Critical grain sizes and generalized flow stress - grain size dependence

TL;DR

This paper presents a generalized equation for yield stress dependence on grain size, identifying two critical sizes where the strengthening mechanism changes, and discusses behavior in nanometer ranges with boundary strength effects.

Contribution

It introduces a unified model describing grain size dependence of yield stress across different regimes, including critical sizes and boundary effects.

Findings

Two critical grain sizes identified for mechanism change

Equation includes Hall-Petch relation for larger grains

Nanometer range behavior varies with boundary strength

Abstract

The generalized eguation that describes the yield stress dependence upon the grain size in the wide range of grain sizes has been obtained. There are two critical grain sizes that corresponds to the changes in strengthening mechanism. The equation includes Hall - Petch relation in the range of d>dcr1. For dcr1>d>dcr2, the power in the Hall - Petch relation varies from -1/2 to -1. In a nanometer (nm) range (d<dcr2) there are posibileties of softerning (in case of "weak" boundaries) as well as significant strengthening (in case of "srtong" boundaries).