Modeling of crack tip high inertia zone in dynamic brittle fracture

A phenomenological modification is proposed to the existing cohesive constitutive law of Roy and Dodds to model the crack tip high inertia region proposed by Gao. The modification involves addition of a term which is attributed to fracture mechanisms that result in high energy dissipation around the crack tip. This term is assumed to be a function of external energy per unit volume input into the system. Finite element analysis is performed on PMMA with constant velocity boundary conditions and mesh discretizations based on the work of Xu and Needleman. The cohesive model with the proposed dissipative term is only applied in the high inertia zone and the traditional Roy and Dodds model is applied on cohesive elements in the rest of the domain. The results show that crack propagates in three phases with a speed of 0.35cR before branching, confirming experimental observations. The modeling of high inertia zone is one of the key aspects to understanding brittle fracture.