Dislocation bowing and passing in persistent slip bands

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.