Advanced crack tip field characterization using conjugate work integrals

TL;DR

This paper introduces a novel integral technique to accurately characterize higher order crack tip fields, improving fracture mechanics analysis by capturing more detailed stress intensity factors.

Contribution

It develops a conjugate work integral method to compute higher order Williams coefficients, advancing beyond classical first order stress intensity factors.

Findings

The integral method accurately computes higher order terms.

Comparison shows the method's advantages over fitting techniques.

Results across various specimen types validate the approach.

Abstract

The quantitative characterisation of crack tip loads is fundamental in fracture mechanics. Although the potential influence of higher order terms on crack growth and stability is known, classical studies solely rely on first order stress intensity factors. We calculate higher order Williams coefficients using an integral technique based on conjugate work integrals and study the convergence with increasing crack tip distance. We compare the integral method to the state-of-the-art fitting method and provide results for higher-order terms with several crack lengths, external forces, and sizes for widely used middle tension, single-edge cracked tension, and compact tension specimen under mode-I loading.