A model emitting dislocation group from crack tip with stress singularity and its application to brittle-ductile transition

Taking into account the stress singularity near the crack tip, computer simulation of dislocation emission and motion has been carried out. A model is proposed in which the source emitting the dislocation group is located near by the crack tip. The numerical method has been used by programming to adjust time increment automatically. By this model and the analytical method, the converged solution has been obtained. The main results are as follows: The region where any dislocation does not exist along the slip plane near the stressed source, namely, dislocation free zone (DFZ) is found to appear. Also it has been found that inverse pile-up of dislocations against the tip of DFZ will appear. The formula is obtained correlating the maximum dislocation density with DFZ length. With increase of stress rate and decrease of the value of μ/τ₀^*, the inverse pile-up at the tip of DFZ becomes more significant. Based on these results, a new fracture criterion for brittle fracture is proposed assuming critical local stress requisites within DFZ, where high stress concentration is induced by dynamic inverse pile-up of dislocations.