Phase-field modeling of anisotropic brittle fracture including several damage mechanisms

Abstract

The present paper aims at modeling complex fracture phenomena where different damaging mechanisms are involved. For this purpose, the standard one-variable phase-field/gradient damage model, able to regularize Griffith's isotropic brittle fracture problem, is extended to describe different degradation mechanisms through several distinct damage variables. Associating with each damage variable a different dissipated fracture energy, the coupling between all mechanisms is achieved through the degradation of the elastic stiffness. The framework is very general and can be tailored to many situations where different fracture mechanisms are present as well as to model anisotropic fracture phenomena. In this first work, after a general presentation of the model, the attention is focused on a specific paradigmatic case, namely the brittle fracture problem of a 2D homogeneous orthotropic medium with two different damaging mechanisms with respect to the two orthogonal directions. Illustrative numerical applications consider propagation in mode I and II as well as kinking of cracks as a result of a transition between the two fracture mechanisms. It is shown that the proposed model and numerical implementation compares well with theoretical and experimental results, allowing to reproduce specific features of crack propagation in anisotropic materials whereas standard models using one damage variable seem unable to do so.

On penalization in variational phase-field models of brittle fracture

“…The (exact) solution of the semi-linear problem in (55) is constructed in Appendix C. It reads (56). More precisely, it highlights the anticipation that the convergence ofx to 2 when r → +∞ must result in the point-wise convergence of α ρ to the corresponding α .…”

“…The final step of the presented analysis is the derivation of the optimal lower bound for r (and, hence, for ρ). As before, we insert (56) into E S (α) in (51) and arrive at…”

“…(a) Sketch of the reference profile α in(34), α ρ in(56) and the corresponding limiting point x : whenx converges to 2 , the point-wise convergence of α ρ to α is expected; (b) The numerical evidence of the convergence behavior of α ρ to α in terms of the penalty parameter r.…”

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

“…Variational approaches based on energy minimization constitute a promising tool to overcome this limitation [17,18]. 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].…”

Phase field modelling of crack propagation in functionally graded materials

“…Variational approaches based on energy minimization constitute a promising tool to overcome this limitation and could, therefore, be particularly useful in modelling crack advance in FGMs [15][16][17]. Specifically, the phase field method has proven to be a compelling technique in modelling brittle fracture [18,19], ductile damage [20,21], fiber cracking and composites delamination [22,23], and hydrogen embrittlement [24,25], among other phenomena. We aim at extending this success by presenting a phase field formulation for fracture in compositionally graded materials.…”