Grain-size dependence of plastic-brittle transgranular fracture

TL;DR

This study computationally investigates how grain size influences fracture toughness in metals, revealing a non-monotonic relationship due to competing mechanisms of failure nucleation and crack propagation resistance.

Contribution

It introduces a combined phase-field and crystal plasticity model to explain the complex grain-size dependence of fracture toughness in BCC metals.

Findings

Failure nucleation follows Hall-Petch law with smaller grains being more failure-prone.

Crack propagation resistance follows inverse Hall-Petch law with larger grains offering more toughness.

The non-monotonic behavior explains contradictory experimental observations.

Abstract

The role of grain size in determining fracture toughness in metals is incompletely understood with apparently contradictory experimental observations. We study this grain-size dependence computationally by building a model that combines the phase-field formulation of fracture mechanics with dislocation density-based crystal plasticity. We apply the model to cleavage fracture of body-centered cubic materials in plane strain conditions, and find non-monotonic grain-size dependence of plastic-brittle transgranular fracture. We find two mechanisms at play. The first is the nucleation of failure due to cross-slip in critically located grains within transgranular band of localized deformation, and this follows the classical Hall-Petch law that predicts a higher failure stress for smaller grains. The second is the resistance to the propagation of a mode I crack, where grain boundaries can potentially pin a crack, and this follows an inverse Hall-Petch law with higher toughness for larger grains. The result of the competition between the two mechanisms gives rise to non-monotonic behavior and reconciles the apparently contradictory experimental observations.