Stefan Sandfeld

Abstract:

Work hardening during plastic deformation of crystalline solids is associated with significant changes in dislocation microstructure. The increase in dislocation density on the specimen scale is accompanied by a spontaneous emergence of regions of low dislocation density and clusters of high density which, to a large extent, persists upon unloading ("dislocation patterns"). Despite a significant degree of morphological variation depending on slip geometry and loading mode (e.g. cell or labyrinth structures, dislocation accumulation in veins or walls), these patterns are characterized by fairly universal scaling relationships, commonly referred to as 'similitude principle', relating the characteristic length of the dislocation patterns to the applied stress and to their average dislocation density. Despite long-standing efforts in the materials science and physics of defects communities, there is no general consensus regarding the physical mechanism leading to the formation of dislocation patterns. We present for the first time dislocation patterning results from a continuum theory capturing the coupled dynamics of statistically stored and geometrically necessary dislocations while accounting for the specific kinematics of curved dislocations. The resulting patterns are automatically consistent with the similitude principle. A surprisingly minimalistic set of 'ingredients' is already sufficient to create patterns: starting with an idealized model in single slip configuration, which allows to comprehend the basic mechanisms of pattern formation, we then turn to more realistic 3D multislip models where latent hardening terms couple dislocation densities on different slip systems through short-range interaction stresses. Our simulations explain how complex cell structures matching experimentally observed structures form - again being consistent with similitude. In addition, we show how data from dedicated discrete dislocation dynamics simulations can be extracted and used for gauging and parametrizing continuum models (e.g. in terms of short range dislocation interactions and reactions). Together with the mechanisms for dislocation pattern formation, we have the key ingredients for the formation of persistent slip bands under cyclic loading conditions.