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

Abstract

In this work, we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials (FGMs). A recovery type error indicator combined with quadtree decomposition is employed for adaptive mesh refinement. The proposed approach is capable of capturing the fracture process with a localized mesh refinement that provides notable gains in computational efficiency.The implementation is validated against experimental data and other numerical experiments on orthotropic materials with different material orientations. The results reveal an increase in the stiffness and the maximum force with increasing material orientation angle. The study is then extended to the analysis of orthotropic FGMs. It is observed that, if the gradation in fracture properties is neglected, the material gradient plays a secondary role, with the fracture behaviour being dominated by the orthotropy of the material. However, when the toughness increases along the crack propagation path, a substantial gain in fracture resistance is observed.

A Unified Abaqus Implementation of the Phase Field Fracture Method Using Only a User Material Subroutine

“…Variational phase field methods for fracture are enjoying a notable success [ 1 , 2 ]. Among many others, applications include shape memory alloys [ 3 ], glass laminates [ 4 , 5 ], hydrogen-embrittled alloys [ 6 , 7 ], dynamic fracture [ 8 , 9 ], fiber-reinforced composites [ 10 , 11 , 12 , 13 ], functionally graded materials [ 14 , 15 , 16 ], fatigue crack growth [ 17 , 18 ], and masonry structures [ 19 ]. The key to the success of the phase field paradigm in fracture mechanics is arguably three-fold.…”

A mechanism-based gradient damage model for metallic fracture

“…A viscoplastic approach shall be adopted to achieve a first-order, self-consistent implementation of MSG plasticity. Recall that the Taylor dislocation model defines the flow stress σ f low to be dependent on both the equivalent plastic strain ε p and the effective plastic strain gradient η p , see (16). It then follows that,…”

“…composite materials [11][12][13], functionally graded materials [14][15][16], shape memory alloys [17], hyperelastic solids [18,19], hydraulic fracture [20,21],…”

Phase field modelling of fracture and fatigue in Shape Memory Alloys

“…Not surprisingly, the method is enjoying great popularity and its success has been extended to numerous applications. Recent examples include fracture of functionally graded materials [24,25], composites delamination [26,27], cracking in solar-grade silicon [28], hydrogen embrittlement [29][30][31], rock fracture [32,33], and fatigue damage [34,35], among others; see [36] for a review.…”