Peter Ispanovity1 Stefanos Papanikolaou2 István Groma1

1, Eotvos University, Budapest, , Hungary
2, West Virginia University, Morgantown, West Virginia, United States

To understand the formation and evolution of dislocation patterns developing during plastic deformation has long been a central aim of materials research. Several continuum theories have been proposed that are able to model different types of dislocation patterns like PSB or fractal structures. Apart from these, discrete dislocation dynamics has also been employed and demonstrated the tendency of dislocation ensembles to form patterns. Embryonic forms of some well-known structures have been directly observed with this method.

In order to identify the necessary ingredients of a continuum theory and their role in patterning in the talk, contrary to previous approaches, we aim at a multi-scale description. We, therefore, parallelly study the patterning phenomenon in a 2D discrete dislocation system and its continuum counterpart. To this end, we develop a two-dimensional stochastic continuum dislocation dynamics theory that is derived by coarse graining the equations of motion of discrete dislocations. The main ingredients of the continuum theory is the evolution equations of statistically stored and geometrically necessary dislocation densities, which are driven by the long-range internal stress, a stochastic flow stress term and, finally, local strain gradient terms, commonly interpreted as dislocation back-stress.

The agreement between the two models is shown primarily in terms of the patterning characteristics that include the formation of dipolar dense dislocation walls that are perpendicular to the slip plane. The length of these walls gradually increase with increasing strain and reach the simulation box size at yielding. Not only the different parameters of the patterns, but also the stress-strain curves exhibit quantitative agreement between the too models.

The multi-scale approach enables us to identify the back-stress term as the main source of the pattering in the continuum description. We will thoroughly discuss the relation of this finding to local stresses, internal correlations and stochastic and intermittent processes.
Connections of our results to theories of kinematic hardening and strain-gradient plasticity as well as to the Bauschinger effect will also be described followed by prospects for generalization to 3D.