Modelling of
Friction Stir Spot Welding
Mr Aidan Reilly MA MEng
Department of Engineering
Sidney Sussex College
University of Cambridge
A thesis submitted for the degree of
Doctor of Philosophy
25 May 2013
ii
Preface
This dissertation sets out my work on friction stir spot welding from 2009 to
2013. Although owing much to many other people, the thesis as set out here
is entirely my own work except where specifically noted. In particular, it
draws heavily on work published by a wide range of other authors for specific
details. These contributions are all noted in the text, with details of sources
given in the section titled ‘References’. The first version was submitted for
examination on 28 March 2013. Following my viva on 22 May, this revised
version was completed on 25 May 2013. This work comprises 56375 words
and 120 figures.
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iv
Acknowledgements
I would like to express my sincere gratitude to everyone who has helped me
in my work and without whom it would not have been possible. There are
too many to name everyone individually, but in particular I would like to
thank my academic supervisor Hugh Shercliff and advisor Graham McShane
for their invaluable advice and assistance throughout the project. I would
also like to thank my parents Tom and Sue for their support, both during
the last four years and before, and I would like to thank my indefatigable
proof-reader Tasha for her patience in reading through many early drafts
and pointing out my mistakes. My sister Alice has provided me with much
encouragement, as has my brother Jonathan, and I hope he is successful with
his own thesis; I am also deeply indebted to Hazel for urging me to finish on
time, and had it not been for her I would probably still be writing.
I would like to thank Bethany Parker and Patryk Je¸drasiak for their
contributions, and I would like to acknowledge the assistance of Yingchun
Chen and Phil Prangnell from Manchester for their collaboration, and for
the many useful discussions.
Finally, I would like to express my gratitude to all my supervisors, tutors
and fellow students at Trinity Hall, without whom I would not have started
my Ph.D., and to everyone at Sidney Sussex College, without whom the last
four years would have been much less fun.
This work was funded by the Engineering and Physical Sciences Research
Council.
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Contents
Preface iii
Acknowledgements v
Summary xi
Nomenclature xiii
1 Introduction 1
1.1 Motivation for the project . . . . . . . . . . . . . . . . . . . . 3
1.2 Friction stir process descriptions . . . . . . . . . . . . . . . . . 5
1.2.1 Friction stir welding . . . . . . . . . . . . . . . . . . . 5
1.2.2 Friction stir spot welding (FSSW) . . . . . . . . . . . . 7
1.2.3 Pinless FSSW . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Comparison between FSSW and other processes . . . . . . . . 10
2 Literature review 13
2.1 Welding process modelling . . . . . . . . . . . . . . . . . . . . 13
2.2 Background to FSSW . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 Development of pinless joining . . . . . . . . . . . . . . 17
2.2.2 Failure modes . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.3 Optimum conditions . . . . . . . . . . . . . . . . . . . 22
2.3 Previous modelling approaches . . . . . . . . . . . . . . . . . . 22
2.3.1 Advantages of modelling . . . . . . . . . . . . . . . . . 22
2.3.2 Introduction to modelling . . . . . . . . . . . . . . . . 23
2.3.3 Friction stir spot welding . . . . . . . . . . . . . . . . . 24
2.3.4 Friction stir welding and related processes . . . . . . . 25
2.3.5 Empirical testing and validation . . . . . . . . . . . . . 39
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2.3.6 Microstructural modelling . . . . . . . . . . . . . . . . 41
2.3.7 Modelling of related non-welding processes . . . . . . . 42
2.4 Constitutive data . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.5 Issues for further study . . . . . . . . . . . . . . . . . . . . . . 45
2.5.1 Need for new techniques . . . . . . . . . . . . . . . . . 46
3 Experimental work 49
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3 Welding parameters . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3.1 Welding time . . . . . . . . . . . . . . . . . . . . . . . 55
3.3.2 Rotation speed . . . . . . . . . . . . . . . . . . . . . . 57
3.3.3 Workpiece material . . . . . . . . . . . . . . . . . . . . 59
3.3.4 Welding time — Al to Fe . . . . . . . . . . . . . . . . . 62
3.3.5 Rotation speed — Al to Fe . . . . . . . . . . . . . . . . 63
3.4 Tool types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.5 Weld quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.6 Sources of error . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.7 Plunge depth and surface finish . . . . . . . . . . . . . . . . . 72
3.8 Backing plate material . . . . . . . . . . . . . . . . . . . . . . 77
3.9 Flow visualisation . . . . . . . . . . . . . . . . . . . . . . . . . 78
4 Thermal modelling 79
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2 Timescale of welding . . . . . . . . . . . . . . . . . . . . . . . 81
4.3 FE model description . . . . . . . . . . . . . . . . . . . . . . . 82
4.4 Axisymmetric modelling . . . . . . . . . . . . . . . . . . . . . 86
4.5 Thermal contact problems in Abaqus . . . . . . . . . . . . . . 89
4.6 Mesh effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.7 Model calibration . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.7.1 Material properties . . . . . . . . . . . . . . . . . . . . 93
4.7.2 Power input . . . . . . . . . . . . . . . . . . . . . . . . 97
4.7.3 Heat losses . . . . . . . . . . . . . . . . . . . . . . . . 106
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4.8 Plunge depth effects . . . . . . . . . . . . . . . . . . . . . . . 112
4.9 Model to experiment comparison . . . . . . . . . . . . . . . . 114
4.10 Optimum welding conditions . . . . . . . . . . . . . . . . . . . 117
4.10.1 A process window for FSSW . . . . . . . . . . . . . . . 117
4.10.2 Alternative backing plate materials . . . . . . . . . . . 122
5 Kinematic model 127
5.1 Model development . . . . . . . . . . . . . . . . . . . . . . . . 129
5.2 Tool contact boundary condition . . . . . . . . . . . . . . . . 132
5.3 Through-thickness heat flow . . . . . . . . . . . . . . . . . . . 136
5.4 Dissimilar joining: aluminium to steel . . . . . . . . . . . . . . 140
5.4.1 Welding Al to uncoated steel . . . . . . . . . . . . . . . 140
5.4.2 Welding Al to galvanized steel . . . . . . . . . . . . . . 142
5.5 Deep plunge welds . . . . . . . . . . . . . . . . . . . . . . . . 144
5.6 Comparison with experiments . . . . . . . . . . . . . . . . . . 147
5.7 Variation in ω¯ for experimental welds . . . . . . . . . . . . . . 152
5.8 Analysis of actual slip conditions during welds . . . . . . . . . 154
5.9 Tool features and hooking . . . . . . . . . . . . . . . . . . . . 155
5.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6 Sequential small-strain analysis 159
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.2 Static plunge modelling . . . . . . . . . . . . . . . . . . . . . . 160
6.2.1 Model setup and initial tests . . . . . . . . . . . . . . . 161
6.2.2 Methods of simulating downforce . . . . . . . . . . . . 162
6.2.3 Mesh sensitivity analysis . . . . . . . . . . . . . . . . . 167
6.2.4 Further investigation of the Boussinesq problem . . . . 167
6.2.5 Plasticity . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.2.6 Analysis of thin plates . . . . . . . . . . . . . . . . . . 172
6.3 Sequential small-strain analysis . . . . . . . . . . . . . . . . . 174
6.3.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
6.3.2 The model . . . . . . . . . . . . . . . . . . . . . . . . . 175
6.3.3 Proof-of-concept . . . . . . . . . . . . . . . . . . . . . 183
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6.3.4 Thin plate welding . . . . . . . . . . . . . . . . . . . . 187
6.3.5 Adaptive timesteps . . . . . . . . . . . . . . . . . . . . 189
6.3.6 Case study and validation . . . . . . . . . . . . . . . . 189
6.3.7 Optimum welding with a copper backing plate . . . . . 192
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
7 Conclusions and further work 199
References 203
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Summary
Friction stir spot welding (FSSW) is a solid-state welding process which
is especially useful for joining precipitation-hardened aluminium alloys that
undergo adverse property changes during fusion welding. It also has potential
as an effective method for solid-state joining of dissimilar alloys. In FSSW,
heat generation and plastic flow are strongly linked, and the scale of the
process in time and space is such that it is difficult to separate and control
the influence of all the relevant input parameters.
The use of modelling is well-established in the field of welding research,
and this thesis presents an analysis of the thermal and mechanical aspects of
FSSW, principally using the finite element (FE) technique. Firstly, a thermal
FE model is shown, which is subsequently validated by reference to experi-
mental temperature data in both aluminium-to-aluminium and aluminium-
to-steel welds. Correlations between high-quality welds and temperature
fields are established, and predictions are made for peak temperatures reached
under novel welding conditions.
Deformation and heating are strongly linked in FSSW, but existing mod-
elling tools are poorly suited to modelling flow processes in the conditions
extant in FSSW. This thesis discusses the development and optimisation of
two novel techniques to overcome the limitations of current approaches.
The first of these uses greatly simplified constitutive behaviour to convert
the problem into one defined purely by kinematics. In doing so, the bound-
ary conditions reduce to a small number of assumptions about the contact
conditions between weld material and tool, and the model calculation time is
very rapid. This model is used to investigate changes in the slip condition at
the tool to workpiece interface without an explicit statement of the friction
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law. Marker experiments are presented which use dissimilar composition but
similar strength alloys to visualise flow patterns. The layering behaviour and
surface patterns observed in the model agree well with observations from
these experiments.
The second approach extends the FE method to include deformation
behaviour without the need for a fully-coupled approach, guided by the
kinematic model. This is achieved using an innovative sequential small-
strain analysis method in which thermal and deformation analyses alternate,
with each running at a very different timescale. This technique avoids the
requirement to either remesh the model domain at high strains or to use an
explicit integration scheme, both of which impose penalties in calculation
time and model complexity. The method is used to relate the purely thermal
analysis developed in the work on thermal modelling to welding parameters
such as tool speed. The model enables predictions of the spatial and tem-
poral evolution of heat generation to be made directly from the constitutive
behaviour of the alloy and the assumed velocity profile at the tool-workpiece
interface. Predictions of the resulting temperature history are matched to
experimental data and novel conditions are simulated, and these predictions
correlate accurately with experimental results. Hence, the model is used to
predict welding outcomes for situations for which no experimental data exists,
and process charts are produced to describe optimum welding parameters.
The methods and results presented in this thesis have significant im-
plications for modelling friction stir spot welding, from optimising process
conditions, to integration with microstructural models (to predict softening
in the heat-affected zone, or the formation of intermetallics at the interface in
dissimilar welds). The technique developed for sequential small strain finite
element analysis could also be investigated for use in other kinematically
constrained solid-state friction joining processes.
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Nomenclature used in this work
Symbol Definition Units
a Thermal diffusivity m2 s−1
a Asymptotic power fraction -
A,B Material fitting parameters Pa
C Specific heat capacity J kg−1 K−1
C Material fitting parameter -
h Heat flow per unit area W m−2
h Workpiece thickness m
hc Contact conductance W m
−2 K−1
h˙ Rate of change of h W m−2 s−1
LP Pin length m
K Bulk modulus Pa
K1, K2 Material fitting parameters Pa
l,m, n Material fitting parameters -
P Instantaneous power W
P0 Initial power W
q Area or volumetric heat input (W m−2) or
(W m−3)
q˙ Rate of change of q W m−2 s−1
Q Heat input W
Q Activation energy J kg−1
Q′ Heat input W
R Specific gas constant J kg−1 K−1
R Radius m
RS Shoulder radius m
t Time s
T Temperature K
Tmelt Solidus temperature K
T0 Room temperature (293 K) K
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Symbol Definition Units
U Internal energy per unit volume J m−3
v′ Slip velocity m s−1
vH Characteristic heat flow speed m s
−1
x, y, z Space dimensions m
Z Zener-Hollmon parameter s−1
α Material fitting parameter -
δ Dimensionless slip rate (see page 34) -
ε Strain -
ε˙ Strain rate s−1
λ Thermal conductivity W m−1 K−1
ν Poisson’s ratio -
ρ Density kg m−3
σ Normal stress Pa
σy Normal stress at yield Pa
σ0 Base stress for material models Pa
σ∞ Limiting stress at large strain Pa
τ Shear stress Pa
τy Shear stress at yield Pa
ω Angular speed or velocity rad s−1
ω¯ Dimensionless angular velocity -
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Chapter 1
Introduction
This project is an investigation into a newly-developed joining technique:
friction stir spot welding, an offshoot of the closely-related (and more es-
tablished) friction stir welding. Friction stir spot welding (FSSW) was first
reported in 2000 (Schiling et al., 2000), and it is commonly used to weld
aluminium and steel. These two processes are illustrated in Figures 1.1 and
1.2, respectively. Both work in a similar fashion: a hard, rotating tool plunges
down into the workpieces to be joined. Energy dissipated by friction and
plastic work heats and softens the material, allowing it to deform. As the
downforces are in general sufficient to produce at least some sticking friction,
the deformation pattern broadly tracks the rotating motion of the tool. They
are versatile and efficient processes that can join sheets of circa 1 to 50 mm
thickness, though because of the equipment requirements (primarily stiffness)
they are currently limited to factory/machine shop use and similar settings.
By comparison with more established welding methods and other join-
Figure 1.1: The FSSW process (image from Bakavos & Prangnell, 2009)
1
Figure 1.2: The FSW process for seam welding (from Smith et al., 2004)
ing techniques, these are poorly understood processes; they are not well-
characterised, and much work remains to be done to develop optimum con-
ditions for many alloys. Owing to the metallurgical advantages conferred by
these processes, there has been significant investment in empirical testing,
however the same attention has not extended to mathematical modelling.
Development of accurate, fast predictive models will enable the optimisation
of current techniques and the application of these joining and processing
techniques to new materials or combinations of materials. In particular,
there are many outstanding issues surrounding joining between dissimilar
alloys, including problems caused by different material strengths and thermal
properties, interfacial reactions leading to embrittlement, and corrosion re-
sistance. However, an efficient method of joining dissimilar metals will allow
greater variation of properties within a product, leading to lower weight,
higher strength, and other benefits. The resulting microstructural changes
can be exploited purely for their effects on mechanical properties, without
being used to create a joint; when used in this way, the technique is termed
friction stir processing. A greater understanding of these processes is of
relevance to many industrial areas, but in particular to the transport sector,
where the ability to use lightweight aluminium alloys, with high strength and
stiffness but low density, is especially important.
2
1.1 Motivation for the project
There have always been incentives to reduce the weight of vehicles, both
because of the costs associated with raw materials for production, and be-
cause of the cost of energy used in transport. More recently, a growing
awareness of the environmental impacts of transport energy use has provided
further pressure to reduce vehicle weight. In developed economies, transport
accounts for approximately a third of all primary energy use, so there is a
clear incentive to reduce the weight of vehicles in order to reduce energy
use. Furthermore, vehicle weight has an impact on many issues besides
fuel consumption and emissions, such as noise pollution, road damage and
the rate of road accident casualties. As the total distance of passenger
journeys correlates strongly with gross domestic product, which is expected to
increase, and fuel reserves become more scarce, there is reason to believe that
these incentives will grow over the short-to-medium term future (Schipper
et al., 1992). Additionally, the increased use of alternative propulsion (i.e.
alternatives to petrol or diesel, such as hydrogen fuel cells or battery-powered
electric motors) could provide an additional push towards lightweight vehicles
(Carney, 2008).
Application to the transport sector leads to a focus on particular materials
that are either already widely used in transport, or are considered important
for the near future. Although specific strength is the overriding performance
criterion for structural components, there are other factors which have a
strong influence including cost, toughness, toxicity1 and ease of processing
and recycling. Steel dominates the automotive industry due to cost, but
aluminium and other light alloys (such as titanium and magnesium) are
widely used in sectors such as aerospace where a higher premium is placed
on performance.
The light alloys are often considered difficult to join, whether consid-
ering welds between the same metal, or to other light alloys or to steels
(Polmear, 1995). Joining these metals to steel is of considerable importance
1For example, beryllium has a low density and high specific strength, but due to its
toxicity its use is limited to specialist applications such as spacecraft and X-ray equipment.
3
within the automotive industry despite the trend towards lighter parts as
key components will continue to be made from steel, even in vehicles that
are predominantly made from other metals, or composites. Although this
discussion focuses predominantly on the transport sector, light alloys are
widespread in many other engineering fields, with aluminium being the most
widely used metal after iron and steel, and the most abundant metal in the
Earth’s crust.
Other alloys of commercial importance include titanium, which has a
very high specific strength, but also a high cost; consequently its use as a
structural material is confined to areas such as high-end aerospace applica-
tions and bicycle frames. It also finds many uses in the chemical industry
due to its corrosion resistance. The most versatile titanium alloys are β-
stabilised2 and heat treatable (Hampel, 1961), of which the commonest alloy
in industrial use is Ti–6Al–4V. Other common alloying elements include
chromium, molybdenum and manganese (Carpenter, 2012).
Magnesium is the lightest structural metal in use. It is usually alloyed
with aluminium and zinc, and its alloys are generally easy to cast; alloys
containing zirconium are also widely used in more specialist applications.
The primary applications of magnesium are in automotive and aerospace
components, and die cast parts for consumer electronics. Its wider use is
limited by its reactivity and poor performance at elevated temperature, with
most alloys only being usable up to 500 K (Magnesium Industry Council,
1962). By comparison, steels typically retain sufficient usable strength up to
at least 700 K.
Friction stir spot welding’s advantages are explored in depth in the fi-
nal section of this chapter (Section 1.3); it is an attractive process for the
transport industry since its inherently low energy use and favourable joint
properties could allow the construction of lighter vehicles with a lower em-
bodied energy. As an example, the energy use of FSSW can be less than 1%
of that required for an equivalent resistance spot weld, the current industry
standard (Iwashita, 2003).
2β-stabilised alloys contain elements that form a solid solution in the β phase, which
stabilise the ductile body centred cubic β phase to lower temperatures.
4
1.2 Friction stir process descriptions
1.2.1 Friction stir welding
Friction stir welding (FSW) is a novel joining process that was patented
by Thomas et. al. in 1992. A diagram of the welding process is shown in
Figure 1.2. This shows a butt joint configuration between two workpieces
and the rotating tool above. The tool rotates at high speed, typically 30
to 300 rad s−1 (300 to 3000 rev/min), and this supplies both the heat and
deformation to create a joint. In FSW, the tool translates slowly along the
joint line (typically at 0.01 to 1 mm s−1). As it does so, the rotation of the
tool forces hot material around it, with most of the metal flowing past on
the retreating side (the side where the translational and tangential velocities
are in opposite directions; the opposite side is the advancing side). The
whole process takes place with the weld material in a solid state, with heat
generated by some combination of friction and plastic deformation. The
balance between these two heat generation effects is a point of debate in the
literature (see e.g. Mishra et al., 2000, Mahoney et al., 2001 and Charit et al.,
2002).
Originally, FSW was developed for Al. Compared to traditional fusion
welding processes, the temperature is lower and so problems associated with
melting do not occur. This is particularly advantageous when working with
heat-treatable, precipitation-hardened alloys such as the 2000, 6000 and 7000
series, which have Cu, Mg and Si, and Zi as the primary alloying elements.
FSW has now been applied to many other metals, including steels, Ti and
Mg. Threadgill et al. (2009) summarised the current state of research into
friction stir welding of many metals in their review.
As well as being used for butt welds, the FSW process can also be used for
other welding geometries, such as lap welds, and it is currently under research
for complicated shapes such as T joints. However, the tooling and parameters
required to make high-quality welds in a lap configuration are substantially
different to those required for butt joints. In general, the joint must be wider
and the range of optimal parameters is narrower for lap welds, owing to the
5
difficulty of breaking up the oxide layer on the two joining surfaces. Despite
these difficulties, FSW is rapidly becoming a standard technique for lap joints
as well as butt joints in many applications.
FSW tooling consists of two parts: the shoulder, which may be flat or
profiled, and the pin, which projects from the shoulder. Various designs have
been used for the pin, from smooth cylinders, through the addition of simple
threads or flukes, through to the complexity of tools like the Triflute (see
Figure 1.3).
For welds in Al and other light alloys, tools are commonly made from
high-alloy steel. However, when welding steel the high wear rate of the
tool is a particular problem (Mandal et al., 2006). While tools may last
for many welds in Al, a single long weld may have a non-negligible proba-
bility of tool failure when welding steel; the much higher strength of steel
at elevated temperatures is compounded by the lower ductility of the tool
materials. For welds in steel, tools based on tungsten or boron nitride are
the most common. Tungsten-rhenium (W-Re) is one of the most durable
tool materials, but is exceptionally expensive and difficult to manufacture,
as is polycrystalline boron nitride (PCBN). W-Re tools can only be ground,
as opposed to conventional machining, and PCBN tools are manufactured
under very high temperatures and pressures.
A large fraction of the wear occurs during the plunge, when the tool
encounters cold base metal. Tool wear with steel workpieces presents a
particular problem, despite the use of special methods to reduce the wear rate.
One of the most promising is the use of pre-drilled holes in the material to
reduce wear during the plunge, but it remains a significant problem (Thomas,
1999, and Thomas et al., 1999).
The reactivity of Mg and Ti presents further problems; tungsten-based
tools are the most common choice for these metals and show promise. Ni-
Fe or Ni-Cu based tools with W particles are under development, and these
tools are substantially cheaper to produce than W base alloys.
6
Figure 1.3: MX Triflute tool (from Mishra & Ma, 2005)
1.2.2 Friction stir spot welding
Friction stir spot welding (FSSW) grew out of FSW in an attempt to transfer
some of the advantages of FSW to spot welding. While it has been used in
production (including for spot welds in automotive bodies: see Bakavos &
Prangnell (2009) and Iwashita (2003)), it is still considered an immature
process. In its simplest form, it comprises 3 phases: a plunge, dwell, and
retraction, with no lateral movement or translation. The process whereby
this forms a joint is similar to that for seam FSW: heat created by friction
and plastic work softens the workpiece material, and the rotation of the tool
causes the workpiece to deform plastically to large strains.
Owing to this development path, initially the same tools and process
parameters were used for FSSW as had been found suitable for FSW. This
has been found to be suboptimal; the key differences between FSW and
FSSW are:
• spot welding is a transient process, while seam welding in many cases
takes place in a steady-state environment;
7
• the demands and loading patterns placed upon a spot weld vary markedly
from those on a seam weld;
• the translation present in seam welding has an influence on the weld,
despite its low speed compared to the tangential tool speed;
• spot welds are often made in thinner sheet than is typical for seam
welds.
Some authors have started to publish studies studying FSSW specifically in
more detail, and these are summarised in detail in Chapter 2.
1.2.3 Pinless FSSW
FSSW is FSW without translation, but this introduces a unique set of dif-
ficulties. One of the issues is the production of a ‘keyhole’, the hole in the
centre of a spot weld left by the tool pin. This is not usually a problem
with FSW; the weld can be continued into a blank, which is then machined
off, or if not, it is often the case that the hole does not necessarily create a
significant loss of strength due to the greater length of the joint. However,
it is a more significant problem for FSSW simply because the hole occupies
a much larger fraction of the joint area and volume. Consequently, current
research is focusing on ways to create a weld without leaving a keyhole at all.
The simplest approach, considered in detail by this project, is to form welds
using a tool with no pin, relying entirely on the shoulder contact to generate
heat and induce deformation in the workpieces. This process is illustrated in
Figure 1.4.
Figure 1.4: The pinless FSSW process (from Bakavos & Prangnell, 2009)
8
Figure 1.5: The refill FSSW process (from Muci-Kuchler et al., 2010)
Another technique that shows promise is refill FSSW, shown in Figure 1.5.
This technique uses an independently movable collar surrounding the main
part of the tool; on contact with the surface, this collar retreats, filling up the
space with extruded workpiece material. The extruded material is then forced
back into the weld zone by the collar as the tool retracts. This approach is
very promising, but at the moment is too expensive and time-consuming
to have been widely adopted for production use. Circular FSSW uses a
conventional tool with a superimposed circular motion to increase the area
of the joint. Using this method a keyhole is still formed, but a smaller hole
is left for the same joint area. Different shapes besides a circular joint have
been investigated, and while no fixed terminology has yet become standard
the term swing FSSW is becoming popular for this method (Badarinarayan
et al., 2007). However, this method — like refill FSSW — is considered too
time-consuming for production use in the automotive industry where cycle
time is considered a critical factor.
9
1.3 Comparison between FSSW and other
processes
Many considerations determine which process is chosen for any particular
application; for welding processes, key factors are the microstructural change
induced by heating during the weld, the bulk property changes thus caused,
and the cycle time of the process.
Conventional fusion welding involves substantial melting, usually of both
workpieces to be joined. The two parts mix in the molten state, and when
the weld nugget cools and solidifies a solid monolithic joint is formed. FSSW
takes place entirely or almost entirely within the solid state (Babu, 2009).
Melting a metal provokes large changes in microstructure, and the resulting
microstructure on resolidifying can be very different from the pre-welded con-
dition, even in a weld between identical alloys. This is especially noticeable
with heat-treatable aluminium alloys; Al alloys also tend to exhibit large
distortions and residual stresses on cooling after being fusion welded (Barnes
& Pashby, 2000).
Heat-treatable Al alloys are those in the 2000, 6000 and 7000 series (with
the primary alloying elements being Cu, Mg and Si, and Zi, respectively).
These derive a significant proportion of their strength from precipitates — in
the case of 6000 series alloys, Mg2Si particles. Upon reheating, the precipi-
tates entirely dissolve, and the weld will require extensive heat-treatment to
return its properties to the pre-weld, parent material state. Such treatment
may be impractical for a large component, so FSSW is particularly beneficial
for these alloys. (Indeed, 2000 and 7000 series alloys are still referred to as
‘unweldable’, although this is no longer strictly the case as these alloys are
quite easily joined with FSSW and FSW (Khalid, 2002).)
Since steel is so widespread many joining techniques were originally devel-
oped for steel. As process parameters have to be adapted before transferring a
joining technique to a different material, it is difficult to be certain about the
potential of a new process without extensive testing and research. However,
one parameter that is comparatively easy to assess is the capability of a new
process to join various thicknesses of material. The capability of FSW is
10
limited primarily by the size and stiffness of equipment required to join large
thicknesses, and buckling/tearing of the workpiece for thin foils. Figure 1.6
shows the range of section thicknesses that can be routinely joined by a range
of metal joining techniques, with selected welding processes highlighted; this
gives a useful indication of the types of process that seam FSW competes
with. FSSW works well for thin sheet, but has not yet reached the same
level of development as FSW for joining thick plates, though no fundamental
limit on this is envisaged beyond practical machine limits. The considera-
tions outlined in this section apply to the use of FSSW for what may be
considered ‘general factory welding’ conditions; in various more specialised
tasks practical considerations may override concerns regarding the optimum
process from a metallurgical point of view. This can work both ways: due
to the equipment involved, FSSW is unlikely to ever become a technology
in use on construction sites, or for field repairs to vehicles, despite current
development work on hand-held FSSW devices. On the other hand, it is
impossible to join closed-section components with resistance spot welds, but
may be possible with FSSW (Zhao et al., 1999).
To be accepted industrially, many demands are made of a joining process
besides the quality of the joint it makes; for example, diffusion bonding can
produce very high-quality joints, but due to the time involved it is unsuitable
for mass-production automotive applications, where joining processes must
be kept below 10 s to be seen as competitive. FSSW is potentially compet-
itive in this regard, although welding time probably represents its greatest
weakness when compared to resistance spot welding (RSW), the dominant
competing technology in the parameter space filled by FSSW.
The comparison with RSW becomes more favourable to FSSW when
discussing light alloys specifically. Light alloys in general, particularly Al
alloys, are much more conductive than steel; they also have a tendency to
degrade electrodes due to their reactivity (Peng et al., 2004). Neither of these
problems apply to FSSW.
Low temperatures and a small weld nugget mean that the heat input
during FSSW is lower than in many other processes. Laser welding, which
can produce high-quality, deep welds with a small heat-affected zone (HAZ)
11
Figure 1.6: Selected joining techniques by section thickness, with welding
techniques shown in blue. Data from CES (Granta Design).
and is capable of joining many light alloys, uses 50 times the energy of
FSW (Mishra & Mahoney, 2007). Laser welding requires exceptionally high
powers to join high-purity Al (1000 series alloys or higher) as they are very
reflective (Mackwood & Crafer, 2005). FSSW uses around 10 % of the energy
of RSW per weld (as an average — this figure can be as low as 1 % in specific
conditions (Iwashita, 2003)), so a dramatic reduction in the energy needed
to fabricate components is possible by switching from RSW to FSSW.
Emission of toxic gases during the process and the requirement for shield-
ing gases to prevent oxidation are two common problems with traditional
arc welding; they increase the difficulty and cost of using these processes
in industrial settings. Arc welding processes convert 0.5 % to 1 % of the
consumables used into gas and dust (Yeo & Neo, 1998). Altogether the
annual emissions of metal oxides caused by welding within the EEC are
around 6 × 106 kg (1998 estimate); a small fraction of total emissions, but
still harmful and locally problematic. FSW avoids entirely the emission of
these gases, which are associated with MIG and MMA welding, and which
are a particular problem when welding Al (and also Cu). Such gases typically
include a high proportion of Si, K, F, Ti, Ca, O3 and oxides of nitrogen. As
FSSW neither emits toxic gases nor requires shielding gases it has a lower
environmental impact than other welding processes. These reasons also make
it an attractive process from a manufacturing point of view, as it is much
easier to handle.
12
Chapter 2
Literature review
This project is about friction stir spot welding, and specifically, it is an
investigation into modelling of thin sheet welding using a pinless tool. The
development of pinless FSSW took place at Manchester University, and this
project is a continuation of that research, in collaboration with the original
developers of the process. Key results that have already been published
by other researchers in the team are included here; further details of their
experimental work, along with experimental work conducted by the author,
are given in Chapter 3.
2.1 Welding process modelling
Welding processes have changed substantially over time, with many new
processes being invented. Arguably the first form of welding invented was
forge welding as practised by blacksmiths for many centuries. However, it
was not until the close of the 19th century that arc, oxyacetylene, thermite
and resistance welding were invented. During the 20th century, many new
welding techniques were invented, and the existing methods were refined
and enhanced. Amongst these new developments, laser welding, the various
forms of friction welding, and the use of shielding gas stand out prominently.
Welding techniques may be usefully categorised in two ways: by grouping
together either those processes where significant deformation is induced or
13
Significant deformation No significant deformation
FSSW & FSW Arc welding
Ultrasonic welding Gas welding
Rotary friction welding RSW
Linear friction welding Electron beam welding
Forge welding Thermite welding
Explosive welding Laser welding
Magnetic welding Plasma welding
Table 2.1: Welding types, categorised by degree of deformation
not (Table 2.1), or by grouping together those where the heat input is
independently adjustable or not (Table 2.2).
The first grouping is probably the most significant if one wishes to group
welding processes by the resultant microstructure; those with no significant
deformation all rely on melting, and mixing between the workpieces occurs in
the molten state. Those where significant deformation processes are involved
often take place in a solid state, and consequently the microstructures formed
by the two groups can be very different. From a modelling viewpoint the
processes that involve no significant deformation — with the exception of
laser and plasma welding — can generally be modelled for most purposes as
a purely thermal problem (laser and plasma welding are exceptions as the
extreme temperatures reached cause evaporation of workpiece metal). Those
processes where deformation takes place require more complicated models.
The grouping shown in Table 2.2 is also directly relevant to modelling,
with the processes in the left-hand column being the easiest to model: for
these types, the heat input is known a priori, so temperatures and material
responses are easy to calculate. For the operations in the right-hand column
the heat input depends on the response of the material, often in a complicated
feedback loop. For example, during resistance spot welding (RSW) the
input voltage and current are known, so the workpiece temperature can be
calculated from a purely thermal model; while in laser welding, the power
absorbed depends on the microstructural state of the metal and on the shape
of the hole formed, which both vary during the course of a weld (Zhao et al.,
1999).
