Notch fracture toughness of glasses: Rate, age and geometry dependence

TL;DR

This paper develops a theoretical framework to understand how the notch fracture toughness of glasses depends on loading rate, age, and notch geometry, emphasizing the competition of timescales and validating predictions with simulations and experiments.

Contribution

It introduces a unified theory linking fracture toughness to timescale competition and validates it through novel 2D computations and experimental data.

Findings

Fracture toughness scales with the square root of notch radius for low timescale ratio.

Toughness exhibits a logarithmic dependence on the timescale ratio in the high regime.

Experimental data supports the theoretical predictions for bulk metallic glasses.

Abstract

Understanding the fracture toughness (resistance) of glasses is a fundamental problem of prime theoretical and practical importance. Here we theoretically study its dependence on the loading rate, the age (history) of the glass and the notch radius $\rho$. Reduced-dimensionality analysis suggests that the notch fracture toughness results from a competition between the initial, age- and history-dependent, plastic relaxation timescale $\tau^{pl}_0$ and an effective loading timescale $\tau^{ext}(\dot{K}_I,\rho)$, where $\dot{K}_I$ is the tensile stress-intensity-factor rate. The toughness is predicted to scale with $\sqrt{\rho}$ independently of $\xi\!\equiv\!\tau^{ext}\!/\tau^{pl}_0$ for $\xi\!\ll\! 1$, to scale as $T\sqrt{\rho}\,\log(\xi)$ for $\xi\!\gg\!1$ (related to thermal activation, where $T$ is the temperature) and to feature a non-monotonic behavior in the crossover region $\xi\!\sim\!{\cal O}(1)$ (related to plastic yielding dynamics). These predictions are verified using novel 2D computations, providing a unified picture of the notch fracture toughness of glasses. The theory highlights the importance of timescales competition and far from steady-state elasto-viscoplastic dynamics for understanding the toughness, and shows that the latter varies quite significantly with the glass age (history) and applied loading rate. Experimental support for bulk metallic glasses is presented.