Crack-tip dislocation emission arrangements for equilibrium—III. Application to large applied stress intensities

Abstract

Bulk {100}<010> oriented Fe 3 wt% Si single crystals have been evaluated with two types of experiments—a detailed TEM analysis of the dislocation structure found at a crack tip loaded to 17 MPa√m, and fracture toughness in the cleavage temperature transition range. Based on observations of crack-tip emitted dislocations along ( 1 ¯ 1 2 ¯ ) and ( 1 ¯ 1 2 ¯ ) planes, a quasi-equilibrium model based on Atkinson and Clement's discretized dislocation analysis modified to contain a tip emission condition is compared to both of these data sets. The first comparison verifies that less than 10% of the observed dislocation density is required for equilibrium, consistent with Weertman's hypothesis of redundant and necessary dislocation densities. The second comparison demonstrates that the crack-tip distance to the last dislocation emitted, while not really a dislocation free zone, is nevertheless critical to the understanding of the tip-emission condition. This is first modeled computationally and then shown that an analogous Mode I analytical formulation to the Mode II, III model of Weertman et al. [ Acta metall. 31, 473 (1983)] describes how the local stress intensity, k tip, varies with yield stress and applied stress intensity. It is further shown that when k tip ⪖ k IG, the Griffith value, cleavage occurs and such a criterion holds over a wide temperature range where fracture toughness varies from 3 to 60 MPa√m. This forms the basis for plastically-induced cleavage.