Fracture Toughness of Crystalline Solids

TL;DR

This paper develops a first-principles thermodynamic dislocation theory to predict the fracture toughness of crystalline solids, successfully matching experimental data across various conditions.

Contribution

It introduces a novel theoretical framework based on thermodynamics and dislocation dynamics to quantitatively predict fracture toughness in crystals.

Findings

Theory matches experimental toughness data for tungsten crystals.

Predicts both brittle and ductile fracture behaviors.

Applicable across wide temperature and loading rate ranges.

Abstract

This paper describes an attempt to construct a first-principles theory of the fracture toughness of crystalline solids. It is based on the thermodynamic dislocation theory (TDT), which starts with the assertion that dislocations in solids must obey the second law of thermodynamics. A second starting assumption is that fracture is initiated when the tip of a notch is driven to undergo a sharpening instability. The results of this analysis are developed in comparison with measurements by Gumbsch and colleagues of the notch toughness of both predeformed and non-predeformed tungsten crystals. The theory includes a mathematical conjecture regarding tip dynamics at small dislocation densities. Nevertheless, its predictions agree quantitatively with the experimental data, including both brittle and ductile fracture, over a wide range of temperatures, loading rates, and initial conditions.