Observations on high strain rate crack growth based on a strip yield model

Abstract

In the past, analytical models have been developed for the study of rapid crack growth in a rate-dependent elastic—plastic material under conditions that permit crack advance in a cleavage mode, and separately for rapid crack advance in an elastic—plastic material when the crack advances by means of a local ductile mechanism. However, models suitable for study of rapid crack growth that permit either mode of crack advance, with the operative mode being determined by which of two competing fracture criteria prevails, have been elusive. Here, the process of dynamic tensile crack growth in a material is studied under small scale yielding conditions with the crack tip plastic zone modeled as a strip yield zone extending ahead of the advancing crack tip. Following Glennie [1] and others, rate dependence of plastic flow is taken into account by assuming that the cohesive stress in the yield zone depends linearly on the local rate of opening of the yield zone. The conditions under which a crack can advance steadily according to either of two criteria are considered. A crack tip opening criterion is identified with a locally ductile mode, and a critical stress condition is identified with a cleavage mode. The analysis leads to conditions among the applied stress intensity factor, the crack speed and the material viscosity that are necessary for sustained crack growth in either case, with the implication that the criterion that is easiest to satisfy will establish the mode by which the crack advances.