Dislocation behavior in fatigue II. Friction stress and back stress as inferred from an analysis of hysteresis loops

Abstract

Fatigue hysteresis loops obtained by three different authors are evaluated to obtain data for the friction stress and back stress acting on the dislocations. Part of the friction stress is equal in magnitude to the back stress and like it rises roughly in proportion to the root of the cumulative plastic strain. The theoretical discussion of this contribution to friction stress will be given in conjunction with the discussion of the back stress in parts III and IV of this series. The smaller part of the friction stress depends more or less linearly on the number of cycles. It is identified primarily with the stress required for dragging the jogs on the screw dislocations which shuttle to and fro in the matrix channels in accordance with the deductions of part I of this series. Additionally, there may be a yet smaller contribution to the friction stress due to dispersed point defects. This, if it exists, comes to saturation after about 12 cycles. The fact that no contribution to the stress can be identified with the back stress due to the glide dislocations which are spun out and taken up again at the channel-loop patch interfaces indicates that their line tension is quite low. This is understandable on account of their arrangement into tilt wall configurations as well as the local screening of their stresses by reorienting loops in their vicinity. Following up on the corresponding hypothesis in part I, it is suggested that the channel widths in the matrix structure adjust such that, on the average, one jog resides on each screw dislocation segment. If so, the channel width should initially decrease inversely with the number of cycles, and then become constant.