Phase field modelling of crack propagation in functionally graded materials
This work provides a computational framework for designing fracture-resistant FGMs, which is relevant for engineers and materials scientists working on graded materials.
The paper presents a phase field formulation for fracture in functionally graded materials (FGMs), demonstrating its ability to capture crack deflections and identify material gradients that enhance crack growth resistance. Numerical experiments over a wide range of gradation profiles and orientations provide insight into crack growth resistance, and predictions are validated against experimental data and alternative methods.
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.