Modeling of a Curvilinear Planar Crack with a Curvature-Dependent Surface Tension

A. Y. Zemlyanova, J. R. Walton

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

An 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. © 2012 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)1474-1492
Number of pages19
JournalSIAM Journal on Applied Mathematics
Volume72
Issue number5
DOIs
StatePublished - Jan 2012
Externally publishedYes

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