On stress singularities and interfaces in linear elastic fracture mechanics

Atkinson, C.

doi:10.1007/bf00034324

Cited by 143 publications

(68 citation statements)

References 7 publications

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“…The oscillatory behaviour can be avoided either by imposing mathematical restrictions at the crack tips (Atkinson 1977;Comninou 1977) or by considering some special classes of nonlinear materials (see Knowles & Sternberg 1983). The aforementioned results have been the subject of intense discussion in the literature.…”

Section: (A) Functions F (T) G(t) and B(t)mentioning

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: (A) Functions F (T) G(t) and B(t)mentioning

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 values for the cubic materials are the average of Solutions to a number of different interface crack problems exist in the literature. See Atkinson (1979) and Park and Earmme (1986) for recent discussions. The complex intensity factors for the two basic problems (Erdogan, 1965;Rice and Sih, 1965) shown in Fig.…”

Section: Applications and Implicationsmentioning

confidence: 99%

Crack Paralleling an Interface Between Dissimilar Materials

Hutchinson

Mear

Rice

1987

Journal of Applied Mechanics

509

171

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“…The first is the complex power singularty at the tip of an interface crack giving oscilations in stresses and crack opening displacements very near the crack tip (e.g., Muskhelishvili (1953a), Erdogan (1965), England (1965), Rice and Sih (1965)). A crack tip contact model has been proposed t o eliminate these oscillations within the context of the linear elastic theory, Comninou (1977), Atkinson (1977).…”

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confidence: 99%

The Crack Problem in Bonded Nonhomogeneous Materials

Erdoğan

Kaya

Joseph

1991

Journal of Applied Mechanics

124

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In this paper the plane elasticity problem for two bonded half-planes containing a crack perpendicular to the interface is considered. The primary objective of the paper is to study the effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors. The two materials are, thus, assumed to have the shear moduli μ0 and μ0exp(βx), x = 0 being the diffusion plane. Of particular interest is the examination of the nature of stress singularity near a crack tip terminating at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r−α, 0<α<1, in this problem the stresses have a standard square root singularity regardless of the location of the crack tip. The nonhomogeneity constant β has, however, considerable influence on the stress intensity factors.

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On stress singularities and interfaces in linear elastic fracture mechanics

Cited by 143 publications

References 7 publications

Effect of surface elasticity on an interface crack in plane deformations

Effect of surface elasticity on an interface crack in plane deformations

Crack Paralleling an Interface Between Dissimilar Materials

The Crack Problem in Bonded Nonhomogeneous Materials

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