Chemical fracture and distribution of extreme values

TL;DR

This paper develops an analytical theory for the probability of chemical fracture in solids, based on extreme value statistics, and confirms it through numerical experiments, highlighting differences from traditional mechanical failure models.

Contribution

It introduces a new analytical model for chemical fracture probability derived from extreme value theory, validated by numerical simulations.

Findings

The theory aligns with numerical experiments on a 2D model.

The analytic law differs from the Weibull law used for mechanical failures.

A three-parameter Weibull fit effectively describes chemical fracture data.

Abstract

When a corrosive solution reaches the limits of a solid sample, a chemical fracture occurs. An analytical theory for the probability of this chemical fracture is proposed and confirmed by extensive numerical experiments on a two dimensional model. This theory follows from the general probability theory of extreme events given by Gumbel. The analytic law differs from the Weibull law commonly used to describe mechanical failures for brittle materials. However a three parameters fit with the Weibull law gives good results, confirming the empirical value of this kind of analysis.