# Microplasticity and yielding in crystals with heterogeneous dislocation distribution

## TL;DR

This paper uses discrete dislocation dynamics simulations to study how heterogeneous dislocation distributions affect the elastic and plastic behavior of face-centered cubic crystals, revealing effects on elastic modulus, yield stress, and hardening.

## Contribution

It introduces a continuum dislocation dynamics model to explain the transition from inversive to non-inversive dislocation motion and analyzes the impact of dislocation density gradients on deformation.

## Key findings

- Effective elastic modulus decreases with dislocation density gradient.
- Yield stress decreases as dislocation density gradient increases.
- Pronounced hardening stage with stress redistribution observed.

## Abstract

In this study, we use discrete dislocation dynamics (DDD) simulation to investigate the effect of heterogeneous dislocation density on the transition between quasi-elastic deformation and plastic flow in face-centered cubic single crystals. By analyzing the stress-strain curves of samples with an initial, axial dislocation density gradient, we arrive at the following conclusions: (i) in the regime of quasi-elastic deformation before the onset of plastic flow, the effective elastic modulus of the simulated samples falls significantly below the value for a dislocation-free crystal. This modulus reduction increases with decreasing dislocation density gradient: crystals with homogeneous dislocation distribution are thus weakest in the quasi-elastic regime; (ii) the transition towards plastic flow occurs first in regions of reduced dislocation density. Therefore, the overall yield stress decreases with increasing dislocation density gradient; (iii) crystals with dislocation density gradient exhibit a more pronounced hardening stage during which stress is re-distributed onto stronger regions with higher dislocation density until the sample flows at a constant flow stress that is approximately independent on dislocation density gradient. We interpret these findings in terms of a continuum dislocation dynamics inspired model of dislocation density evolution that accounts for inversive dislocation motions. The transition between quasi-elastic and plastic deformation is interpreted as a transition from inversive to non-inversive dislocation motion, and the initial differences in elastic modulus are related to a density dependent polarizability of the dislocation system. The subsequent plastic flow behavior is analyzed in terms of a modified version of Mughrabi's composite model.

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Source: https://tomesphere.com/paper/1812.11427