A gradient-enhanced damage model for anisotropic brittle fracture with interfacial damage in polycrystalline materials

Abstract

This article presents a nonlocal gradient-enhanced damage model that uses direction-dependent damage evolution and interfacial damage to predict transgranular and intergranular cracks in polycrystalline materials at the microstructural level. The distinct grains within the polycrystalline morphology are modeled as anisotropic linear elastic domains with random spatial orientation and cubic symmetries. Transgranular micro-cracks are assumed to occur along specific preferential cleavage planes within each randomly oriented crystal and are described using a bulk damage variable. For intergranular fracture, a smeared description of interface decohesion is incorporated through an interface damage variable which depends on the modified interface kinematics based on a cohesive law that uses a smoothed displacement jump approximation. The coupled system of equations in the proposed computational framework is decoupled using an operator-split methodology to ensure a robust and straightforward computational implementation. Several numerical examples are presented, and simulations are performed on single crystal, bicrystals, and polycrystalline domains to demonstrate the capabilities and validation of the proposed model.