Inelastic rotations in crystal plasticity

Considerable efforts have been recently devoted to the task of small-scale modeling of crystal
plasticity at a reasonable computational cost. A fully detailed description of plastic flows in
crystals is possible only by molecular dynamics (MD) approaches, which accurately represent
micromechanisms of plastic response while relying minimally on phenomenology. However, in
most applications, such an approach is prohibitively computationally expensive, even if one deals
with ultrashort timescales and ultrasmall samples. The discrete dislocation dynamics (DDD)
approach was created to overcome the short-scale focus of atomistic methods and inform
various classical continuum models. However, the DDD models contain many parameters since
the processes of dislocation nucleation, interaction with defects, self-locking, climbing, etc., have
to be prescribed phenomenologically through specific local rules coming from independent
phenomenological constructs. Other major challenges in the DDD framework include accounting
for large plastic distortions and incorporating the effects of anisotropic elasticity.
To achieve a compromise between more and less coarse-grained models, we adopt a novel
approach known as the mesoscopic tensorial model (MTM). It represents a crystal as a collection
of homogeneously deforming elastic elements whose nonlinear elastic response is governed by
globally periodic potential defined in the space of metric tensors. The potential is designed to
respect the geometrically nonlinear kinematics of the lattice. From the perspective of the ensuing
Landau-type model, the elastic potential has an infinite number of equivalent energy wells, and
therefore plastically deformed crystals can be viewed as coherent mixtures of equivalent
‘phases’. In this work, we apply the MTM approach to the study of microstructure formation in
crystals during plastic deformation. These microstructures are composed of randomly rotated
patches of the unstressed lattice. We will show that while such ’patches’ disguise themselves as
an elastically neutral rotation, behind it is an inherently dissipative, dislocation-mediated process.
We then investigate dislocation core properties along these grain boundaries. Finally, we
compare our results with MS simulations