14
Heating controlled independently Heating primarily via a
dependent process
Arc Laser
Gas Explosive
RSW Magnetic
Thermite Rotary friction
Forge Linear friction
Electron beam FSSW & FSW
Plasma Ultrasonic
Table 2.2: Welding types, categorised by the existence or otherwise of a
feedback loop controlling the heat input during welding
The welding processes which fall into the right-hand column of Table
2.1 and the left-hand column of Table 2.2 are, in many respects, easier to
model than the others. In these processes, the dominant effect is melting
of the workpieces due to a known, controllable power input, and hence
these welding operations may be modelled by numerical implementations
of Fourier’s Law, or by analytical models of the type described by Rosenthal
(1946). Although such models necessarily avoid much of the detail of the
process, they are nevertheless accurate and robust enough to produce useful
results, for example as the basis for microstructural models. By contrast, with
processes like explosive and forge welding it is difficult to estimate the power
input, making microstructural modelling very difficult. However, Rosenthal’s
work provides a starting point for a thermal analysis of FSW, as carried out
by Russell (2000) (described later).
Meanwhile, even a thermal model for the other processes listed can be
difficult to implement as the power is an unknown quantity. In this regard,
these processes are similar to FSSW in that the heat input is coupled to
deformation of the workpiece in some way. As an example, laser welding is
one of the most difficult processes to analyse, and so an extensive body of
literature is dedicated to coupled models including a range of physical effects.
Although some progress has been made, particularly the finding that power
absorption is strongly linked to the presence of volatile materials in the sur-
face layer of the workpiece, detailed modelling still involves computationally
15
intensive fully coupled FE models; these take of the order of many months or
even years to simulate a full weld (Katayama, 1996, Bachmann et al., 2012,
Gatzen & Chongbunwatana, 2012 and Balasubramanian, 2012).
The models that are most similar to FSSW fall into the same columns
in both tables: linear and rotary friction welding, and ultrasonic welding,
are likewise based on a friction process so the similarities between these
types are the strongest. These processes are shown schematically in Fig-
ures 2.1, 2.2 and 2.3.
Figure 2.1: Rotary friction welding (image from TWI Ltd.)
Figure 2.2: Linear friction welding (image from TWI Ltd.)
16
Figure 2.3: Ultrasonic welding (image from Haddadi, 2012)
2.2 Background to FSSW
2.2.1 Development of pinless joining
The concept of pinless FSSW seems simpler than FSSW with a pin; nev-
ertheless, it was almost discovered by chance, as part of a study into the
optimum pin length in FSSW by Bakavos & Prangnell, 2009. The reason
for the lack of interest or development in the most obvious pinless approach
appears traceable to a conference paper (Addison & Robelou, 2004), from
which it was generally assumed that the pin had to penetrate into the bottom
sheet by at least 25 % of the sheet thickness to form a successful lap joint.
Many authors have cited this paper (see e.g. Valant et al. (2005); Fratini
et al. (2007) and Buffa et al. (2008)), but the only other study to indepen-
dently examine the effect of pin length appears to be that by Bakavos and
Prangnell. This work examined the effect of pin length on the shear strength
of lap joints in AA6111. While other authors have looked at this effect, like
Addison & Robelou (2004) they did not control for the plunge depth of the
shoulder. Bakavos and Prangnell suggest that the strengthening effect seen
by Addison et al. is due to a correlation between shoulder plunge and joint
strength, rather than pin length per se. In their study, Bakavos and Prangnell
controlled for shoulder plunge by using a selection of different tools, each
17
with a different pin length. In this way, the shoulder plunge depth could
be maintained constant, or nearly so, between welds. This gives a better
measure of the effect of increasing the tool pin length independently from
other parameters. Their results, for lap welds in 0.9 mm sheet, are shown in
Figure 2.4; this figure shows a clear trend towards decreasing joint strength
as the pin length is increased.
A number of authors are generally cited as having studied the effect of
pin length; however, these studies are more properly described as varying the
plunge depth. For example, Mitlin et al. (2006) studied the failure strength
of lap joints in AA6111. Although their work is described as varying the
pin penetration depth, they used the same geometry tool for all welds. As
the shoulder was in contact with the workpiece in each of their welds, the
shoulder plunge depth was also being varied.
Figure 2.4: Variation of joint strength with tool pin length for lap welds
between two 0.9 mm thick sheets (from Bakavos & Prangnell, 2009)
2.2.2 Failure modes
Part of the complexity in indentifying trends in the strength of joints made
by FSSW is that there are a number of distinct modes by which a joint can
fail. Mitlin et al. found the failure mode of the joint changed from brittle
pull-out fracture for small plunges to ductile fracture around the edge of the
nugget for large plunges. They found a peak in shear strength for the joint,
18
increasing then decreasing with increasing plunge depth, and suggest that
the joint strength increases because the area of full metallurgicial contact
increases (see Figures 2.5, 2.6 and 2.7). Bakavos and Prangnell put forward
the theory that this is due to the influence of the shoulder rather than pin
penetration.
Tozaki et al. (2007b) identified three modes of failure of lap joints:
• Shear failure/debonding: in this type of failure, the joint comes apart
along the line of the original interface between the two sheets. It is more
commonly seen in thicker plate since with thin sheet the off-centre shear
loading tends to peel the sheets apart, rather than causing a pure shear
load; however, it can occur with very weak welds in thin sheet material.
• Nugget pull-out: in this failure mode, the nugget pulls cleanly out of
one sheet, with a ductile failure occuring in a ring around the edge
of the nugget. Typically, this will occur in the top surface, though
the fracture would presumably form in the lower sheet under the right
conditions.
• Combined debonding and pull-out: where failure begins in the manner
of a pure shear failure, but then a portion of the nugget is pulled out
at a smaller diameter than the tool shoulder. This usually occurs when
the pin (if present) has penetrated into the lower sheet.
Of these three failure modes, that which involves a pull-out of the whole
nugget usually has the highest performance. Peak failure forces can be similar
to that of the combined debonding/pullout failure, but the failure energy is
highest in the case where the whole nugget pulls out. Images of the post-
failure surface for welds in thin sheet AA6111 are shown in Figure 2.8.
The presence and thickness of the surface oxide layer is thought to play a
strong part in determining the quality and strength of the metallurgical joint
(Badarinarayan et al., 2009). A requirement of a joining process that relies on
forming a chemical bond between metals (such as FSSW) is that it breaks up
the surface oxide layer on both surfaces. This is seen in other applications,
for example in diffusion bonding where reactive metals like titanium must
19
Figure 2.5: Micrograph of a kissing bond and partial metallurgical contact
(from Mitlin et al., 2006)
Figure 2.6: Micrograph of full metallurgical contact (from Mitlin et al., 2006)
Figure 2.7: Variation of full metallurgical contact area with tool penetration
(from Mitlin et al., 2006)
20
Figure 2.8: Failure modes in thin sheet AA6111 joints (from Bakavos &
Prangnell, 2009)
21
have their oxide layers removed and be joined in an oxygen-free atmosphere.
FSSW relies on tool-induced deformation to break up the oxide layers.
2.2.3 Optimum conditions
There seems to be a requirement for deformation to reach the interface in
order for a proper joint to form. However, once this point is reached there is
then a balance between longer, hotter and deeper welds, which increase the
surface area of the full bond and the joint strength (after Mitlin et al., 2006),
and thinning of the workpiece caused by a deeper plunge (after Bakavos &
Prangnell, 2009). In general, thinning of the workpiece dominates, so the
optimum weld appears to be one where the deformation is just sufficient to
reach the interface, but no more. Other considerations also tend to favour
using the smallest plunge possible which will produce a weld: larger plunges
lead to greater surface imperfections, larger forging forces and a weaker HAZ
(Nishihara & Nagasaka, 2003, and Johnson et al., 2001).
2.3 Previous modelling approaches
2.3.1 Advantages of modelling
Empirical experimental investigations are the foundation of many areas of
scientific endeavour, and welding research is no different. However, experi-
ments in welding present a unique set of challenges, and modelling efforts are
used extensively in all branches of welding research to investigate welds on
scales and in ways that are impossible or impractical experimentally (Cerjak
& Bhadeshia, 2002). In FSSW, many of these challenges are magnified:
• it is a short duration process: typically a weld takes of the order of 1 s
• it involves high forces, of the order of 10 kN
• the rotational speeds are high, of the order of 200 rad s-1 (2000 rpm)
• complex flow patterns develop during the weld
22
• steep thermal gradients occur, both in time and space
• the volume of the total weld zone is small
Owing to these characteristics, developing a thorough understanding of
the process through experiments alone is fraught with difficulty. For example,
simply measuring temperatures accurately is itself an experimental challenge:
the smallest thermocouples reasonably available are around 0.5 mm in width,
while temperature gradients can be as much as 100 K mm-1; thermocouples
are destroyed if placed too close to the weld stir zone; and thermal cameras
are somewhat unreliable and in any case can only measure temperatures on
exposed surfaces. Flow visualisation is even more difficult, as flow patterns
inside solid metal are very difficult to observe. Finally, the process outputs
(in terms of temperatures and flow patterns) depend on a complex interplay
of many different factors (such as tool downforce, tilt angle, rotation speed,
clamping forces and material properties) such that it can be very difficult to
produce exact repeat experiments.
For all these reasons, modelling FSSW is vital to develop a greater un-
derstanding of the process.
2.3.2 Introduction to modelling
Weld modelling may be divided into two categories: analytical models, in-
volving continuous equations to describe the temperature field, power input
and other parameters, and numerical solutions that work with a mesh or
similar discrete representation of a weld and calculate a solution at finite
time steps. Analytical models provide broad insight into the process, and
in general the solution time is much shorter. However, analytical solutions
struggle to represent many of the features in real welds, such as finite tool
sizes, contact conditions and heat losses to a backing plate, and irregular
geometries. By contrast, numerical models cope well with such finite effects.
Numerical models, however, require much greater computing resources, and
are less suitable for providing broad process windows of the kind that may be
desired when introducing a new alloy, for example. Since numerical models
23
do not provide the same degree of insight into the process, it is often difficult
to estimate the influence of any particular parameter on the final solution.
This kind of work is particularly important for judging the sensitivity of a
model to variations in input data. The time or computing resources required
to carry out large numbers of similar calculations means that this important
step is often not conducted, leading to less robust and less reliable predictions
(Mishra & Mahoney, 2007, Colegrove & Shercliff, 2006).
As all types of FSW, but in particular FSSW, are comparatively new
welding techniques most analytical approaches are based on a model of the
thermal field alone, since these techniques were developed for analysing fusion
welds where the flow pattern is not usually important. Consequently, many
models only look at this side of the problem and do not attempt to include
flow effects. This is not necessarily a big drawback, depending on the aims
of the model: understanding the evolution of the temperature field is a very
important outcome, as it strongly affects the behaviour and properties of the
workpiece material.
2.3.3 Friction stir spot welding
The only detailed models of FSSW to date are based on numerical ap-
proaches; so far, no analytic models have been developed. It is worth noting
that FSW and FSSW are both processes in which the flow is kinemati-
cally constrained rather heavily, making analytical models more promising.
Fully-coupled thermomechanical models have been produced for FSSW, al-
though a lot of the parameters are unknown. For example, Awang et al.
(2005) developed a thermomechanical model using Abaqus Explicit. In this
model, the heat input is assumed to be generated by Coulomb friction with
a temperature-dependant coefficient of friction. A convection coefficient (of
30 W m-2 K-1) is used for heat losses from the workpiece-air interfaces, but
there is little indication that this value is correct. Although this model gives
believable results for the flow pattern (which are hard to verify experimen-
tally), the temperatures calculated are far higher than generally accepted
peak temperatures for FSSW. They calculate a peak temperature of 1200 K
24
for FSSW in AA6061, which is far above the melting point. Some experi-
mental results have found structures consistent with local melting (Park et
al. and Sato et al., 2002), but there is no possibility that temperatures so far
in excess of the solidus can be reached during FSW or FSSW, so such studies
must be dismissed.
Temperature regime in which FSSW operates
It is well-established that the peak temperature during FSW is limited at
the solidus temperature (Ts), due to a great reduction in material flow stress
at Ts. This also applies to FSSW. The majority of published literature
supports this, with most authors finding a peak temperature close to the
solidus. Gerlich et al. (December 2005) review a number of other authors’
work in their paper, including Colegrove and Shercliff’s work on AA7075 and
Su et al.’s work (2006) on 6061, 7075 and 2024 alloys; these authors report
peak temperatures around the solidus. Murr et al. (1998a) report a peak
temperature of 0.7Ts and Somasekharan & Murr (2004) report a peak tem-
perature of 0.8Ts. Gerlich et al. measured peak temperatures during FSSW
of 6111 and 2024 Al alloys and AZ91 Mg, and found temperatures within
6 % of the solidus temperature (0.94Ts for Al alloys and 0.99Ts for Mg).
It is uncommon to find temperature measurements taken during dissimilar
FSSW; Prangnell et al. measured the temperatures during dissimilar FSSW
and found temperatures substantially below the solidus, though these mea-
surements were taken away from the tool (so peak weld temperatures would
be higher). Park et al. (2004) and Sato et al. (2004) observed microstructures
in AA1050/AZ31 welds consistent with melting and mixing, implying higher
temperatures were achieved in these welds than in welds of either material
to itself. However, no direct temperature measurements were made during
these welds.
2.3.4 Friction stir welding and related processes
There is relatively little literature devoted specifically to FSSW and much
more to seam FSW. Given the similarities in the two processes, there is much
25
that can be learnt from a study of this larger body of work. Other modelling
techniques may also be relevant, and likely processes can be selected by
choosing those that operate in a similar parameter space. Peak temperatures
reached in FSSW are generally of similar magnitudes to the solidus temper-
ature of the alloy being welded, due to the negative feedback mechanisms
discussed earlier. There is some discussion in the literature regarding the
strain rates reached, with authors claiming strain rates for Al welding from
20 s−1 (Frigaard et al., 2001) up to 500 s−1 (Colegrove & Shercliff, 2006).
Rotary friction welding (RFW) operates in similar regimes of temperature
and strain rate (with strain rates of up to 1000 s−1 being found by Midling
& Grong, 1994). Modelling of RFW tends to use similar approaches to those
used for FSSW and FSW (with heat and flow models linked in some manner),
and consequently has similar difficulties regarding temperature measurements
for validation of models and selection of appropriate constitutive laws.
Analytical models
Heat flow during welding is governed by Fourier’s 2nd law (Equation 2.1).
Analytical solutions to this problem are known for many different boundary
conditions, including various scenarios representative of welding. The seminal
work in this area is that by Rosenthal (1946), who presented an analytical
model for heat flow through conducting plates from a moving heat source (see
also Rosenthal (1941) and Rosenthal and Schmerber (1938); and see Grong
(1997), for an extensive rework of Rosenthal’s solutions and broadening of
their application). The motivation behind this work was the intention to
develop a model for arc welding, however, the models developed by Rosenthal
have since been applied to other welding situations, including seam FSW
(Gould et al., 1996, Russell et al., 1997, Russell, 2000, and Shercliff &
Colegrove, 2002).
ρC
∂T
∂t
= λ
(
∂2T
∂x2
+
∂2T
∂y2
+
∂2T
∂z2
)
+ q (2.1)
Rosenthal’s solutions are divided into 3 categories depending on the work-
26
piece thickness. These are:
• a thick plate solution, which assumes that the workpiece is a semi-
infinite solid with a heat source on the surface;
• a thin plate solution, which assumes that all heat flow is within the
plane of the plate (i.e. there is no through-thickness variation in tem-
perature);
• a medium thickness solution.
The medium plate solution is the most general (and consequently the most
complex). In the case of seam welding at sufficiently high welding speeds the
heat source travel time is short compared to the heat diffusion time. In this
case, the thick plate solution simplifies to a 2D calculation and the thin plate
solution to a 1D case. Grong’s process map was considered in relation to
FSW by Russell (2000). This work provides a map of the conditions under
which each model is accurate based on the dimensionless thickness, power
and peak temperature (Figure 2.9).
Grong’s work also provides useful insight into the timescales associated
with various processes. While steady-state solutions are often considered for
seam welding, these generally take 10 s or more to become established under
typical conditions, indicating that a transient solution will be necessary for
spot welding.
A complicating factor in applying Rosenthal’s work to FSSW is that it
assumes constant material properties, while the thermal properties of Al
vary with temperature. This variation is commonly ignored to reduce the
complexity of the calculation. Sometimes room-temperature properties are
assumed for the whole calculation, and sometimes average values over the
temperature range of interest are used. An additional reason for using room-
temperature properties, is the difficulty of measuring the correct properties at
elevated temperature: most measurements of properties take place after long
hold times. This allows equilibrium microstructures to form, which may not
happen during welding. Indeed, Colegrove & Shercliff (2006) found a better
match to experimental data using room-temperature values, rather than
27
Figure 2.9: Rosenthal solution map (image after Grong, 1997)
values for equilibrium microstructures at the correct temperatures (though
this was with a numerical, rather than analytical, model).
Numerical modelling
The most common class of numerical models, by far, consists of those based
on a finite grid representation of the deforming material. Grid-based models
use either an Eulerian mesh, where the grid is fixed and material flows
through the grid (the typical approach for fluid dynamics), or a Lagrangian
approach, where the grid deforms with the material (typically used for small-
strain, quasi-static problems such as elastic structural analysis). These mod-
els can either calculate the coupled behaviour taking into account thermal
properties and constitutive behaviour, or examine only one aspect of the
problem — typically the thermal problem in isolation. In the latter case,
it is common to neglect heat transfer by convection, and solve for a purely
conductive problem represented by a fixed grid in a rigid solid, using the
28
FE method. Fully-coupled models need a representation of the material
constitutive behaviour. This may either by derived empirically, or be derived
by modelling the microstructural changes. One of the difficulties in modelling
the microstructure during the process is that, owing to its transient nature,
the material is often very far from equilibrium.
Although finite element models are the most common by a large margin,
models based on the finite difference method are also in use (Frigaard et al.,
2001).
Thermal modelling
All thermal modelling is, at its heart, an attempt to find solutions to Fourier’s
2nd law (Equation 2.1), with appropriate boundary conditions.
Unlike many thermal processing problems (including most other welding
processes — see Section 2.1), in FSSW the heat input is not an independent,
adjustable parameter, but is intricately bound up with the flow pattern and
deformation forces in the stir zone. Nevertheless, many approaches treat the
thermal field as a separate problem, and develop a solution based around
a volumetric or, more commonly, surface heat input, such as the models
described by Colegrove & Shercliff, 2006, Colegrove et al., 2007, Khandkar
et al., 2003, Russell & Shercliff, 1999, Lambrakos et al., 2003, Frigaard et al.,
1999 and others. One major problem with this approach is the need to
fix parameters for the heat input. For example, the common parameters
used to control FSW are the downforce or plunge depth, traverse speed and
rotation speed, with the latter usually kept constant throughout a weld.
Torque or power are not normally measured, at least not unless the weld is
being conducted under experimental conditions. This leaves the power, in a
purely thermal model, to be fixed by reference to the temperatures that are
the outputs of the model. Experimental welds with power measurement have
been modelled, but there is still considerable freedom to fit other parameters,
as seen for example in Khandkar et al.’s 2003 paper where the power input
is fixed, but heat losses (modelled therein as convective backing plate losses)
are freely adjustable.
29
A recent modification to the FSW process is the development of torque
control (Longhurst et al., 2010). This is described in the literature as having
promising applications for automation; additionally, it could make rapid mod-
elling of welds in a commercial environment easier by depositing a constant,
known, power into the weld, removing a free input variable from the model.
Heat losses
Heat loss to the backing plate or anvil is an important factor in FSSW
and FSW, and it is vital to incorporate it into a model to make accurate
predictions of heat flow. Many different ways of describing heat losses within
models are described in the literature, and there is no consensus as to the
best approach. These methods are summarised here.
Some models include the backing plate explicitly in the model domain;
such models require a gap conductance for the contact between the workpiece
and backing plate, and a boundary condition for heat loss from the backing
plate to machine bed interface. Some models do not include the backing plate,
but instead model heat loss to the backing plate as a boundary condition at
the edge of the workpiece. The latter approach is more common in fully
coupled models, as there is a greater computation penalty for including the
backing plate in the meshed domain. Though it is possible (see, for example,
Ulysse, 2002), models including the backing plate tend to be thermal-only
models.
For models which include the anvil explicitly, the gap conductance be-
tween the workpiece and backing plate is an input parameter to the model.
However, it is not usually possible to measure this directly. It can be esti-
mated from the downforce and a knowledge of the contact mechanics at the
interface, and interface pressure is widely recognised as a key parameter in
the contact conductance between smooth surfaces. Cooper et al. (1969) and
Mikic (1974) explore the pressure dependency of thermal contact conductance
at length. However, this simply shifts the problem back a step, as the required
pressure is also locally unknown and will vary strongly during the course of
a weld. Owing to the elastic nature of forces in the vertical direction, it is
30
not possible to calculate such forces from a CFD calculation. An uncoupled
elastic analysis is also probably unable to predict the contact forces with
sufficient accuracy as plastic deformation is significant. Schmidt et al. (2004)
developed an analytical model for the heat flow during a weld based on the
contact forces, and the gap conductance typically increases during a weld as
the hot weld metal conforms more closely to the backing plate.
Another approach is to estimate the heat flow to the backing plate using
experimental measurements of the backing plate temperature. This can be
achieved by placing thermocouples in the backing plate — this has been
carried out at Cambridge (Dickerson, 2002) and Manchester (Prangnell &
Bakavos, 2010, and Chen, 2010). Wang et al. (2013) extend this approach
using an artificial neural network, described below.
Despite these difficulties, Soundararajan et al. (2005) used a constant
gap conductance in a fully coupled model and report predictions of the
thermal field that are within 10 % of measured values. Colegrove et al.
(2007) state that better thermal contact is achieved between the backing
plate and the workpiece after welding, due to flattening of surface asperities.
They incorporate this into their model of seam welding by adjusting the
contact conductance, setting it to be high under and behind the tool and
low elsewhere. This model is used to predict temperatures at thermocouple
points to within about 10 K. However, one effect that is not captured is the
non-uniform temperature field (it is not symmetric about the weld line, with
an 18 K difference between the advancing and retreating side). They suggest
that this is due to deflection of the tool towards the retreating side (thereby
making the retreating side thermocouple closer to the actual weld line than
thought).
In the work by Wang et al. (2013), experimental temperature measure-
ments were combined with results from numerical models as the inputs to an
artificial neural network. Various features of the temperature curves (such
as peak temperature, cooling rate, or total integral) were used to estimate
contact conductance values in a more systematic way than by trial and error.
The contact conductance model used in this work split the metal-to-metal
contacts into two zones, a high-conductance and a low-conductance zone,
31
with temperature-dependent values.
Heat is lost to the surroundings through the backing plate, from the
top surface to the surrounding air, to the tool and to the clamps. Heat
loss from the model boundary is often modelled by a convective heat flow.
Heat loss to the air is a convective solid-fluid heat transfer problem, but
for solid-solid contacts this is not a physically realistic model; therefore,
it is not possible to measure this parameter directly. The problems with
including parameters such as unknown gap conductance and/or convective
heat transfer are illustrated by Khandkar et al. (2003). In an attempt to
improve confidence in FSW/FSSW models they measured the power input to
the workpiece and used this to fix the power input to their model, rather than
adjusting the power input based on the recorded temperatures. However, the
convective heat loss from the backing plate was still unknown, and had to be
adjusted to fit the calculated temperatures to the measured data. Although
there may still be confidence in the heat flow profiles so produced, it is very
difficult to generalise such a model to accurately predict weld temperatures
under other welding conditions or geometries.
Models for contact conditions and heat generation
During FSSW, heat is generated through a combination of surface friction
and bulk heating due to deformation. Many welding studies use simplified
models where the heat is assumed to be supplied by a point heat source, and
the exact details of how the heat is generated are ignored. This provides
acceptable results for the temperature field at a large distance from the tool,
but the accuracy decreases as the distance from the tool decreases. In FSSW
it is often temperatures in the HAZ that are of interest (as this is the region
of weakest material in the post-welded state — see e.g. Bakavos & Prangnell,
2009). Models of finite-sized contact patches were used by Colegrove, and
other authors have used similar approaches for other types of welding: Ion
et al. (1992) analyse a distributed source for modelling laser welding, and
Midling & Grong (1994) use this approach with rotary friction welding of
bars. This last is of particular relevence for the present work, as rotary
32
friction welding bears many similarities to FSSW: in both, frictional heating
causes a loss of strength and possible asperity melting with bulk material
remaining solid, and the dimensions, rotation speeds and forces involved are
very similar. Midling & Grong (1994) examine friction welds in AA6082,
updating Rykalin’s 1971 solution for an infinite rod to account for finite
geometries, and they introduce a steady-state phase where the contact surface
is held at a constant temperature. This latter approach accords better with
the qualitative opinion of many authors that melting does not take place in
FSSW due to a negative feedback loop as the solidus is approached, which
occurs since loss of strength in the material leads to a lower heat input. (It
should be noted that, in a later study, Midling & Grong (1994) did in fact
find evidence of melting, but this was confined to very small regions around
asperities.)
Russell & Shercliff (1999), Colegrove et al. (2000), and Upadhyay &
Reynolds (2012) have all examined the contact condition at the interface
between the tool and the workpiece, as this is critically important for under-
standing the mechanisms of heat generation. Schmidt et al., 2004 summarised
many of the existing approaches. They define a dimensionless slip parameter
as:
δ =
vw
vt
(2.2)
where vt is simply the velocity of the tool at that point (i.e. vt = ω× r) and
vw is the velocity of workpiece material directly under that point on the tool.
The possible states of the system and the corresponding values of this
parameter are given in Table 2.3.
Condition Matrix velocity Shear stress State variable
Sticking vworkpiece = vtool τfriction > τyield δ = 1
Sticking/sliding vworkpiece < vtool τfriction ≥ τyield 0 < δ < 1
Sliding vworkpiece = 0 τfriction < τyield δ = 0
Table 2.3: Definition of contact condition, velocity/shear relationship and
state variable (dimensionless slip rate), after Schmidt et al., 2004
33
Which of these states applies in any particular case depends on the relative
values of the contact friction and yield stresses; it seems probable that the tool
interface may typically pass through all stages over the course of a single weld,
with different parts of the tool interface in different states at any instant. For
a thermal model, the heat input is often assumed to be a surface heat flux
lying between the two extremes of a fully sticking contact and a fully sliding
contact. A sticking contact model generally assumes a constant shear stress
over the tool surface; such models are used by Song & Kovacevic (2003a),
Zhu & Chao (2002), Khandkar et al. (2003) and Bastier et al. (2006):
Q =
2pi
3
τωR3s (2.3)
where Q is the input power, Rs is the radius of the shoulder, τ is the shear
stress and ω is the angular speed.
Though this can be used to predict the heat input from known material
parameters under the conditions of temperature and strain rate commonly
found in FSW, it requires an estimate of the shear stress. It has been
suggested that the best experimental method to measure the desired material
properties might be to use the FSW process itself (Schmidt & Hattel, 2005
and Schmidt & Hattel, 2008). The relationship in Equation 2.3 above may
also be used to predict the shear stress from a known power input (the power
is quite easily measured with a dynamometer). If one assumes yield takes
place according to the Tresca criterion with uniform contact pressure and
material state (temperature), Equation 2.3 becomes:
Q =
pi
3
σyωR
3 (2.4)
Russell, 2000 uses this approach to estimate the contribution to heating
from 3 regions in conventional seam FSW: the pin, the shoulder, and bulk
deforming of the workpiece. The contribution from the shoulder is as given
in Equation 2.4, that from the pin and the workpiece is shown overleaf (the
slip surface for the workpiece region is assumed to be a vertical surface, with
radius R3).
34
QP =
pi
3
σyωR
2
PLP (2.5)
QW =
pi
3
σyωR
2
3LP (2.6)
where QP and QW are the powers dissipated by slip lines along the pin and
within the workpiece, respectively, RP and LP are the pin radius and length,
and R3 is the radius of the deforming region of the workpiece.
Using typical values for 2000 series alloy, Russell finds that the contribu-
tion from the shoulder is around 90 % in 2 mm plate, 75 % in 4 mm plate and
65 % in 6 mm plate. However, it should be noted that this analysis provides
an overestimate of the power required since the proposed mechanism activates
redundant slip surfaces — if the shoulder and pin are sliding with δ = 0 there
will be no workpiece deformation. In such a case QW = 0. With partial slip,
all the mechanisms will be active to some extent, but the applicable value
of ω will be different in each term (and unknown, if the degree of slip is
unknown).
Despite the assumptions in previous analyses, the power input will not be
evenly spread over the entire tool area; one approach is to model the power
input as a linear function of power density with radius, from a known total
power (Schmidt & Hattel, 2005 and Schmidt & Hattel, 2008):
q(r) =
3Qr
2piR3s
(2.7)
where q is the power input per unit area as a function of radius and Q is the
total power; other variables are as defined previously.
Colegrove & Shercliff (2005 and 2007) used the above relationship, but
truncated the power input function at a smaller radius than that of the
shoulder. This was justified by them by reference to experimental tempera-
ture measurements; based on the accuracy of their predictions, it seems likely
that this is a good match for the power input function. This could indicate
a boundary between different power dissipation mechanisms — i.e. between
stick and slip — occurs at this point. The issue of stick vs. slip, and its
impact on heat generation, are therefore central to modelling processes such
as FSSW.
35
Flow modelling
Models have been developed to investigate the flow pattern during FSW. Ac-
curate numerical models that incorporate fully-coupled interactions between
temperature and strain must take account of elastic and plastic strains, heat
losses, and the response of the material as a function of strain rate and
temperature. There are two major issues with running fully-coupled models:
firstly, it is rare that the boundary conditions and material constitutive
model are known with sufficient accuracy to produce a generally applicable
integrated model; and secondly, such a model is very labour-intensive to
create and computationally expensive to run. A simplified approach to
modelling the flow pattern is to neglect elastic strains and to import a prior
calculation of the thermal field into a flow model (e.g. using CFD) to deter-
mine the material deformation at each point. This method is demonstrated
by Colegrove and Shercliff (2007).
Examples of fully-coupled calculations applied to seam FSW are the
arbitrary Lagrangian-Eulerian (ALE) finite element models developed by
Schmidt and Hattel (2005). This work looked at the conditions under which
a void will form during FSW, modelling in detail the welding of a sample
of AA2024 using Abaqus Explicit. By comparison with their earlier, purely
Eulerian CFD models, and experimental results, they find that the ALE
approach makes more accurate predictions but at a heavy computational
price. The greatest error with the CFD models was due to the assumption
of incompressibility, which leads to unrealistically low predicted pressures
behind the pin. (The assumption of incompressible flow is reasonable for
metals in the plastic regime, but it is a poor model for elastic regions, given
that Poisson’s ratio is around 0.33 for most metals.)
The plunge stage of FSW is essentially identical to the FSSW process,
although the goals of modelling each are different. Modelling of the plunge
stage of FSW is usually approached with a view to understanding tool wear
(because most tool wear occurs during the plunge), with its effect on the
workpiece of somewhat secondary importance. Tool wear is fastest during
the early part of the weld as the workpiece is strongest when cold. Both
36
solid mechanics and fluid mechanics approaches have been attempted as
methods of modelling the plunge, and each approach has its advantages and
disadvantages. One of the main problems with simulating the plunge using
solid mechanics approaches is the large deformation during this stage of the
process, which causes excessive mesh distortion when attempting traditional
FE analysis. However, as the elastic forces are important, computational fluid
dynamics (CFD) is also somewhat limited. Nevertheless, Gerlich et al. (2005)
presented a CFD approach to the problem. Kakarla et al. (2005) investigated
the behaviour during the plunge using an isothermal FE solid mechanics
model, in Abaqus Explicit. The behaviour during the plunge is very poorly
characterised and this work adds to the available knowledge; however, it is
unlikely that an isothermal model can give accurate quantitative predictions
of the wear rate as attempted in their paper. As temperature rises from
room strength to the solidus, the workpiece yield stress can fall by a factor
of 20 or more (Colegrove et al., 2007), and this will strongly influence the
wear rate. Attempts have also been made to model the plunge stage of seam
FSW using fully-coupled models, such as that by Mandal et al. (2008). This
work is applicable to FSSW also, since the tool does not translate during the
plunge.
