Effective mobility of dislocations from systematic coarse-graining. (1st June 2015) - Kooiman, M; Hütter, M; Geers, MGD
Abstract: The dynamics of large amounts of dislocations governs the plastic response of crystalline materials. In this contribution we discuss the relation between the mobility of discrete dislocations and the resulting flow rule for coarse-grained dislocation densities. The mobilities used in literature on these levels are quite different, for example in terms of their intrinsic the stress dependence. To establish the relation across the scales, we have derived the macroscopic evolution equations of dislocation densities from the equations of motion of individual dislocations by means of systematic coarse-graining. From this, we can identify a memory kernel relating the driving force and the flux of dislocations. This kernel can be considered as an effective macroscopic mobility with two contributions; a direct contribution related to the overdamped motion of individual dislocations, and an emergent contribution that arises from time correlations of fluctuations in the Peach–Koehler force. Scaling analysis shows that the latter contribution is dominant for dislocations in metals at room temperature. We also discuss several concerns related to the separation of timescales.