Modeling of a curvilinear planar crack with a curvature-dependent surface tension

TL;DR

This paper introduces a curvature-dependent surface tension model for curvilinear cracks that removes classical crack-tip singularities and aligns with empirical crack opening observations.

Contribution

It extends fracture modeling by incorporating curvature-dependent surface tension, eliminating stress singularities at crack tips for curvilinear cracks.

Findings

Eliminates crack-tip stress singularities of order 1/2

Results in sharp crack opening consistent with experiments

Some weaker logarithmic singularities remain for general curvilinear cracks

Abstract

IAn approach to modeling fracture incorporating interfacial mechanics is applied to the example of a curvilinear plane strain crack. The classical Neumann boundary condition is augmented with curvature-dependent surface tension. It is shown that the considered model eliminates the integrable crack-tip stress and strain singularities of order 1/2 present in the classical linear fracture mechanics solutions, and also leads to the sharp crack opening that is consistent with empirical observations. Unlike for the case of a straight crack, for a general curvilinear crack some components of the stresses and the derivatives of the displacements may still possess weaker singularities of a logarithmic type. Generalizations of the present study that lead to complete removal of all crack-tip singularities, including logarithmic, are the subject of a future paper.