New mesoscopic approach to crystal plasticity

We discuss a novel mesoscopic tensorial model (MTM) of crystal plasticity which allows one to capture in a geometrically precise way the role of crystallographically-specific lattice invariant shears. It represents a crystal as a collection of deforming elastic elements whose nonlinear elastic response is governed by globally periodic potential defined in the space of metric tensors. The ensuing Landau-type model with infinite number of equivalent energy wells effectively views a plastically deformed crystal as a mixtures of equivalent “phases”. Plastic yield is interpreted as an escape from the reference energy well, and plastic ‘‘mechanisms’’ are linked to low-barrier valleys of the energy landscape. Rate-independent dissipation emerges due to the well-switching events describing elementary plastic slips. While the MTM approach is formulated in terms of macroscopically measurable quantities (stress and strain), it can handle the short range interactions, involved in the dislocation nucleation and in the interaction of dislocations with various obstacles, without introducing ad-hoc relations. In contrast to physical experiments, the MTM modeling allows one to track the deformation history of individual elastic elements. Using this capability of MTM, we were able to trace how  various  microtwin laminates  self-organize to present themselves macroscopically as pseudorigid rotations. The dissipative, dislocation-mediated nature of such self-organization suggests that at least some of the macroscale textures, sometimes naively associated with purely elastic or even rigid rotations, have their origin in collective motion of dislocations.  The quantitative statistical analysis of the emerging spatial correlations suggests that the underlying process of dislocational self-organization  resembles fluid turbulence.