Physical scaling laws in dislocation microstructures and avalanches from dislocation dynamics simulations

TL;DR

This study uses 3D dislocation dynamics simulations to identify invariant power law exponents in crystalline plasticity and establishes quantitative scaling laws for avalanche behavior across dislocation densities.

Contribution

It reveals that the power law exponent is invariant to dislocation density and loading direction, and provides new scaling laws for avalanche cutoff and triggering stresses.

Findings

Power law exponent approximately 1.6 is invariant across densities and directions.

Dislocation density controls avalanche cutoff scaling as b/√ρ.

Correlations between slip system activities evolve with avalanche size.

Abstract

Avalanche-like plastic bursts in crystalline materials follow power law statistics, but the scaling exponents and cutoff parameters vary widely in the literature ($\alpha$ ranging from 1 to 2.2), hindering predictive modeling. Since distributions do not follow Gaussian behavior, the average of plastic kinetics is not correctly defined. Larger-scale models that rely on average behavior are therefore fundamentally flawed. {We performed extensive three-dimensional Dislocation Dynamics simulations} of FCC Cu deformation across three orders of magnitude in dislocation density ($\rho = 5 \times 10^{10} \ \text{to} \ 2 \times 10^{12} \ \text{m}^{-2}$) under constant strain rates. Our results demonstrate that the power law exponent ($\alpha \approx 1.6 \pm 0.1$ ) is invariant to both dislocation density and loading direction, resolving previous inconsistencies. However, dislocation density strongly controls the power law truncation scaling ($\Delta \gamma_{max} \propto \ b/\sqrt{\rho}$) and the distribution of avalanche triggering stresses. We quantify correlations between slip system activities and show how individual system contributions evolve with avalanche size. These findings reconcile experimental scatter in avalanche statistics and provide quantitative scaling laws for mesoscale-to-continuum plasticity models.