Interaction between emission and cleavage at crack tips

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Abstract
Whether a crack cleaves first or instead emits a dislocation has been explored extensively to understand the ductile and brittle nature of crack response. Recently, Rice and co-workers have used a single-plane Peierls approach to identify a critical energy release rate for dislocation emission from a crack tip in terms of γ, the maximum unit area energy required to uniformly shear a candidate slip plane, and SI, a Schmid-type factor to resolve the mode I crack loading onto the candidate slip plane. Comparison with a separate cleavage analysis based on surface energy γs yields an approximate single-plane condition γus/2γs = S 2 1, to distinguish between emission and cleavage. This work attemps to assess this result by treating dislocation emission and cleavage as interacting rather than isolated processes. In particular, two nonlinear Peierls-type planes are considered as in a similar model by Beltz and Schmauder, so that the interactive competition between cleavage and dislocation emission on different planes can be studied. Results for one combination of Peierls plane orientations show that the critical ratio of γus/2γs for transition may deviate from the approximate single-plane value by about −25% to +35%, as the coupling that occurs between opening and shearing of modes on a Peierls-type plane is increased. Profiles of the shear and opening distributions on the competing cleavage and slip planes show large interaction, particularly near instability. Ledge effects, which are not included here, are expected to enhance the interaction between competing cleavage and dislocation emission processes on different planes.