Phase field modelling of crack propagation in functionally graded materials

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.

Phase field predictions of microscopic fracture and R-curve behaviour of fibre-reinforced composites

“…The discretised forms of the field equations are solved by using a staggered solution scheme [16,27].…”

Adaptive phase field modelling of crack propagation in orthotropic functionally graded materials

“…The spatial variation of the elastic and fracture properties inherent to functionally graded materials (FGMs) can be incorporated following the pioneering work by Hirshikesh et al [33]. Variational phase field fracture methods are particularly suited to capture the complex crack trajectories that are observed in FGMs due to the inherent crack tip mode mixity [33,44,45].…”

“…The spatial variation of the elastic and fracture properties inherent to functionally graded materials (FGMs) can be incorporated following the pioneering work by Hirshikesh et al [33]. Variational phase field fracture methods are particularly suited to capture the complex crack trajectories that are observed in FGMs due to the inherent crack tip mode mixity [33,44,45]. As described below, we introduce a history field H to prevent damage irreversibility and we adopt the so-called hybrid model [46] to absence of inertia and body forces is given by [46,47]:…”

“…Specifically, the phase field method (PFM) has proven to be efficient technique in modelling brittle fracture [19][20][21], ductile damage [22,23], dynamic fracture [24], fracture properties prediction of nanocomposites [25], fiber cracking and composites delamination [26][27][28], plates and shells [29,30] and hydrogen embrittlement [31,32], among other phenomena. Recently, the success of phase field fracture methods has been extended to modelling cracking in isotropic FGMs by Hirshikesh et al [33].…”

Comparison of peridynamic and phase-field models for dynamic brittle fracture in glassy materials

“…Phase-field formulation can be implemented in any FEM commercial software, like ABAQUS [73][74][75][76] or open source FEM package [77]. Phase-field modeling is inherently a multi-field problem.…”