Material-independent crack arrest statistics: Application to indentation experiments

TL;DR

This study demonstrates that crack arrest statistics in brittle materials can be described by a universal distribution derived from depinning models, enabling scale-invariant predictions of crack behavior across different materials.

Contribution

The paper introduces a universal crack arrest distribution model based on depinning phenomena, applicable across multiple brittle materials and scales.

Findings

Crack length statistics are material-independent.

Crack arrest follows a universal distribution characterized by two parameters.

Knowledge at one scale predicts behavior at all scales.

Abstract

An extensive experimental study of indentation and crack arrest statistics is presented for four different brittle materials (alumina, silicon carbide, silicon nitride, glass). Evidence is given that the crack length statistics can be described by a universal (i.e. material independent) distribution. The latter directly derives from results obtained when modeling crack propagation as a depinning phenomenon. Crack arrest (or effective toughness) statistics appears to be fully characterized by two parameters, namely, an asymptotic crack length (or macroscopic toughness) value and a power law size dependent width. The experimental knowledge of the crack arrest statistics at one given scale thus gives access to its knowledge at all scales.