A theoretical model for roughness induced crack closure

Abstract

A theoretical model for the effects of grain size on the magnitude of roughness induced crack closure (RICC) at fatigue crack growth threshold has been proposed. With the basic configuration of a crack propagating incrementally along planar slip bands and deflecting at grain boundaries, an idealized zig-zag crack path is considered. The effective slip band length is considered to be equal to grain size. It is assumed that the dislocations emitted from the crack tip upon loading to form the pile-up are completely irreversible to produce a comnined mode I and mode II displacement at the crack tip. The assumption of continuously distributed dislocations in the pile-up facilitated the calculation of crack tip sliding displacement (CTSD) along the slip plane from which the mode I closure disregistry just behind the crack tip can be calculated. The closure stress intensity factor at threshold, Kel,th could then be expressed as a function of critical resolved shear stress, average macroscopic yield stress, angle subtended by the slip plane with the crack plane and the length of the slip band. Comparisons of the predicted trends with experimental data from various alloy systems indicate good agreement.