Intermittency in crystal plasticity informed by lattice symmetry

TL;DR

This paper introduces a nonlinear 3D phase field model for crystal plasticity that incorporates lattice symmetry, revealing complex energy landscapes and scale-free slip avalanches influenced by symmetry and dislocation interactions.

Contribution

The model uniquely accounts for the lattice symmetry group G, enabling the simulation of dislocation dynamics and slip processes without auxiliary hypotheses.

Findings

Reveals scale-free intermittency in plastic flow with power-law slip avalanche statistics.

Shows the influence of lattice symmetry and compatibility on dislocation behavior.

Captures long-range elastic fields and complex dislocation distributions.

Abstract

We develop a nonlinear, three-dimensional phase field model for crystal plasticity which accounts for the infinite and discrete symmetry group G of the underlying periodic lattice. This generates a complex energy landscape with countably-many G-related wells in strain space, whereon the material evolves by energy minimization under the loading through spontaneous slip processes inducing the creation and motion of dislocations without the need of auxiliary hypotheses. Multiple slips may be activated simultaneously, in domains separated by a priori unknown free boundaries. The wells visited by the strain at each position and time, are tracked by the evolution of a G-valued discrete plastic map, whose non-compatible discontinuities identify lattice dislocations. The main effects in the plasticity of crystalline materials at microscopic scales emerge in this framework, including the long-range elastic fields of possibly interacting dislocations, lattice friction, hardening, band-like vs. complex spatial distributions of dislocations. The main results concern the scale-free intermittency of the flow, with power-law exponents for the slip avalanche statistics which are significantly affected by the symmetry and the compatibility properties of the activated fundamental shears.