Sheared Solid Materials

TL;DR

This paper introduces a time-dependent Ginzburg-Landau model for nonlinear elasticity in solids, capturing dislocation formation, shear banding, and effects of free volume, with applications to alloys and aging phenomena.

Contribution

It develops a novel model incorporating lattice periodicity and free volume, enabling simulation of dislocation dynamics, shear banding, and phase interface behavior in solids.

Findings

Dislocation dipoles and slips form under shear in the model.

High-density dislocations lead to shear banding and strain localization.

Dislocation pinning and aging effects depend on free volume accumulation.

Abstract

We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. We assume that the elastic energy density is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure. With this new ingredient, solving the equations yields formation of dislocation dipoles or slips. In plastic flow high-density dislocations emerge at large strains to accumulate and grow into shear bands where the strains are localized. In addition to the elastic displacement, we also introduce the local free volume {\it m}. For very small $m$ the defect structures are metastable and long-lived where the dislocations are pinned by the Peierls potential barrier. However, if the shear modulus decreases with increasing {\it m}, accumulation of {\it m} around dislocation cores eventually breaks the Peierls potential leading to slow relaxations in the stress and the free energy (aging). As another application of our scheme, we also study dislocation formation in two-phase alloys (coherency loss) under shear strains, where dislocations glide preferentially in the softer regions and are trapped at the interfaces.