Interfacial thermal stress analysis of an elliptic inclusion with a compliant interphase layer in plane elasticity

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

doi:10.1016/s0020-7683(01)00033-6

Cited by 26 publications

(9 citation statements)

References 29 publications

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“…Considering only the first-order effect of a linear spring-layer interface, Qu [6] first derived the expression of a modified Eshelby tensor for an ellipsoidal inclusion and then used this expression in some classical micromechanical schemes to estimate the effective moduli of composites under consideration. A semi-analytical solution was presented by Shen et al [39] for an elliptical inclusion with a spring-layer interface. In the works by Hashin [5] and Lipton [40], the classical variational principles of linear elasticity were extended to composites with linear stringlayer interfaces, and the lower and upper bounds on the effective moduli of these composites were obtained.…”

Section: Introductionmentioning

confidence: 99%

Three‐dimensional numerical modelling by XFEM of spring‐layer imperfect curved interfaces with applications to linearly elastic composite materials

Zhu

Yvonnet

et al. 2011

Numerical Meth Engineering

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SUMMARYThe spring-layer interface model is widely used in describing some imperfect interfaces frequently involved in materials and structures. Typically, it is appropriate for modelling a thin soft interphase layer between two relatively stiff bulk media. According to the spring-layer interface model, the displacement vector suffers a jump across an interface whereas the traction vector is continuous across the same interface and is, in the linear case, proportional to the displacement vector jump. In the present work, an efficient three-dimensional numerical approach based on the extended finite element method is first proposed to model linear spring-layer curved imperfect interfaces and then applied to predict the effective elastic moduli of composites in which such imperfect interfaces intervene. In particular, a rigorous derivation of the linear spring-layer interface model is provided to clarify its domain of validity. The accuracy and convergence rate of the elaborated numerical approach are assessed via benchmark tests for which exact analytical solutions are available. The computated effective elastic moduli of composites are compared with the relevant analytical lower and upper bounds.

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Section: Introductionmentioning

confidence: 99%

Three‐dimensional numerical modelling by XFEM of spring‐layer imperfect curved interfaces with applications to linearly elastic composite materials

Zhu

Yvonnet

et al. 2011

Numerical Meth Engineering

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“…The computations performed in Shen et al (2000c) show no significant difference between the results for the cases h 1 = h 2 and h 1 = 3h 2 (as discussed in Hashin, 1991b). …”

Section: Internal Stress Distribution Along the Interfacementioning

confidence: 82%

“…we finally obtain the following form of the interface condition (2.9) (seeShen et al, 2000c for details):…”

mentioning

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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“…The physical reasoning for this seemingly unacceptable overlapping phenomenon has been explained in detail in [33]. Figure 5 shows that the shear stress attains its maximum value when x ≈ 0.6y 0 to y 0 .…”

Section: Discussionmentioning

confidence: 96%

“…the same degree of imperfection is realized in both the normal and tangential directions). This imperfect interface description has been shown (numerically) to capture the major qualitative features of the general imperfect interface model (see [33] for details). Hence, it is found from equation (20) that λ 1 = ρλ 2 for ρ ≥ 1 (or λ 2 = ρλ 1 for ρ ≤ 1) when α = β yields the result that φ 2 (z) = 0 (see equation (29)).…”

Section: Complex Potential Solutionmentioning

confidence: 96%

Elastic fields in two imperfectly bonded half-planes with a thermal inclusion of arbitrary shape

Wang

Sudak

2006

Z. angew. Math. Phys.

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A general method is presented for the rigorous solution of Eshelby's problem concerned with an arbitrary shaped inclusion embedded within one of two dissimilar elastic halfplanes in plane elasticity. The bonding between the half-planes is considered to be imperfect with the assumption that the interface imperfections are uniform.Using analytic continuation, the basic boundary value problem is reduced to a set of two coupled nonhomogeneous first-order differential equations for two analytic functions defined in the lower half-plane which is free of the thermal inclusion. Using diagonalization, the two coupled differential equations are decoupled into two independent nonhomogeneous first-order differential equations for two newly defined analytic functions. The resulting closed-form solutions are given in terms of the constant imperfect interface parameters and the auxiliary function constructed from the conformal mapping which maps the exterior of the inclusion onto the exterior of the unit circle.The method is illustrated using several examples of an imperfect interface. In particular, when the same degree of imperfection is realized in both the normal and tangential directions between the two half-planes, a thermal inclusion of arbitrary shape in the upper half-plane does not cause any mean stress to develop in the lower half-plane. Alternatively, when the imperfect interface parameters are not equal, then a nonzero mean stress will be induced in the lower halfplane by the thermal inclusion of arbitrary shape in the upper half-plane. Detailed results are presented for the mean stress and the interfacial normal and shear stresses caused by a circular and elliptical thermal inclusion, respectively. Results from these calculations reveal that the imperfect bonding condition has a significant effect on the internal stress field induced within the inclusion as well as on the interfacial normal and shear stresses existing between the two half-planes especially when the inclusion is near the imperfect interface. (2000). 30B40, 74B05. Mathematics Subject Classification

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Interfacial thermal stress analysis of an elliptic inclusion with a compliant interphase layer in plane elasticity

Cited by 26 publications

References 29 publications

Three‐dimensional numerical modelling by XFEM of spring‐layer imperfect curved interfaces with applications to linearly elastic composite materials

Three‐dimensional numerical modelling by XFEM of spring‐layer imperfect curved interfaces with applications to linearly elastic composite materials

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

Elastic fields in two imperfectly bonded half-planes with a thermal inclusion of arbitrary shape

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