Analysis of Plane-Strain Crack Problems (Mode-I &amp; Mode-II) in the Presence of Surface Elasticity

Kim, C. I.; Schiavone, Peter; Ru, C. Q.

doi:10.1007/978-94-007-1884-5_26

Cited by 4 publications

(10 citation statements)

References 29 publications

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“…In this paper, we refine the classical LEFM model to incorporate surface mechanics using a version of the surface model proposed by Gurtin & Murdoch (1975) (see Ru 2010). The latter has been used extensively in a number of studies including several problems dealing with fracture mechanics (see Wang et al 2008;Kim et al 2010;Ru 2010 and references therein). The model developed in this paper is sufficiently general to incorporate the most general cases, where the upper and lower surfaces of the crack as well as the separate materials comprising the bulk have distinct material properties (see Sharma & Ganti 2004).…”

Section: Introductionmentioning

confidence: 99%

Effect of surface elasticity on an interface crack in plane deformations

Kim

Schiavone

2011

Proc. R. Soc. A.

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We consider the effect of surface elasticity on an interface crack between two dissimilar linearly elastic isotropic homogeneous materials undergoing plane deformations. The bimaterial is subjected to either remote tension (mode-I) or in-plane shear (mode-II) with the faces of the (interface) crack assumed to be traction-free. We incorporate surface mechanics into the model of deformation by employing a version of the continuum-based surface/interface theory of Gurtin & Murdoch. Using complex variable methods, we obtain a semi-analytical solution valid throughout the entire domain of interest (including at the crack tips) by reducing the problem to a system of coupled Cauchy singular integrodifferential equations, which is solved numerically using Chebychev polynomials and a collocation method. It is shown that, among other interesting phenomena, our model predicts finite stress at the (sharp) crack tips and the corresponding stress field to be size-dependent. In particular, we note that, in contrast to the results from linear elastic fracture mechanics, when the bi-material is subjected to uniform far-field stresses (either tension or in-plane shear), the incorporation of surface effects effectively eliminates the oscillatory behaviour of the solution so that the resulting stress fields no longer suffer from oscillatory singularities at the crack tips.

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Section: Introductionmentioning

confidence: 99%

Effect of surface elasticity on an interface crack in plane deformations

Kim

Schiavone

2011

Proc. R. Soc. A.

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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%

“…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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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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“…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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Analysis of Plane-Strain Crack Problems (Mode-I & Mode-II) in the Presence of Surface Elasticity

Cited by 4 publications

References 29 publications

Effect of surface elasticity on an interface crack in plane deformations

Effect of surface elasticity on an interface crack in plane deformations

A mode-III crack with variable surface effects

A crack with surface elasticity in finite plane elastostatics

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