Cohesive and gradient damage coupling applied to the propagation of microcracks in layered materials

In this study, we present a new phase field model (PFM) (inspired by the gradient damage model) combined with the cohesive zone model (CZM) to capture the mixed-mode fracture. The cohesive zone law is modified using shape parameters to consider different normal and tangential traction separation behaviors. The model uses a volumetric–deviatoric (V–D) split to account for the mixed-mode fracture in layered materials. A coupled exponential cohesive model is adopted to account for normal and tangential displacement jumps. The model uses two different phase field parameters for the diffused crack and interface. The fracture energy considered depends on the angle of the direction of the damage gradient of the material. This paper demonstrates the different cases of instability in layered materials during crack propagation. The working of a mixed-mode fracture PFM coupled with an exponential cohesive law using several numerical examples. The numerical examples show instability in crack propagation, including mixed-mode fracture in brittle materials and layered materials, penetration and deflection in a bi-material interface, and intergranular–transgranular fractures in a bicrystalline material.