Dislocation bowing and passing in persistent slip bands

Interactions of glide dislocations in a channel of a persistent slip band

“…The results of Mughrabi and Pschenitzka [9] motivated Brown to further improve the model [2]. He considered the dislocation shape changes in the vicinity of the walls more carefully.…”

“…(As shown by Mughrabi and Wang [1] the saturation stress lies actually below the endurance limit as the latter requires additionally a crack formation and their propagation.) Brown [2] has summarized four possible contributions to the endurance limit: (i) the stress required to make screw dislocations of opposite sign pass one another during their shuttle in a channel of a persistent slip band (PSB); (ii) the stress required to bow-out the screw dislocations between the PSB walls; (iii) the internal stress resulting from inhomogeneous plastic deformation, caused by the resistance to plastic flow of the walls; and (iv) the friction stress which might come from dislocation debris left between the walls by the shuttling glide dislocations. The model proposed in the present paper is used to simulate the escape stress consisting of contributions (i) and (ii), as well as to estimate the influence of boundary conditions partly addressed in item (iii).…”

“…Approximate analytical solutions of this problem involving the coupled contributions (i)-(iii) were presented in the recent papers by Brown [2,8] and Mughrabi and Pschenitzka [9]. Similarly as in [4,13], Brown [8] assumed that the bowing stress is equal to the passing stress, and that the two contributions to the escape stress should be added together; the contribution (iii) was neglected.…”

An interpretation of the Haasen–Kelly effect

“…The bowing stress is equal to the nominal passing stress if the dipole is about ( ) 17 1 8 ≈ −ν π times longer than its height. Under these circumstances, it is easy to use the calculations of Brown (2006) to estimate the reduction in passing stress: it is reduced by about 50%. However, the diagram of Fig.…”

Exact solution for dislocation bowing and a posteriori numerical technique for dislocation touching-splitting

“…In Section 2, to focus on these phenomena, a local coordinates will be introduced between two circular obstacles, that is, we will consider evolving open curves with two endpoints moving along each circle, and an exact solution will be constructed. To the best of our knowledge, no one has studied evolving curve connecting two circles; on the other hand, fixedendpoints case has been studied extensively by various authors (e.g., [3][4][5][6]). …”