An elliptic inclusion with imperfect interface in anti-plane shear

Shen, H.; Schiavone, Peter; Ru, C. Q.; Mioduchowski, A.

doi:10.1016/s0020-7683(99)00174-2

Cited by 45 publications

(31 citation statements)

References 11 publications

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“…This fact can be clearly observed from the additional terms on the right-hand side of equation (3.11) which are due to imposed eigenstrains. In fact, our analysis also suggests that the correspondence principle in Shen et al [21] is no longer valid for a non-elliptical inhomogeneity with a homogeneous spring-type imperfect interface. Using the Peach-Koehler formula [1], the image force acting on the screw dislocation in the presence of remote uniform loading and imposed eigenstrains can be simply derived from equation (3.10) as…”

Section: (B) Complex Variable Formulationmentioning

confidence: 63%

“…This fact implies that the induced elastic fields both in the inhomogeneity and in the surrounding matrix are size-dependent. The above analysis also indicates that when discussing an inhomogeneity with interface stresses, there is no correspondence principle for the internal stress field between remote loading and imposed eigenstrains on the inhomogeneity unlike the case of an elliptical inhomogeneity with springtype imperfect interface [21]. This fact can be clearly observed from the additional terms on the right-hand side of equation (3.11) which are due to imposed eigenstrains.…”

Section: (B) Complex Variable Formulationmentioning

confidence: 93%

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Interaction of a screw dislocation with a nano-sized, arbitrarily shaped inhomogeneity with interface stresses under anti-plane deformations

Wang

Schiavone

2014

Proc. R. Soc. A.

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We propose an elegant and concise general method for the solution of a problem involving the interaction of a screw dislocation and a nano-sized, arbitrarily shaped, elastic inhomogeneity in which the contribution of interface/surface elasticity is incorporated using a version of the Gurtin-Murdoch model. The analytic function inside the arbitrarily shaped inhomogeneity is represented in the form of a Faber series. The real periodic function arising from the contribution of the surface mechanics is then expanded as a Fourier series. The resulting system of linear algebraic equations is solved through the use of simple matrix algebra. When the elastic inhomogeneity represents a hole, our solution method simplifies considerably. Furthermore, we undertake an analytical investigation of the challenging problem of a screw dislocation interacting with two closely spaced nano-sized holes of arbitrary shape in the presence of surface stresses. Our solutions quite clearly demonstrate that the induced elastic fields and image force acting on the dislocation are indeed size-dependent.

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Section: (B) Complex Variable Formulationmentioning

confidence: 63%

Section: (B) Complex Variable Formulationmentioning

confidence: 93%

Interaction of a screw dislocation with a nano-sized, arbitrarily shaped inhomogeneity with interface stresses under anti-plane deformations

Wang

Schiavone

2014

Proc. R. Soc. A.

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“…Next, as in Shen et al (2000a), we substitute the following expression for 1 + b * sin 2 θ into (2.26): …”

Section: H Shen Et Al Zampmentioning

confidence: 99%

Effects of a compliant interphase layer on internal thermal stresses within an elliptic inhomogeneity in an elastic medium

Shen

Schiavone

et al. 2001

Z. angew. Math. Phys.

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This paper studies the effect of a compliant interphase layer on internal thermal stresses induced inside an elliptic inhomogeneity embedded within an infinite matrix in plane elasticity. The compliant interphase layer between the inhomogeneity and the surrounding matrix is modeled as a spring layer with vanishing thickness. The behavior of this interphase layer is based on the assumption that tractions are continuous but displacements are discontinuous across the layer. Complex variable techniques are used to obtain infinite series representations of the internal thermal stresses (specifically, the mean stress and the von Mises equivalent stress) which, when evaluated numerically, demonstrate how the internal thermal stresses vary with the aspect ratio of the inhomogeneity and the parameter h describing the interphase layer. These results are used to evaluate the effects of the interphase layer and the aspect ratio of the inhomogeneity on internal failure caused by void formation and plastic yielding within the inhomogeneity. Remarkably, the mean stress and von Mises equivalent stress are both found to be non-monotonic functions of the parameter h. Consequently, we identify a specific value (h * ) of h which corresponds to the maximum peak (mean or von Mises) stress inside the inhomogeneity. We also obtain another value (h R ) of h below which the peak (mean or von Mises) stress within the inhomogeneity is smaller than that corresponding to the case of a perfect interface (that is, in the absence of the compliant interphase layer). These special values h * and h R of the parameter h depend on the aspect ratio of the elliptic inhomogeneity. In particular, when the interphase layer is designed so that the value of h is close to unity, the internal peak thermal stress is reduced to a fraction of its original value obtained in the absence of the interphase layer. Mathematics Subject Classification (2000). 73K20, 73V35, 73C02, 30B40.

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“…When all the three interface parameters are zero, the imperfect interface will be fully debonding. By utilizing the above stated spring-like model, a considerable amount of investigations involving the calculations of physical quantities [16][17] and the interactions of an inclusion or dislocations with the imperfect interface [18][19][20][21] were made. Here, our interest is in the interaction of a crack and the imperfect interface.…”

Section: Introductionmentioning

confidence: 99%

Fracture analysis of mode-II crack perpendicular to imperfect bimaterial interface

Zhong

Zhang

2012

Appl. Math. Mech.-Engl. Ed.

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The problem of a mode-II crack close to and perpendicular to an imperfect interface of two bonded dissimilar materials is investigated. The imperfect interface is modelled by a linear spring with the vanishing thickness. The Fourier transform is used to solve the boundary-value problem and to derive a singular integral equation with the Cauchy kernel. The stress intensity factors near the left and right crack tips are evaluated by numerically solving the resulting equation. Several special cases of the mode-II crack problem with an imperfect interface are studied in detail. The effects of the interfacial imperfection on the stress intensity factors for a bimaterial system of aluminum and steel are shown graphically. The obtained observation reveals that the stress intensity factors are dependent on the interface parameters and vary between those with a fully debonded interface and those with a perfect interface.

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An elliptic inclusion with imperfect interface in anti-plane shear

Cited by 45 publications

References 11 publications

Interaction of a screw dislocation with a nano-sized, arbitrarily shaped inhomogeneity with interface stresses under anti-plane deformations

Interaction of a screw dislocation with a nano-sized, arbitrarily shaped inhomogeneity with interface stresses under anti-plane deformations

Effects of a compliant interphase layer on internal thermal stresses within an elliptic inhomogeneity in an elastic medium

Fracture analysis of mode-II crack perpendicular to imperfect bimaterial interface

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