Stress Intensity Factor of Mode III Cracks in Thin Sheets

TL;DR

This paper provides exact analytical expressions for the stress intensity factor of Mode III cracks in thin elastic sheets, enhancing the limited set of known solutions in Linear Elastic Fracture Mechanics.

Contribution

It introduces new exact solutions for the stress intensity factor in Mode III crack problems in thin plates, which were previously unavailable.

Findings

Exact analytic expressions derived for the stress intensity factor

Universal form of the stress field at crack tips in thin sheets

Dependence of the stress intensity factor on crack length and boundary conditions

Abstract

The stress field at the tip of a crack of a thin plate of elastic material that is broken due to a mode III shear tearing has a universal form with a non-universal amplitude, known as the stress intensity factor, which depends on the crack length and the boundary conditions. We present in this paper exact analytic results for this stress intensity factor, thus enriching the small number of exact results that can be obtained within Linear Elastic Fracture Mechanics (LEFM).