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Phase field modelling of crack propagation in functionally graded materials

Accepted version
Peer-reviewed

Type

Article

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Authors

Hirshikesh 
Natarajan, Sundararajan 
Annabattula, Ratna K 
Martínez-Pañeda, Emilio  ORCID logo  https://orcid.org/0000-0002-1562-097X

Abstract

We present a phase field formulation for fracture in functionally graded materials (FGMs). The model builds upon homogenization theory and accounts for the spatial variation of elastic and fracture properties. Several paradigmatic case studies are addressed to demonstrate the potential of the proposed modelling framework. Specifically, we (i) gain insight into the crack growth resistance of FGMs by conducting numerical experiments over a wide range of material gradation profiles and orientations, (ii) accurately reproduce the crack trajectories observed in graded photodegradable copolymers and glass-filled epoxy FGMs, (iii) benchmark our predictions with results from alternative numerical methodologies, and (iv) model complex crack paths and failure in three dimensional functionally graded solids. The suitability of phase field fracture methods in capturing the crack deflections intrinsic to crack tip mode-mixity due to material gradients is demonstrated. Material gradient profiles that prevent unstable fracture and enhance crack growth resistance are identified: this provides the foundation for the design of fracture resistant FGMs. The finite element code developed can be downloaded from www.empaneda.com/codes.

Description

Keywords

Phase field, Functionally graded materials, Fracture, Finite element analysis, Damage

Journal Title

Composites Part B: Engineering

Conference Name

Journal ISSN

1359-8368
1879-1069

Volume Title

Publisher

Elsevier BV
Sponsorship
E. Martínez-Pañeda acknowledges financial support from the Royal Commission for the 1851 Exhibition through their Research Fellowship programme (RF496/2018).