FE modelling of small-scale hot deformation testing
This report presents a finite element model of small-scale hot compression testing, using a dilatometer in loading mode. The main goal is to correct the true stress-strain hot constitutive response as a function of temperature and strain-rate, accounting for friction between the platens and workpiece, and the temperature gradient along the sample. The model also provides quantitative prediction of the spatial and temporal variation in strain-rate and strain throughout the sample, which is needed to correlate the local deformation conditions with the microstructure/texture evolution. The study is based on a detailed series of 144 hot compression tests of a zirconium alloy (Zr-2.5Nb), at strain-rates ranging from 10-2.5 to 10s-1, and temperatures between 650°C to 850°C, with duplicate tests at all nominal test conditions. The Zr alloy is an important wrought material in its own right, in the context of the nuclear industry, but also serves as an analogue for other high temperature alloys (notably titanium) which show a dual - phase microstructure in a comparable temperature range. The finite element model of the dilatometer test demonstrated that deformation conditions in the sample were substantially non-uniform, compared to the nominal temperature and strain-rate. The heating and cooling capabilities of the dilatometer were able to maintain reasonably isothermal conditions at the centre of the sample at moderate strain-rates, but not at rates of 1s-1 or above; but in all cases the temperature gradient and friction led to inhomogeneous deformation and barrelling. To account for these factors, a novel method is presented for correcting the true stress-strain (i.e. from the notional response allowing only for the idealised change in sample length and area), to give a true constitutive response over the full range of temperatures, strain-rates and strain. The analysis in this report includes a number of alternative approaches to capturing the material constitutive data in equations or look-up tables, and also detailed sensitivity analysis on the FE-predicted spatial histories of deformation, as a function of the assumed material model and friction coefficient, for different test temperatures, temperature gradients and strain-rates. The FE-corrected constitutive data have been applied for a number of applications, for example, the generation of “processing maps” for Zr-2.5Nb, demonstrating the importance of allowing for inhomogeneity and meaningful statistical fitting of the data; this work is presented in more detail elsewhere .