Universal Power-Law Strengthening in Metals?

TL;DR

This paper proposes a universal model explaining power-law scaling of metal strength across various microstructures by linking dislocation network properties with critical stress distributions, unifying different strengthening paradigms.

Contribution

It introduces a model that quantitatively predicts the scaling exponent for metal strength, applicable across diverse microstructures and experimental data.

Findings

The model accurately predicts the power-law scaling exponent.

It unifies Hall-Petch and small-scale plasticity paradigms.

The approach explains strength scaling over six orders of magnitude.

Abstract

The strength of most metals used in daily life scales with either an internal or external length scale. Empirically, this is characterized by power-laws persisting to six orders of magnitude in both strength and length scale. Attempts at understanding this scaling have generally been based on a specific mechanism. However the wide applicability of material type and microstructure to this phenomenon suggests a single mechanism is unlikely to capture the observed trend. Here we develop a model which gives quantitative insight into the scaling exponent using the known universal properties of a dislocation network and the leading order stress dependence of an underlying critical stress distribution. This approach justifies a value for the scaling exponent for virtually any experimental data set within the frameworks of both Hall-Petch strengthening and the "small is stronger" paradigm of small scale plasticity.