DISLOCATION PILEUPS AND THE HALL–PETCH RELATION

Abstract

The strength of a linear dislocation pileup depends on the nature of its barrier. Analysis is given for the case in which the barrier is a second-phase particle and for that in which the barrier is a locked dislocation with a different Burgers vector.In the first case, where pileups lie in front of hard inclusions, it is shown that the Hall–Petch relation is valid and that the Petch slope increases as the ratio of the inclusion/matrix shear moduli increases. For a screw dislocation pileup, the Petch slope increases by a factor of about 2 for a modulus ratio of 3 and by about a factor of 3 for a ratio of 7. The increase for edge pileups is somewhat higher.In the second case, where the barrier is a locked dislocation with a different Burgers vector, the Petch slope may be increased (or decreased) by a factor of √m, where m is the ratio of the Burgers vector of the locked dislocation resolved in the slip plane to that of the free dislocations in the pileup.