Statistical mechanical model for crack growth

TL;DR

This paper develops an analytical approximation for thermally activated crack growth rates using statistical thermodynamics, validated against simulations and experiments, aiding fracture modeling.

Contribution

It introduces an asymptotic theory to derive analytic crack growth rate relations from fundamental principles, improving understanding of fracture mechanics.

Findings

Analytic crack growth relations are derived and validated.

The approach aligns well with Monte Carlo simulations and experimental data.

Encourages future modeling of complex fracture mechanisms.

Abstract

Analytic relations that describe crack growth are vital for modeling experiments and building a theoretical understanding of fracture. Upon constructing an idealized model system for the crack and applying the principles of statistical thermodynamics, it is possible to formulate the rate of thermally activated crack growth as a function of load, but the result is analytically intractable. Here, an asymptotically correct theory is used to obtain analytic approximations of the crack growth rate from the fundamental theoretical formulation. These crack growth rate relations are compared to those that exist in the literature and are validated with respect to Monte Carlo calculations and experiments. The success of this approach is encouraging for future modeling endeavors that might consider more complicated fracture mechanisms, such as inhomogeneity or a reactive environment.