Dislocation ‘pile-ups’ occurred in crystals when a number of similar dislocations, gliding in a common slip plane, were driven by an applied stress towards an obstacle that they could not overcome. In contrast to dislocation walls, pile-ups gave rise to a long-range stress field, and their properties strongly influenced the plastic behaviour of the crystal as a whole. The analytical model of a pile-up (due to Eshelby, Frank and Nabarro) was applied to a cubic crystal. Full anisotropic elasticity was used, and the model was extended to predict the plastic displacement generated by a dislocation source during the formation of a pile-up. The results were applied to Fe close to the temperature of the α–γ phase transition, where the inclusion of anisotropy led to a strikingly different prediction from that of the isotropic approximation.

Dislocation Pile-Ups in Fe at High Temperature. S.P.Fitzgerald, S.L.Dudarev: Proceedings of the Royal Society A, 2008, 464[2098], 2549-59