Dislocation bowing and passing in persistent slip bands

Abstract

In response to a recent paper by Mughrabi and Pschenitzka (Phil. Mag. 85 3029 (2005).), an estimate is given of the saturation stress in cyclic plasticity, assuming only the bowing of screw dislocations and the simultaneous passing of them at a critical separation determined by their cross-section for mutual annihilation by cross-slip. Although, as Mughrabi and Pschenitzka show, the simple addition of the two stresses is a poor approximation, if the bowing stress is made equal to the passing stress, the equations governing the saturation stress and the associated average plastic strain in a persistent slip band are scarcely altered from earlier work (Phil. Mag. 84 2501 (2004).). A comparison between theory and experiment shows good quantitative agreement. Finally, an estimate is made of the alternating internal stress in a band, and reasons suggested for why it does not contribute to the saturation stress.

Acknowledgements

It is a pleasure to thank Prof. Carl Holste for his thoughtful criticism of these ideas, and Prof. Hael Mughrabi for showing me his pioneering paper with Pschenitzka prior to publication. Volume 11 in Nabarro's series Dislocations in Solids has proved immensely helpful by providing a concise summary of various authors’ views of a contentious and difficult field: I owe an immense debt to him for encouragement and criticism. I am grateful to Robinson College and to the Cavendish Laboratory for support.