Schmidt et al. (2005) modelled the plunge using an arbitrary Lagrangian-
Eulerian mesh to cope with the large strains. The constitutive behaviour
assumed for this work includes the Norton-Hoff model for viscoplastic flow
at high temperatures, whereas most other models assume Johnson-Cook
behaviour; these laws both relate flow stress to temperature and strain rate,
however the latter is a poor representation of the measured response for Al
alloys. The divergence of the Johnson-Cook model from measured behaviour
is greatest near the solidus — precisely the region of interest for FSSW. This
is explored further in Section 2.4. The work by Mandal et al. is of particular
note as it compares calculated results to experimental measurements (both
their own, and previously published work by Feng et al., 2005).
Arbitrary Lagrangian-Eulerian (ALE) models are, as the name suggests, a
hybrid between those two methods (i.e., between Lagrangian (‘solid’) meshes
and Eulerian (‘fluid’) ones — explained in more depth in Section 2.3.4).
37
Developed for solving multiphysics problems that could not be reasonably
solved using either discretisation technique on its own, they are commonly
used for situations with a free surface, or with a moving interface between
a solid and a fluid. Guerdoux et al. (2004a) have compared similar models
using both Lagrangian and ALE methods; in their later work (Guerdoux
& Fourment, 2007) they apply this to a full seam weld using the Forge3
code. A Lagrangian mesh is used to model the plunge and a fixed mesh is
used to model the steady-state phase. However, the model shows extreme
void formation and flash extrusion during the plunge to a degree that is not
observed during real welding.
Another class of modelling approach is smoothed particle hydrodynamics.
This is a mesh-free numerical method that has seen use in time-dependent
fluid mechanics problems, and to a more limited extent in solid mechanics
work. Recently, some authors have taken this method and applied it to FSW.
Bhojwani (2007) developed a 2D smoothed particle hydrodynamics (SPH)
model of the flow problem during FSW and attempted quantitative analyses,
but this work is still at a very early stage.
Tartakovsky et al. (2006) published one of the earliest reports of SPH
applied to FSW, developing 2D and 3D models of various tool shapes, though
in their paper they only report qualitative comparisons with experiment. Das
& Cleary (2007) developed a single-phase SPH model of fusion welding, which
captures both elastic and plastic behaviour and predicts temperatures and
deformation.
The SPH approach holds considerable promise for future modelling, as it
has no problems associated with large deformations, but the mathematical
underpinnings are not yet as robust as for FE and CFD codes. In other fields
where it is used (primarily those dealing with hypersonic flow problems) it is
generally considered to be a much faster modelling approach than grid-based
solvers, though less accurate.
38
2.3.5 Empirical testing and validation
The power input is an important parameter for all modelling. With some
experimental welds, the power is known, being measured by a dynamometer
or other means. For other cases it must be estimated somehow, either from
the weld parameters or from measured temperatures. A flow model may be
able to predict the heat generation, as shown by Colegrove and Shercliff (2003
& 2006), and Colegrove et al. (2007), whereas for a purely thermal model it
is an imposed boundary condition as discussed earlier.
Colegrove et al. (2007) modelled the heat input by assuming contact
between the tool and workpiece only up to a certain fraction of the shoulder
radius, and found that this improved agreement with experimental results.
However, there are no direct measurements of the spatial power distribution
available in the literature; most of these assumed profiles come from theoret-
ical considerations, and their validity derives from the ability of the models
to predict the final temperatures. A knowledge of how the profile influences
the final weld will be useful for designing new tools both to improve the weld
properties and to reduce tool wear.
On the other hand, the temporal variation in power input is much more
easily measured. A good example of such work is that by Gerlich et al.
(2005), who measured the downforce and torque during FSSW, as shown
in Figure 2.10. This clearly illustrates the softening of the workpiece as the
temperature rises (the drop in axial force and torque from about 3 s onwards,
at constant displacement). The two peaks in force are due to the pin and
shoulder respectively.
There is a strong tendency within the existing literature to use numerical
approaches, particularly thermal FE and fully-coupled FE models, to produce
models of particular welding cases without much regard to their experimental
accuracy. Substantial numbers of papers can be easily found that present
the results of a finite element model without any experimental results for
comparison, or by comparing predicted temperature outputs at a point with
a single thermocouple measurement, often for one single weld.
The author does not consider single output thermocouple locations, nor
39
Figure 2.10: Sample downforce and torque measurements from FSSW
(figure from Gerlich et al., 2005)
unvalidated FE calculations, to be sufficiently reliable as to form the basis of
further work without much more extensive experimental comparisons. One
of the few papers with a more through investigation into the accuracy of
modelling approaches is by Su et al. (2006a), wherein an attempt is made to
verify model approaches by measuring the total heat input into the workpiece
by calorimetry. This is done by using an oil bath to measure the heat content
of the workpiece at the end of welding. These calorimetry results are of
particular interest, as they found that a low fraction of the input energy
is deposited in the workpiece, with the rest of the energy being lost to the
tool, backing plate, anvil and other surroundings. 12.6 % of the energy was
deposited in the tool with a steel backing plate, and 50 % with a mica backing
plate (for AA6111 welds). During plunge testing, around 4 % of the total
input energy was used in stir zone formation. Although FSSW is already
a low-power and efficient process by comparison with its main competitor
RSW, these results raise the possibility that further reductions in energy
input may be possible.
In a separate paper (Su et al., 2006b), the same authors report on exper-
imental visualisation of the flow pattern during FSSW using two techniques:
40
firstly, etching of dissimilar welds between AA5754 and AA6111 (where the
different etching characteristics show the final pattern), and secondly by using
finely-dispersed particles of alumina in an AA6111 weld.
Given the lack of existing validated approaches within the literature, an
important component of this present work will be to examine the robustness
of FE models and estimate their reliability.
2.3.6 Microstructural modelling
In practice, it is rarely worth the complexity of using a dynamic microstruc-
tural model to determine the constitutive behaviour, and this is measured
experimentally and fed into the deformation analysis. Microstructural models
are then incorporated as a post-processing step, using the calculated thermal
history.
Kamp et al. (2006a,b) demonstrated the application of a kinetic reac-
tion model to a FSW thermal cycle by using the Kampmann and Wagner
method to model the response of AA7449 to FSW. This method is based on
classical nucleation and phase transformation theory, is capable of tracking
the precipitate size distribution over the course of a non-isothermal heat
treatment. They used both isothermal holds and Jominy end quench tests
for calibration. This model has been used extensively to model thermal cycles
due to other welding processes (see e.g. Myhr et al. (1997, 1998), who applied
it to AA6082).
A simpler model has been developed by Hyoe et al. (2003) that only
takes account of the thermal effects, and does not account for the effect of
deformation on the reaction kinetics. This model assumes that the precipitate
content is at a maximum prior to welding (and is therefore only applicable
to certain tempers). Nevertheless, this model predicts hardnesses that are in
good agreement with experimental results.
Robson et al. (2007) used a semi-empirical properties model linked to a
thermal model developed by Mackwood (2001) to predict hardness profiles
in 7449 and 6013 Al alloys, and found agreement with experimental results.
Their model can predict the microstructure and properties of age-hardenable
41
alloys after non-isothermal heat-treatment, based on work by Kampmann
& Wagner (1991) who developed a microstructural model to predict the
evolution of precipitates in the HAZ. It relies on calibration data derived
from isothermal experiments on the same alloys, and can predict the form of
hardness profiles with some degree of success. As expected from the general
consensus in the literature, hardness in the HAZ is found to depend strongly
on the peak temperature, with hold times at lower temperatures having a
much smaller effect, due to the reaction rate terms containing a 4th order
dependence on temperature.
Deschamps et al. (2005) studied the problem of independently measuring
the parameters applicable to non-isothermal kinetic models in substantial
depth, using less complex thermal histories than those imposed by FSW to
study precipitation. Other models of microstructure evolution in Al welding
have been developed by Grong (1997), Bjorneklett et al. (1999), and more
recently Babu (2009) and Mathon et al. (2009), but substantial research
remains to be done in this area.
2.3.7 Modelling of related non-welding processes
Non-welding processes that involve deformation, heating, and deformation-
induced heating of Al include extrusion and forging. Section 2.3.3 discussed
the temperature and strain rate regime in which FSSW operates; both extru-
sion and forging tend to operate at much lower levels — strain rates of 1 s−1
are generally considered high for both processes (Ferrasse et al., 1997, Prasad
et al., 1984), so models for these processes will have only limited applicability
to FSSW.
2.4 Constitutive data
All the modelling approaches described here share one thing in common: they
require accurate material models to produce useful, realistic results. For the
conditions that prevail during FSSW, it is difficult to obtain accurate material
data, and data for many materials is lacking. The range of temperature
42
(up to the solidus, for Al, around 800 K), strain-rate (from quasi-static up
to around 1000 s−1) and strains (many times the strain to first yield) are
difficult to reproduce in any environment apart from that of friction welding
processes, although hot-working deformation testing machines such as the
GleebleTM system may be able to with careful setup, at least for Al. However,
even when the desired test conditions are obtained, there are problems with
knowing what the correct outcome measures are. Material models used in
these ranges include, amongst others, the Zener-Hollomon model and the
Johnson-Cook model. Each of these was originally derived for specific metals
under specific conditions, and the extrapolation of any of them outside these
conditions is problematic. Voce’s equation (given in Equation 2.8 from Voce,
1955) incorporates a strain dependent term and has been cited in later work,
but is clearly not suitable for present purposes as it does not include a strain-
rate dependent term.
σ = σ∞ − (σ∞ − σ0)e−(ε/εc) (2.8)
Ludwik’s equation is widely used in the literature on casting and forging
in an effort to include the effects of creep and strain hardening, which are
applicable in different but overlapping temperature regimes. (See, for exam-
ple, measurements of the Ludwik parameters for 3000, 5000 and 6000 series
Al alloys, including AA6111 in Alankar & Wells, 2010). Work hardening
is strongest at low temperatures, creep at high temperatures. However,
Ramaekers and Veenstra (1970) find that, using reasonable experimental data
for steel, Ludwik’s original equation (Equation 2.9) leads to a prediction of
negative yield stress when large deformation data is included in the dataset.
This has led to the adoption of a modified Ludwik equation (Equation 2.10)
which is extensively used in casting and forging.
σ = σ0 +K1[ε¯]
l (2.9)
σ = K2(εp + εp0)
n(ε˙p + ˙εp0)
m (2.10)
where K1, K2, l, m and n are empirically measured material parameters.
43
The Johnson-Cook model (Equation 2.11, below) is one of the most
commonly-used material models in the literature on FSSW and FSW. It
is widely used in the ballistic and impact testing community, and because of
this, it is also used extensively in FE simulations of slower processes — such
as FSW — but its use at lower strain-rates is questionable. Furthermore, the
Johnson-Cook model was initially developed for austenitic steel, and this is
the only material for which extensive tests of the model exist in the literature.
However, it is important to document it here since many authors use it in
FSSW modelling (e.g. Schmidt & Hattel, 2005 and Awang & Mucino, 2010,
both of which are regarded as key papers in the field).
σ = (A+Bεnp )(1 + C ln
ε˙
ε˙0
)
(
1−
[
T − T0
Tmelt − T0
]m)
(2.11)
where A, B, C, m and n are material parameters and other symbols have
their usual meanings.
Like Johnson and Cook’s work, the Zener-Hollomon law was also origi-
nally developed for steel (Zener & Hollomon, 1944). Many constitutive laws
are derived purely from experimental correlations; unlike these, the Zener-
Hollomon law is based on an assumption that mechanical flow properties have
associated activation energies, and depend on a dimensionless group such
that the temperature and strain rates are linked to the flow stress through a
single parameter as seen in Equation 2.12. Sellars & Tegart (1972), proposed
a relationship between this parameter and the strength of Al which has the
form given in Equation 2.13 (as modified by Sheppard & Wright, 1979). This
relationship has been successfully used in previous studies of seam FSW (e.g.
Colegrove et al., 2007 and Frigaard et al., 2001) and is widely accepted in
the literature as a suitable material model for Al under the conditions that
prevail during FSSW.
Z = ε˙e
Q
RT (2.12)
Z = A sinh(ασ)n (2.13)
where A, n and α are material constants.
44
Figure 2.11: Zener-Hollomon and Johnson-Cook models for AA2024
The Zener-Hollomon and Johnson-Cook laws give very different results in
the temperature region of interest for FSSW. See Figure 2.11 for a comparison
of these two models for AA2024: as temperatures approach the solidus, the
models diverge even further. An advantage of the Johnson-Cook model
is that it includes strain-dependent behaviour, which the Zener-Hollomon
model neglects, though this is not an issue for Al alloys during FSSW.
2.5 Issues for further study
Initial studies, such as those by Bakavos & Prangnell (2009) and Bakavos
et al. (2011) described earlier, have investigated the variation of weld strengths
and failure energies with sets of welding parameters, and also looked at the
flow patterns and microstructures produced. However, there remains a lack
of understanding regarding exactly how changes in process variables affect
welds, and also regarding the mechanisms by which FSSW forms successful
joints. A systematic and structured experimental programme can address
these issues to some extent, however, there remain three main areas of
study which cannot be understood exclusively by reference to experiments
45
at present.
The first of these is to develop a detailed understanding of heat flow
within the workpiece (and the tool, to a lesser extent). While thermocouple
measurements are reliable, practical limitations mean that the details of heat
flow in weld nuggets cannot be resolved at present. It is precisely this region
under the tool where the temperatures are of most interest, but the spatial
resolution of the thermocouples available (0.5 mm at best) and their fragility
makes them unsuitable for this purpose. Other measurement techniques are
available, notably thermal cameras, but these all have their own particular
limitations. Thermal cameras can only measure surface temperatures, and
for this purpose they are not as precise as thermocouples, nor as reliable with
aluminium. An accurate thermal model can be used in models of microstruc-
ture evolution to understand the processes taking place at a microscopic level.
The second aim of modelling efforts must be to understand the flow
pattern. Etched images of interrupted welds between AA6111 and 6082
are innovative and very useful in this regard, but again the experiments
alone are insufficient to establish an understanding of the flow. In this
case, practical limitations on the number of experiments and the difficulty
inherent in interrupting a weld at a specific point are the limiting factors.
The experiments conducted so far have provided evidence for what structures
form, but there is a gap of knowledge regarding how they form and what
behaviour gives rise to what weld features.
The final modelling goal is to link the flow behaviour to heat generation,
torque and power via the constitutive law of the material (or materials) being
welded. This will ‘close the loop’ between models, experiments and produc-
tion welding, and lay the foundation for both an enhanced understanding of
the process at a fundamental level.
2.5.1 Need for new techniques
As described, many different modelling techniques already exist, including
those developed specifically for welding (such as Rosenthal and Grong’s
work), and those of more general application such as FE and CFD codes.
46
Unfortunately, none of these are entirely suitable for modelling FSSW, for
the reasons discussed above.
Analytical models of heat flow, for example, do not capture sufficient
detail to be used for accurate predictions of specific welds, such as are required
for microstructural models; analytical flow models are not available. (This
is not entirely true, as it could be argued that applying the Navier-Stokes
equations with correct boundary conditions would solve the flow problem.
While this view is possibly correct, a general solution to the Navier-Stokes
equations is not known, and in any case there would remain the problem of
finding the correct boundary conditions.)
Numerical models have already been used extensively to model FSW, and
these techniques can be applied to FSSW. However, they do not provide a
physical understanding of the problem, and are in general very sensitive to the
constitutive law chosen for the model. Furthermore, the run times for these
modelling techniques, particularly for fully-coupled 3D welding simulations,
are very large. While quoted values for runtimes are of only limited utility
(since hardware differences, reductions in model complexity due to symmetry,
and changes in mesh parameters have enormous influence over the time
taken), simulation times of over a month are seen in the literature, and
anything less than a week is generally considered reasonably quick. A large
parametric study might involve four or five variables, each taking three or four
values, which would be impractically long — especially when an experimental
program could run as many experiments in a few hours or less.
Consequently, there is a need for two types of model, which do not yet
exist so far as can be reasonably ascertained. Firstly, an analytical model
of the flow behaviour that can give insights into the trends and patterns
associated with the kind of flow that occurs in FSSW. It would be useful if
this could include thermal effects, but the primary requirement of this model
would be to accurately represent flow features. Secondly, a comparatively
fast model, which can be used to examine the trends that occur with changes
in welding conditions. This latter model should include as much of the
real behaviour as is necessary to produce an accurate model, but no more.
Simplified numerical methods, e.g. taking account of the symmetry in the
47
problem or intelligently handling the kinematic constraints show the most
promise in this regard.
Such models may turn out to have wider applicability, since there are a
number of other processes, friction and ultrasonic welding foremost amongst
them, which exhibit similar combinations of strong kinematic constraints,
friction and deformation processes, and intense thermal transients.
48
Chapter 3
Experimental work
3.1 Introduction
This thesis is part of a joint EPSRC-funded project with Manchester
Materials Science Centre. Experimental work was predominantly conducted
at Manchester, with additional joint experiments conducted at TWI with the
author. While the author carried out some experiments at Manchester, the
modelling work drew heavily on experiments conducted by other members
of the group, and it is most convenient to summarise all of the experimental
work together. The primary collaborators were Yingchun Chen and Dim-
itrios Bakavos (University of Manchester) and Nathan Horrex (TWI Ltd.)
for the instrumented weld experiments, and Bethany Parker (University of
Cambridge) for the hardness tests and weld profile measurements. For the
welding experiments, the author was involved in all of the experiments that
took place at TWI (see Table 3.3), and the experiments at Manchester using
the flat tool. The remainder were carried out by the collaborators named
above. The author set up the Talysurf machine for the weld profile tests and
performed the first two experiments, the rest of the profiles were measured
by Parker. Except as noted in relevant figure captions, data extraction and
plotting was carried out by the author, and the interpretation of the work is
the author’s own.
This chapter draws together a range of experiments with different goals:
some of the experiments presented here were conducted with the express goal
of understanding the behaviour of aluminium and steel when subjected to the
49
FSSW process, and with a view to supporting the modelling work presented
in later chapters. Some of the experiments were conducted for related but
different purposes, such as optimising tool settings, producing high-quality
welds in different materials or finding a viable parameter space for alternative
tool types, but are nevertheless useful from a modelling perspective and so are
presented here alongside the other work. The primary aim of this chapter is
to collate these experiments and organise them to develop a coherent picture
of FSSW at a fundamental level.
3.2 Methodology
Friction stir spot welds were performed on two machines for this series of
experiments; the machines in question were a CS Powerstir machine at
Manchester, and a custom-built machine at TWI. The CS Powerstir machine
is shown in Figure 3.1, and it is capable of producing a maximum power
output of 25 kW and a maximum downforce of 100 kN, with tool speeds
ranging from 0 to 2000 rev/min. The experiments at TWI used the Artemis
instrumented tool connector between the tool and the machine; identical
tools were used on both machines.
The workpieces were machined into 100 mm x 25 mm coupons for lap
welding. For the double lap/butt flow visualisation experiments (described
later), 25 mm x 30 mm Al coupons were used. The sheets were all nominally
0.91 mm thick; a sample of sheets were measured to 0.01 mm precision and
found to be accurate to their nominal dimension. The arrangement of the
tool, workpieces and clamps for a lap weld is shown in Figure 3.2; that for a
butt weld was identical except for the horizontal position of the workpieces.
Thermocouples were used to measure temperatures in the welds; these
were K-type (NiCr–NiAl bimetallic) thermocouples of 0.5 mm diameter.
Grooves were cut into the backing plate and holes were drilled into the
workpieces to allow the thermocouples to be located at the appropriate
positions, shown schematically in Figure 3.3.
The materials used were AA6111-T4 and AA6082 Al alloys, and DC04
mild steel. The nominal compositions of these materials are given in Table
50
Figure 3.1: CS Powerstir machine
Figure 3.2: Welding setup
Figure 3.3: Thermocouple locations; typical parameters were r1 = 0,
r2 = 4, r3 = 8 and h = 0.1 (dimensions in mm), with specific values
for each weld given in Table 3.3.
51
3.1, and their standard properties are given in Table 3.2. All coupons were
machined from the same batch to minimise variation between samples. Ex-
perimental welds covered a range of rotation speeds, material combinations,
plunge depths, dwell times and tool types. A summary of the welds made at
Manchester and TWI is given in Table 3.3.
Various tool types were used for welding. The most extensive series
of experiments were conducted with a flat tool; a tool with wide grooves
(‘flutes’) extending over approximately 80 % of the tool radius was also used
for a large number of welds. This tool was termed the ‘wiper’ tool and was
found to produce stronger joints in Al to Fe welds than the flat tool. A
number of other shoulder surface profiles were tested, and these are shown in
Figure 3.4; a fuller discussion of their characteristics is given in Section 3.4.
Figure 3.4: The different pinless tool designs compared in this work,
from Bakavos & Prangnell (2009): (a) the featureless flat tool, (b)
the short flute wiper tool, (c) the long flute wiper tool, (d) the fluted
scroll tool, and (e) the proud wiper tool
52
Alloy Cu Si Zn Fe Mg Mn Cr Ti Al
6082 <1 7–13 <2 <5 6–12 4–10 <2.5 <1 balance
6111 5–9 6–11 <1.5 <4 5–10 1–4.5 <1 <1 balance
C Mn P S Fe
DC04 <0.8 <4 <0.3 <0.3 balance
Table 3.1: Nominal material composition of the alloys used in this study,
in % by weight; composition data from the Aluminium Association
and SSAB Tunnplat.
Alloy Density
Thermal
conductivity
Specific heat
capacity
0.2 % proof
stress∗
kg m-3 W m-1 K-1 J kg-3 K-1 MPa
6111 2700 143 800 149
6082 2690 172 870 149
DC04 7850 47 419 310
Table 3.2: Material properties of the materials used in this study, at
room temperature. High-temperature properties were used in some
models, and are given in the relevant chapters. Data from Mills
(2001), the Aluminium Association and SSAB Tunnplat.
∗The AA6082 used for these experiments was artificially aged to give the
same room-temperature hardness as AA6111-T4.
53
Top sheet
material
Bottom sheet
material
Tool type Tool speed Dwell time
Plunge
depth
Backing
plate
material
Thermocouple
distances from
centreline
Thermocouple
depths from
top surface
Institution
rev min-1 s mm mm mm mm
AA6111 AA6111 Flat 2000 2.5, 5, 30 0.2 steel 0 1.8 Manchester
6111 6111 Flat 2000 2.5, 5, 30 0.2 Macor 0 1.8 Manchester
6111/6082 6111 Flat 2000 2.5 0.2 steel 2.5, 5, 10 1.7 Manchester
6111/6082 6111
Short flute wiper
(CW & ACW)*
2000 2.5 0.2 steel 2.5, 5, 10 1.7 Manchester
6111/6082 6111 Scroll 2000 2.5 0.2 steel 2.5, 5, 10 1.7 Manchester
6111/6082 6111 Proud wiper 2000 2.5 0.2 steel 2.5, 5, 10 1.7 Manchester
6111/6082 6111 Long flute wiper 2000 0.5, 1, 2.5 0.2 steel 2.5, 5, 10 1.7 Manchester
6111 DC04 Flat 1600 1
0.1, 0.3,
0.5, 0.7
steel - - Manchester
6111 DC04 Flat & wiper 2000 1 0.5 steel 0, 2.5 1 Manchester
6111 DX54Z Flat & wiper 2000 1 0.5 steel 0, 2.5 1 Manchester
6111 DC04 Flat
800, 1200,
1600, 2000
1 0.5 steel in tool in tool Manchester
6111 6111 Flat
400, 800,
1200, 1600,
2000, 3000
1 0.2 steel 2, 6, 10 1.8 TWI
6111 6111 Flat 800 2 0.2 steel 2, 6, 10 1.8 TWI
6111 6111 Flat 2000 1, 2, 4, 6 0.2 steel 2, 6, 10 1.8 TWI
6111 6111 Wiper 800, 2000 2 0.2 steel 2, 6, 10 1.8 TWI
6111 6082 Flat 800 2 0.2 steel 2, 6, 10 1.8 TWI
6111 6082 Wiper 800 2 0.2 steel 2, 6, 10 1.8 TWI
6111 DC04 Flat 800 2 0.2 steel 2, 6, 10 1.8 TWI
6111 DC04 Wiper 800, 2000 2 0.2 steel 2, 6, 10 1.8 TWI
6111/6082 DC04 Flat 800, 1600 0.5, 1, 2, 4 0.2 steel 2, 6, 10 1.8 TWI
6111/6082 DC04 Wiper 800 2 0.2 steel 2, 6, 10 1.8 TWI
Table 3.3: Summary of experimental welds
*Clockwise and anti-clockwise
3.3 Welding parameters
A parametric investigation was undertaken to examine the influence of se-
lected independent welding variables. These experiments were all conducted
with the same geometry as specified in Section 3.2, with 2 sheets of AA6111
in a lap configuration as the default case. The standard weld was a 1 s weld
at a rotation speed1 of 2000 rev/min, with a 0.2 mm nominal plunge depth
using a flat H13 steel tool. The welding parameters were all kept constant
except for the one variable at a time being tested. The variables studied were
workpiece material, dwell time and rotation speed.
3.3.1 Welding time
The effect of dwell time on peak temperature, and on the form of the tem-
perature rise, was examined. The variation of temperature with dwell time
was examined for the standard case, with dwell times of 1, 2, 4 and 6 s; these
results are shown in Figure 3.5. Temperatures at the 2 mm thermocouple
(the hottest out of the locations measured) increased slightly between 1 s and
2 s, but then remained constant within the bounds of experimental error.
The conclusions that can be drawn from Figure 3.5 are that the solidus
is reached at the interface within a short time (probably less than 1 s),
and that the temperature field remains fairly static after about 2 s. This
indicates that steady-state conditions are reached by this time. This ties in
well with post-weld strength tests conducted by Bakavos and Chen, where
optimum strengths were found at 1 s. It appears likely that the joint is
entirely formed by this time, with longer dwells simply causing a loss of
strength in surrounding HAZ material via processes such as coarsening of
precipitates.
Full thermocouple histories for these welds are shown in Figure 3.6. These
1Although the SI unit is radians per second, many experimental papers still use
revolutions per minute, therefore the older unit is used here where appropriate to conform
to stylistic conventions in the field. (The conversion factor is 1 rev/min ' 0.10472 s−1,
∴ (800 to 2000) rev/min ' (84 to 210) s-1.)
55
Figure 3.5: Variation in peak temperature with dwell time for the
standard welding case
Figure 3.6: Thermocouple histories at 3 thermocouple locations for dwell
times of 1, 2, 4 and 6 s
56
results confirm the previous conclusions — at least in terms of the temper-
ature field, it is apparent that steady-state conditions have been established
certainly by the 4 s point for the thermocouples nearest the weld. The 10
mm thermocouple continues to experience a slight temperature rise even at
6 s; as discussed, at this distance the characteristic heat flow time is more
similar to the welding time, so it is expected that steady-state conditions will
take longer to become established at this distance. This thermocouple is also
closer to the edge of the workpiece, and it is possible that edge effects are
becoming significant.
Bakavos and Chen have extended this series of welds up to 30 s; steady-
state temperatures are definitely reached after 10 s, and the temperature
after 1 s is within 5 % of this value.
3.3.2 Rotation speed
The next parameter to be varied was the angular speed of the tool. Speeds
tested covered the range from 400 to 3000 rev/min (42 to 315 s-1). All these
tool speeds produced a weld, although of varying quality, with the exception
of the 400 rev/min (42 rad/s) case. This failed to produce a weld at all,
and the two workpieces fell apart post-weld. On inspection of the surface,
it appeared that the tool had achieved only a negligible plunge into the top
surface, and the interface between the two workpieces underneath the tool
showed no sign of deformation. It seems that at this low rotation speed either
the heat produced is not sufficient to soften the workpiece and allow the tool
to grip, or simply that the forces are insufficient to produce deformation, or
both. It is highly likely that a different mechanism is involved in dissipating
the power at this speed (i.e. pure surface friction, with no associated plastic
work).
The corresponding peak temperatures measured are shown in Figure 3.7.
These are the peak temperatures measured by a thermocouple 2 mm from the
weld centreline. The temperature would be expected to be higher at higher
welding speeds, and this is seen in the results. However, the quantitative
form of the relationship between tool speed and temperature is not obvious,
57
Figure 3.7: Variation in peak temperature with tool speed
due to the interaction between heat input and softening. If the torque was
the same in each weld, then the heat input would be proportional to the
speed; it clearly is not, indicating that the softening effect is important (as
expected).
Fitting functions were plotted on these results, and R2 values for linear,
logarithmic and quadratic fitting functions are 0.59, 0.85, and 0.77. If the
400 rev/min case is ignored the correlation coefficient for the logarithmic
case can be improved to 0.99. There is reason to think this is valid, since at
400 rev/min no weld was formed, as described above.
The fact that the torque is not constant, indicates that very simple models
that assume heat generation entirely by friction not only ignore the physics of
the problem, but that they are not even good approximate empirical models
of the overall heat input. Even where models have accounted for additional
effects over and above simple Coulomb friction, there is no simple dry friction
law which would give rise to a logarithmic variation in power with surface
velocity. This is discussed in more detail in the chapters on modelling.
It is surprising that the logarithmic function is such a good fit. This
indicates that the torque drops off very steeply as the tool speed increases,
58
as otherwise the increase in power and peak temperature with speed would
be greater than that observed; this tends to support the assumption in
much of the literature that peak temperatures at the interface are very
close to the solidus over a wide range of welding conditions. If the interface
temperatures were substantially below the solidus at low speeds, then an
increase in tool speed should more than compensate for the drop in torque
caused by softening, and the total power (and hence peak temperature)
should increase; if the lower speed is sufficient to bring a layer of material up
to the solidus, then an increase in speed will result in a drop in torque such
that the total power is largely unaltered.
3.3.3 Workpiece material
The workpiece material has perhaps the largest influence over the behaviour
of a weld out of all the variables studied. Chapter 2 describes other studies
where the FSSW process is implemented in a wide range of materials; for the
purposes of this study, three materials were experimentally tested: AA6082
and AA6111 aluminium alloys, and DC04 steel. Their compositions are given
in Table 3.1.
Some of the welds were arranged in a double lap/butt configuration. The
weld material in these cases comprised two sheets of Al above a sheet of
either Al or steel. The two sheets of Al were made from the alloys AA6082
and AA6111, aged to give the same room-temperature hardness in each.
The primary purpose in using AA6082 alongside AA6111 was to deter-
mine the flow pattern: the use of the different alloys makes it possible to
section them post-weld and examine the final distribution of the initial sheets.
As the strengths are the same, the expectation is that this will produce a
weld that is very similar to a single lap weld of Al over Fe.
AA6082 and AA6111
The two Al alloys used were treated to have the same room-strength hardness;
despite this, other differences between the two alloys could cause different be-
haviour under otherwise identical welding conditions. Because of the possible
59
differences in their high-temperature properties, it was necessary to evaluate
welds made in these two alloys to see if they did in fact behave similarly, in
order to use them in later Al to Fe experiments.
Temperature histories for these welds are shown in Figure 3.8. These
welds have identical parameters, except for the workpiece material. Both
welds used AA6111 for the top sheet, while the bottom sheet was either
another sheet of 6111, or 6082. These two welds produced thermocouple
temperature histories that were identical within the bounds of experimental
variation identified in Section 3.6; therefore it is concluded that there is no
significant difference between these two alloys under these welding conditions.
Aluminium and steel
The combination of Al and Fe is of particular importance in the automotive
industry. An important part of this experimental programme is to study
FSSW as a joining method for these two materials, especially AA6111 (as a
typical medium-strength, heat-treatable alloy) and DC04 as a representative
mild steel.
The standard case for these welds was a 2 s weld at 800 rev/min. (This
is different to the Al to Al case, since good-quality welds were desired for
the reference cases with each material, and these conditions were required to
produce good-quality welds due to the lower conductivity of Fe compared to
Al). Under otherwise identical conditions, the peak temperatures recorded
at the 2 mm thermocouple were approximately 30 K lower in the weld with
an Fe lower workpiece than an Al one (see Figure 3.9). The same difference
was observed at the second thermocouple, however, the 10 mm thermocouple
measurements were essentially identical.
