Crack-Tip Blunting Versus Cleavage Extension
Suppose that a crystal containing a cleavage crack is subjected to a stress. The crystal may fail in a ductile manner, with blunting of the crack, or it may fail in a more or less brittle manner by cleavage extension of the crack. Under what conditions will one or the other behaviour occur? In a classic paper Rice and Thomson1 addressed this question by considering whether spontaneous emission of a dislocation was possible from the tip of a sharp crack loaded to the critical condition for cleavage, according to the Griffith criterion for supply of the intrinsic surface energy. In practice however, brittle cleavage, especially in metals, is often accompanied by a considerable amount of dislocation activity. Emission of a single dislocation may therefore not be a sufficient condition for continued blunting to occur. We must ask whether limited blunting combined with cleavage extension is possible. To address this question, we attempt in this note to extend the analysis of Rice & Hiomson, to see whether the presence of one or more emitted dislocations affects the competition between further emission and cleavage. Note that we do not consider the alternative possibility of cleavage accompanied by dislocation generation and motion in the bulk which does not blunt the tip.
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