A simple elastic cell model of cleavage fracture in the presence of dislocation plasticity

The current analysis is prompted by the recent recognition that an elastic core embedded about the crack tip in a plastic medium affords a mechanism for cleavage-type crack growth with significant plastic dissipation [Beltz et al., Acta metall. mater., submitted (1995)]. We build upon recent notions that recognize the large disparity between relevant length scales involved in plastic Bow processes around cracks in metals and on metal-ceramic interfaces. A simple, continuum-based model that assumes the presence of a dislocation-free core of dimension R(c) is used. The crack tip is assumed not to emit dislocations. The core size is chosen in a self-consistent manner by identifying a maximum equivalent stress in the plastic zone with that predicted by the phenomenological hardening law having the form sigma(flow) = alpha Eb/R(c). When the inner elastic stress field is matched with the approximate stress field within the plastic zone, it is found that the applied energy release rate needed to initiate crack extension is several orders of magnitude greater than the ideal work of fracture. This apparent shielding of the crack tip is found to strongly depend on the ideal work of fracture, indicating a possible mechanism for segregation-induced interfacial embrittlement.