Clearly, the lower conductivity of Fe as compared to Al has an influence;
as the thermocouples are located in the steel sheet, the peak temperatures
would be expected to be lower. Correspondingly, the peak temperatures in
the upper (Al) workpiece are probably higher (since heat is being conducted
away more slowly). Importantly, this will also raise the temperature at the
tool–workpiece interface. Since the Al sheet will be hotter in the case of a
60
Figure 3.8: Thermocouple histories for 2 s welds at 800 rev/min, between
AA6111 and itself (black curves) and 6082 and 6111 (red curves)
Figure 3.9: Thermocouple histories for 2 s welds at 800 rev/min, between
AA6111 and itself (black curves) and 6111 and DC04 (red curves)
61
dissimilar weld, the deformation pattern could be significantly affected (since
most of the deformation occurs in the Al sheet — see Chapters 5 and 6).
What is unknown from the experimental data alone, is if the total heat input
remains the same as in the Al to Al case, or if it falls due to greater softening
of the Al, or if it rises due to some deformation taking place in the lower
sheet (which is much stronger in the dissimilar case). As the power input is
not known the temperatures in the Al workpiece are not necessarily hotter
— it is possible that the power input is lower in the dissimilar case. The fact
that the peak temperature recorded at 10 mm from the tool is very similar
in the two cases might suggest that the heat input is the same; however, the
volumetric heat capacity of the steel workpiece is higher (by approximately
50 %) than that of the Al one, the diffusivities are different, and the contact
conductances likely vary too, so this cannot be resolved without thermal
modelling. This is explored in Chapter 4.
3.3.4 Welding time — Al to Fe
In Section 4.2, the relationship between welding time and the characteristic
heat flow time is discussed. In the context of a steel lower sheet, Equations
4.1 to 4.4 indicate that the two thermocouples nearest the weld centre can
be considered to be a short distance from the heat source. The corollary
of the argument presented in Section 4.2 is that long dwell time thermal
histories appear to be extensions of shorter ones. To check this assumption,
thermocouple histories were measured for Al to Fe welds at 0, 1, 2 and 4 s.
(NB: all these times are the dwell times after completion of the plunge, when
tool vertical motion is nominally zero — hence the weld time in each case
is approximately 1/2 s longer than the quoted time; this cannot be quoted
exactly for each weld as the contact time between the tool and the workpiece
also depends on the time taken to retract the tool, which in turn depends on
the plunge actually achieved — see Section 3.7 and Chapter 5.)
These temperature histories are plotted in Figure 3.10. From this figure,
it is possible to see that the assumption that the thermocouples are close to
the heat source is valid. Indeed, the temperature histories for the two closest
62
Figure 3.10: Thermocouple histories for welds between Al and Fe at
1600 rev/min, at 0, 1, 2 and 4 s dwell time
thermocouple points lie almost on top of one another, and those at the 10
mm location are also very close. In addition to confirming the validity of the
analysis in Section 4.2, this makes the modelling task easier as short-duration
welds can be treated simply as truncated versions of long-duration welds.
3.3.5 Rotation speed — Al to Fe
The previous analysis for welds made at different speeds was repeated with
dissimilar materials. Due to the clamping arrangements and the smaller
parameter space available for producing actual welds between Al and Fe (as
compared to Al to itself), the range of speeds covered was smaller than in the
study of Al to Al welds, covering only 800 to 1600 rev/min (84 to 168 rad/s).
A similar trend was found as for the previous study: the peak temperature
reached increased with welding speed at the bottom end of the viable speed
range, reaching a plateau. Temperature histories are shown in Figure 3.11
for the same locations as previously; there is no significant difference between
the measured histories for the 126 and 168 rad/s cases. While the number
63
of data points is not sufficient to establish a quantitative trend, the previous
assumed logarithmic fit is at least consistent with these new results. Again,
this supports assumptions in the literature that peak temperatures in FSSW
are usually at or very close to the solidus.
Figure 3.11: Thermocouple histories for 1 s welds between Al and Fe
64
3.4 Tool types
Welding tools for FSSW and FSW come in a range of sizes and geometries,
with patterns on the shoulder and pin and changes in the pin length, quite
apart from radically different tool types such as self-reacting bobbin tools
(only used for seam welding) and refill FSSW tools. Pin features can include
round pins, threaded pins, and more complex helical patterns, while shoulders
can have a variety of patterns inscribed on the surface. This study used five
different tool types, which are all shown in Figure 3.4. The 2 recessed wiper
(long and short) tools have wide grooves cut into the surface, and the scroll
tool has longer but narrower grooves. The proud wiper tool has ridges raised
out of the surface of the shoulder, with a similar width. These tool designs
produce distinct thermal fields in the weldzone, shown in Figure 3.12. The
short wiper tool was used twice (once clockwise, once anticlockwise, looking
down on the tool). The results for the long wiper are not presented as they
were very similar to the results from the short wiper, but the strength of joints
made with the short wiper was significantly higher. The welds produced by
the proud wiper were not considered to be of acceptable quality; only a very
limited range of conditions resulted in a joint at all, and the welds that did
form were of very low strength. The tool was described by one investigator as
‘in hindsight, more like a milling tool than a welding tool’. The results from
the scroll tool were also found to be rather poor, so further work concentrated
entirely on the flat tool and the clockwise wiper tool.
The data presented in Figure 3.12 are only based on one weld run for each
case, so there is some uncertainty in each curve. Nevertheless, the maximum
temperatures measured in welds with different tools differ by around 50 K;
this is greater than the weld-to-weld variability as observed in Figures 3.14
and 3.15 (discussed later).
The difference in tool design could affect the temperature field in various
ways. Features on the tool could influence the flow pattern, thus changing
the distribution of heat as it flows with the material, or they could change
the heat input distribution (and total power input) by altering the contact
conditions at the tool–workpiece interface. Both of these effects probably
occur.
65
Figure 3.12: Temperature histories measured in the backing plate for
various tool types
66
3.5 Weld quality
Experimental work, primarily carried out by Bakavos and Chen, identified
the conditions under which ‘good-quality’ welds could be formed. Good-
quality welds were those that were free of obvious defects such as cracks
and voids. Once the parameters required to form good-quality welds had
been determined, tensile tests were conducted with a number of sample
welds. These initial tests were straight pull tests, with shims placed in the
machine clamps in an attempt to produce as close to pure shear conditions
as possible across the weld interface. The highest strengths were associated
— as expected — with nugget pull-out; hybrid failures gave rise to lower
failure loads and fracture energies while shear failures across the line of the
original interface between the two workpieces resulted in very low strengths.
Tool rotation speeds from 800 to 2000 rev/min were found to produce good-
quality welds in AA6111 workpieces of 2 mm thickness. Force–displacement
curves are shown for these tests in Figure 3.13a; these are used as opposed
to stress–strain curves as (in order to assess the quality of a joint) the total
force carried by a spot weld is often of more interest than the peak stress.
A second measure of weld quality is the fracture energy, which is the area
under the force–displacement curve.
The variation of peak load with rotation speed over this range is shown
in Figure 3.13b for a constant weld time of 2.5 s. From this figure it can
be seen that welds giving rise to the highest failure loads were produced at
750 rev/min, i.e., the lowest rotational speed used that gave rise to a good
weld. (Welding was also attempted at 400 rev/min, but at this speed no weld
was formed and the parts remained unjoined.) These welds also showed the
highest strain to failure.
67
Figure 3.13: Load testing results for selected FSSW joints.
a. (upper): Load-displacement (figure provided by collaborators at
Manchester)
b. (lower): Peak force (data collected by collaborators at Manchester
68
Figure 3.14: Measured temperatures at 2, 5 and 10 mm from the weld
centre for nominally identical welds (AA6111, 2000 rev/min)
Figure 3.15: Measured temperatures at 2, 5 and 10 mm from the weld cen-
tre for nominally identical welds (AA6111 over 6082, 800 rev/min)
69
3.6 Sources of error
In order to compare experimental and model results, it was necessary to
understand and quantify the various sources of error in the experimental
measurements (modelling errors are discussed in the relevant chapters). The
potential sources of error and an a priori estimate of the importance of
each is shown in Table 3.4. Quantitative estimates were made of the total
contribution of all errors by looking at the variance in results: a number of
repeat welds were produced at TWI for nominally identical conditions and
the measurements compared.
Many of the welds made were repeated twice as a check; two welding
conditions were repeated more extensively. These were 2000 rev/min (210
rad s-1) with AA6111 and 800 rev/min (84 rad s-1) with AA6082 over 6111
(with 8 and 4 repeats, respectively). Plots of the temperatures recorded at
three locations in each weld are shown in Figures 3.14 and 3.15. Temperature
measurements were chosen as the appropriate comparison for a number of
reasons, both experimental and practical: temperature histories are of great
importance for weld modelling, as reaction rates and the rate of growth
of intermetallic compounds (IMCs) depend strongly on temperature, while
thermocouple data can pick up variations in a wide range of other parameters
that may not be measured. It is unlikely that any other parameters of interest
could vary independently without affecting the temperature.
Figures 3.14 and 3.15 show substantial variation in peak temperature,
and also in the time taken for the weld. The variation in peak temperature
near the centre of the weld (the hottest thermocouples) is around 15 K; the
variation at the 10 mm location is much larger, about 30 K. Fortunately the
hotter temperatures are of most interest, and these seem to experience less
variation than the other locations (these temperatures are more important,
since at the lower temperatures further from the centre — typically around
430 K at 10 mm — there will be very little reaction between the workpieces,
when considered on welding timescales2). Taking into account all relevant
factors and looking at the possible sources of error it Table 3.4, it seems that
2Precipitates in Al alloys only start to dissolve above about 450 K.
70
Source of errors Mitigation attempts and qualitative estimate
of magnitude
Workpiece thickness
variation
A selection of samples were measured with
callipers; all tested samples were 0.91 mm to
0.01 mm accuracy. The flow pattern could
be very sensitive to thickness, so even this
variation could be significant.
Workpiece in-plane
dimensional tolerance
Not measured, but FE thermal modelling in-
dicates that a variation of up to 1mm (which
would be detected by eye when aligning sheets)
is not significant.
Variation of
workpiece properties
(especially
temper/aging time)
Potentially significant; all samples were taken
from the same batch, so in practice the varia-
tion is likely to be small.
Clamping force Workpieces were held in place by hand-
tightened bolts; torque was not measured, and
so considerable variability was likely. Its influ-
ence is unknown at present.
Machine compliance Significant, between machines, and likely to
form a major contribution. For this reason,
caution should be exercised when comparing
results from two different machines (this is
noted in the text wherever relevant).
Thermocouple errors The K type thermocouples used are generally
considered reliable and accurate to within 1 K.
Occasional errors caused by non-functioning
thermocouples or thermocouples damaged or
destroyed during welding were usually obvious
in the data.
Thermocouple
location
Estimated to be accurate to within 0.5 mm;
owing to the steep thermal gradients, this
could be a significant (and possibly the domi-
nant) source of error.
Ambient temperature Not significant considering the temperatures
reached in welding; recorded prior to each
weld.
Table 3.4: Sources of experimental errors
71
errors in the thermocouple location could be responsible for most of the vari-
ation seen between different welds. Weld modelling (see Chapter 4) indicates
a comparatively flat temperature gradient for the central half diameter or so
of the weld, with the steepest gradients occurring at about 5 mm from the
weld centre. Slight errors in alignment of the tool with the expected central
point on the workpiece could cause similar effects to those seen; however, the
larger error at the 10 mm location does not correspond well to this (since the
temperature gradient here is fairly shallow).
Clamping force affects the temperature by altering the contact conduc-
tance to the backing plate, and variations in clamping force would affect
temperatures far from the weld centre more strongly since the tool itself
provides a large downforce at the centre. The effect of altering this is explored
in more detail in Chapter 4; together these two effects can account for the
majority of the variation seen in temperature measurements.
The welds between AA6082 and 6111 (Figure 3.15) show less variation
than those between two sheets of AA6111. The former series were carried
out a lower rotation speed; it is likely that the higher speed magnifies small
inconsistencies in e.g. thermocouple placement or sample thickness, leading
to greater variation in these welds.
3.7 Plunge depth and surface finish
The plunge depth has a large influence over most of the processes taking
place in a weld. The forging force is a crucial component in spot welding,
and this force varies strongly with plunge depth. While the forging force has
been commented on with respect to seam FSW, since seam welding usually
reaches a steady state variations in plunge depth have not received much
attention. It is likely that variations in downforce and/or plunge depth affect
the flow pattern directly; these variations will also affect the temperature
field, particularly temperatures at the interface (since any heat generated at
the interface between tool and workpiece is closer to the weld centre, with a
deeper plunge weld). However, due to the finite stiffness of the machine, the
clamping arrangements, and the tool itself, as well as the time-dependant
72
softening of the workpiece, the plunge actually achieved is not always the
same as the nominal plunge. All these effects are magnified with thin-sheet
welding: the overall distance from the tool to the weld interface is shorter, so a
given change will be a greater proportion of this distance, and the workpiece
material is more strongly constrained than with a thick workpiece, so its
apparent stiffness will be higher.
To begin the investigation into the effect of plunge depth, and the rela-
tionship between target plunge depth, forging force, and temperature, final
plunge depths were measured for a number of samples after welding. These
samples included welds made with a variety of conditions, but all had a
nominal plunge of 0.2 mm. The surface profiles of the tool contact patches
were measured on a Taylor-Hobson Talysurf. From this data both average
plunge depths and surface roughness values could be calculated. Figure 3.16
shows a typical surface profile, in this case from a weld that appeared to be of
good quality (the surface finish was comparatively smooth, the flash was not
excessive, and there was no visible distortion or slip between the workpieces
— such characteristics are indicative of a strong weld). Points of interest on
this figure are the average plunge (the distance between the far workpiece
surface, represented by the dashed red line, and the surface represented by
the solid black line), and the two deeper areas at the edges of the contact
patch. These deeper areas are part of a ring in plan section extending round
the edge of the contact patch, and have been termed overplunge, although
their significance is unknown at present and has not been discussed by other
authors.
Not all the samples exhibited such a smooth surface finish as that in
Figure 3.16, some were much rougher; in addition, few of the samples had a
final plunge close to 200 µm. The mean depth was 100 µm and the standard
deviation was 89 µm. These differences appear to be systematic: welds
made with identical conditions produced similar plunge depth measurements,
with the maximum difference in depths for identical welding conditions being
40 µm.
Various correlations between the average final plunge and the welding
parameters were studied; the strongest was between plunge depth and tool
73
Figure 3.16: Sample weld profile (from Parker, 2011)
rotation speed. This correlation improved further if the correlation was
calculated separately for different values of the other parameters (workpiece
material and welding time), and a plot of this is shown in Figure 3.17.
These correlations all suggest that there could be a link between temper-
ature and plunge depth. This is plotted in Figure 3.18, where the blue data
points show results for Al to Al welds and the red points show results for Al
to steel welds. These are plotted as separate series, since the temperature
measurements are not directly comparable between the two cases (the ther-
mocouples were placed at the base of the bottom sheet, hence temperatures
nearer the nugget and the weld interface will be higher with an Fe lower
workpiece, for the same temperature measured at the thermocouples).
From this figure, there is a clear link between the temperature and the
measured plunge depth. This makes sense: due to the finite stiffness of the
tool and machine, the finite forging force available, and the response time of
the machine feedback systems, the increased softening of the workpiece at
higher temperatures results in plunges closer to the nominal plunge: the tool
can embed further into softer material. Given that the interface temperatures
depend strongly on the distance from the tool to the weld interface, modelling
should take account of the fact that the plunge is usually less than the
74
Figure 3.17: Variation in plunge depth with tool rotation speed for a
nominal plunge of 0.2 mm
nominal value (in particular, assuming that the plunge is constant and equal
to the target plunge is unlikely to be correct).
The previous discussion concerned plunge depth data for welds made with
flat tools only. When the same analysis was conducted with the wiper tool,
a different phenomenon was observed: the welds made with the wiper tool
all had a negative plunge depth, i.e., the final surface of the nugget was
above that of the surrounding parent material. The height reached was up
to 120µm, of the same order as the target depth. As the tool cannot have
welded the material at this height, some pulling-up effect must have occurred.
The most likely explanation is that workpiece material stuck to the tool as
it was withdrawn. As the back of the lower workpiece remains level after
welding, by conservation of material the wiper tool must form voids in the
weld. This was confirmed by imaging the samples in a 3D X-ray machine. In
most cases this void took the form of an approximate crescent shape under
one half of the shoulder contact area. A particularly large void was formed
at 2000 rev/min, and a slice showing a section through such a weld is shown
in Figure 3.19.
This is surprising, even more so given that the wiper tool generally
75
Figure 3.18: Variation in plunge depth with temperature.
Figure 3.19: X-ray slice showing voiding in a weld produced by the wiper
tool (the slice shown is from 0.39 mm below the joint interface; the
image is approximately 20 mm across)
produces strong welds, yet voids are usually assumed to indicate poor quality,
very weak welds.
Roughness measurements were made of the tool contact areas on all of
these welds. The surface roughness of the samples using the wiper tool
was slightly more than twice that of those made using the flat tool. This
is consistent with sticking between the workpiece and the tool as the tool
withdraws and the workpiece cools. However, at present there is no further
explanation as to why the wiper tool grabs material on withdrawal in this
manner.
76
3.8 Backing plate material
Bakavos & Prangnell (2009) conducted a study into the effect on welding
of two different anvil materials. They conducted two identical sets of ex-
periments: one with a conventional steel backing plate, and one with the
same backing plate but coated with 4 mm of Macor ceramic. This has a
low thermal conductivity, of 1.46 W m-1 K-1. The ceramic anvil produced
consistently lower-strength welds for all except the pinless case, for which the
strengths were almost identical; the results of the strength tests are shown
in Figure 3.20. The thermal diffusivity of the backing plate strongly affects
the thermal cycle experienced by the workpiece, but experimental data alone
is not sufficient to explain the strength difference. This is studied in more
detail in Chapters 4 and 6.
Figure 3.20: Comparison of failure strengths for steel and ceramic backing
plates
77
3.9 Flow visualisation
Flow visualisation has been accomplished on experimental welds made be-
tween AA6082 and 6111. The different copper content of these two alloys
gives them different appearances when etched. These images are very useful,
in combination with flow models, for understanding what deformation takes
place. In turn, this provides useful insight into conditions during welding and
how the joining process works. Sample images are shown in Figures 3.21; this
method is discussed in more detail in Chapter 5.
Figure 3.21: Left: Top surface view of the contact patch, post-weld, show-
ing a typical onion-ring pattern, and right: Section view through a
weld, showing layering between AA6082 and 6111
78
Chapter 4
Thermal modelling
4.1 Introduction
As discussed in Chapter 2, there are two broad classes of model: analytical
and numerical. The advantages and disadvantages of each type are discussed
at more length in the relevant sections of Chapter 2. Analytical models are
quick to calculate and provide insight into the mechanics of the process, but
they struggle to represent features, such as finite geometries, that can be
important in real welds. Within the class of numerical models, finite element
(FE) modelling is a mature, well-developed field, and is the dominant mod-
elling technique used by other authors (see for example Colegrove & Shercliff,
2006, Awang et al., 2005 and Schmidt & Hattel, 2008). Consequently, an FE
model was selected for this problem, supplemented by analytical models of
specific features as appropriate. An analytical model is presented first to
examine the influence of welding time.
Existing FE models for seam welding usually concentrate on the steady-
state phase of welding, as the majority of time making long seam welds is
indeed spent in — or almost in — steady-state conditions. Where a dwell
phase with pre-steady-state conditions is considered, this is usually only used
to estimate the time needed for steady-state conditions to form. An FE model
is presented here that can accurately predict temperatures in a spot weld;
this model is then used to examine possible variations in welding conditions
79
and to understand how these changes can affect the temperatures reached in
the weld.
Two further objectives are to produce a model of sufficient accuracy:
(a) to combine with a new sequentially coupled thermal and mechanical
analysis (described in Chapter 6); (b) to predict thermal histories in the heat-
affected zone, particularly at the weld interface, as inputs to microstructural
models being developed by the project partners at Manchester University.
One drawback of FEA is the calculation time involved, with some models
taking many hours to model a single weld of a few seconds’ duration. This is
especially important for parametric studies like those in Section 4.10, where
numerous calculations must be performed for various load cases, material
combinations, and interface conditions. Although hardware capabilities and
software performance can vary substantially, there is a common factor across
all platforms: a reduction in model complexity can speed up calculation
times, often dramatically. Computing resource requirements are strongly
linked to mesh characteristics such as the number of elements and the size of
the smallest element (which affects the timestep size required for stability).
Dimensional reduction, such as the switch from 3D to 2D, can considerably
reduce the number of elements required and the running time of the model.
The FSSW process is an axisymmetric one, therefore an axisymmetric model
is the logical choice (even though the geometry of the workpieces is not
axisymmetric). Before an axisymmetric model can be relied upon, it must
be tested to ensure the simplification is accurate. This can be assessed
by comparing outputs, primarily temperature, from 3D and axisymmetric
models. There are a number of features in the experimental welds described
in Chapter 3 that are not in fact axisymmetric: comparing 2D and 3D models
will show if these features significantly affect the weld and the temperatures
reached. This does not, of course, say anything about whether either model
is an accurate model of experiments, but that is a separate question, which
is addressed in Section 4.9.
80
4.2 Timescale of welding
When considering the effect of dwell time on temperature, there are two
possible extreme cases. The first is to assume that the heat source is close
to the thermocouples; the second is to assume that it is at a large distance.
If the heat source is very close to the measurement point, and the welding
time is much longer than a characteristic heat diffusion time over the distance
between the two, then the temperature at the measurement point will be
approximately proportional to the temperature at the heat source at all times.
In such a case, a 1 s weld will look exactly like the first 1 s of a 2 s weld, and
similarly for any longer time.
If, on the other hand, the measurement point is a long way from the
heat source, then this will not be the case. ‘Long’, in this context, means
that the characteristic heat diffusion time (given by Equation 4.4) between
the two points is much longer than the welding time. If the weld geometry
and welding time fall into this parameter space, then the heat input can be
approximated by a delta function. In this case, the heat equation (Equa-
tion 4.1) has the solution in Equation 4.3, and a doubling of the welding
time is seen at the measurement point as a doubling of the total heat input,
but the temporal variation of the power is unimportant. Put another way, at
a location far from the heat source, an increase in the welding time results
in an increase in the temperature, but not in the shape of the temperature
rise experienced at that point.
Unfortunately for this analysis, the typical thermocouple locations are at
neither a short nor long distance from the heat source. An order-of-magnitude
estimate of the characteristic heat flow time can be made from Equation 4.4,
which, for a thermocouple 10 mm from the weld centre in AA6111, gives a
time of about 1.5 s. This is not short enough to treat the heat input as a
delta function. However, for short welds, or for thermocouples closer to the
centre than 10 mm (which is true for most of the measurements made in this
project — 10 mm was the greatest distance used) it may be reasonable to
approximate longer welds as extensions of shorter welds. Using Equation 4.4
in reverse, gives a distance of about 8 mm for a 1 s weld in AA6111. This
81
suggests that the nearest thermocouples may, in fact, be considered to be a
short distance from the heat source for welds of 1 s or longer. As AA6111 is
the highest diffusivity material used, this will also be valid for Fe workpieces.
∂T
∂t
= a
∂2T
∂x2
(4.1)
T =
Q
2pi
∫ ∞
∞
e−a
2teix d (4.2)
∴ T = Q
2
√
piat
e
−
(
x2
4at
)
(4.3)
t =
x2
a
(4.4)
Q is the total heat input in this case, and all other symbols have their usual
meanings.
4.3 FE model description
The finite element modelling software chosen was Abaqus, in ‘standard’ (i.e.
implicit) mode. The energy balance equation is given in Equation 4.5. The
implicit solver uses the backward Euler method (Equation 4.6) to calculate
the solution incrementally. The use of the backward Euler method ensures
that the calculation is stable. Differentiating 4.5 and substituting 4.6 into
the result gives Equation 4.7; this is discretised and an approximate solution
is found at each timestep.∫
V
U dv =
∫
S
h ds+
∫
V
q dv (4.5)
U is the internal energy (U = ρu), h is the heat flow per unit area due to the
temperature gradient and q is the external heat input per unit volume.
dU
dt
∣∣∣∣
t+∆t
=
Ut+∆t − Ut
∆t
(4.6)
82
1∆t
∫
V
Ut+∆t − Ut dV =
∫
S
h˙ ds+
∫
V
q˙ dv (4.7)
The elements used were linear heat-transfer elements, of Abaqus type
DC2D4 for the 2D model, and DC3D6 and DC3D8 for the 3D model. Au-
tomatic time stepping was used for all calculations. Using automatic time
stepping, the time increment for each step is calculated automatically and
may vary within each calculation. When using this method, a value is chosen
for the temperature change per increment. If the change in temperature
at any node exceeds this value during a single analysis step, the step is
halted, and attempted again with a new (smaller) timestep. If the maximum
temperature change is smaller than the allowable value, the timestep is
increased slightly for the subsequent step. For all calculations in this work
other than those described in Section 4.5 the maximum allowable change was
set at 1 K per step.
Descriptions of the materials used and the experimental setup are given
in Section 3.2; the simulations described in this chapter were based on this
arrangement. Models were built in 2D and 3D; a section view through the
3D model showing the parts is given in Figure 4.1. The 2D model can be seen
in Figure 4.2, showing the parts, interfaces and a typical mesh1. Dimensions
are shown in Figure 4.3.
Figure 4.2 shows a model with zero plunge. This was used for early work
which compared the 2D and 3D models, and for the examination of mesh size
effects. Calibration to experimental data used models with a plunge equal to
the nominal plunge during welding (i.e. these later models assumed that the
tool arrived instantly at the final plunge depth at the start of the weld).
The material properties that are relevant to thermal modelling are sum-
marised in Table 4.1, and these constant property values were used for
all models except where noted in the text. The use of constant versus
temperature-dependent property values is discussed further in Section 4.7.1.
1The mesh illustrated is described as a coarse mesh in Section 4.6 — see that section
for details of the influence of element size.
83
Figure 4.1: Example thermal model in 3D showing the parts and interfaces
Material Density Thermal Specific heat Diffusivity
conductivity capacity (calculated)
kg m-3 W m-1 K-1 J kg-3 K-1 m2 s-1×106
AA 6111 2700 143 800 66.2
AA 6082 2690 172 870 73.5
ES EN DC04 7850 47 419 14.3
SAE 4340 7850 44.5 475 11.9
SAE H13 7860 29 495 7.46
Alumina 95% dense 3900 27 900 7.7
Pure copper 8700 400 385 119
Table 4.1: Thermal properties of the materials used, at room temper-
ature. Data from Mills (2001), Hector et al. (2004) and Ashby &
Cebon (2009).
84
Figure 4.2: Example thermal model in 2D, showing the parts, interfaces
and an example mesh
Figure 4.3: Model dimensions and temperature output locations
85
4.4 Axisymmetric modelling
FE models of the weld were built in 2 and 3 dimensions. Components not
essential to the core of the thermal model (i.e. the tool, backing plate and top
clamps) were added to the model sequentially. In this model, the workpieces
both had the properties of AA6111 Al alloy, the tool was H13 steel and
the backing plate and clamps were 4340 steel. A constant (in time) and
uniform (in area) heat input was applied to the whole of the tool-to-workpiece
contact patch. In the 2D model, the workpieces were represented as discs of
12.5 mm radius (so the diameter is equal to the width of the workpieces
in the experimental setup); in the 3D model they were the full size of the
experimental coupons (100 mm × 25 mm). In both models the thickness was
0.9 mm, the same as the experimental sheets. The workpieces were initially
thermally tied: the temperatures at the nodes on either side of the interface
were constrained to be the same, representing perfect heat transfer between
the two parts. As new parts were added in, they were initially tied to the
existing parts at the interfaces; a more detailed discussion of metal-to-metal
contact is given is Section 4.7.3.
Virtual thermocouple outputs were taken at the base of the lower work-
piece at 0, 2.5 and 5 mm from the centre of the weld. Using t = x2/a
gives a time of about 2.4 s as a characteristic heat flow time between the
centreline and the edge. Consequently, it was expected that there would be
some difference between the temperatures reached in the two models for long
welds, and during the cooling phase, but for welds of much less than 2 s the
results should be very similar.
Temperatures at the points of the virtual thermocouples are plotted for
the 2D and 3D models in Figure 4.4 for a 1 s weld with a 1 kW power input.
As the workpieces are insulated from the surroundings in this model, the
final temperature rise can be calculated by dividing the energy input by the
heat capacity of the workpieces — these values are plotted as asymptotes
in the figure. The 2D and 3D models match closely for the initial slope of
the temperature rise, although there is a difference of 50 to 100 K in the
predicted peak temperature; the temperatures diverge significantly after the
86
end of the heating phase, which is as expected as the long-term asymptote
for the 3D case is much lower (as the volume of material included in the
model domain is much greater). Clearly, if this had been a representation of
a real weld then the 2D model would not be accurate enough for temperature
predictions.
The next stage of the comparison was to add extra features into each
model, and again examine the differences between the two. Figure 4.5 shows
temperature outputs for the same locations as before: this time, the model
includes the backing plate as well (with perfect thermal contact everywhere
between the workpiece and backing plate).
This case shows much closer agreement between the two models than the
previous one, presumably as the backing plate provides a large heat sink in
both cases, thus limiting the overall average temperature rise. The overall
energy input is sufficient to raise the temperature of the entire domain by only
3.3 K in the 2D case and 1.3 K in the 3D case — although the temperature
rise in the 2D model is still over twice that of the 3D case, the absolute
difference is small. It is of interest to note that the greatest difference in
temperature profiles under these conditions is found at the 0 and 2.5 mm
locations, while the temperature 5 mm from the weld centreline is almost
identical in the two models.
A further calculation was performed with each model with the addition of
the top clamp to the model domain. The results for this case appeared very
similar to those for the previous case with the backing plate; since little heat
flows into the top clamp, it makes only a minor difference to the solution.
These results show that the assumption of axisymmetry produces results
that are in close agreement with a 3D model, and a 2D model may be
used with confidence for short welds. However, owing to the divergence
between the two cases at longer times — caused by ’heat reflection’ from
the boundaries, which are nearer in the axisymmetric case than in reality —
the 3D model will be used for modelling longer welds (experimental welds
included dwell times of up to 6 s).
87
Figure 4.4: Comparison between 2D and 3D models: workpieces only
Figure 4.5: Comparison between 2D and 3D models: with backing plate
88
4.5 Thermal contact problems in Abaqus
The model was built up in stages so that additions could be checked for
problems more easily. The first stage included just a single workpiece, then
two workpieces tied together, then two workpieces with imperfect thermal
contact, then a tool was added into the model. Without the tool present, the
input power had to be reduced by a factor to allow for heat loss to the tool;
with the tool present, this heat flow could be calculated directly in the model
(and in this case the factor could vary throughout the course of a weld). When
the tool was incorporated into the model, it was initially included with its
surface temperatures tied to the temperature of the workpiece at that point,
simulating perfect thermal contact between the two parts.
A more realistic way to model all the metal-to-metal interfaces is to use a
thermal contact conductance, which is defined by Equation 4.8. Since contact
between the tool and workpiece in the real process is lost at the end of the
dwell time, the initial model imposed a step change in contact condition at
this interface from thermal conductance to insulated. This coincided with
the step change in power input to zero.
hc =
q
∆T
(4.8)
Switching instantaneously from an imperfect contact to no contact demon-
strated a problem in the way Abaqus handles step changes in thermal bound-
ary conditions. Figure 4.6 shows the problem, which is that the predicted
temperature of the workpiece falls below its initial (ambient) value.
