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 ela stic core embedded about the crack tip in a plastic medium affords a m echanism for cleavage-type crack growth with significant plastic dissi pation [Beltz et al., Acta metall. mater., submitted (1995)]. We build upon recent notions that recognize the large disparity between releva nt length scales involved in plastic Bow processes around cracks in me tals 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 eq uivalent stress in the plastic zone with that predicted by the phenome nological hardening law having the form sigma(flow) = alpha Eb/R(c). W hen the inner elastic stress field is matched with the approximate str ess 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 shiel ding of the crack tip is found to strongly depend on the ideal work of fracture, indicating a possible mechanism for segregation-induced int erfacial embrittlement.