A multiscale two-dimensional finite element incorporating the second-order Cauchy–Born rule for cohesive zone modeling: Simulation of fracture in polycrystalline materials

Abstract

In this work, a multiscale cohesive zone model is developed by elaborating the second-order Cauchy–Born (CB) rule to simulate crack growth in polycrystalline solids. To do so, a two-dimensional domain is discretized with bulk elements and finite width cohesive zone interphase. As polycrystalline materials are considered, the grain boundaries are meshed with cohesive zone interphase elements, allowing crack to propagate in the boundaries as well as through the grains. The correlation between the micro and the macroscale material properties is specified using CB rule, as the first-order CB is utilized in the bulk elements, and the second-order CB is utilized in the cohesive interphase elements. An extensive numerical study has been performed for understanding the effect of (1) the boundary conditions, (2) the integration scheme, and (3) the mesh refinement. Moreover, a comparison between the proposed method and the one elaborating the depletion potential for cohesive zones calculations has been performed. Also, the applicability of the model to predict fractures due to defects and vacancies is studied, which shows the ability of the model to predict both brittle and ductile fractures. It should be noted that the proposed model elaborates the same constitutive relations for the bulk elements and the cohesive zone elements, making this model a consistent one, unlike most of other cohesive zone models that employ different laws depending on the different element types.