Modeling Growth Paths of Interacting Crack Pairs in Elastic Media

TL;DR

This paper develops an analytical framework to predict the complex growth paths of interacting crack pairs in elastic media, using boundary integral and perturbation methods, with three simplified models validated against exact and experimental results.

Contribution

It introduces the first analytical models for curved En-Passant crack paths and proposes three hierarchical methods, including an asymptotic matching approach, for crack path prediction.

Findings

All three methods agree within their applicable limits.

The asymptotic matching method effectively predicts crack paths.

Models are validated against exact solutions and experimental data.

Abstract

The problem of predicting the growth of a system of cracks, each crack influencing the growth of the others, arises in multiple fields. We develop an analytical framework toward this aim, which we apply to the `En-Passant' family of crack growth problems, in which a pair of initially parallel, offset cracks propagate nontrivially toward each other under far-field opening stress. We utilize boundary integral and perturbation methods of linear elasticity, Linear Elastic Fracture Mechanics, and common crack opening criteria to calculate the first analytical model for curved En-Passant crack paths. The integral system is reduced under a hierarchy of approximations, producing three methods of increasing simplicity for computing crack paths. The last such method is a major highlight of this work, using an asymptotic matching argument to predict crack paths based on superposition of simple, single-crack fields. Within the corresponding limits of the three methods, all three are shown to agree with each other. We provide comparisons to exact results and existing experimental data to verify certain approximation steps.