A numerical investigation of the interplay between cohesive cracking and plasticity in polycrystalline materials

Abstract

The interplay between cohesive cracking and plasticity in polycrystals is herein investigated. A unified finite element formulation with elasto-plastic elements for the grains and interface elements for the grain boundaries is proposed. This approach is suitable for the analysis of polycrystalline materials with a response ranging from that of brittle ceramics to that of ductile metals. Crystal plasticity theory is used for 3D computations, whereas isotropic von Mises plasticity is adopted for the 2D tests on plane strain cross-sections. Regarding the grain boundaries, a cohesive zone model (CZM) accounting for Mode Mixity is used for the constitutive relation of 2D and 3D interface elements. First, the analysis of the difference between 3D and 2D simulations is proposed. Then, considering all the nonlinearities in the model, their interplay is numerically investigated. It is found that the CZM nonlinearity prevails over plasticity for low deformation levels. Afterwards, plasticity prevails over CZM. Finally, for very large deformation, failure is ruled by the CZM formulation which induces softening. The meso-scale numerical results show that the simultaneous use of cohesive interface elements for the grain boundaries and plasticity theory for the grains is a suitable strategy for capturing the experimental response of uniaxial tensile tests.