Plastic deformation as a phase transition: a combinatorial model of plastic flow in copper single crystals

TL;DR

This paper models plastic deformation in copper single crystals as a phase transition using a discrete mesoscale approach, revealing complex microstructural evolution and different phase behaviors under stress.

Contribution

It introduces a novel discrete exterior calculus-based model for plastic flow, capturing microstructural phases and phase transitions in copper crystals beyond continuum models.

Findings

Identification of multiple phases with distinct slip network arrangements.

Observation of both first-order and second-order phase transitions.

Correlation of phase behaviors with crystallographic phenomena.

Abstract

Continuum models of plasticity fail to capture the richness of microstructural evolution because the continuum is a homogeneous construction. The present study shows that an alternative way is available at the mesoscale in the form of truly discrete constructions and in the discrete exterior calculus. A pre-existing continuum mean-field model with two parameters is rewritten in the language of the latter to model the properties of a network of plastic slip events in a perfect copper single crystal under uniaxial tension. The behaviour of the system is simulated in a triangular 2D mesh in 3D space employing a Metropolis-Hastings algorithm. Phases of distinct character emerge and both first-order and second-order phase transitions are observed. The phases represent arrangements of the plastic slip network with different combinations of collinear, coplanar, non-collinear and non-coplanar active slip systems. Furthermore, some of these phases can be interpreted as representing crystallographic phenomena like activation of secondary slip systems, strain localisation and fracture or amorphisation. The first-order transitions mostly occur as functions of the applied stress, while the second-order transitions occur exclusively as functions of the mean-field coupling parameter. The former are reminiscent of transitions in other statistical-mechanical models, while the latter find parallels in experimental observations.