In this communication, we summarize the current advances in size-dependent
continuum plasticity of crystals, specifically, the rate-independent
(quasistatic) formulation, on the basis of dislocation mechanics. A
particular emphasis is placed on relaxation of slip at interfaces. This
unsolved problem is the current frontier of research in plasticity of
crystalline materials. We outline a framework for further investigation,
based on the developed theory for the bulk crystal. The bulk theory is based
on the concept of geometrically necessary dislocations, specifically, on
configurations where dislocations pile-up against interfaces. The average
spacing of slip planes provides a characteristic length for the theory. The
physical interpretation of the free energy includes the error in elastic
interaction energies resulting from coarse representation of dislocation
density fields. Continuum kinematics is determined by the fact that
dislocation pile-ups have singular distribution, which allows us to represent
the dense dislocation field at the boundary as a superdislocation, i.e., the
jump in the slip filed. Associated with this jump is a slip-dependent
interface energy, which in turn, makes this formulation suitable for analysis
of interface relaxation mechanisms.
Plasticity of crystals and interfaces: From discrete dislocations to size-dependent continuum theory
