Anisotropic Damage Constitutive Law for Cleavage Failure in Crystalline Grain by Cohesive Zone Model

Abstract

The objective of this study is to propose new anisotropic damage constitutive law that represents the separation process on cleavage plane in a polycrystalline aggregate. The proposed law is formulated by embedding of an exponential type of the cohesive zone model (CZM) in a standard crystal plasticity constitutive law. The separation of the cleavage plane can be realized by exponential type of the CZM based on an atomic potential. On the other hands, the crystal plasticity constitutive law is used to simulate the deformation due to the crystalline slip on each crystallographic system. Thus, the proposed damage constitutive law is capable of representing the microscopic mechanism characterized by both the fracture behavior of the cleavage plane and the plastic deformation of the crystallographic slip. Several numerical simulations are conducted to demonstrate the capability of the proposed damage constitutive law. In particular, it is confirmed that the proposed model enables us to simulate the crack propagation in arbitrary directions, and the resultant anisotropic strength in a single crystal grain.