Clearly, this is wrong, as the temperature of the workpiece cannot fall
below that of the surroundings in the cooling phase. In this model, no
heat loss to the surroundings is considered – all boundaries are specified
as being perfectly insulated. This leaves only three possibilities (or, perhaps,
a mixture of the three):
• the outer boundaries are not behaving as insulators, as specified;
• the boundary between the tool and the workpiece is not being treated
correctly, and the heat is flowing into the tool against the thermal
gradient;
89
• energy in the system is not being conserved (i.e. the temperature of
some nodes is falling without the heat flowing out or being accounted
for).
Figure 4.6: Non-physical cooling effects in Abaqus
Further investigation shows that the problem is related to the step change
imposed in the load and interface conductance. Figure 4.7 shows the heat
flux vectors calculated by Abaqus for one increment in the cooling phase of
the weld. The nominal interface condition at this point is one of perfect
insulation between the tool and the upper workpiece, however, this is not
being respected: there should be no heat flow across the boundaries, yet the
heat flux vectors in the region of the (removed) tool clearly show heat flow out
of the model domain. This situation is not peculiar to an isolated increment,
and heat continues to flow out of the model throughout the cooling phase.
It appears that heat continues to flow into the tool, from the workpiece,
even after the tool has been removed from the model (which is done using
*MODEL CHANGE,REMOVE in the input file). Although the cause of
this is unclear, it may be avoided by adding an extra step to the analysis,
between the heating and cooling phases. During this phase, the conductance
and power inputs are ramped down smoothly throughout the step, rather
90
Figure 4.7: Heat flow in Abaqus after an instantaneous change in
boundary conditions
than being turned off as a step change; the tool is then removed at the start
of the third step (or it may be left in the analysis as a disconnected region,
if tool temperatures during the cooling phase are desired). This second step
can be made very short: 0.05 seconds is sufficient to eliminate the problem.
4.6 Mesh effects
The precision of an FE model depends strongly on the nodal density. A dense
mesh produces more accurate solutions, but takes more computing power, or
more time to run. The causes are twofold: firstly, with more nodes, the
matrices are larger and more operations are required for each increment.
Secondly, the stable time increment is smaller with smaller elements.
In order to check that the mesh density was not adversely affecting the
accuracy of the output, a model was run for a 1 s weld with three different
mesh densities, with a factor of approximately 5 increase in the number
of nodes between each density. Temperature outputs for the centre of the
weld at the interface are shown in Figure 4.8. This location was chosen
as a critical point of interest in the weld. The mesh density check was
performed prior to the analysis and calibration of the model, hence the power
input (and temperatures reached) are not realistic. The difference in peak
91
temperature between the medium and fine meshes corresponds to 0.04 %,
which was deemed sufficiently small that the medium-density mesh could be
used for the rest of the analysis.
Figure 4.8: Mesh sensitivity analysis
4.7 Model calibration
The FSSW process has numerous input parameters, only some of which
are independently adjustable. Many of these parameters, such as interface
conductance values, are difficult to measure. Others (such as the total power
input) are superficially simple to measure, however the accuracy of these
measurements is low. In the case of the total power input, this was measured
experimentally but factors such as the machine idling torque and the low
sampling rate rendered the data of limited use.
Fortunately, temperature measurements contain a wealth of information
about the weld properties: temperature measurements across interfaces can
feed into models of contact conductance, the ratio of thermocouple mea-
surements at various radii depends most strongly on the shape of the power
distribution, the shape of temperature histories with time is influenced by
the variation in the power input, and the total power strongly influences the
92
peak temperature reached. All these factors are related, but an iterative
process can find values of each parameter that lead to a self-consistent model
capable of predicting temperatures with accuracy.
4.7.1 Material properties
The thermal properties of Al are widely known to depend on temperature.
Both the conductivity and the specific heat capacity vary with temperature,
increasing over the range from room temperature to the solidus. While
for pure Al both properties increase monotonically with temperature, the
presence of alloying elements produces multiple local maxima in both. The
underlying reasons depend on an interaction between the precipitate distri-
bution, dissolved solutes and phase changes; the exact effects depend on the
alloy composition. Temperature-dependent values of specific heat capacity
and thermal conductivity for AA6111 measured after 1 hour hold times are
shown in Figures 4.9 and 4.10. Since they both increase with temperature,
the overall variation in diffusivity (Figure 4.11) is smaller than that in either
the conductivity or heat capacity alone. This data is representative of that
available in the literature — measurements of the thermal properties exist
for all common alloys, but currently extant data is generally measured at
long hold times, typically one hour or more, to allow time for the material
to approach equilibrium at temperature before measurements are taken.
Owing to the rapid thermal cycle in FSSW, the use of data measured
after 1 hour hold times is not necessarily appropriate for modelling purposes;
some authors use room temperature data, and this subject remains a matter
of debate. Which of these values is most accurate, or whether an intermediate
or different value should be used, depends on the reaction kinetics.
The rate of change of properties will also vary with temperature. The rate
of change will be highest in the nugget (as the peak temperatures are highest),
and lower in the surrounding HAZ; the nugget is characterised by dissolution
and recrystallisation, while precipitates in the HAZ exhibit coarsening; these
will affect the materials’ properties in different ways.
93
Colegrove & Shercliff (2006) performed FE calculations using both room-
temperature data and values for Al in equilibrium at high temperatures.
They found that the former provided a better match for the conditions pre-
vailing during seam FSW, based on a comparison of predicted temperatures
with experiments. This would seem to indicate that room-temperature data
is also appropriate for FSSW. Since the heat input as a function of time
is calibrated in the model, it may be argued that some of the uncertainty
arising from the use of constant thermal properties is absorbed within this
calibration. There is little justification for the additional complexity of
notionally greater precision in the thermal properties, when the heat input
is adjusted empirically in this way.
Definitive property values can only be found by measuring the heat ca-
pacity and conductivity during a very rapid temperature rise, but this is
not practical at present. Differential scanning calorimetry can be used to
pinpoint the phase transitions and measure the heat capacity by reference to
a known sample, but the rate of heating in such experiments remains orders of
magnitude below that applied during welding. A non-equilibrium test on an
alloy of interest was conducted by Dutta & Allen (1991), who measured the
heat capacity of ice-quenched AA6061 during a continuous temperature rise
at a rate of 0.167 K s-1; this is shown in Figure 4.12 as a difference between
that and the values for equilibrium (overaged) samples. This shows a small
discrepancy over most of the range (the maximum difference is approximately
10 %, which occurs at circa 575 K). Despite the comparatively high heating
rate in this experiment, it was still only 10−3 times that during FSSW. It
may be that the best approach possible at present is to use FE models of the
FSSW process, or other rapid heating processes, and compare the outputs
for different material laws against experimental temperature measurements.
94
Figure 4.9: Thermal conductivity of AA6111 as a function of temperature
(data from Khanna et al., 2005)
Figure 4.10: Specific heat capacity of AA6111 as a function of tempera-
ture (data from Khanna et al., 2005)
95
Figure 4.11: Thermal diffusivity of AA6111 as a function of temperature
(derived from Khanna et al., 2005)
Figure 4.12: Differential scanning calorimetry thermogram of AA6061,
showing four precipitate formation peaks, a to d, and one dissolution
peak, e. (Image from Dutta & Allen, 1991)
96
4.7.2 Power input
The power input to the weld can vary in both time and space.2 As described
in the literature review, other authors have discussed to some extent the
spatial variation of the power input function, mostly in the context of seam
FSW, but as many studies use steady-state models, variation in time has not
received the same study.
Spatial variation
The most common assumptions are to assume that the power input is either
uniform over the contact patch between the tool and workpiece, or that it
scales with the local tool velocity (so that it varies linearly with radius, as
used by Schmidt & Hattel, 2008). This has the form given in Equation 2.7
(reproduced below in Equation 4.9).
q =
3Qr
2piR3S
(4.9)
where q is the power input per unit area, Q is the total power, r is radial
position and RS is the shoulder radius.
Colegrove & Shercliff (2006) used a similar model, but by calibrating
the total power to experimental temperature measurements found the best
match was obtained by truncating the power input function at a fraction of
the shoulder radius. This gives the new power input as shown in Equation
4.10.
q =

2Q′r
3piR3S
, r ≤ RS′
0 , r > RS′
(4.10)
where Q′ satisfies
∫ RS
0
q dr = Q (4.11)
2For the sake of brevity, ‘power distribution’ is used in this work to refer to the spatial
distribution of power input, and ‘power profile’ to refer to the shape of the power vs. time
curve.
97
Models of other friction-based processes usually assume a uniform in-
put power; for example, thermal models of rotary friction welding still use
Rykalin’s solution for the heat flow in a bar (Rykalin, 1951). While this so-
lution to Fourier’s Law (shown in Equation 4.12) is accurate for the assumed
boundary conditions, the assumption of uniform heat input is likely to be
wrong.
∆T =
−Q
2Aρc
√
pia
∫ t
0
 1√te
−x2
4piat

 dt (4.12)
(Equation 4.12 concisely demonstrates why lateral heat flow and a time-
varying power are important for FSSW. Putting in material data for AA6111
with a 5 mm radius bar and a 1 kW heat source — typical of FSSW — gives
temperature rises at the surface of the workpiece shown in Table 4.2. These
temperature rises, certainly for longer times, are much higher than those
measured experimentally.)
Given the number of competing suggestions for the power distribution in
the literature on seam FSW, and the transient nature of spot as opposed to
seam welding, additional investigation was warranted to examine which (if
any) of these would be most appropriate for FSSW. This was carried out
using the basic Abaqus model (described previously), with the backing plate
and clamping arrangements included and perfect thermal contact between all
parts. Four power distributions were modelled, and virtual thermocouple out-
puts compared. The power was adjusted in each case to keep the total energy
input constant. The four power distributions that were used are described
Welding time (s) Temperature rise (K)
1 338
2 478
4 677
Table 4.2: Temperature rises in an Al bar with a uniform 1 kW heat
source (as given by Equation 4.12)
98
in Equations 4.13 to 4.16 and illustrated graphically in Figure 4.13. The
uniform and ‘top hat’ (truncated uniform) distributions are not considered to
be realistic models, as they are not physically representative of the underlying
physics. Since they are used by many authors, they are nevertheless included
here for comparative purposes.
Distribution 1: q =
Q
piR2S
(4.13)
Distribution 2: q(r) =

16Q
9piR2S
, r ≤ 3
4
RS
0 , r > 3
4
RS
(4.14)
Distribution 3: q(r) =
3Qr
2piR3S
(4.15)
Distribution 4: q(r) =

32Qr
9piR3S
, r ≤ 3
4
RS
0 , r > 3
4
RS
(4.16)
The factor of 3
4
was chosen based on kinematic modelling work (Chap-
ter 5) and an extensive study of the location that gave the best prediction
of experimental temperatures; this latter work is given in more detail in
Je¸drasiak et al. (2012).
Temperature measurements at the same three locations were used to
compare the results from these 4 power distributions; these are shown in
Figure 4.14. As can be seen in the figure, all these cases give very similar
results for the 10 mm location. This is as expected, since a simple analy-
sis (given in Chapter 3, based on an x =
√
at calculation) shows that at
Figure 4.13: Power distributions
99
Figure 4.14: Predicted temperature outputs for 4 input power distribu-
tions at 0, 5 and 10 mm locations
this distance treating the heat input as a point source is a reasonable first
approximation. Comparing the ratio of the temperatures at the two closer
thermocouples gives a metric that can be used to quantify the effect of each
power distribution on the temperature distribution. Values of this metric for
each case are given in Table 4.3. These can be compared to values for the
same metric calculated from experimental data, shown in Table 4.4.
If the top hat distributions are discounted (as they are unrealistic, dis-
cussed previously) and the variation of power per unit area with radius is
taken to be linear, this analysis allows selection of the peak in heat input to
Power distribution 0 mm temperature 5 mm temperature Ratio
K K
1 619 513 1.21
2 656 494 1.33
3 603 525 1.15
4 637 595 1.29
Table 4.3: Power distribution metrics — calculated data
100
Tool type Average ratio
Flat 1.23
Short wiper 1.27
Long wiper 1.29
Scroll 1.33
Proud wiper 1.06
Table 4.4: Power distribution metrics — experimental data
match the distribution generated by each tool. This has been done for the
flat and wiper tools, the wiper tool generating a peak at a smaller radius
than the flat tool. (The anomalous result for the proud wiper tool is not
considered important; it has very poor joining ability, discussed in Section
3.4, and produces very different results to the other tools.)
Variation with time
Generally speaking, FSSW takes place at constant rotation speed. As the
workpiece heats up, the flow stress falls, leading to a fall in torque and power
input. Unfortunately, although the torque was measured in experiments at
Manchester, the power losses in the machine were so high, and the sampling
rate so low, as to render this data unusable. Torque data was also measured
during the experiments at TWI, but owing to software limitations data
was only available at intervals of 1 s. However, thermocouples placed in
the workpiece respond very quickly to changes in total power input, so
it is possible to extract meaningful information about the power input by
looking at the temperature histories, in combination with an accurate model.
Torque data is also available from other published work, such as that carried
out by Gerlich et al. (2005) which is presented in Chapter 2. Figure 2.10
shows a typical torque history, exhibiting an exponential shape once complete
shoulder contact is made (after point F2 in the figure, at around 3 s).
To investigate the effects of fluctuations in the total power input, three
different power profiles were tested. Other parameters were kept constant,
using those of the standard case for the thermal model (a lap weld between
101
two AA6111 coupons of the standard geometry, with perfect thermal contact
to a 4340 steel backing plate; the spatial power distribution had a linear
variation with radial position, as described earlier). The three power profiles
used were a constant power, an exponential decrease, and an impulse. An
ideal impulse cannot be represented easily in a numerical calculation, so
instead a finite-duration impulse was used of 0.1 s. The exponential profile
lies between the two extremes, and is probably the most realistic, as discussed
later. The three profiles were adjusted so that the total input energy was the
same in each case. The exponential power profile has the form P = P0 e
(−t/tc)
where t is time and tc is the time constant. For the case presented here,
P0 = 1.5 kW and tc = 5 s.
The temperature outputs are shown in Figure 4.15; it is clear from this
figure that variation in the power profile has a great effect on the peak
temperatures produced in the workpiece, even for equal total energy inputs.
Compared to an exponential profile, a constant power input delivers a larger
proportion of energy towards the end of the weld, resulting in higher peaks
near the tool and lower peaks further from the tool, whereas with the ex-
ponential input the bulk of the energy is delivered earlier, so it has spread
Figure 4.15: Temperature outputs at 0, 5 and 10 mm
102
further through the workpiece by the end of the dwell time. The case of an
impulsive heat input is not physically realistic, and the peak temperatures
calculated are far too high.
An exponentially-decreasing power input ties in with current literature
about how the process works: as the weld heats up, the flow stress de-
creases, and hence the heat generation for a constant deformation pattern
will decrease, and the process is to a large extent self-limiting. The plasticity
analysis in Chapter 6 also confirms that there is a strong physical basis
for this profile. Refinement of the power input and study of experimental
welds showed that a pure exponential function could not match the observed
temperature measurements for welds at longer dwell times. A revised form
was chosen, with P = P0(a e
(−t/tc) + (1− a)).
Total input power
From the two preceding sections, the overall form of the power input can be
determined. The form that best matches experimental temperature measure-
ments is a linear power distribution with a cutoff, as given by Equation 4.16,
that varies in time as an exponential function with an asymptote. This still
leaves a number of variables to be determined by reference to experiments,
but has markedly reduced the overall complexity of the problem. The power
input can now be completely described by four variables: the initial power;
the asymptotic power; the time constant; and the radial cutoff (assumed to
be 3
4
RS in Equation 4.16).
Assuming that a 1 s weld is the same as the 1st 1 s of a 2 s weld, etc., the
most useful approach is to use welds with the longest dwell time available for
the initial calibration — this will allow the most accurate estimation of the
time-varying parameters. Shorter welds can be used to assess the accuracy
of the calibration.
A summary of all experimental welding conditions is given in Chapter 3.
Dwell times up to 6 s were modelled in AA6111 to AA6111, with a shallow
plunge (of 0.2 mm) and welding speeds of 800 or 2000 rev/min. The metal-
to-metal contacts under the tool were treated as perfectly conducting as
103
the tool downforce applies a high pressure to this contact, and the metal
rapidly softens in this region; for the contact between the workpiece and
backing plate over the rest of the surface, a value of 100 W m-2 K-1 was used,
after Colegrove & Shercliff (2006). Calculations were run for the standard
welding cases, keeping the radial cutoff at 3
4
RS, and adjusting the other
three parameters describing the power input (initial and asymptotic powers,
and the time constant) to best match the peak temperatures. Temperature
outputs were taken from locations at 1, 6 and 10 mm from the centre of the
weld, to correspond with thermocouple measurements made in experimental
welds. The three parameters describing the input power were adjusted in
an iterative process to provide the best match between the FE predictions
and measured temperatures. The power input parameters found to give the
best match between model and experiment were a peak power of 1200 W, an
asymptotic power fraction of 0.45, and a time constant of 2.3 s. The power
profile matching these parameters is shown in Figure 4.16.
After optimising these parameters, the temperature outputs in Figure 4.17
were obtained. These outputs are shown alongside thermocouple data from
experiments. This figure shows a very close match for the two thermocouples
closest to the weld. The calculated temperature at 10 mm from the weld is
lower than that measured, however. This occurs due to the unrealistic contact
conductance used in the model; this is explored further, and more accurate
values for the conductance are estimated, in Section 4.7.3.
Figure 4.16: Power profile showing the best-match parameters with
P0 = 1200 W, a = 0.45 and tc = 2.3 s for a 4 s weld
104
Figure 4.17: Comparison of temperature histories for model and exper-
iment, using the best-match power input profile; weld with a 6 s
dwell time
To test to see if the adjusted power input fitted data from other welds,
predictions of the temperature histories at the same points were calculated for
other welding times. The only parameter that was adjusted for these welds
was the welding time, all other parameters were kept constant. A comparison
between these predictions and experimental measurements for a 1 s dwell
weld is shown in Figure 4.18; this shows a good match for both the heating
rate and the peak temperatures within the nugget. Temperatures further
out are, again, lower in the model than in experiments, and the cooling
rate is higher than that measured. Further validation was performed against
separate welds, and the results of this analysis are shown in Section 4.9.
The higher cooling rate in the model is interesting — this is a feature
of many thermal models; for example, temperatures calculated by Colegrove
et al. (2007) showed very good agreement with experiments for the heating
rate and peak temperature, but diverged slightly during cooling.
As the reaction kinetics have a very strong dependence on temperature,
the cooling rate has less influence on the microstructure than the peak
temperature. The cooling rate is also not needed for a deformation model.
105
Figure 4.18: Comparison of predicted temperature histories with experi-
mental measurements for a 1 s weld
Therefore, the divergence of temperatures during cooling is not considered
to be a critical flaw in the model.
4.7.3 Heat losses
During FSSW, heat is lost from the workpiece by conduction and radiation.
Convection in the surrounding atmosphere will also play a role by altering
the temperature gradient in the air in contact with the metal parts. To
build an accurate and fast model, it is important to take account of the
most important sources of heat loss, and to discount those effects that are
insignificant. Heat is lost to two main sources during FSSW: the tool and the
backing plate. Minor heat losses also occur to the other clamping metal in
contact with the workpiece, and through the surfaces of the workpiece that
are exposed to air. The model presented so far has only taken account of
conduction effects.
106
Radiation and convection
Radiation and convection both play only a minor role in FSSW. The emissiv-
ity of Al is very low: even when heavily oxidised its emissivity is rarely above
0.3. Taking the area to be twice that of the shoulder (to represent heat loss
from both sides of an exposed workpiece) and the temperature to be 820 K,
P = σAT 4 gives P ' 1.2W. Consequently, radiation may be neglected in the
analysis of FSSW.
Various treatments of thermal losses to the atmosphere from welding are
found in the literature. Most of these studies involve FSW, as during FSSW
the clamping arrangements are more extensive, and these usually minimise
the area of exposed workpiece. The most common approach is to define a
convection coefficient and ambient temperature for losses to the surrounding
air, with values of the convection coefficient during FSSW typically ranging
from 30 to 300 W m-2 K-1. This coefficient is usually chosen by matching
temperature measurements to those observed experimentally. Some models
(see e.g. Awang et al., 2005) additionally use a convection coefficient to model
heat losses to the backing plate; this is done for reasons of speed, but in the
present case the backing plate is explicitly included in the model domain.
With the weld geometry being studied in the present case, very little of
the workpiece is exposed to the atmosphere (only the gap between the tool
and the top clamping plate is directly exposed). The temperature at the
top edge of the top clamp is sufficiently low that heat loss from here to the
surrounding air will be negligible. The only surface where the temperature is
high enough for heat losses to air to possibly be important are the edges of the
tool, and the gap between the tool and the top clamping plate. This latter
gap is filled by flash during the weld, hence calling for a more complicated
treatment than just consideration of the heat loss.
A rough estimate of the heat lost from the tool to the atmosphere can be
made by making an assumption about the thickness of the thermal bound-
ary layer. Assuming that this is at least 1 mm makes the thermal gradi-
ent less than 5 × 104 K m-1; taking the thermal conductivity of air to be
0.024 W m-1 K-1 then over the heated, exposed area of the tool the steady-
107
state heat loss would be around 0.4 W. This is so much lower than the
power input that heat losses here, like the radiative losses, can reasonably be
neglected.
Contact conductance at metal-to-metal interfaces
As mentioned, in most of the models considered in this chapter the backing
plate is included in the meshed domain. The heat loss across the interface
between backing plate and workpiece is calculated as a function of the tem-
perature gradient and contact conductance. Accurate values for the contact
conductance are crucial, for the interface between bottom workpiece and
anvil, and also values for contacts between the two workpieces, and between
the tool and the top workpiece. These interfaces are illustrated in Figure 4.19.
These interfaces are important because they strongly affect the temperature
in the workpiece: realistic contact conductances, based on values found in
the literature, can alter the peak temperature reached at the interface by
250 K. However, it is a difficult aspect to model accurately, as can be seen
from the range of values quoted in previous studies.
While contact conductances have received extensive study, it is difficult to
make any predictions about the conductance due to the number of variables
involved. The value of the conductance at any given interface is a function
of the conductivity, surface finish, flatness and hardness of both materials
in contact and their oxide layers, and of the contact pressure, temperature,
and heat flux, as well as the properties of trapped fluid (air) between the
Figure 4.19: Model setup, with interfaces highlighted
108
surfaces in contact (Rohsenow & Hartnett, 1998). Increasing downforce
and temperature make the workpiece conform better to the profile of the
backing plate on a small scale, increasing heat transfer, and both downforce
and temperature change substantially during welding. Rohsenow & Hartnett
(1998) quote values of contact conductance for contacts between Al sheets
that vary by a factor of 4 depending on surface roughness, for the same alloys
and with all other conditions held constant. Given the variation in contact
pressure and surface properties during the course of a single weld, it is not
thought possible to make an a priori estimate of the contact conductances
during FSSW. However, it is possible to estimate the mean conductances
from instrumented welds, by comparing FE models using a range of values
for the contact conductance to experimental measurements.
A study was conducted to examine the influence of contact conductance.
Conductance values were varied at each interface in turn, and temperature
histories at selected points were examined. The power profile and distri-
bution used were those found in Section 4.7.2. As might be expected, this
study found that the temperatures away from the tool were more sensitive
to the conductance to the backing plate, while those nearer the tool were
more sensitive to the heat input. Calculations were performed varying each
interface by a factor of 10 from 10 to 1010 W m-2 K-1; the extreme values
are essentially indistinguishable from no heat transfer and perfect contact
respectively. Time-varying conductance was an additional complication that
was not considered.
The optimum values were those that gave the closest match between pre-
dictions and measured data. These were found to be 106 for the conductance
under the tool and 103 elsewhere. The calculations are shown in Figures 4.20
and 4.21, along with the experimental results. As more energy was lost to
the surrounding clamping arrangements with higher conductance values, the
total energy had to be increased to keep the peak temperature predictions
for the central node in line with experimental values. The total power had to
be increased by 6% when using the best-match conductances, as compared
to 100 W m-2 K-1. Fortunately, the value of conductance required under the
tool is so high as to approximate perfect conductance. This is useful, since
109
it makes the temperature outputs much less dependent on the details of the
contact than was first thought. However, temperatures remain sensitive to
conductance values outside the direct contact patch.
These calculations were done in 3D so as to properly account for edge
effects; a similar study was carried out by Parker (2011) using a 2D model,
for the same welds presented here. This study found that the contact conduc-
tances that best matched the experimental data were 105 W m-2 K-1 under
the tool and 103 W m-2 K-1 elsewhere. For the high conductance patch under
the tool, even though the values used differ substantially between the 2D and
3D cases (by a factor of 10), they are both sufficiently high as to be almost
perfectly conductive, and it is difficult to differentiate accurately between
such high values.
These values, even the low values for poor contact, are substantially higher
than those used in most of the literature on seam FSW. Seam FSW tends
not to use such high clamping forces near the tool as were used in these ex-
periments (seam welds are usually done without any top clamp arrangement
at all), and contact conductance is strongly dependant on pressure, so this is
the likely source of this difference.
110
Figure 4.20: Comparison of predicted temperature histories with ex-
perimental measurements for a 1 s weld, with adjusted contact
conductance values
Figure 4.21: Comparison of temperature histories for model and experi-
ment for a 6 s weld, with adjusted contact conductance values
111
4.8 Plunge depth effects
The typical weld profile for these spot welds is a relatively fast plunge and
then a comparatively long dwell, and early thermal modelling work assumed
that the tool arrived quickly at the target plunge and remained there for the
dwell time; this was modelled by placing the tool at the final plunge depth
for the whole duration of the weld. However, the work in Section 3.7 shows
that this is not the case, as the actual plunge depth is often less than the
target. It is likely that the plunge depth continues to increase during the
whole weld, i.e. the tool continues to descend. In addition to this, some of
the experimental work was conducted at a much deeper plunge in order to
bring the tool closer to the weld interface (this was required in some cases to
produce a strong joint, such as short-duration welds between aluminium and
steel). As a consequence, further modelling was carried out (in Abaqus) to
examine the influence of the plunge depth. Although the actual plunge depth
cannot be controlled or predicted accurately, it can at least be measured with
reasonable confidence during welding. In order to reduce complexity the tool
does not move in the thermal model; tool locations that broadly corresponded
to a small, medium and large overall plunge were chosen to provide upper
and lower limit estimates of the peak temperature profile.
Three Abaqus models with plunge depths of 200, 400 and 600 µm were
chosen, with otherwise identical parameters of heat input, weld duration
(0.5 s) and thermal contact conditions between each part. The change in
geometry required changes to the mesh. The mesh for the case of a 600 µm
plunge is shown in Figure 4.22. Flash height was adjusted to conserve the
volume of material in the workpiece. While some of the flash is expelled from
the weld zone, this is a comparatively small quantity. In any case, this is hot
material which is being expelled at some stage during the weld, so it is more
realistic to keep such material in the model than to ignore it entirely.
Figure 4.23 shows predicted temperatures at the joint interface, for a
radial line extending from 0 to 5 mm from the weld centre. The temperature
histories at the 5 mm location are very similar. However, the difference at
the 2.5 mm thermocouple position, of around 70 K, is significant and would
correspond to a large change in the reaction rate and intermetallic layer
thickness.
112
Figure 4.22: Image of a deep plunge weld model; the colours correspond
to the peak temperature reached
Figure 4.23: Peak temperatures reached at the interface, for various
plunge depths
113
4.9 Model to experiment comparison
Experimental validation was conducted using a separate series of experiments
to those used for model calibration. These models used the values found
previously: a peak in the power distribution at 0.7RS, total power input
parameters of 1200 W, 0.45 and 2.3 s, and the contact conductances found in
Section 4.7.3. This validation was performed on a number of different welds.
Firstly, it was performed on a 2 s weld made in the lab at Manchester.
This weld used the same machine as the earlier 1 s and 6 s calibrations,
the same speed (2000 rev/min) and the same nominal plunge (0.2 mm). An
important difference with this weld is the location of the thermocouples,
which were at 2, 5 and 10 mm from the weld centre at the top of the
backing plate (as opposed to 1, 6 and 10 mm from the centre with the
thermocouples in contact with the bottom of the workpiece, which were the
locations used in the previous comparison). The calculation is presented
alongside experimental thermocouple data in Figure 4.24. This figure shows
a very good correspondence between the calculation and the measured data
for most of the weld, with only a slight divergence visible during the cooling
phase. That the model can predict these temperatures with such a high
degree of accuracy, indicates that the values found earlier for the adjustable
parameters are sufficiently accurate.
Following this, a series of experiments were carried out at TWI for the
same nominal conditions. The machine used here is much larger and po-
tentially stiffer, so it is possible that some factors — particularly the actual
plunge — differ somewhat from the welds made at Manchester. However,
a good test of the model is to see if it can accurately model welds with a
range of different parameters. These experiments were all instrumented at 0,
4 and 8 mm from the weld centre. Figures 4.25 and 4.26 show comparisons
between FE simulations and the TWI experiments for a range of welding
times. More extensive comparisons covering a range of welding parameters
are presented in Je¸drasiak et al. (2012) and Je¸drasiak (2012). As well as
variations in welding speed and plunge, these two papers also cover Al to Fe
welds. The model as presented here has been shown to predict temperatures
in experimental welds with good accuracy.
114
Figure 4.24: Comparison between model and experimental temperature
histories for a 2 s weld, with thermocouples at 2, 5 and 10 mm from
the weld centre
Figure 4.25: Temperature histories for model and experiment, in a 1 s
weld made at TWI (thermocouple locations as indicated)
115
2 s dwell
4 s dwell
6 s dwell
Figure 4.26: Comparisons between FE calculations and experimental
results, for thermocouples at the base of the backing plate at 0,
4 and 8 mm.
4.10 Optimum welding conditions
An area where modelling can be of great use is in a parametric study to
examine the influence of varying welding parameters. Although a programme
of experimental work could be devised to cover a range of values for each
parameter, it is expensive to conduct experimental trials without any sense of
the likely impact on the outcome of each possible combination of parameters.
4.10.1 A process window for FSSW
A process window can be defined for all welding parameters in terms of
their effects on the peak interface temperature. This can describe how one
parameter can be varied in order to compensate for a change in another –
for example, how the speed could be altered to compensate for a reduction
in welding time, in order to maintain the same joint strength. From a purely
thermal perspective, the variables of importance are input power and dwell
time. The variation of input power with rotation speed and downforce is
examined in depth in Chapter 6; for the present discussion, all welding
parameters apart from dwell time will be lumped together and represented
by altering the power.
The assumption made here, examined in detail in Chapters 5 and 6, is
that a certain minimum temperature must be reached at the weld interface.
This minimum temperature must allow the metal to soften sufficiently so
that deformation can break up the oxide layers at the interface.
As discussed in Chapter 2, the HAZ is usually the weakest point of
the weld. Bjorneklett et al. (1999) summarised the loss of strength in the
HAZ in precipitate-hardened Al: ‘Particle dissolution is the main factor
contributing to strength loss during welding. At the same time, growth of the
remaining particles occurs during cooling, leading to solute depletion within
the aluminium matrix. This, in turn, reduces the precipitation potential
and contributes to the development of a permanent soft zone within the
partly reverted region after prolonged room-temperature aging’. This loss of
strength is particularly severe in 6XXX-T6 alloys due to reversion of the β′′
precipitates.
117
Both the size of the HAZ and the loss of strength within it can be
minimised by minimising the energy input to the weld. However, a cer-
tain minimum temperature must be reached in order for a joint to form
at all. Peak temperature greatly influences microstructural changes, and as
discussed in Chapter 2 has more of an effect than variation in the hold time at
temperature. Consequently, the production of optimum-strength welds relies
on reaching a certain minimum temperature in the nugget, while keeping
temperatures in the HAZ below a maximum. This description is supported
by strength-testing results presented in Chapter 3, where it was shown that
maxima exist for the variation of joint failure load with welding time, or
rotation speed.
Peak temperatures at the weld interface can be predicted from the cal-
ibrated model. (It is very difficult to measure peak temperatures at the
interface as thermocouples placed here are usually destroyed by the welding
process.) Peak temperatures are shown in Figure 4.27 for five different cases.
Considering only the Al to Al welds in this figure, hotter (i.e. longer) welds
are associated with lower failure loads.
