# Yielding Transitions and Grain-Size Effects in Dislocation Theory

## TL;DR

This paper applies a statistical-thermodynamic dislocation theory to analyze yielding transitions and grain-size effects in polycrystalline copper, challenging traditional views on the Hall-Petch effect and predicting stress behaviors based on dislocation source strengths.

## Contribution

It introduces a novel explanation for the Hall-Petch effect, attributing it to dislocation source strengths at grain edges rather than boundary resistance.

## Key findings

- Hall-Petch effects linked to dislocation source strengths
- Theory predicts grain-size dependence of yield and flow stresses
- Rapid elastic-plastic transition at yield points

## Abstract

The statistical-thermodynamic dislocation theory developed in previous papers is used here in an analysis of yielding transitions and grain-size effects in polycrystalline solids. Calculations are based on the 1995 experimental results of Meyers et al. for polycrystalline copper under strain-hardening conditions. The main assertion is that the well known Hall-Petch effects are caused by enhanced strengths of dislocation sources at the edges of grains instead of the commonly assumed resistance to dislocation flow across grain boundaries. The theory describes rapid transitions between elastic and plastic deformation at yield points; thus it can be used to predict grain-size dependence of both yield stresses and flow stresses