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

A. Y. Zemlyanova; J. R. Walton

doi:10.1137/110860100

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

A. Y. Zemlyanova, J. R. Walton

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24 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 language	English (US)
Pages (from-to)	1474-1492
Number of pages	19
Journal	SIAM Journal on Applied Mathematics
Volume	72
Issue number	5
DOIs	https://doi.org/10.1137/110860100
State	Published - Jan 2012
Externally published	Yes

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10.1137/110860100

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title = "Modeling of a Curvilinear Planar Crack with a Curvature-Dependent Surface Tension",

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. {\textcopyright} 2012 Society for Industrial and Applied Mathematics.",

author = "Zemlyanova, {A. Y.} and Walton, {J. R.}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: Received by the editors December 22, 2011; accepted for publication (in revised form) June 25, 2012; published electronically September 27, 2012. This work was supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1137/110860100",

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AU - Zemlyanova, A. Y.

AU - Walton, J. R.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: Received by the editors December 22, 2011; accepted for publication (in revised form) June 25, 2012; published electronically September 27, 2012. This work was supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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N2 - 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.

AB - 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.

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

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