Thermal conditions in the nugget and HAZ were characterised by the
temperatures T1 and T2 respectively. These were the peak temperatures
at two locations: the centre of the weld (T1), and 5 mm from the centre
(T2), located 0.9 mm above the backing plate (i.e. at the joint interface).
Comparing temperatures at these locations with strength data for the same
welds suggests that the temperatures that give rise to a high-strength joint
are T1 > 670 K and T2 < 605 K. This allows weld modelling to take place to
examine the combinations of power input and dwell time that could give rise
to optimum welds.
Simulations were run covering a range of welding times, and the peak
power was adjusted in each case by a trial and error process until T1 = 670 K.
For this series of calculations, the workpieces both had the properties of
AA6111 and the plunge was kept constant at 0.2 mm. The power profiles
and distributions were otherwise kept constant. The resulting combinations
of peak power and dwell time that give rise to a peak temperature of 670 K
at the weld centre are shown in Figure 4.28. This indicates the minimum
118
Figure 4.27: Peak temperatures at the interface, selected welding conditions
power required at each dwell time to produce sufficient softening at the weld
centre.
The same process was carried out looking at the 5 mm location instead
of the weld centre, and combination of dwell time and peak power such that
T2 = 605 K are shown in Figure 4.29. This gives the maximum power possible
at each dwell time without causing overheating.
These boundaries can be used to define the edge of a process window
for optimum welds: the combination of power and dwell time must be such
that peak temperatures satisfy T1 > 670 K and T2 < 605 K. These limits
are plotted in Figure 4.30. From this figure, the optimum power required
for a certain dwell time can be found. Not only does the power required
increase as dwell time decreases, but the process window becomes larger —
i.e. the range of power that will produce a joint without causing overheating
in the HAZ increases. The converse is also true, to the extent that beyond
approximately 2.4 s optimum welds are no longer possible: a sufficient energy
input to soften the deformation zone will cause excessive overheating in the
HAZ.
These results match well with experimental data, in which dwell times
need to be at least 1 s to form welds, and at longer times the weld strength
falls. There is a very sharp increase in the required power for welds of less
119
Figure 4.28: Combinations of peak power and dwell time for equivalent
temperatures at the weld centre
Figure 4.29: Combinations of peak power and dwell time for equivalent
temperatures 5 mm from the weld centre
120
Figure 4.30: Processing window for optimum strength welds (Al to Al).
The blue line indicates the minimum power required to satisfy
T1 > 670 K, and the red line indicates the maximum power
permissible to satisfy T2 < 605 K.
121
than 1 s duration, a power that cannot be applied even at very high rotation
speeds (see Figure 3.7), or at least, it is impractical to generate such a power
using currently-available equipment. At times longer than 2 s, there is very
little change in the peak power required — the weld has almost reached a
steady-state, and the bulk of any additional energy supplied is lost to the
anvil and surroundings.
This analysis suggests that the strength of Al to steel welds could also
be improved by reducing the energy input. However, the process window in
dissimilar welds is much narrower, owing to the lower conductivity of steel.
Further study could refine the exact values of T1 and T2 needed to produce
optimum welds in various materials. This would not need to be done through
FSSW: with extensions to the deformation models in Chapters 5 and 6, it
may be possible to define these temperatures based purely on the softening
and aging characteristics of the particular alloys being welded, with reference
to kinetic models of their microstructures. However, that is beyond the scope
of this present study, for which it is sufficient to define T1 and T2 by reference
to experimental FSSW data.
4.10.2 Alternative backing plate materials
Various backing plate materials have been used in experiments in the liter-
ature, but the approach seems to have been scattered, with no systematic
studies reported. Complicated setups involving heated plates, or plates with
cooling pipes, have been used, and their effects on weld strength and quality
reported, but no attempt to understand the mechanisms involved is discussed.
A study is presented here which modelled an otherwise identical weld with
four different backing plates. These were made from steel, alumina, copper,
and a theoretical material with zero conductivity. Except in the last case, the
contact conductivity was not altered, and the previous values found by Parker
(2011) and Je¸drasiak (2012) for contact conductance were used. The perfect
insulator was modelled by removing the backing plate from the model. The
top clamp and tool were kept the same in each case, with the properties of
steel, as given previously. (The thermal properties of all materials are given
in Table 4.1.)
122
Figure 4.31: Temperatures histories at the weld interface, for 4 different
backing plate materials
Temperature histories for each of these cases are shown in Figure 4.31.
The difference between the peak temperatures reached in the steel and alu-
mina cases is smaller than may be expected from looking just at their relative
conductivities; this is because, as noted, FSSW is a highly transient process
and so heat flow is dominated by the diffusivity rather than the conductivity.
The perfect insulator creates a higher temperature rise, but perhaps of more
note is the copper case: the peak temperature reached in this model is only
429 K, barely enough to produce softening in the workpieces. These results
are more extreme than could be achieved experimentally, as the model does
not take into account the feedback loop — in experiments, the power would
drop off in the case of an insulator as the temperature approached the solidus,
and in the copper case the power would be much higher (assuming the tool
could grip the workpiece and force it to deform in the same manner).
Strength tests on welds made with a homogeneous steel and a Macor-
coated steel backing plate were presented in Chapter 3. In these results, the
use of the ceramic coating produced lower-strength welds in most cases.
High-diffusivity backing plates reduce T2 compared to T1, all other pa-
rameters being equal; consequently, this increases the parameter space (in
123
terms of power input and dwell time) that can give rise to optimum welds.
To test this in quantitative terms, analysis from Section 4.10.1 was repeated,
with T1 = 670 K and T2 = 605 K, but with a copper instead of steel anvil.
Based on the same assumptions as in Section 4.10.1, the range of optimum
welding conditions using a copper backing plate is shown in Figure 4.32. This
shows that the viable processing window is much larger than with a steel
anvil. A drawback of using a backing plate with higher diffusivity is that
doing so reduces the proportion of energy retained in the weld. Hence, the
input power and the total energy input increase dramatically. This has a
number of drawbacks, but it appears to be an unavoidable trade-off.
A surprising result is noticeable in Figure 4.32: not only is the range
of power that gives rise to optimum welds increased, but it continues to
increase as the welding time is increased. This is in contrast to using a steel
backing plate, when there is a time (estimated as about 2.4 s) beyond which
optimum welds are impossible with any power input. This situation arises
due to the significantly greater thermal diffusivity of Cu as compared to Al: it
is possible, with a Cu anvil, to set up steady-state conditions with the weld
centre at 670 K and the temperature at the 5 mm location below 605 K.
(‘Possible’ meaning, in this context, there is a solution to the equations of
heat transfer that makes the above statements true, not that it can necessarily
be achieved with actual welding equipment.)
This is useful; although it may not be precise enough to make exact
predictions of the optimum parameters, it indicates where experiments should
be focussed within the overall parameter space. One possible drawback was
noted above: with a copper backing plate, the power required increases.
Furthermore, as shown in Figure 4.33, although the process window covers
a wider range of powers at longer times, longer welds also increase the total
energy required. Figure 4.33 shows contours of constant weld energy. This
places a limit on dwell times that will be practical, in addition to produc-
tion considerations. Nevertheless, high-diffusivity backing plates could be a
subject for productive future research.
124
Figure 4.32: Process window for optimum welding, with a copper backing
plate
Figure 4.33: Process window for welding with a copper backing plate,
showing contours of constant weld energy at 3, 6 and 12 kJ.
125
126
Chapter 5
Kinematic model
Friction stir spot welding is a flow process involving heating and deformation.
This chapter is primarily concerned with the flow aspect, which has few
similarities with flow in other processes. Kinematically, FSSW is a highly con-
strained process, especially when used with thin sheet workpieces. Although
there is intense deformation in the nugget, there is solid, undeforming mate-
rial only a short distance outside the tool shoulder radius, and the tool and
backing plate remain solid and elastic (and therefore essentially undeformed,
by comparison with the plastic strains involved). These kinematic constraints
mean that the flow, despite its complexity, can be adequately described by
a relatively small number of parameters. As a consequence of the boundary
constraints, the flow is predominantly cylindrical, i.e. tangential to the tool
radius at any point. However, patterns evident in the deformation zone after
welding are not simply uniform layers as might be na¨ıvely expected under
these flow conditions. Imaging studies, such as those carried out by Bakavos
et al. (2011) using dissimilar alloys show features referred to as hooking and
dishing that are commonly taken to be a result of vertical and radial flow
during welding. This present work shows that tangential flow alone can give
rise to many of these features, and they cannot necessarily be taken as signs
of more complex flow patterns.
Even with the presence of asymmetric tool features (seen, for example,
in the MX Triflute tool) the flow constraints are comparatively simple, and
127
a great deal of the complexity in the process arises from the constitutive
behaviour of the material. Earlier flow models have relied on computationally
intensive CFD or FE simulations; however, by making some simplifying
assumptions about the material properties a simple deformation model can
be developed based on the kinematic constraints imposed on the flow. In
particular, by constraining the material to only flow tangentially at any
point, a kinematic model can still reproduce many of the post-weld features
previously thought to be indicative of more complex flow behaviour.
This approach allows investigation of the contact conditions at the tool-
to-workpiece interface, and the influence this has throughout the weld. The
degree of slip is closely linked to the flow pattern and heat generation;
these parameters are used as an input into many thermal models, however
at present such models rely on fitting parameters, such as a correlation
between the torque and the heat input determined from reference welds (see,
for instance, Khandkar et al., 2003, who summarise a number of similar
approaches). Obviously, this approach has substantial limitations, not least
of which is the fact that so many parameters may be adjusted in opposition to
each other. For example, in Chapter 4 increasing both contact conductance
and power input had similar effects on weld temperatures, requiring multiple
thermocouple measurements from a number of welds to identify accurate
values for both parameters. In general, fully-coupled FE models are also
unable to model the slip, as the friction coefficient depends strongly on many
factors that are not usually incorporated into such models, and which can be
impossible to measure during welding, such as surface finish and roughness.
The simplified approach presented in this chapter is a novel approach to weld
modelling, and provides many insights into the behaviour of FSSW.
128
5.1 Model development
As FSSW is so highly constrained, there is a fairly narrow range of possible
flow patterns that satisfy continuity. As the process takes place in thin
sheet material, the steel tool and backing plate constrain the bulk of the
flow to be predominantly in-plane. The shoulder diameter to sheet thickness
ratio is typically of order 5, so radial flow is constrained by friction against
the tool and backing plate. The tool and backing plate are made of much
harder and stiffer material than the workpiece and the stresses within these
components remain elastic, so these boundaries may be treated as entirely
non-deforming for large-strain analyses. Additionally, there is non-deforming
parent material only a short distance outside the shoulder radius, which
strongly influences the flow pattern. The process is axisymmetric (at least
for the case of a flat shoulder). The angular velocity at any point on the
interface can be conveniently described by the degree of slip at that point (this
applies to both the tool–workpiece interface, and the workpiece–backing plate
interface). For the top interface, a convenient measure of slip is the speed of
the workpiece surface as a fraction of the tool speed at the same radius; for
the bottom interface, the speed itself is the appropriate measure of slip (as
the backing plate is static). In the case of full sticking at the tool–workpiece
interface, v = ω× r at any point; however, at some radius Rs (close in value
to the tool shoulder radius) the velocity must fall to zero. Hence, there must
be a transition region between a sticking region and the periphery, giving a
region of slip, where the tool moves faster than the workpiece it is in contact
with. A kinematic model was developed in Matlab to visualise the flow based
on these constraints using greatly simplified constitutive behaviour.
Firstly, by assuming uniform strength in the material, a torque applied
to a cylinder gives rise to uniform twist and shear strain along its length.
Consequently, the position of any point after a certain twist is applied to the
top surface is a function purely of its initial position and the twist angle. The
model presented here takes the kinematic equations of motion for each point
in an initial point cloud, and tracks the position of each point throughout
the course of a weld. If, for example, the point cloud specifies points that
129
initially lie in a single plane, the position of these points at a later time shows
where that plane has moved to. The relationship between the whole weld, the
nugget, and the tracked plane is shown graphically in Figure 5.1 for a butt
weld configuration. In a butt weld, the two colours in this figure represent the
two different workpieces, and each coloured plane in later figures represents
the advancing front of that workpiece. In a lap weld, the same flow pattern
occurs, though it is not seen in experimental weld sections as there is no
physical joint to see in the vertical plane.
The output from the model is a graphical representation of the final
positions of the points being modelled. In the first and simplest case, a
uniform angular velocity is imposed on the top surface of the stir zone. The
bottom sheet is stuck to the backing plate, and the outer boundary of the
nugget is allowed to slip freely. The series of images shown in Figure 5.2
represents two alloys being joined in a butt weld configuration. Each image
shows the position of the interface between the two alloys as welding time
increases. In these views, each colour represents the advancing front of one
workpiece, i.e., the region behind the red surface and in front of the blue is
filled by the red workpiece.
The model need not be restricted to modelling points in a plane, but may
also model points filling the whole stir zone (or any arbitrary region desired).
If a ‘solid’ point cloud (i.e. a cloud of points evenly distributed throughout
the stir zone) is used, then the resulting graphical output may be sliced either
horizontally or vertically to produce top-down or section views. Examples of
these views, for the same velocity profile, are shown in Figures 5.3 and 5.4.
Figure 5.1: Expanded 3D view of the kinematic model, showing a
schematic of the whole workpiece, the weld stir zone, and a cut-
away view of the stir zone
130
Figure 5.2: Open corkscrew series, isometric view for 0, 1
6
, 1
4
, 3
4
and 1.5
rotations (dimensions in mm)
Figure 5.3: Open corkscrew series, top-down view, for 0, 1
6
, 1
4
, 2.5 and
10 rotations; the top down view is indistinguishable from rigid-
body rotation for this case, and is shown here only for completeness
(dimensions in mm)
Figure 5.4: Open corkscrew series, section view, showing layering (for 0,
1
6
, 1
4
, 2.5 and 10 rotations)
131
5.2 Tool contact boundary condition
The model presented in the preceding section serves to outline the concept of
the model, but it is not an accurate representation of reality. In particular, it
does not satisfy continuity. The boundary conditions that must be satisfied,
for all welding conditions, are:
• a fixed boundary at some radius (this is RS at the surface, but the fixed
boundary need not be vertical);
• a boundary at the interface between the workpiece and tool that may
be fully stuck, fully slipping, or partially slipping at any point, as a
function of radius;
• a boundary condition between the workpiece and backing plate similar
to that between the workpiece and tool.
The previous model imposed a velocity of v = ω× r across the whole surface
of the stir zone, out to r = RS. In conjunction with the condition v = 0 at
r > RS this gives rise to a discontinuity at r = RS. A step change in strain
within a solid body is a crack; as cracks are not generally observed at this
position in real welds, the assumed boundary conditions cannot be correct.
To remedy this, the top surface boundary condition was altered to reduce
to zero velocity at the edge of the tool shoulder (RS). Three new profiles
for the top surface velocity were modelled, shown in Figure 5.5. These all
satisfy continuity, and so are more realistic than the open corkscrew case.
The first of these profiles has v = ω×r for r
RS
< 0.9, with v then falling back
linearly to zero at r = RS. This is not thought of as a particularly realistic
profile, but is a sort of ‘minimum required’ case, in that it is probably the
simplest case that satisfies the continuity requirements (other than the trivial
v = 0 everywhere case). The point outside which the workpiece is no longer
in sticking contact with the tool is labelled r1.
The second and third profiles were created based on FE modelling work
described in Chapters 4 and 6. The reasoning set out here describes why
they were chosen for investigation. It is not intended to show that these
132
slip profiles are necessarily realistic — this justification comes later, via
the accurate predictions they produce. Extensive empirical calibration work
carried out by Je¸drasiak et al. (2012) looked at the detailed effect of varying
the heat input location on the peak temperatures reached at various virtual
thermocouple points. This work was all carried out as a finite element study
(in the same manner as described in Chapter 4); in particular, it looked at
the influence of surface and volumetric heating. Previous work by Russell
(2000) made some simple slip surface estimates of the relative proportions of
power contributed due to deformation around the pin and shoulder in seam
FSW. Je¸drasiak et al. found that a heat input with a peak at r = 0.7RS
was able to provide the most accurate prediction of temperature data across
a range of welding conditions. Based on this work, and previous work by
Colegrove & Shercliff (2006) and Colegrove et al. (2007), two other velocity
profiles were developed: the first simply sets the point of inflection, or point
of maximum velocity, r2, in the velocity profile to be 0.7 (this is profile 2);
the second relies on a knowledge of the stress under the tool (developed with
the aid of an FE deformation model described in Chapter 6) to estimate the
slip condition required to give rise to the thermal profile found by Je¸drasiak
et al. This third profile introduces a change in gradient, i.e. a change in the
rate of slip increase with radius. This point is labelled r1, and is set to 0.5RS.
All three top surface boundary conditions can all be described by a single
piecewise equation shown in Table 5.1. The innermost zone is a region of no
slip, and in the middle and outermost zones the slip velocity varies linearly
with radius.
Because of the flow pattern produced by these profiles, the isometric
view is not such a useful output (see Figure 5.6: the interface has a vertical
component which hides the inner zone of greatest interest). The top-down
Region Slip velocity (relative velocity between tool and workpiece)
r < r1 v
′ = 0
r1 < r < r2 v
′ ∝ (r − r1)
r > r2 v
′ ∝ (r − r1) +
(
r−r2
RS−r2
)
Table 5.1: Top surface slip velocity
133
Figure 5.5: Velocity profiles applied to the top surface of the stir zone
and section views are much more informative, and so these are the only views
that will be presented further; these views have the additional advantage that
they can be easily compared with experimental metallographic sections.
A series of top-down and section views showing the differences between
the velocity profiles in Figure 5.5 is shown in Figures 5.7 and 5.8. From the
top-down views the effect of decreasing r2 can be clearly seen: this profile
leads to a weld with wider spirals and a smaller central region (the region of
no slip). Decreasing r1 below the value of r2 leads to a still smaller region of
no slip, and a slight change in the shape of the spirals.
The differences are more apparent in the section views. While all of
the profiles give rise to broadly similar forms — interlocking layers of the
two alloys — increasing the size of the slip zone produces more rounded,
bowl-shaped layer boundaries, rather than the hard-cornered layers seen with
velocity profile 1. In terms of the local shear strain experienced by the
material, profile 1 leads to a much more concentrated shear zone, with very
intense deformation in the region where r > r2.
134
Figure 5.6: Isometric view for 0.75 and 1.5 rotations, with top surface
velocity profile 1; compare with the figures in 5.2 and note that now
most of the weld is hidden by the outer ring.
Figure 5.7: Velocity profiles 1 to 3 at 1, 2 and 4 rotations — top-down view
135
Figure 5.8: Velocity profiles 1 to 3 at 1, 2 and 4 rotations — section view
5.3 Through-thickness heat flow
Initially, the model represents an autogenous weld with uniform material
flow properties that are independent of time and position. The physical
interpretation of this is that there is no allowance for temperature dependent
properties, or alternatively, that the material is all at a uniform temperature
for the whole duration of the weld. These two statements are equivalent,
and the result of assuming either is that temperature effects do not affect the
flow of material. The feedback loop between temperature and deformation is
a critical mechanism in FSSW and an understanding of this interaction is a
major goal of modelling. Hence, a model that does not capture these effects
can only capture a limited part of the behaviour of interest.
A refinement of the model is presented here that can account, in a reduced
fashion, for through-thickness heat flow. Radial heat flow is not modelled here
(see Section 2.3.4 for an explanation of why this is valid, and the conditions
under which it is appropriate; in summary, the parameter space in which
FSSW mostly operates is one of 1D heat flow in the nugget).
136
The feedback loop is incorporated into the present model by changing the
constitutive behaviour and making a simplifying assumption about the heat
flow. The constitutive law adopted is a simple rigid–perfectly plastic model
where the rigid–plastic transition is purely dependant on temperature. The
heat flow is assumed to be 1D in the through-thickness direction, from the
tool to the backing plate. This is similar to the conditions applicable to the
bottom right of Grong’s condition map (Figure 2.9), i.e. a thin workpiece
made from high strength, high conductivity material. (Note that the con-
dition map shown in that figure does not correspond exactly to the FSSW
process, as there is no translation in FSSW. The heat flow is dominated
by flow downwards from the top surface, where the workpiece is in contact
with the tool.) The effect of introducing this constitutive behaviour and
vertical heat flow, is that at time t = 0 all deformation is restricted to
a thin layer at the top of the workpiece; the rest of the weld material
remains rigid. As welding progresses, the deforming zone spreads through the
thickness, capturing the effect of material softening as heat diffuses through
the workpiece. This is modelled by assuming a linear increase in deformation
depth with time.
Although the number of layers does not alter when this material behaviour
is assumed, the relative thickness of each layer depends on the relationship
between heat flow and rotation speed. This is characterised by a dimen-
sionless group labelled here as ω¯ : alternatively interpreted, this is the time
taken for sufficient heat to reach the bottom of the workpiece to allow it to
deform, compared to the time taken for one rotation of the tool. The rate of
heat flow is governed by the weld material’s thermal properties, specifically,
the diffusivity; the rotation speed is a welding parameter. The ‘speed of
propagation of heat’, vh, is found from the rise time of the temperature at
a distance x from a heat source, as a solution to the error function. An
order-of-magnitude estimate of this rise time is given by t = x
2
a
. This allows
the welding parameters to be linked to the material properties through the
use of ω¯ and vH , as in Equation 5.3. The parameter ω¯ is then the ratio of
the maximum linear tool speed (i.e. the speed at the edge of the shoulder)
to the mean speed of propagation of heat through the workpiece (vH). This
137
propagation speed is assumed to be constant, so the onset of deformation
progresses linearly through the workpiece until the influence of the tool
reaches the bottom of the workpiece and the whole stir zone starts deforming.
Although a non-linear function could easily be introduced into the model,
there is at present no information about how it may evolve with time, so a
linear function is assumed as the simplest case.
In the model, vh is a kinematic parameter that is specified directly, but
the use of ω¯ allows it to be linked to real welding conditions. A more accurate
estimate of vH could be obtained from, for example, an FE model of the heat
flow, which could be used to improve the accuracy of the kinematic model,
and in such a case it may become appropriate to consider a time-varying vH .
ω¯ =
ωh
vH
(by definition) (5.1)
vH ∼ a
h
(from x =
√
at ) (5.2)
∴ ω¯ ∼ ωh
2
a
(5.3)
(In this equation, h is the workpiece thickness, a is the thermal diffusivity and
vH is a characteristic heat propagation speed, or thermal diffusion velocity,
defined as vH =
h
t1
where t1 is the time between the onset of heating and the
temperature rise at the far surface of the workpiece.)
A series of section views showing the effect of varying the ω¯ parameter is
shown in Figure 5.9. The figure shows a series of stills at increasing times
(corresponding to increasing numbers of tool rotations) from left-to-right
and at increasing values of ω¯ from top-to-bottom. These are all shown for
velocity profile 3 (Figure 5.5), as this is the best experimental match to the
flow pattern (see Section 5.6). The top row is the result of models run with
ω¯ = 0; this is the same as seen in Figure 5.8. As ω¯ is increased, the layers
become increasingly concentrated, and also thinner. While those of ω¯ = 0
and ω¯ = 30 appear very similar for times after t = 0.5 s, in the bottom row
(where ω¯ = 300) deformation has not reached the bottom of the sheet even
after 20 rotations. Qualitatively, the effects are clear: increasing the heat
flow time, analogous to modelling a material with a lower thermal diffusivity,
138
compresses the layers into the upper region of the workpiece. Importantly,
the number of layers remains the same — this is a characteristic of each weld
that is independent of a.
The calculation of ω¯ for a dissimilar workpiece combination is slightly
more complicated due to the non-linear variation in mean heat propagation
speed with h. For two layers, let h1, h2, t1 and t2 be the thicknesses and
characteristic heat flow times of each layer. In that case, vh is given by
Equation 5.5 and ω¯ for the whole weld is given by Equation 5.6.
vh =
h1 + h2
t1 + t2
(5.4)
∴ vh ∼ h1 + h2h21
a1
+
h22
a2
+ 2h1h2
a2
(5.5)
∴ ω¯ ∼ ω ×
(
h21
a1
+
h22
a2
+
2h1h2
a2
)
(5.6)
Figure 5.9: Section views showing the changes in layering caused by
varying ω¯ (ω¯ values of 0, 30 and 300 for 2, 5 and 20 rotations)
139
5.4 Dissimilar joining: aluminium to steel
All the analysis so far has been conducted for butt welds between identical
workpieces, or alloys with very similar strengths (as in the case of AA6111 and
6082). There is no change in the flow pattern between a butt weld and a lap
weld between two Al sheets — the layering pattern continues through both
the top and bottom sheets, showing that sticking friction conditions exist
at the interface between the two sheets almost immediately, and continue
throughout the weld. This has been shown experimentally with ‘dual-lap’ or
‘semi-lap/semi-butt’ welds, i.e. with three sheets forming a butt joint over
the top of a lap joint (or with four workpieces forming a ‘double-butt’ joint
as in Figure 5.10.
However, as discussed in Chapter 1, one of the key benefits of FSSW over
other welding processes is its ability to easily join dissimilar metal combina-
tions, therefore extending the model to handle these cases is important. A
case of particular interest is joining Al and Fe. In a lap weld configuration,
this combination can be welded either ‘classically’, i.e. with the Al sheet on
top, or inverted, with the Fe on top. Only classical welds will be considered
in this section. Owing to the strength difference between Al alloys and
steels — which becomes more pronounced at elevated temperatures — most
deformation during dissimilar welding takes place in the Al workpiece (see e.g.
Chen & Lin, 2010). In section views of these welds the layering pattern ceases
at the Al to Fe interface. As a first approximation, therefore, the previous
kinematic model can be run assuming that all the deformation takes place in
the top sheet.
In the present work, welds with AA6111 to both uncoated and galvanised
low-carbon steel sheets are considered. The presence of the zinc layer has a
significant effect on the flow pattern.
5.4.1 Welding Al to uncoated steel
In the case of a weld between Al and Fe, the strength difference at temper-
ature is so marked that the Fe does not deform plastically, at least in bulk.
Micrographs indicate that the oxide layer is broken up, and the intermetallic
140
Figure 5.10: Illustrative figure of a ‘double-butt’ weld
layer between the two workpieces shows that the temperature rise is sufficient
to cause significant reaction and diffusion. However, for the purpose of
modelling the bulk material, these welds can be modelled by assuming that
all the deformation takes place in the Al layer. In the case of a plain DC04
steel sheet for the lower workpiece, the hypothesis is that friction at the
interworkpiece interface is sufficient to prevent movement of the base of the
upper layer. In this case, the section views look the same as for Al to Al welds,
except the deformation is confined to the top sheet, and hence the layers are
one half as thick — in Figure 5.11, compare the bottom row of images to
the top row. Apart from the interface and the fact that the bottom sheet is
non-deforming, the boundary conditions are the same in the two cases.
Figure 5.11 is for ω¯ = 0. However, the earlier discussion concerning ω¯
still applies. Essentially, the Fe sheet plays no part in the deformation, and
the flow is confined to the upper (Al) sheet. The flow patterns look similar
to Al to Al cases, but squashed. This is as expected: the materials and
forces involved in the contact between the Al and Fe sheets are the same as
for a contact between an Al sheet and the backing plate, so the friction and
slip velocity will also be similar. The only differences are due to the hotter
interface in the case of a steel workpiece (since the distance from the tool is
less), the surface finish, and differences due to a difference in alloy between
the workpiece and the backing plate (both are mild steel in the experiments
conducted in this project; greater differences may be expected with high alloy
steels). This similarity was even more apparent when conducting deliberately
over-hot welds; in a few experimental cases joining Al to Al the workpieces
were inadvertently welded to the backing plate.
141
Figure 5.11: Section views showing a model of a 4-sheet double-butt weld,
in AA6111 aluminium to itself (upper series) and on top of DC04
steel (lower series) for 1, 2 and 4 rotations
5.4.2 Welding Al to galvanized steel
Galvanized steel is widely used for its corrosion resistance, which makes it an
obvious choice in combination with Al for parts in corrosive environments.
Welding experiments have been tried using both hot-dip galvanized and
zinc electrocoated steels as the bottom workpiece; these two processes both
produce a zinc coating with an Fe/Zn intermetallic layer between the parent
material and the bulk of the Zn, although the hot dip process produces a much
thicker zinc layer. These welds are qualitatively different from those with
ungalvanized steel, since the zinc softens and melts, forming a lubricating
layer at the joint surface. This is an exception to the general rule that FSSW
is a solid state process, and the situation arises because the melting point of
Zn is lower than that of the Al. Because of this, further heat generation can
take place in the top sheet even after the zinc layer has reached its solidus
and experienced the loss of strength that this entails.
A modification to the kinematic model extends it and makes it suitable
for modelling these welds. This is studied by reference to Al and Zn welding,
but is also applicable for other situations where a layer (or the bottom sheet)
has a lower solidus temperature than the upper sheet; the same situation can
arise, for example, when welding Al to Fe in the ‘inverted’ case, i.e. with Fe
as the upper worksheet (Chen, 2010 and Chen & Lin, 2010).
142
As a limiting case, a molten layer can be modelled by relaxing the con-
straint at the bottom of the upper (Al) sheet entirely. This gives rise to
the section views shown in Figure 5.12. In this case, the only restraint to
motion is the contact between the nugget and the surrounding material in
the top workpiece, and the joint line deforms but remains vertical, as seen in
the figure. This is representative of an entirely lubricated layer between the
two workpieces throughout welding. However, a galvanised workpiece will
provide some restraint — the Zn will provide a measurable friction contact
between the two sheets until it reaches its solidus. This can be modelled more
realistically by allowing a sticking frictional contact between the two layers
until some time, then releasing the contact after that to simulate melting of
the interface.
This is done in the Figure 5.13, which shows images from simulated welds
at a speed of 84 rad s-1. The two section views in this figure are taken after 20
rotations of the model. The image on the left shows the result of full sticking
at the interface, simulating plain steel on the lower sheet; as discussed in
the previous section, this looks very similar to the case of a weld between
two Al sheets, but with the layers confined to the top sheet. Again, for this
weld ω¯ = 0.
The image on the right of Figure 5.13 shows the effect of a zinc layer
between the upper and lower sheets; the layer provides sticking friction until
it reaches its solidus, then no resistance to sliding. For this simulation, the
zinc melting time was set (somewhat arbitrarily) to 0.4 s after the start of the
weld. The change in contact condition at this interface creates a discontinuity
Figure 5.12: Section views showing a lubricating layer between the two
sheets (2, 5 and 20 rotations)
143
Figure 5.13: Section views after 20 rotations for a zinc layer that melts
after 0.4 s (at 84 rad s-1)
in the layering pattern when viewed in section. In Figure 5.13, it can be seen
that the effect of the melting is to reduce the number of layers in the central
portion of the nugget and increase the angle of the outer portion of the layers
from horizontal. The horizontal layers form while the interface is a sticking
contact, then once the zinc layer has melted the outer 50 % of the stir zone
experiences horizontal shearing, forming vertical bands, but superimposed
on the pre-existing horizontally-layered structure. The central portion of the
nugget undergoes a rigid body rotation once the base has melted.
5.5 Deep plunge welds
The previous analysis focussed on spot welds where the plunge is sufficiently
shallow by comparison with the overall depth of the combined workpieces
that the change in geometry can be ignored. While this is often true for
aluminium welds, the search for stronger welds between Al and Fe has led to
the production of welds with much deeper plunges. In a weld, this has two
advantages: firstly, it increases the temperature at the joint, as the tool is
brought closer to the interface. Secondly, it increases the shear strain gradient
at the interface, which helps break up the oxide layer and encourage mixing.
These two effects have to be balanced against the loss of strength that can
be caused by joint thinning and overheating. Bringing the tool closer to the
joint interface will clearly increase the local strain rate (although this is not
mentioned in published literature); this is supported by the kinematic model,
which shows higher strain rates at the base of the upper layer as the plunge
depth increases.
