From microstructural features to effective toughness in disordered brittle solids

TL;DR

This paper theoretically investigates how microstructural parameters influence the macroscopic toughness of disordered brittle solids, revealing two regimes of crack propagation and emphasizing the importance of micro-to-macro scale transition.

Contribution

It introduces a theoretical framework linking microstructural toughness parameters to macroscopic toughness, distinguishing between collective and individual pinning regimes.

Findings

In the collective pinning regime, toughness depends on average, standard deviation, and correlation lengths.

In the individual pinning regime, the full toughness distribution is necessary for prediction.

The study highlights a complex filtering process from microscale to macroscale in disordered systems.

Abstract

The relevant parameters at the microstructure scale that govern the macroscopic toughness of disordered brittle materials are investigated theoretically. We focus on planar crack propagation and describe the front evolution as the propagation of a long-range elastic line within a plane with random distribution of toughness. Our study reveals two regimes: in the collective pinning regime, the macroscopic toughness can be expressed as a function of a few parameters only, namely the average and the standard deviation of the local toughness distribution and the correlation lengths of the heterogeneous toughness field; in the individual pinning regime, the passage from micro to macroscale is more subtle and the full distribution of local toughness is required to be predictive. Beyond the failure of brittle solids, our findings illustrate the complex filtering process of microscale quantities towards the larger scales into play in a broad range of systems governed by the propagation of an elastic interface in a disordered medium.