A mode III arc-shaped crack with surface elasticity

Wang, Xu

doi:10.1007/s00033-014-0482-x

Cited by 33 publications

(9 citation statements)

References 15 publications

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“…The high surface area to volume ratio present at the nanoscale dictates that any continuum-based model of deformation should incorporate the separate contribution of surface mechanics (Sharma and Ganti, 2004). Recently, the continuum-based surface/interface model proposed by Gurtin, Murdoch and co-workers (Gurtin and Murdoch, 1975; Gurtin et al, 1998) has been incorporated in the analysis of several typical crack problems (see for example, Kim et al, 2010Kim et al, , 2011aAntipov and Schiavone, 2011;Wang, 2015;Wang andSchiavone, 2015, 2016). It was first proved by Walton (2012) and later corroborated by Kim et al (2013) that the contribution of surface elasticity (based on the Gurtin-Murdoch model) to LEFM would, at best, reduce the classical strong square root singularity to a weaker logarithmic singularity.…”

Section: Introductionmentioning

confidence: 99%

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A mode-III crack with variable surface effects

Wang¹,

Schiavone²

2016

jtam

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We study the contribution of variable surface effects to the antiplane deformation of a linearly elastic material with a mode-III crack. The surface elasticity is incorporated using a modified version of the continuum based surface/interface model of Gurtin and Murdoch. In our discussion, the surface moduli are not constant but vary along the crack surfaces. Using Green's function method, the problem is reduced to a single first-order Cauchy singular integro-differential equation, which is solved numerically using Chebyshev polynomials and a collocation method. Our results indicate that the gradient of the surface shear modulus exerts a significant influence on the crack opening displacement and on the singular stress field at the crack tips.

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Section: Introductionmentioning

confidence: 99%

“…In recent studies, the incorporation of surface elasticity into LEFM models has been confined to the simple case in which the surface moduli are constant along the crack surfaces (Kim et al, 2010(Kim et al, , 2011aAntipov and Schiavone, 2011;Wang, 2015;Wang andSchiavone, 2015, 2016).…”

Section: Introductionmentioning

confidence: 99%

A mode-III crack with variable surface effects

Wang¹,

Schiavone²

2016

jtam

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“…[14][15][16]. The Gurtin-Murdoch surface elasticity model has been adopted in the analysis of a crack in isotropic homogenous materials and bimaterials under uniform or nonuni form remote antiplane and in-plane stresses [17][18][19][20][21][22][23],…”

Section: Introductionmentioning

confidence: 99%

Interaction Between an Edge Dislocation and a Crack With Surface Elasticity

Wang

Schiavone

2015

Journal of Applied Mechanics

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We undertake an analytical study of the interaction of an edge dislocation with a finite crack whose faces are assumed to have separate surface elasticity. The surface elasticity on the faces of the crack is described by a version of the continuum-based sur face/interface theory ofGurtin and Murdoch. By using the Green's function method, we obtain a complete exact solution by reducing the problem to three Cauchy singular integrodifferential equations of the first-order, which are solved by means of Chebyshev polynomials and a collocation method. The correctness of the solution is rigorously veri fied by comparison with existing analytical solutions. Our analysis shows that the stresses and the image force acting on the edge dislocation are size-dependent and that the stresses exhibit both the logarithmic and square root singularities at the crack tips when the surface tension is neglected.

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“…Most recently, various authors (see, for example, [Kim et al 2010b;2010a;2011a;2011b;2011c;Antipov and Schiavone 2011;Wang 2015]) have incorporated the continuum-based surface/interface theory of Gurtin and Murdoch [1975;1978;Gurtin et al 1998] into the fracture analysis of linearly elastic solids. It was shown that the incorporation of the Gurtin-Murdoch surface model can suppress the classical strong square-root stress/strain singularity at the crack tip predicted in linear elastic fracture mechanics (LEFM) to the weaker logarithmic singularity [Walton 2012;Kim et al 2013].…”

Section: Introductionmentioning

confidence: 99%

A crack with surface elasticity in finite plane elastostatics

Wang

Schiavone

2015

Math. Mech. Compl. Sys.

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We consider the effect of surface elasticity on a finite crack in a particular class of compressible hyperelastic materials of harmonic type subjected to uniform remote Piola stresses. The surface mechanics is incorporated into the model of finite deformation by employing a version of the continuum-based surface/interface theory of Gurtin and Murdoch. A complete solution valid throughout the entire domain of interest is obtained by reducing the problem to two series of coupled Cauchy singular integrodifferential equations that are solved numerically using a collocation method. Our model predicts that, in general, the size-dependent Piola stresses exhibit a weak logarithmic singularity at the crack tips. For a crack in a special class of materials subjected to mode II loading, the stresses are bounded whereas the deformation gradients exhibit a logarithmic-type singularity at the crack tips.

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A mode III arc-shaped crack with surface elasticity

Cited by 33 publications

References 15 publications

A mode-III crack with variable surface effects

A mode-III crack with variable surface effects

Interaction Between an Edge Dislocation and a Crack With Surface Elasticity

A crack with surface elasticity in finite plane elastostatics

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