144
From a modelling point of view, a number of simplifying assumptions can
be made which allow the kinematic model to be adapted to model deep plunge
welds. An unconstrained homogeneous cylinder under pure axial compression
will deform outwards. The radial expansion ∆r will be independent of z,
since the stress state is purely a function of radius, and will depend only on
the overall change in height. For a weld, the deforming zone is constrained
by surrounding parent material. The only way the tool can plunge into the
workpiece is by expelling material and forming flash on the top surface. The
material most easily expelled is that near the surface, as lower material is
more heavily constrained, much like a punch indentation problem. At the
bottom interface, the workpiece is stuck to the backing plate and surrounded
by cooler, stronger material, so a reasonable first approximation is to assume
that the radial velocity scales linearly with height above the bottom surface.
The volume of material expelled is found by volume conservation (as Poisson’s
ratio ν = 0.5 for plastic deformation).
These boundary conditions will lead to the upper layers of the cylinder
deforming outwards more than the lower. As a first approximation, this
variation can be assumed to be linear, i.e. ∆r ∝ z, as in the series of graphics
in Figure 5.14. In practice, the cold outer material prevents bulk radial
expansion of the weld nugget, and instead the material expelled from this
volume is forced upwards, forming flash. The ultimate effect of this is that
the final weld nugget, in the post-weld state, is formed from material that
originally occupied the shaded volume in Figure 5.15.
Figure 5.14: Assumed flash extrusion profile
145
Figure 5.15: Weld nugget volume before a deep plunge weld: the shaded
region represents the material that will make up the final volume of
the nugget
Together with the original axisymmetric flow pattern, the assumption
that the radial expansion is proportional to z is sufficient to specify the
radial and vertical motion entirely: as the process is axisymmetric and the
flow pattern is incompressible, then for any given plunge rate the radial
velocity can only take one value to satisfy continuity. This value is given by
Equation 5.7, which comes from equating the volume of the initial cylindrical
volume under the tool and the final truncated cone that this material would
occupy if the surrounding material did not force it upwards to form flash.
dr
dt
=
(
r2 (h1 − h2)
h32/3 + r1h22
)
dz
dt
(5.7)
Deep plunges can be incorporated into the kinematic model by imposing
a radial and vertical velocity at each point. This is shown in Figure 5.16
for an Al to ungalvanized Fe weld. Within the final nugget volume, to a
first approximation the deeper plunge has no effect beyond stretching the
layers already formed; importantly, the number of layers will be the same
regardless of the plunge depth. This is illustrated in Figure 5.16. At least
with a flat tool, the essential flow features of a weld as observed in section
are not significantly altered by increases in the plunge depth.
This proposed mechanism of flash formation could be tested empirically
by measuring the volume of flash produced and comparing that to the volume
‘excavated’ by the tool during the plunge. However, practical limitations have
so far prevented this. Comparison with the model provides a way to check: if
the number and form of layers in a weld section agrees with the model output,
then the flow pattern assumed in the model is very likely to be correct.
146
Figure 5.16: Section view through a deep plunge weld
5.6 Comparison with experiments
A number of weld coupons were used in flow visualisation experiments;
these were etched according to the description given in Chapter 3. The
configuration for these welds was that of a double lap joint, using AA6111 and
AA6082 aluminium alloys in a butt weld configuration, over a sheet of DC04
steel. These two Al alloys have different appearances when etched, which
allows the flow pattern to be observed both with through-thickness sections
and intact views of the top surface of the finished weld. The tempers of the
aluminium alloys were chosen to give the same room-temperature hardness
value for each, ensuring that as far as possible their behaviour during the
weld is similar. As a result the weld is essentially the same as a single lap
weld with Al over Fe. The kinematic model treats both materials as identical.
A sample image from one of these welds (from Chen, 2010) is shown
in Figure 5.17a. AA6111 contains a higher proportion of copper (typically
0.75 % by weight compared to <0.1 % for AA6082) and is a lighter colour
when etched. The two alloys form distinct regions in the post-weld state,
and the top-down view shows a clear spiral pattern. The alloys are not
thoroughly mixed but form interlocking regions that are substantially one
alloy or the other. (Diffusion between the two alloys can of course occur, but
this is insignificant on this time and length scale.)
Figure 5.17b shows a model top view, from a simulation using velocity
profile 3 (i.e. r1 = 0.5RS and r2 = 0.7RS). By comparison with Figure 5.17a
147
Figure 5.17: a (left): Top-down view of an experimental weld between
AA6111 and 6082 over DC04, showing the top surface in the post-
weld condition, and b (right): Top-down view of the kinematic
model, run with velocity profile 3 for 10 rotations
it can be seen that the kinematic model produces results that are broadly in
agreement, at least qualitatively, with experiment. Moreover, it is possible to
use this model, in combination with weld metallography, to infer what contact
condition must have existed between the tool and top workpiece during the
weld.
Figure 5.18 shows the same top-down view of the experimental weld as
Figure 5.17a, but with the central portion highlighted. The edge of the
highlight indicates the boundary between a heavily-strained outer region and
a much less deformed inner zone. The central region shows very little mixing;
this is in accordance with the model (the fact that the centre of this region
appears slightly offset from the centre of the contact patch could be due to a
number of factors, most likely a slight difference in thickness between the two
alloys forming the upper sheet). The diameter of this region is approximately
2.5 mm. The model predicts a region of comparatively little deformation out
to a radius of r1 — in this case, 2.5 mm. Consequently, it is possible to infer
with a high degree of confidence that sticking conditions existed during the
148
Figure 5.18: Top-down view of the experimental weld (as in Figure 5.17a)
with the sticking region highlighted
experimental weld between the tool and the workpiece surface out to 2.5 mm.
The velocity profiles in Figure 5.5 were initially generated based on an
analysis of the heat flow, and an assumption that the spatial distribution
of heat input could relate to the slip condition. The consistency between
the patterns in Figure 5.17 suggests that the velocity profile that applies is
indeed close to profile 3. This is the first known work to provide a direct
method of estimating the surface slip, and it is independent of any estimate
(or measurement) of the local pressure or temperature. Furthermore, this
lends support to the original assumption that the heat distribution correlates
well with the surface strain-rate.
The effect of r2 is harder to measure from these views, and no detailed
conclusions can be drawn about the form of the slip profile outside 2.5 mm,
beyond the recognition that the distance between each layer boundary on the
surface reduces towards the outer radius. This suggests a surface velocity
profile similar to profile 3 is correct, but the precision of this method is not
adequate at this stage to say whether the slope beyond r1 is linear or if it
takes some other form.
In addition to the top-down views, similar welds with the same materials
149
and configuration were cut vertically to show a section view, etched in a
similar manner to the top views. A sectioned view of an experimental weld
interrupted after approximately 10 revolutions is shown in Figure 5.19. This
image shows alternating layers of the two alloys in a very similar fashion to
that predicted by the model. Again using surface velocity profile 3, a sectional
view of the model after 10 tool revolutions is shown in Figure 5.20. In this
image the model output figure is not stretched on a vertical axis as previous
ones have been, but is displayed on an equal axis to facilitate comparison
with the experimental figure.
There are lots of similarities between these two figures. The first key point
to note is that the number of layers is either identical or almost identical in
both cases; the second is that the shape of the layers matches reasonably
closely. The kinematic model specifies tangential flow at all points; there is
no radial or vertical flow in the model. The fact that these constraints can
give rise to such similar features as those seen in experimental welds strongly
suggests that the dominant flow in experimental welds is tangential. If there
is any radial or vertical flow, this is not required to produce the features seen
in real welds.
This comparison between model and experiment definitively fixes the
surface slip condition. In the model, layers are produced by tool rotation,
and the number of horizontal layers near the centre of the weld cannot be
greater than twice the number of rotations plus one (it may be less, in the
case of slipping at the base, and the total number of layers may be greater,
in the case of melting of an interface coating, depending on the path along
which layers are counted). The number of tool rotations in the experimental
welds is known, and the number of layers is at or very close to the limit
predicted by the model. This shows that a sticking contact exists almost
Figure 5.19: Section view through a weld between AA6111 and AA6082,
showing layering
150
Figure 5.20: Expanded section view through the kinematic model show-
ing bowl-shaped layers
immediately, and this is common regardless of the tool type or downforce.
There is essentially no ‘pre-dwell’ phase where the workpiece is being heated
purely by friction, but instead the tool grabs the surface as soon as contact is
made (or at least, within less than one revolution). The progressive increase
in the number of layers, and the thinning of existing layers as new layers
are added, is also seen experimentally. Figure 5.21 shows section views for
shallow-plunge welds after 0, 0.5 and 1 s of post-plunge dwell time (with a
plunge of around 0.3 s). Although the resolution of these images is lower
than of Figure 5.19, distinct layers can be seen in the lower portion of each
weld. The number of layers within the dashed boxes increases from 0.5 to
1 s. The interface between the upper and lower sheets remains essentially
horizontal.
This is an intriguing result, and one that would not necessarily be ex-
pected. Owing to compliance in the tool, machine and clamping arrange-
ments, there is some vertical slack in the system, and the tool is approaching
comparatively slowly (at 1.55 mm s-1 in the weld in Figure 5.19). Due to
these factors, the downforce does not undergo a step change, but ramps up
slowly as the tool continues to plunge (see Figure 2.10 and Section 3.7 for a
fuller discussion of this effect). This suggests that even when cold, a Coulomb
friction model would provide a poor match for the conditions prevailing at
the tool–workpiece interface.
151
Figure 5.21: Section view showing the increase in the number of layers
as determined experimentally (from Bakavos & Prangnell, 2009)
5.7 Variation in ω¯ for experimental welds
The value of ω¯ depends on a combination of welding parameters and material
properties. Values of ω¯ for various welding conditions are shown in Table 5.2
(with ω¯ calculated according to Equation 5.3). The corresponding welds
were either conducted as part of this project or reported by other authors,
as noted.
From this table, it can be seen that, for practical welds, ω¯ generally
lies between 30 and 50. This is an intriguing result, and indicates that
there is a fundamental balance that must be found to produce good-quality
welds. Work carried out for this project found that 84 rad/s was about the
lower limit at which good-quality welds could be formed in 0.9 mm thick
AA6111; below this speed, no joint formed at all, presumably because the
rate of heat diffusion at this lower power was sufficient to cool the contact
patch enough to prevent softening. Attempted welding at speeds below this
produced fretting on the top surface, but the two sheets fell apart after the
process was complete. At the highest rotation speeds attempted (up to 315
152
Workpiece material and welding conditions ω¯ Data source
AA6111, 210 rad/s, 2 no. 1 mm thick work-
pieces, 5 mm radius tool
32 Present work
AZ31 (1.6 mm) to low-carbon steel (0.8 mm),
25 rad/s, 15 mm radius tool
43 Chen & Nakata
(2009)
AA6061, 2 mm workpieces, 210 rad/s, 15 mm
diameter tool
49 Awang et al. (2005)
1 no. 1 mm Al sheet on top of 1 no. 1 mm
Mg sheet, 9.5 mm tool diameter, 108 rad/s
38 Choi et al. (2011)
1.3 mm thick PM2000 ODS steel, 63 rad/s,
12 mm diameter tool
34 Mathon et al. (2009)
6.3 mm thick AA6061, 210 rad/s, 4 mm
diameter tool
40 Su et al. (2006a)
Lower limit on rotation speed for forming
welds (limiting criterion: sufficient heating)
in AA6111 with 2 no. 0.9 mm thick work-
pieces and a 5 mm radius tool
13 Present work
Upper limit on rotation speed (criterion:
avoid cracking), conditions as above
40 Present work
Table 5.2: Values of ω¯ for various reported welding conditions
153
rad/s) final welds were observed to be of poor quality, with excessive flash
formation and visible defects on the weld surface. This model provides some
insight into the reasons for this — it seems to indicate that the reason that
higher speeds fail, is that at these speeds heat does not have time to diffuse
down into the bulk of the material. As a result, deformation is concentrated in
the upper portion of the workpiece, while the lower portion is comparatively
undeformed.
5.8 Analysis of actual slip conditions during
welds
As mentioned, the degree of slip between the workpiece and tool is of critical
importance for the behaviour of FSSW. Analysis of the slip condition that
exists during FSSW is a topic of debate in the literature, but there have
been as yet no attempts to measure it directly (due in no small part to the
difficulty inherent in doing so). Where an estimate is required, e.g. for a
numerical calculation, friction is assumed to follow a law such as Coulomb
friction, that is very well established for certain regimes, but for which the
appropriate parameters are often not known (in particular, the pressure as
a function of time and radius is not known with any accuracy, and is often
assumed to be constant — this is an especially poor model, as discussed
in Chapter 6). The kinematic model is especially useful in this regard, as
the amount of slip may be inferred by comparing outputs from the model
with experimental weld sections. This is something that is not possible with
more complicated flow models such as numerical FE or CFD codes. (In
FE models, the slip may be calculated rather than specified directly as an
input, but in order to do this assumptions are still required regarding the
friction law and values of parameters, e.g. the pressure, which are often not
known with accuracy, under the conditions of strain rate and temperature
applicable during FSSW.) As discussed in the preceding section, an estimate
of the radius outside which slip occurs is comparatively easy with this model.
An accurate measure of the slip outside r1 is more difficult, but could in
154
principle be possible with appropriate image analysis techniques to measure
the average thickness of each ring in the top-down view.
The other parameter that appears to be of great importance is the di-
mensionless group expressed here as ω¯ . This relates the mean speed of heat
propagation through the thickness of the weld to the maximum tangential
velocity of the tool, and has been shown to take only a small range of values
for all good-quality welds — the range of ω¯ is far smaller than the range in
any of tool speed, tool diameter, material diffusivity or workpiece thickness.
An experimental definition of ω¯ would be the time taken for the base of
the workpiece to soften sufficiently to deform, under the torque being applied
by the tool at that velocity. An estimate of this experimental definition of
ω¯ could be made from weld sections, from figures such as Figure 5.19). The
kinematic model predicts a layer thickness which alters with time, and the
rate of change of this thickness depends on ω¯ . If the layer thickness can be
measured accurately from image analysis, then the experimental value of ω¯
can be compared with that calculated in Equation 5.3, and the accuracy of
the dimensionless group as a predictor of the value actually occurring can be
calculated.
A more detailed study with higher-resolution experimental images could
analyse the other tunable parameters in the model (e.g. to get a much more
accurate assessment of r1 and r2 than is possible when estimating them by
eye, and the variation of ∂r
∂t
with z during the plunge) to estimate their values
in a range of welding environments.
5.9 Tool features and hooking
If other tool types do produce vertical flow, then by conservation, they
must also produce radial flow. It is likely that the causality of this is
reversed — looking at the surface of the ‘wiper’ tool (in Figure 5.22), for
example, it has features which can be easily imagined to produce some
degree of radial flow, even if this is at a substantially lower speed than the
tangential/circumferential flow. This radial flow would then produce vertical
flow by the requirements of continuity (since the workpiece is essentially
155
incompressible). This is supported by images of welds showing hooking
behaviour — this occurs more readily for tools with patterned shoulders than
for flat tools. Figure 5.23 shows the existence of hooks in 3 welds made with
profiled tools, while no hook is produced with a flat tool under identical
conditions, showing that pins are not required to produce vertical flow.
Unfortunately, radial and vertical flow does not have such simple kinematic
constraints as purely circumferential flow, and this tool type requires a more
complicated analysis. Analysis of these tool types is undertaken with a finite
element model, described in Chapter 6.
Figure 5.22: Surface view of the ‘wiper’ tool
156
Figure 5.23: Hooking behaviour for 4 tool types under identical welding
conditions
157
5.10 Conclusions
This model comprehensively proves that features seen in experimental welds,
like the bowl-shaped layers in Figure 5.19, can be produced entirely by
tangential flow at every point in the weld. No radial or vertical flow is
required. The general assumption by authors in the field is that vertical flow
is promoted by pin features, and that this enhances weld quality by producing
patterns that add to the strength of a joint. As vertical flow is not required
to produce the observed patterns, it is quite likely that tool features that
promote vertical mixing do not strengthen joints in this manner at all. If true,
this would explain the somewhat counter-intuitive observation that pinless
tools (which, by their nature, can promote only very limited vertical flow)
produce unexpectedly strong joints. It may be the case that tool features
actually promote enhanced mixing by increasing the circumferential velocity
deeper within the body of the weld, increasing the strain rate near the actual
joint line.
158
Chapter 6
Sequential small-strain analysis
6.1 Introduction
The preceding chapters have presented models for the behaviour of metal
during FSSW based on thermal and kinematic analyses. This leaves out one
key aspect that is important to the process: those aspects of deformation
and flow that depend on the material properties, rather than being governed
exclusively by the kinematics. As summarised in Chapter 2, other authors
have approached this problem by using fully-coupled FE models, but these
are computationally intensive and sensitive to the boundary conditions cho-
sen. The goal of the present work is to capture sufficient detail of the plastic
flow to predict the heat generation and flow pattern, making the model as
simple as possible while retaining accuracy.
To this end, a novel snapshot FE method has been developed, which
takes account of the material model while affording a dramatic reduction in
run-time as compared to fully-coupled models. The operation of this model
is presented, along with more detailed predictions about the copper backing
plate welds modelled in Chapter 4. Additionally, a conventional FE model of
the plunge is presented; this latter is presented first, as the conclusions are
useful when considering the snapshot model.
159
6.2 Static plunge modelling
In Section 3.7 the results of actual, measured final plunge depths were pre-
sented. Accurate plunge depths are most important with pinless tools and
thin sheet, as the plunge depth can be a significant fraction of the sheet
thickness (typically at least 10%, often as high as 50%). The highest values
are typically used in an attempt to create defect-free joints between Al and Fe,
in an attempt to heat and deform the interface while minimising overheating
in the HAZ.
In addition to identifying the factors that govern the plunge depth, it
is important to understand the interaction between plunge forces and in-
plane deformation during FSSW. Unlike seam welding, FSSW cannot be
considered as a steady-state process, and the stress state of the weld metal
is strongly influenced by the downforce. An effort was made to understand
the plunge further by modelling it using the finite element method, using the
commercially available software package Abaqus.
The plunge modelling study covered the following work: firstly, it ex-
amined ways of representing the tool, and how this affects the model (for
example, is the tool best modelled as a fixed displacement applied to the top
surface of the weld, as a fixed pressure, or is it necessary to include a realistic
tool, including its own deformation behaviour?). Secondly, it looked at the
effect of a near boundary in the z direction (i.e. the influence of a backing
plate, and workpiece thickness).
An initial FE model was developed to model the plunge as a forging
process, with no rotation from the tool. As the deforming domain has an
axis of symmetry, it is possible to use a 2D model; however, the elements must
also be capable of deforming in the tangential direction (to allow for later
calculations using the same model). The model consists of a 2D axisymmetric
model, built in Abaqus using 2D elements capable of twist distortion (i.e.
deformation about the central axis of symmetry). For the first calculations,
the twist is constrained to be zero, so the model can only move radially and
vertically.
160
Initially, the physical boundary conditions of the model were a symme-
try boundary at the axis (i.e. no movement in the radial nor out-of-plane
directions) and an encastre base and far-field boundary (set at twice the tool
radius). The upper surface was entirely free to deform. For this stage of
the model, the workpiece was represented by a single block of homogeneous
material, with boundary conditions representing the backing plate and tool
(the backing plate was modelled as a rigid boundary; various boundary
conditions were used to represent the tool, which are discussed in following
sections). The model geometry and restraints are shown in Figure 6.1, though
the tool and backing plate were not included in all stages of the model.
Figure 6.1: Constraints applied to the plunge model (tool and anvil not
included initially, shown for reference to their position only)
6.2.1 Model setup and initial tests
A load was applied to a contact patch on the upper surface; this load was
set to be sufficient to produce a displacement of around 0.1 mm as the mean
vertical displacement of the contact patch (this being a typical value of the
plunge during actual welding). The initial material properties specified were
those of ‘elastic Al’: a density of 2700 kg m-3 and Young’s modulus of 70
GPa, with no yield point.
Two calculations were carried out for results that could be computed by
hand as a ‘sanity check’ on the FE output. The first calculation was for a
161
uniform pressure load. A load of 7 GPa was applied to the top surface over
the inner 5 mm of the radius (the unrealistically high value for the pressure
load is required to produce high values of deformation in this non-yielding
material). The downforce should then be 549.76 kN (from F = pA); the
downforce calculated by Abaqus with a moderate density mesh was 549.78
kN. Running the model again with a mesh 5 times denser in each linear
dimension (i.e. 25 times the number of nodes) produced an identical result.
This indicates that the error is not due to a discretisation problem but is
instead something more fundamental to Abaqus. However, the error is small
enough (34.6×10−6) that other outputs from the model can be regarded with
high confidence.
The next case modelled was an imposed uniform displacement over the
surface of the shoulder. Imposing a uniform vertical displacement of 0.1 mm
produced a net reaction force of 754 kN. However, forcing a flat displacement
everywhere under the shoulder caused much higher stresses at the corner, and
it also created a ripple effect related to the mesh size. Close inspection of the
vertical displacement in the first case, of a uniform pressure, revealed that it
was not level under the tool, but varies from about 0.08 mm at the centre to
0.09 mm, then ramped up at the edge of the shoulder to meet the unloaded
material.
The actual case in practice must lie somewhere between the two extremes
of a uniform displacement (corresponding to an infinitely stiff tool) and a
uniform pressure (corresponding to a zero-stiffness tool), as the tool has a
finite stiffness. In the case of a steel tool and an Al workpiece, the tool is
approximately 3 times stiffer than the workpiece. As the goal is to develop
an elastic-plastic model below the tool, these initial trials suggest that it
is necessary to take a closer look at the stress state under the tool, before
rotation is imposed.
6.2.2 Methods of simulating downforce
Four different methods of modelling the tool loading on the workpiece were
simulated. In the order in which they are presented, these are: a uniform
162
pressure over the contact patch; a uniform displacement over the contact
patch; a distributed pressure load corresponding to a modified solution of
the Boussinesq problem; and a finite stiffness tool with a uniform pressure
applied to its top (i.e. the tool is explicitly included in the FE model). These
loading cases are shown graphically in Figure 6.2. These four loads were
applied in turn to a large, homogeneous block of AA6111 and the stress
fields produced in this block compared. The total load was kept constant in
all cases at 7.85 kN, a typical downforce for FSSW. The boundary conditions
were kept the same as in Figure 6.1, i.e. an encastre base and far-field r
boundary, a symmetry axis with no vertical restraint, and a free top surface
outside the contact patch.
The calculation was performed as a 3D static analysis in Abaqus using
an implicit formulation. The tool loading was applied to a patch of 5 mm
radius (the same area as the tool shoulder in experiments). The contact
between workpiece and tool, where this was explicitly included, was set as
frictionless. The elements were 4-node linear stress elements, and the model
initially comprised 270 elements with a bias distribution in both axes to
enhance the resolution of the solution near the tool contact patch.
The uniform pressure and uniform displacement load cases are self-
explanatory; case 3 requires more explanation. The load applied in case
3 is a modification of the pressure produced by a uniform displacement. The
pressure distribution used is based on Sneddon’s solution of the Boussinesq
problem for a cylindrical punch. This result (from Sneddon, 1965) gives the
pressure under a cylindrical punch into an elastic half-space as:
σzz(r) =
−2Kd
pi(1− ν) × (R
2
S − r2)−
1/2
(6.1)
with σzz as vertical stress or pressure, r radial position, RS tool radius, ν
Poisson’s ratio, K bulk modulus and d as plunge depth of the punch.
The problem with this distribution is that it leads to infinite stresses
under the corner of the tool (or under the edge of a displacement boundary
condition). To circumvent this issue, the distribution above is modified by
taking r(max) = 0.95R to ensure the distribution as used has a finite maximum
163
Figure 6.2: Loading cases for the static plunge model
Top left: uniform pressure; Top right: uniform displacement; Bot-
tom left: modified Boussinesq problem; Bottom right: explicit
inclusion of the tool
(adjusted by a constant to keep the integral — the total force — the same
as in the other cases). This pressure distribution is shown in Figure 6.3
alongside Sneddon’s solution.
Each load case was applied to the model in turn, to find the steady-state
stress and strain fields. Vertical deflection and Mises stress fields for each of
the load cases are shown in Figure 6.4.
These results show a surprising difference in both the displacement and
stress produced in the four cases. The far-field, beyond about a tool diameter
from the centre of the contact, is the same in all cases, but there is a
substantial difference between all the cases in the region closer to the centre.
The near-field, or nugget and TMAZ, is the location of interest.
The analytical solution to the uniform displacement case (case 2) gives
rise to infinite stresses at the edge of the tool, as in Sneddon’s solution. The
FE solution, as expected, gives rise to very large stresses at the edge of the
164
Figure 6.3: Solutions to the Boussinesq problem for the pressure under
a flat cylindrical punch in an elastic aluminium half-space at a
displacement of 0.0018 mm. The black line gives Sneddon’s solution,
the blue line gives the distribution used in the present work to avoid
infinite stresses under the tool edge.
contact patch. The values produced for the stress here are not reliable and
depend on the mesh size chosen (the values increase without limit as the
mesh size is decreased), so this load case is not suitable for further analysis
of the problem.
Case 1, which models the workpiece as subject to a uniform pressure,
closely matches the Hertz distribution of stresses under a spherical contact
between hard surfaces (which gives the maximum stress at a distance of
r
2
below the centre of the contact). However, it is clear that a uniform
pressure does not agree well with the other results; neither the stresses nor
the displacements produced agree closely, and so this case must be discounted
for modelling welds where the tool is significantly stiffer than the workpiece.
The modified Sneddon distribution produces results that are surprisingly
different from those produced by a uniform displacement, as in evident in
both the displacement and Mises stress fields. This indicates that the very
high stresses around the rim of the contact are making a significant contri-
bution to the overall load, despite the small area over which they act.
165
Boundary condi-
tion at the con-
tact patch
Vertical displacement Mises stress distribution
Uniform
displacement
Uniform
pressure
Modified Sneddon
pressure distribu-
tion
Frictionless con-
tact with a tool
made from H13
tool steel
Scale
µm
Figure 6.4: Vertical displacement and Mises stress for 4 load cases,
normalised by downforce
166
The final case considered is that of a finite stiffness tool. As can be seen
from the figure, this appears on a cursory inspection to lie somewhere be-
tween the cases for a finite displacement boundary and the modified Sneddon
pressure.
To obtain realistic results for this simulation, the tool must be modelled
in a more realistic fashion than either the uniform displacement or uniform
pressure loads allow. The tool must either be included explicitly, or the
modified Sneddon solution with a value of R(max) greater than 0.95 could
provide a good match.
6.2.3 Mesh sensitivity analysis
A mesh sensitivity calculation was performed for the model with the tool
explicitly included (with a tied contact). The mesh for the weld nugget was
seeded with both double and half the linear dimensions of the standard case,
giving an approximate factor of 8 either way in the number of elements (with
825, 5565 and 40470 elements in each case, respectively). Plots of the Mises
stress field for each density are shown in Figure 6.5. From this figure, the
maximum stress predicted by the model with the coarsest density mesh is
about 217 MPa. Although the intermediate mesh stress field looks broadly
similar, the peak stress is 270 MPa, significantly different. Going to a finer
mesh decreases this stress slightly to 265 MPa. This is close enough to the
value for the intermediate mesh to give confidence that the dependence on
mesh density at these values is low; more importantly, it shows that the
predicted stress has reached a maximum and will not continue to increase
monotonically without limit as the mesh density is reduced. The initial,
intermediate-density mesh was used for further calculations as a compromise
between speed and accuracy.
6.2.4 Further investigation of the Boussinesq problem
The differences between the stresses produced by the uniform displacement,
modified Sneddon pressure, and explicit tool model load cases were much
greater than anticipated, and warranted further investigation. Using the
167
Figure 6.5: Mesh sensitivity analysis for case 4 (Mises stress)
Top: coarse mesh; middle: intermediate mesh; bottom: fine mesh
168
mid-sized mesh (found to be adequate for all except the fixed-displacement
case) the peak pressures were analysed to see how closely Abaqus conformed
to the analytical solution. Two versions of the modified Sneddon solution
were used, with r(max) = 0.95Rs and r(max) = 0.99Rs. These cases are shown
in Figure 6.6.
The peak pressure (σz) in each case is:
• Sneddon solution with r(max) = 0.95RS: 158 MPa;
• Sneddon solution with r(max) = 0.99RS: 178 MPa;
• explicit inclusion of a finite-stiffness tool: 288 MPa.
There is a surprisingly large difference between the stresses in the 95 %
and 99 % cases, and between those and the explicit case. This shows that
the very high stresses at the edge influence the behaviour far more strongly
than was anticipated, even when keeping the total force the same. This
shows that the pressure at the edge of the tool contact is very sensitive to
the exact tool geometry and stiffness, and it will be necessary to include
the tool explicitly in the FE model to produce accurate results. Fortunately
this is possible without adding a great deal of complexity to the model since
the tool remains elastic and does not require a very dense mesh over its
volume. Furthermore, despite the sensitivity of the displacement boundary
condition to the mesh size, it is possible to create a sufficiently fine mesh (as
in Figure 6.5) to capture a finite-stiffness tool accurately without excessively
complicating the model.
One difficulty that remains and that cannot be easily eliminated from
modelling is the sensitivity of the peak stresses at the edge of the contact
to the exact tool geometry. All the results presented so far have been for a
square corner. In practice, most tools will have a somewhat rounded edge,
which could evolve over time as the tool wears. To accurately model this
would require a knowledge of the exact profile of the particular tool used.
Fortunately however, this problem is expected to become much less important
when yielding behaviour is introduced to the workpiece, since a small region
of yield is likely with any tool, limiting the peak stress.
169
Figure 6.6: Comparison of the Mises stress produced under an explicit
tool model, and 2 modified Sneddon solutions
Top: 95 % Sneddon solution;
Middle: 99 % Sneddon solution
Bottom: explicit tool model.
170
6.2.5 Plasticity
In order to produce more realistic results, the yield behaviour of the material
must be included. The material was modified to behave according to an
elastic-plastic stress-strain curve with no failure, with a yield stress of 60
MPa. A small amount of work-hardening was added (equal to 0.6 MPa for
a plastic strain of 1) to avoid numerical instabilities and localisation effects,
as previous work had shown that without work-hardening the deformation
could entirely localise into a thin deforming layer one element thick, with
the rest of the workpiece remaining elastic. This is lower than the room-
temperature yield strength of the alloys of interest but is more representative
of their strength at higher temperatures. More detailed models with realistic
constitutive behaviour are presented later.
The contact between the tool and workpiece was modelled as both a
frictionless contact and a tied contact. In the frictionless case the workpiece
was unconstrained radially; including friction at this interface is more re-
alistic, but the frictionless case is better for comparison with other loading
patterns. Once this comparison had been established (as in Figure 6.4) a
new calculation was performed with a tied contact at this interface. This
represents sticking friction (although still in the case of a non-rotating tool).
A slipping contact will lie somewhere between these two extremes. The stress
fields caused by these two cases differ significantly, as shown in Figure 6.7.
Consequently, an analysis of the flow pattern must include some allowance
for the radial constraint, as is done in the kinematic model for deep plunge
welds.
Figure 6.7: Mises stress fields under (left) a frictionless contact and
(right) a tied contact with a steel tool
171
6.2.6 Analysis of thin plates
Following on from the previous section, a study was conducted to assess
the effects of a near-field z boundary, as the stresses in a thin sheet can be
very different to those in a thick plate when subject to the same loading.
The same load cases as in the previous section were applied to a 2 mm
thick Al workpiece, with a rigid boundary at the base representing a stiff
backing plate. In this case, it was observed that the precise details of the
loading condition actually had very little influence over the stresses and
strains produced, unlike the model with the thicker plate. The four cases
produced almost identical displacement fields, and the stress fields were also
very similar. The only significantly different result was for the uniform
imposed displacement case, where again the peak stress was a function of
mesh size. Nevertheless, even for this case the overall stress field looked
broadly similar, except for a narrow ring near the edge of the contact patch.
Results for a uniform imposed displacement and pressure (the two extreme
load cases) are shown in Figure 6.8 and Figure 6.9.
