A study of dynamic crack growth in elastic materials using a cohesive zone model

Abstract

The problem of a semi-infinite mode III crack dynamically propagating in a two-dimensional linear elastic infinite body is considered. The crack tip is assumed to be a cohesive zone whose (finite) size is determined so as to cancel the classical crack tip stress singularity caused by the applied loads. The cohesive zone behavior is assumed rate dependent and is characterized by a thermodynamically based constitutive equation. A new semi-analytical solution method has been formulated to solve the resulting initial value problem. The proposed solution method offers the capability to analyze the entire crack growth phenomenon (acceleration-steady state-arrest), without requiring special assumptions, neither on the crack propagation mode (e.g. steady state or assigned crack tip velocity), nor on the space-time discretization, so to obtain solutions that are not affected by grid size effects. Several solutions, corresponding to various values of the initial and boundary conditions as well as cohesive zone constitutive properties, are presented and analyzed.