Dislocation generation instability and the brittle-to-ductile transition

We propose a new model for the brittle-to-ductile transition based on a statistical mechanics description of dislocation generation. We begin with a summary of the deformation and fracture behavior of titanium trialuminides to illustrate the need for a new approach to understanding the ubiquitous brittleness of intermetallic compounds. We then describe the important features of the new model, which is applicable not only to intermetallic compounds but also to the wider class of crystalline materials that exhibit the brittle-to-ductile transition. In two dimensions the onset of the ductile behavior corresponds to a cooperative dissociation instability of many dislocation dipoles driven primarily by thermal fluctuations and assisted by the applied stress. The mutual interactions between the dipoles are taken into account using the Kosterlitz-Thouless concept of thermally induced dislocation screening. The predictions of the transition temperature for several materials are discussed.