As including the tool explicitly remains the best model, this ought to
be done if possible. However, in cases where model complexity and speed
is of great importance, in simulations of thin plate welding the tool can be
replaced with an optimised Sneddon-solution pressure without any significant
loss of accuracy. In a simulation of thicker plate it may still be necessary to
include the tool, depending on the goals and desired accuracy of modelling.
Figure 6.8: Displacement in a thin workpiece (µm) under (top) a uniform
displacement and (bottom) a uniform pressure
172
Figure 6.9: Mises stress fields in a thin workpiece under (top) a uniform
displacement and (bottom) a uniform pressure
173
6.3 Sequential small-strain analysis
6.3.1 Aim
A major drawback with current FE approaches is the computational effort
needed to capture the very large strains in friction stir (FS) processes. A
typical fully coupled analysis requires a new mesh every time the geom-
etry changes significantly; this means that a traditional fully coupled FE
simulation involves remeshing many times per revolution, leading to large
computational loads. It is possible to model seam FSW with an arbitrary
Lagrangian–Eulerian approach, but this is very computationally intensive. In
contrast, computational fluid dynamics approaches handle the large deforma-
tions much better than FE methods, but these methods lose the elastic-plastic
nature of the metal, treating the alloys as viscous liquids. CFD can predict
traverse forces during seam FSW, but not downforce, since the elastic stress
field makes a significant contribution. The new approach presented here
offers the advantage of being able to predict the downforce, while reducing
the computational load and avoiding remeshing.
Work by Colegrove & Shercliff (2006) found that the predicted material
condition during welding is very sensitive to the detail of the constitutive
law chosen. Nonetheless, the deformation conditions are self-limited in FS
processing to some extent. Firstly, the process is tightly constrained kinemat-
ically: the maximum strain-rate will be of an order given by the maximum
surface velocity divided by the thickness of the deformation layer: (ω× r)/h.
Secondly, FS processing is to a large extent self-limiting in temperature due to
the negative feedback loop between power input and temperature, which are
linked via the material’s constitutive law: as the material heats up it becomes
softer, so less energy is dissipated when it deforms. This is particularly the
case at temperatures near the solidus where the strength falls rapidly.
Sequential small-strain analysis (SSsA) is a novel calculation method
developed specifically for FSSW and similar processes. It uses small-strain
elastic-plastic FE analysis to capture enough of the flow behaviour to under-
take computation of the coupled metal flow, heat generation and heat flow
174
in FS processing. The analysis relies on the fact that deformation occurs
on much shorter timescales than heat flow, so any one point will undergo
significant strain (much more than the maximum elastic strain) at nearly
constant temperature.1
Furthermore, provided the material is not undergoing work hardening the
heat generation rate does not depend on the strain; this assumption is valid at
the temperatures of interest during FSSW in Al. Consequently, it is possible
to run a small-strain implicit analysis to produce a ‘snapshot’ of the heat
generation rate and its spatial distribution for a fraction of one tool rotation,
and to use this estimate of the power distribution in a thermal model running
with much longer update intervals.
This approach allows the temperature and deformation fields to interact in
a realistic manner, but is a computationally frugal approach when compared
to fully coupled FE models. The method is presented here for friction stir
spot weld models, but it could in principle be used for any process that shares
the same characteristics of a constrained geometry, with rapid deformation
processes, and heating processes characterised by longer timescales.
6.3.2 The model
The SSsA procedure is to calculate the instantaneous stresses and strain-
rates using a stress-strain FE simulation, then run a purely thermal analysis
with the calculated power for a longer timestep. In this way, the effects of
compressing and deforming the workpiece can be captured, while avoiding a
model with very large deformations. This is desirable because remeshing and
other techniques usually used for large deformation models tend to reduce
both model speed and/or accuracy.
During the deformation calculation, downforce and rotation are applied to
the workpiece. During the first timesteps, deformation in the workpieces will
1The choice of natural scales with which to compare heating and deformation rates is
not obvious. However, choosing the time taken to double both temperature and strain
seems reasonable. By this measure, deformation is occurring on the order of 50 to 100
times as fast as heating: the temperature doubles in 0.5 to 1 s, and the strain rate is of
order 100 s-1.
175
be predominantly elastic, and during later steps, there will be little change in
the elastic strain and most of the additional movement will be due to plastic
strain (once most of the deforming material has reached yield). Plotting the
plastic strain rate for any point as a function of time should then show an
asymptote. The asymptotic value matches the strain rate at that location at
that time, as during the actual weld elastic strains will also be negligible by
comparison with plastic strains.
The procedure for SSsA is as follows:
1. apply a loading condition including both rotation and downforce
2. calculate the output power based on the stress and strain-rate fields at
the end of the analysis step
3. impose the power generation distribution (as a function of position) on
a thermal model
4. run the thermal model
5. import the temperature field back into the deformation model for the
next interval, and rerun.
As applied here to FSSW, the elastic-plastic analysis runs for a rotation of
around 2◦, taking about 0.2 ms at 200 rad/s (1910 rev/min). The deformation
and heat generation thus calculated are assumed to remain constant for
some longer time (typically 0.1 s). The calculated strain-rate and stress
fields are used to calculate the power dissipation by plastic work for each
element. After this, the deformation model is run again under the new
temperature conditions, and new stress and strain-rate fields are calculated.
The process continues, to estimate the strain-rate field and heat generation
by plastic work for the whole duration of a weld. This enables predictions
of the power generation and flow patterns without the need for a complete,
computationally expensive, coupled thermal-stress FE simulation of the full
weld.
The overall modelling procedure is summarised in Figure 6.10. The key
innovation in this model is the decoupling of the thermal and deformation
calculation steps, whilst maintaining an accurate temperature field at all
176
Figure 6.10: Calculation process for the snapshot model
times. This is important, since the workpiece properties depend strongly on
temperature, both during the weld and for the final microstructure. Each
step is explained in more detail below, where the process is illustrated for
two theoretical welds, the first in a thick block of aluminium, the second in
thin sheet material. The weld chosen for the initial model was a shallow
plunge weld of 1 s duration at 760 rev/min (∼80 rad/s); these conditions
were chosen as representative of practical welding conditions.
Material model
The snapshot model can incorporate realistic material behaviour, including
flow stress that depends on temperature and strain-rate. Strain dependence
cannot be included (so Johnson-Cook models cannot be used), but any
other constitutive law that can be implemented in Abaqus is theoretically
possible, subject to stability constraints regarding temperature and strain-
rate dependence (material models that weakened at increasing strain-rates,
or hardened with increasing temperature, would be unstable). The lack
of strain-hardening is not a problem for Al: constitutive data for Al at
temperatures typically encountered in FSSW does not show any great degree
of strain hardening, and the flow stress is strongly dependent on strain-rate
and temperature.
177
For the present work, a sample material was needed. AA7449 was chosen
as it is an important high strength aerospace alloy and is often considered
to be difficult to weld due to its heat-treatable properties. It was modelled
using Zener-Hollomon behaviour in the high temperature regime and single
yield point non-strain-hardening plasticity for the low temperature regime.
The use of this constitutive law for AA7449 in this regime follows work by
Colegrove & Shercliff (2006). Zener-Hollomon behaviour is described by:
Z = ε˙e(
Q/RT) = A sinh(ασ)n (6.2)
The values used for each of the parameters in Equation 6.2 are given
in Table 6.1; these values were derived at strain rates of 0.1 to 25 s1 and
temperatures of 625 to 710 K (using results provided by Alcan). Zener-
Hollomon strain-rate hardening is assumed for all strain rates above 10−3 s-1.
Below this strain-rate quasi-static behaviour with a yield stress that depends
only on temperature is assumed. Zener-Hollomon behaviour has been shown
to hold up to strain-rates of 100 s-1 in 7000 series alloys and up to 1000 s-1 in
1000 series (commercially pure Al). Above this rate Johnson-Cook models
are usually used. These predict greater increases in flow stress with strain-
rate, but these strain rates are above those found in FSSW.
A key issue in friction process modelling is the behaviour of the material
near the solidus temperature, at which point melting commences and the
viscosity will drop significantly. Classical Zener-Hollomon behaviour does not
take account of phase changes, so another approach is required. Colegrove
et al. (2007) used a model proposed by Seidel and Reynolds which predicts
enhanced softening with temperature as compared to the standard Zener-
A Q n α
Softening Solidus Low T
temperature temperature yield stress
kJ K K MPa
2.226× 1012 156 6.81 1.1× 10−8 768 773 590
Table 6.1: Zener-Hollomon parameters for AA7449 (data from Colegrove
& Shercliff, 2006)
178
Hollomon model, with a linear reduction in flow stress as the temperature
approaches the solidus (typically over an interval of up to 50 K). Above the
solidus the material is assumed to have negligible shear strength. The flow
stress for AA7449 using the parameters in Table 6.1 is illustrated in Figure
6.11.
Figure 6.11: Flow stress against temperature at various strain-rates for
AA7449
Thermal model and initial power estimate
The thermal model was built in Abaqus, as a 3D implicit finite element
calculation using 8 node linear (hex) elements. The mesh is illustrated in
Figure 6.12. As this model simulates a purely thermal problem, the runtime
is comparatively fast, and it can include many of the features of real welds,
such as backing plate, clamping arrangements and flash formation. The heat
input is modelled in two parts, part as a surface power input and part as a
volumetric power (split into 12 regions). The outer boundaries are all treated
as insulating, with no heat losses across them.
For this study the ‘weld’ comprised a tool plunging with constant force
into a homogeneous block of aluminium. In the first case, a semi-infinite
179
Figure 6.12: Mesh for the thermal model
block was modelled; semi-infinite in this context refers to a block of such a
depth that the temperature rise at the far surface remained less than 1 K for
the entire duration; in practice, this meant a model thickness of 20 mm for
a 1 s weld, (twice the tool diameter).
In the first instance as a proof-of-concept, an initial estimate of the
heat input was applied for 0.5 seconds, before switching to iterative heat
generation and thermal models. While this may over- or under-estimate the
weld temperature (and thus subsequent heat input), it provided a useful
intermediate computation to test the effect of varying the duration of the
deformation and thermal calculation steps. Subsequent refinement of the
model enabled iterative calculations from cold; this work is presented in the
case study modelling experimental welds in thin sheet.
This initial estimate was needed to bring the model into a stable regime.
The value of this initial power was estimated from thermal modelling of
AA6111 and 6082, and scaled by the relative strengths of the materials at
room temperature. This power was initially applied as a surface heat flux
to simulate frictional heating of the workpiece material from the cold state.
The peak power applied was 1.5 kW; the shape and distribution of the power
input was an exponential function as described in Chapter 4.
180
Deformation model
The deformation model was a stress calculation, again carried out in Abaqus
implicit. The simulated time for each run of the deformation model was
200 µs, corresponding to a rotation of 0.016 rad (0.9◦) at 760 rev/min
(80 rad/s). This rotation is large enough to ensure that the strains in most
of the deforming zone are well beyond the elastic limit, but small enough
to ensure sufficient accuracy without needing to remesh the model domain
during the calculation. At the end of each deformation calculation (i.e.
after 200 µs) the power generation was estimated, and used in the next
step of the thermal calculation. This was done for each timestep of the
deformation model using the Abaqus variable ALLPD. ALLPD is the plastic
work dissipation per element, but here the nugget is divided into 12 zones
rather than into individual elements for simplicity.
Because the analysis starts from a zero-stress state, the plastic work
increases throughout the calculation as the elastic strain component becomes
negligible and a greater proportion of the deforming region starts to deform
plastically. The plastic work rate increases towards an asymptote during the
calculation, and it is this asymptotic value that is used as an input into the
thermal model.
The loading applied to the top of the workpiece consists of downforce and
horizontal velocity. The downforce is as found in Section 6.2. The surface
velocity fields are the same as that used in the kinematic model, shown in
Figure 5.5 (reproduced here as Figure 6.13). Each velocity distribution was
applied in turn to test the sensitivity of the resulting heat generation to the
slip condition.
Running this model calculates the strain throughout the model domain,
including elastic and plastic components. The plastic strain components
calculated under velocity distribution 3 are plotted in Figure 6.14 for 3
selected points. From this graph, the plastic strain-rate at the final increment
can be calculated as the gradient of each line; the final strain-rate is the
asymptotic value given by the straight line segment of each graph. The
strain-rates caused by each surface velocity distribution are shown in Table
6.2.
181
Figure 6.13: Velocity profiles applied to the tool contact patch
The velocity field chosen for further calculations was Profile 3, as this
gave the most realistic results with the kinematic model in Chapter 5.
As well as calculating the strains, these models calculate the stress. Both
downforce and rotation are crucial to the stress state in FSSW. The con-
tribution of each can be assessed by looking at the Mises stress under the
tool. Plots of the Mises stress are shown in Figure 6.15 for three situations:
the case of 100 MPa downforce, but no rotation (top figure, identical to the
output from the static plunge model presented in Section 6.2); the case of
rotation, but only 10 MPa downforce (middle figure); and for rotation with
100 MPa downforce (bottom figure).
r=2.5, z=0 r=5, z=0 r=5, z=0.5
Profile 1 102 50 25
Profile 2 152 20 9
Profile 3 138 13 6
Table 6.2: Plastic strain rates during the final increment, at selected
locations (dimensions in mm)
182
Figure 6.14: Plastic strain at locations indicated
This series of figures shows the importance of including downforce in
models of FSSW. A 100 MPa pressure load alone only produces yield in a
very small region using this material. Rotation alone causes yield in a slightly
larger zone, but one that is constrained to lie near the surface. Both a large
downforce and rotation together cause a large yielding zone, causing different
behaviour to either rotation or downforce alone.
6.3.3 Proof-of-concept
The snapshot modelling approach was used first to model welding in a thick
plate of AA7449. The thermal model was run initially for 0.5 s then with
intervals of 0.1 s, and the deformation model was run for 0.2 ms each time.
An example of the predicted power dissipation is shown in Figure 6.16. This
figure was produced by the deformation model, running with the temperature
field calculated as the output of the thermal model at 0.5 s. The top surface
boundary condition was velocity distribution 3. This figure shows the power
183
Figure 6.15: Mises stress fields
Top: downforce, no rotation
Middle: rotation, minimal downforce
Bottom: downforce and rotation
184
dissipated within the workpiece due to plastic work at each step of the
deformation model. By 0.2 ms, the power reached a steady-state, at an
asymptotic value of 1500 W.
This model not only produced an estimate of the total power, but could
calculate the power on an-element-by-element basis. Due to the manual steps
required, rather than actually using the result for each element, the deforming
region of the workpiece was divided into 12 regions, and the power calculated
for each of these. The power density distribution predicted by the model is
shown in Figure 6.17.
The total power input to the weld includes contributions from plastic
work (shown in Figure 6.16) and frictional heating. The frictional heating
contribution is calculated as:
Pf = 2pi
∫ RS
0
τz,θ . ω×r . |r| . δ dr (6.3)
where P f is the total frictional heating power, τz,θ is the shear stress in the
(z, θ) direction, ω is the rotation speed, r the radius and δ is the interface
slip factor.
Like the plastic work, P f can be calculated on an element-by-element
basis. The total power contribution from both sources is shown in Figure
6.18 for each run of the deformation model, for 0.5 to 1 s.
This correctly predicts the drop-off in power that occurs as the workpiece
heats up and softens. What is clear from this figure, and has not been
established in the existing literature (either experimentally or from other
modelling approaches), is the split between the friction and plastic work
contributions. The top surface of the workpiece reaches a temperature very
close to the solidus very early on in the weld, and then remains almost
at a constant temperature as heat diffuses away from the hottest regions.
Consequently, the power dissipated by friction also remains nearly constant
after the very early part of the weld. Even if the assumed surface velocity
profile is not exactly correct, the conclusion that most of the input power is
dissipated as bulk heating stands.
185
Figure 6.16: Power dissipated within the workpiece at 0.5 s
Figure 6.17: Power dissipation density within the workpiece at 0.5 s; the
top three layers are deforming plastically, with the majority of the power
dissipation occurring in the top layer. Power densities given in W mm-3.
Figure 6.18: Total power dissipation, by plastic work & surface friction
186
6.3.4 Thin plate welding
As in the study of plunge effects with a static workpiece, modelling progressed
from the case of a thick workpiece to more realistic geometries. To test the
application of this method to other geometries, a model was developed for a
2 mm thick workpiece. All other properties were kept constant.
As in the case of the thick plate, the thermal model was run for 0.5 s using
an initial estimate of the power input. The temperature field calculated from
this model was used as an input into the deformation model, and the power
dissipation in each of 12 sections was calculated. The power dissipation
increased at each timestep of the deformation model, reaching an asymptote
which was then used as the input to the next stage of the thermal model.
The total power dissipated in the weld is shown in Figure 6.19, and
the corresponding temperature field is shown for three times in Figure 6.20.
Under these conditions, the total power dissipation predicted by this model
was lower than that predicted for the case of a thick plate, however, the power
dissipated through frictional heating on the surface was slightly higher. This
is due to the greater restraints to deformation that are present in the thin
sheet case. Despite this, the majority (circa 85 %) of the power was still
dissipated by plastic heating in the bulk of the nugget.
Although the surface slip profile must be assumed as an input, the exact
form of this profile has relatively little bearing on the powers produced, and
hence the temperatures reached. For the two most extreme power profiles
considered as realistic (profiles 1 and 3 in Figure 6.13) the power difference
for these conditions amounts to about 150 W, or roughly 10 % of the total
power dissipation. As seen more clearly with the kinematic model presented
in Chapter 5, the slip profile affects the flow pattern substantially, and
where mechanical locking is significant it will affect the strength of the joint
substantially. However, it is interesting that the precise details of the flow
have comparatively little influence over the total power dissipation.
187
Figure 6.19: Total power dissipation, by plastic work and surface friction
for thin sheet AA7449
Figure 6.20: Temperature field for a weld in thin sheet AA7449
a: 0.5 s; b: 1 s; c: 1.5 s
188
6.3.5 Adaptive timesteps
In the previous section, the problem of ‘cold start’ conditions was identified.
The problem arose because, during the early part of a weld, the contact con-
ditions and power input evolve very rapidly. This led to numerical problems
with resolving early stages of welds. The problem was resolved by reducing
the time between each run of the deformation model; this ensured that
the calculation was stable, and allowed successful calculation of solutions.
However, the reduction in time interval required was substantial: at 760
rev/min (80 rad/s), successful cold start calculations required an update
interval of 0.01 s.
Running the deformation model at such short intervals corresponds to
running deformation calculations multiple times per revolution (every 48◦ at
800 rev/min). Although this still offers a significant reduction in calculation
over fully-coupled models, it adds unnecessary calculations later in the weld
when additional precision is not required. Furthermore, it is not feasible at
present to run a model with so many stages as human intervention is required
at each stage. The use of adaptive timesteps allows enhanced precision where
necessary during the early stages and longer intervals between deformation
calculations where this is possible in later steps. A number of schemes are
possible to calculate the optimum timestep; the method proposed here, which
is sufficient for present purposes, is to take the gradient of the power vs. time
curve and extrapolate it to estimate the time interval required for a 10 %
reduction in power.
A reduction in timestep is also necessary to maintain accuracy as the
solidus is approached. The solution near the solidus is stable, but if the time
increments between thermal updates are too long, ‘ringing’, or oscillation
about the true steady-state power, can occur.
6.3.6 Case study and validation
Experiments were conducted at TWI covering a range of experimental con-
ditions, as detailed in Chapter 3. A full simulation was performed of the
standard case: two sheets of Al, at 760 rev/min (80 rad/s), for 1 s. Although
189
the experiments being modelled used both AA6111 and 6082, these are very
similar alloys and the samples used were heat-treated to have the same room-
temperature hardness.
Material data was taken from Sheppard & Jackson (1997). The material
model used was, again, the Zener-Hollomon model, and a plot of flow stress
against temperature for various strain-rates is given in Figure 6.21. Assuming
the two alloys have the same strength at high temperature allows continued
use of the previous axisymmetric model, and should involve no great loss of
accuracy. A linear reduction in flow stress was imposed over the 50 K interval
below the solidus, with the strength becoming negligible at the solidus itself.
With adaptive timesteps, the model was able to simulate an entire weld
from start to finish. The total powers are shown in Figure 6.22, including
the contributions from bulk deformation and surface heating. This enhanced
model predicts that surface friction contributes a much larger fraction of the
total power than previous uses of the model. However, the conclusion that
most power is dissipated by plastic work still holds.
Experimental welds were made at TWI with identical conditions to those
applied in this model. Temperature outputs from the model at locations 2,
6 and 10 mm from the weld centre, 0.1 mm from the base of the workpieces,
are shown in Figure 6.23 alongside thermocouple measurements for the same
locations in an experimental weld. This simulation ran entirely from cold:
the only specified parameters concerning the power input were the tool speed,
the slip profile as a function of radius, and the material properties. The model
was able to predict the observed temperature rise reasonably closely.
Predicted temperatures during the cooling phase are less accurate. This
is probably due to changes in contact conductance that occur as the tool is
removed: contact across the joint is essentially perfect as the two parts have
been welded, but away from the weld it is likely that the conductance falls
as the downforce is removed. However, accurate predictions of the cooling
rate are unimportant from a microstructural point of view, so this does not
represent a serious flaw in the model.
Temperature predictions can be made for locations at the welding in-
terface, where thermocouples cannot be placed as they would be destroyed
190
Figure 6.21: Flow stress against temperature at various strain-rates for
AA6082
Figure 6.22: Predicted power dissipation by surface friction and plastic
work for a weld in AA6082 at 760 rev/min (80 rad/s)
191
Figure 6.23: Temperature predictions (red) and experimental measure-
ments (black) for a weld in AA6082
by the welding process. Peak temperatures at the centre and 5 mm from
the centre are 660 K and 574 K, respectively — these fall just outside the
regime identified as giving rise to optimum welds in Chapter 4, which matches
well with weld strength tests. It is suggested that weld strengths could be
improved slightly by increasing the power input.
6.3.7 Optimum welding with a copper backing plate
In Section 4.10.1, an optimum process window was found for welds using a
copper backing plate. As that was a purely thermal model, the parameter
space was described in terms of time and power input. However, in FSSW
the power input is not an independently controllable parameter. Rather
than assuming a power input distribution, the semi-coupled model presented
in this chapter can analyse welds using a specified rotation speed. In Section
4.10.2, a copper anvil was suggested as a way to improve weld quality. This
present section examines the powers, torques and temperature that arise
when using a Cu anvil.
The thermal analysis indicates that higher powers are required with a
192
Cu backing plate. The variation of input power with rotation speed is not a
fixed function, but varies depending on the backing plate material; a rotation
speed of 160 rad/s (1528 rev/min) was selected for this analysis as a likely
estimate.
As the steady-state heat flow was greater for the new case, the temper-
ature field was more sensitive to the power input. Consequently, smaller
timesteps were required. The calculated power at each step is shown in
Figure 6.24.
There are two contributions to heat flow in the nugget: the conductive
component (to the outer workpiece and backing plate), and the heat capacity
term (representing heating of the nugget). With a Cu anvil, the former rep-
resents a greater proportion of the total. Consequently, the power dissipation
drops off more slowly. As a result, the process window developed in Chapter
4 is no longer completely accurate: Figure 4.32 assumed that the shape of
the power profile remained constant, increasing or decreasing by a uniform
factor. The work in this chapter produces a more accurate power profile for
high-speed welding with a copper anvil.
In Chapter 4, peak temperatures at the centre of the weld and 5 mm from
the weld centre (both on the interface line) were used as a proxy for weld
quality. A good-quality weld was defined as one with a high T1 and a low
T2. Peak temperatures at these locations for the two welds simulated here
are given in Table 6.3.
The ratio ηT (see Equation 6.4 for a definition) is a useful measure of
how effective the welding conditions are at raising the nugget temperature
without causing overheating in the HAZ. For the steel backing plate weld,
ηT = 1.64 and for the copper backing plate weld, ηT = 1.67. This suggests
that the copper backing plate would cause a slight improvement in this ratio,
Backing plate Nugget HAZ
Steel 659 516
Copper 523 431
Table 6.3: Peak temperatures (K) in the nugget and HAZ, on the joint line
193
Figure 6.24: Predicted power for a weld with a copper backing plate, at
160 rad/s
however, the difference is minimal. This suggests that the benefit of switching
to copper anvils may not be as large as first thought.
ηT =
T1 − T0
T2 − T0 (6.4)
In Chapter 4, tentative values of T1 and T2 were suggested for high-
strength welds based on experimental data. The suggested limits were
T1> 670 K and T2< 605 K; for the present weld, T1 = 523 K and T2 = 431 K,
so the nugget is colder than desired. With a copper backing plate, steady-
state conditions are reached very quickly: by 0.5 s, the temperature field is
already stable and the temperature at the tool to workpiece interface is very
close to the solidus. Under these conditions, more heat cannot be added to
the weld: an increase in tool speed reduces the flow stress, limiting the heat
input, and increasing the duration of the weld simply maintains the extant
temperature field for longer. Consequently, the results for T1 and T2 from
this simulation suggest that welding under these conditions will not heat the
interface sufficiently to produce a joint, and all deformation will be confined
to the top sheet.
194
To circumvent this problem, other welding parameters may be varied: for
example, the use of the wiper tool or deeper plunges (both of which extend
the deformation zone deeper into the workpieces — see Chapters 3 and 5)
may be needed. Of course, practical limitations may prevent the use of
certain conditions, and one of the main constraints with FSSW is the torque
capabilities of the machine. For example, the CS Powerstir machine used at
Manchester has a maximum rated torque of 100 Nm (it is designed primarily
for seam FSW, and is capable of welding thicker plate than used in these
experiments — the power and downforce limits are far in excess of those
required for thin sheet FSSW). The snapshot model can be used to calculate
the required torque; the torque during the previous two simulations is shown
in Figure 6.25. From these, it can be seen that the average torque required
for welding with a copper backing plate is actually lower than with steel,
despite the higher power. A lower average torque may well lead to lower
tool wear and increase the life of the machine. However, it may be the peak
torque that is more relevant, and this is very similar in both cases.
The reduced torque with a copper backing plate is beneficial, but the
higher weld energies required represent a cost. In purely financial terms, this
may be offset by lower tool wear; in environmental terms, it may be harder
to justify. The analysis in Section 4.10.2 suggested that high-conductivity
backing plates could bring about significant improvements in the strength of
FSSW joints. The present chapter indicates that these improvements may lie
outside the physically possible parameter space. Further analysis is needed
to assess whether such welds are possible, and if so, whether the compromises
entailed are justified.
195
Figure 6.25: Predicted torque histories for a weld with a steel anvil at
80 rad/s (760 rev/min), and with a copper anvil at 160 rad/s (1528
rev/min)
196
6.4 Conclusions
The plunge analysis conducted in the first part of this chapter shows that an
accurate representation of the tool is necessary. Even for a non-rotating case,
surface friction affects the stress by constraining deformation of the workpiece
— especially when, as in FSSW, the tool is much stiffer than the material
to be welded. Neither a uniform pressure nor a uniform displacement, as
sometimes used by previous modelling approaches, can be relied upon as
accurate boundary conditions; only a finite-stiffness tool gives rise to realistic
stresses in the workpiece.
The second part of this chapter introduced the sequential small-strain
analysis method. This method appears to be an effective means of studying
deformation and predicting power requirements during FSSW, provided that
the slip condition at the interface and the material behaviour are both known.
Even with an unknown slip condition — as is generally the case in practice
— a degree of self-balancing occurs: if the model underestimates strain-rates
in the bulk, there is correspondingly more slip (and heat generation) at the
surface. A finer timestep and a finer grid would improve the accuracy but
the method is practical in principle, and takes far less computation time
than fully coupled models to solve similar problems. The only input data
required concerns the weld geometry, an initial power estimate, a surface slip
profile, and material constitutive data. Using the method to predict peak
weld temperatures to within 30 K can be considered a substantial success.
Although not as accurate as thermal models using measured or calibrated
input powers, the snapshot model is also able to predict tool torques, and
stresses and strains in the workpiece.
The novel sequentially coupled FE model therefore shows the potential to
link the constitutive behaviour to the heat generation in a computationally
efficient manner, and to shed light on the nature of the stick-slip behaviour
under the tool. Further development of the approach depends on well-
instrumented experiments to quantify the downforce and torque as functions
of time, and independent measurement of the constitutive behaviour for the
range of temperatures and strain-rates experienced in friction stir processing.
197
Following development of the model, the same method was used to analyse
temperatures in the nugget and HAZ for novel welding conditions. The
use of the snapshot model, combined with the process window developed
earlier, shows that welding with high vertical heat flow conditions can lead to
temperature fields that give rise to high-strength welds. A possible practical
weld using AA6082 and a copper backing plate was simulated from a cold
start, and the model was used to predict temperature, torque and power data.
The use of a copper backing plate may be an effective method to increase the
strength of joints in thin-sheet 6000 series aluminium alloys, although doing
so requires higher weld energies.
The same techniques could be applied to the analysis of other geometries
and alloy combinations to design effective experimental programmes for weld
optimisation.
198
Chapter 7
Conclusions and further work
FSSW is a comparatively new and poorly-understood process. While much
research has been carried out on continuous seam welding, including FSW,
FSSW is a fast transient process where the heat flow and deformation are
strongly linked. As a consequence, existing assumptions about input param-
eters result in poor models. In Chapter 4, the FE method was applied to
simulate FSSW as a purely thermal process, and in doing so, a greater under-
standing of the boundary conditions present in FSSW was developed. This
knowledge was applied to model a wide range of welds and develop a process
window, which describes the relationship between power input and welding
time that gives rise to optimum-strength welds. The analysis was extended
to produce a second process window for welding with a copper backing plate,
which illustrates the advantages of using high-diffusivity materials such as
copper.
An analysis of heat flow in the weld could be successfully tackled with
existing FE tools; however, material flow during welding is more complicated,
and existing tools were poorly-suited to the task of modelling deformation.
Two new approaches have been devised and developed: the kinematic method
and sequential small-strain analysis.
The kinematic model involved a set of assumptions about the weld bound-
ary conditions that, when applied together, led to a substantially simplified
model of the welding process. The model could simulate flow in welding and
199
the resulting flow patterns were governed by a small number of dimensionless
groups. The most important of these was ω¯, the ratio of the speed of rotation
to the progression of the onset of deformation. The method was shown to
produce weld images that agree with the patterns found in experimental
welds, for top-down and section views, under a wide range of conditions. This
shows that the underlying assumptions used to develop the model are likely
to be correct, in particular, that metal flow during the process is primarily
axisymmetric and highly constrained by surrounding cold material. The
kinematic model was used to show a number of effects in more detail than
can be seen in experimental welds, including the effects of a molten layer
of zinc when welding galvanised steel and the flow patterns caused by deep
plunge welding.
The second new approach developed was the sequential small-strain anal-
ysis method (SSsA), a form of sequentially-coupled FEA which can take
account of elastic stresses and plastic flow caused by tool downforce and
rotation. Welding simulations using this approach enabled predictions to be
made of the spatial and temporal evolution of heat generation, directly from
the constitutive behaviour of the alloy and the assumed velocity profile at
the tool-workpiece interface. SSsA was used to model welds in thick and thin
plate AA7449 as a proof-of-concept, and was then extended to simulate ex-
perimental welds in AA6082. The method produced temperature predictions
that were compared to experimental thermocouple measurements, and that
agreed well.
Early experimental work indicated that high-conductivity backing plates
could give rise to high-strength welds. However, it was not possible to develop
an understanding of the mechanisms involved from experimental work alone.
The modelling work presented here explained the observed effects, and was
used to model novel conditions and extend the process window to include
simulated welds with copper backing plates. The SSsA model supported the
conclusions of the thermal FE work, although it also showed that there could
be practical difficulties involved in delivering sufficient power to the weld
when using a copper anvil.
200
Overall, these three sets of analyses contribute to an enhanced under-
standing of the FSSW process. The models are fast, and well-suited for
integration with microstructural models, such as models of HAZ softening
or the formation of intermetallics at the interface in dissimilar welds. The
techniques developed for sequential small strain FE analysis could also be
investigated for use in other kinematically constrained solid-state friction
joining processes.
201
202
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