Dislocation pile-ups in Fe at high temperature

Dislocation 'pile-ups' occur in crystals when a number of similar dislocations, gliding in a common slip plane, are driven by an applied stress towards an obstacle that they cannot overcome. In contrast to dislocation walls, pile-ups give rise to a long-range stress field, and their properties strongly influence the plastic behaviour of the crystal as a whole. In this paper, we apply the analytic model of a pile-up (due to Eshelby, Frank and Nabarro) to a cubic crystal. Full anisotropic elasticity is used, and the model is extended to predict the plastic displacement generated by a dislocation source during the formation of a pile-up. The results are applied to Fe close to the temperature of the alpha gamma phase transition, where the inclusion of anisotropy leads to a strikingly different prediction from that of the isotropic approximation.