Dynamic formation and release of a dislocation pile-up against a viscous obstacle

Abstract

Abstract The behaviour of a single-ended pile-up of mobile dislocations against a removable viscous obstacle is investigated by a numerical technique. The dislocations are assumed to obey an exponential stress-velocity law. The obstacle is represented by a step increase in the drag stress acting at the lead dislocation and is located at a certain distance from a dislocation source. Dynamic yielding is assumed to occur when the obstacle can no longer support the pile-up. At that instant, the pile-up is allowed to by-pass the obstacle and is rapidly released because of the re- duction of the drag stress on the lead dislocation. Sample calculations were made to simulate three dynamic constant-stress tests and four constant strain-rate tests on a high-carbon, high-manganese steel. The position, velocity and effective stress associated with each dislocation in the pile-up were evaluated during both the pre- and post-yield flow. The shear stresses acting at the lead dislocation at yield were found to bo not larger than three to four times the applied resolved shear stress.