Dislocation dynamic modelling of the brittle-ductile transition in tungsten

Brittle-ductile transitions in metals, ceramics and semiconductors are closely connected with dislocation activity emanating near to crack-tips. We have simulated the evolution of crack-tip plasticity using a two-dimensional dislocation dynamics model which has been developed to include two symmetric slip planes intersecting the crack-tip, and applied to single-crystal tungsten. The dislocation mobility law used was physically based on double-kink nucleation on screw dislocations, with an activation energy reduced by the local stress. Even in the strong stress gradients near a crack-tip, the dislocations are found to self-organise so that the internal stress in the array is effectively constant with time and position over a wide range of strain rates and temperatures. The resultant net activation energy for dislocation motion is found to be constant and close to the activation energy experimentally measured for the brittle-ductile transition. Use of a fracture criterion based on the local crack-tip stress intensity factor, as modified by the stresses from the emitted dislocations, allows explicit prediction of the form and temperature of the brittle-ductile transition. Predictions are found to be in very close agreement with experiment.