Double slip plane crack model

Abstract

In this paper a simple crack model is proposed and the behavior of this crack under stress is explored. The crack consists of an ordinary Griffith crack, but on either side of this crack, at a distance w, exist two slip planes that are parallel to the crack plane. It is assumed that slip can only take place on these two planes. Elsewhere the material is elastic. When w is set equal to zero the crack becomes a Bilby-Cottrell-Swinden crack. This crack model simulates in a simple way the elastic crack tip enclave model of a crack. Because w has a finite value the material around the crack tip is elastic. The crack is considered to be stressed in either mode II (plane strain shear) or mode III (anti-plane strain shear). It is found that for a virgin, stationary crack the stress intensity factor at the crack tip is equal to the conventional stress intensity factor when the stress is raised under a monotonically increasing load. However, when the crack tip advances under such a load the crack tip stress intensity factor is smaller than the conventional stress intensity factor. The fracture stress is proportional to the surface energy of the solid raised to a power. In general, this power is not equal to one half. For cyclic loading by using qualitative arguments it is shown that the crack can grow an incremental distance each cycle, and the growth law is a fourth power Paris equation.