# Phase field modelling of crack propagation in functionally graded materials

## TL;DR

This paper introduces a phase field model for fracture in functionally graded materials, accounting for spatial property variations, and demonstrates its effectiveness through various case studies and comparisons.

## Contribution

The study develops a novel phase field formulation for FGMs that incorporates homogenization theory and validates it with multiple case studies and benchmarks.

## Key findings

- Material gradients can prevent unstable fracture.
- The model accurately predicts crack trajectories in graded materials.
- The phase field method captures complex crack paths in 3D FGMs.

## 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.