Failure Probabilities and Tough-Brittle Crossover of Heterogeneous Materials with Continuous Disorder

TL;DR

This paper presents an exact recursive method to analyze failure probabilities in heterogeneous 1D systems with continuous disorder, revealing how fracture behavior depends on system size, stress, and boundary conditions, including a crossover from tough to brittle regimes.

Contribution

Introduces a new recursive approach to exactly compute failure probabilities in heterogeneous systems with continuous disorder, accounting for boundary effects and fracture crossovers.

Findings

Failure probabilities follow a modified-Gumbel distribution in brittle regimes.

Fracture behavior exhibits crossovers based on system size and applied stress.

Surface effects significantly influence failure probabilities under various boundary conditions.

Abstract

The failure probabilities or the strength distributions of heterogeneous 1D systems with continuous local strength distribution and local load sharing have been studied using a simple, exact, recursive method. The fracture behavior depends on the local bond-strength distribution, the system size, and the applied stress, and crossovers occur as system size or stress changes. In the brittle region, systems with continuous disorders have a failure probability of the modified-Gumbel form, similar to that for systems with percolation disorder. The modified-Gumbel form is of special significance in weak-stress situations. This new recursive method has also been generalized to calculate exactly the failure probabilities under various boundary conditions, thereby illustrating the important effect of surfaces in the fracture process.