Computing stress intensity factors for curvilinear cracks

TL;DR

This paper develops a family of auxiliary and material variation fields for the interaction integral to accurately compute stress intensity factors for curvilinear cracks, achieving optimal convergence rates.

Contribution

It introduces a new formulation of interaction integral fields tailored for curvilinear cracks, enhancing convergence and ease of implementation.

Findings

Stress intensity factors converge at twice the rate of stress fields.

Method is robust to domain size and accounts for crack face tractions and body forces.

Numerical examples demonstrate the effectiveness and convergence of the proposed approach.

Abstract

The use of the interaction integral to compute stress intensity factors around a crack tip requires selecting an auxiliary field and a material variation field. We formulate a family of these fields accounting for the curvilinear nature of cracks that, in conjunction with a discrete formulation of the interaction integral, yield optimally convergent stress intensity factors. We formulate three pairs of auxiliary and material variation fields chosen to yield a simple expression of the interaction integral for different classes of problems. The formulation accounts for crack face tractions and body forces. Distinct features of the fields are their ease of construction and implementation. The resulting stress intensity factors are observed converging at a rate that doubles the one of the stress field. We provide a sketch of the theoretical justification for the observed convergence rates, and discuss issues such as quadratures and domain approximations needed to attain such convergent behavior. Through two representative examples, a circular arc crack and a loaded power function crack, we illustrate the convergence rates of the computed stress intensity factors. The numerical results also show the independence of the method on the size of the domain of integration.