Asymptotic Crack Tip Fields in Linear and Nonlinear Materials and Their Role in Crack Propagation

Abstract

The famous Wieghardt, Griffith and Irwin criteria predict the onset of fracture in linear elastic materials. They have to be supplemented by appropriate criteria for predicting the path that the fracture will follow until the failure of the structure. These require the knowledge of the stress and displacement fields at the front of propagating fracture which depend on the actual loading on the structure and its boundary conditions. In this paper we shall review these fields in brittle and quasi-brittle materials. In the latter materials, a traction-free fracture front often has a large process zone ahead of it in which the material experiences progressive softening. Such a mixed traction-free and process zone is also called a cohesive crack. Over the process zone the material is able to transfer some tractions across the crack faces depending upon how much the faces have separated or slid relative to each other. In the famous Barenblatt model the process zone was very small in comparison with the traction-free crack so that the actual traction-separation relationship in the process zone was not explicitly involved. However, in real quasi-brittle materials the size of the process zone can be commensurate or even larger than the traction-free crack. It is therefore necessary to know this relationship explicitly in order to determine the corresponding stress and displacement fields at the front of the propagating cohesive crack. The asymptotic fields at the front of a crack in brittle materials were obtained by Williams and those for quasi-brittle materials by Xiao and Karihaloo.