The focus of the paper is on the study of the dynamic steady-state propagation of interfacial cracks in anisotropic bimaterials under general, non-symmetric loading conditions. Symmetric and skew-symmetric weight functions, defined as singular non-trivial solutions of a homogeneous traction-free crack problem, have been recently derived for a quasi-static semi-infinite crack at the interface between two dissimilar anisotropic materials. In this paper, the expressions for the weight functions are generalised to the case of a dynamic steady-state crack between two anisotropic media. A functional matrix equation, through which it is possible to evaluate stress intensity factors and the energy release rate at the crack tip, is obtained. A general method for calculating asymptotic coefficients of the displacement and traction fields, without any restriction regarding the loading applied on the crack faces, is developed. The proposed approach is applied for computing stress intensity factors and higher order asymptotic terms corresponding to two different examples of loading configurations acting on the crack faces in an orthotropic bimaterial. arXiv:1305.0486v4 [physics.class-ph]
The focus of this paper is on the analysis of a semi-infinite crack lying along a perfect interface in a piezoelectric bimaterial with arbitrary loading on the crack faces. Making use of the extended Stroh formalism for piezoelectric materials combined with Riemann-Hilbert formulation, general expressions are obtained for both symmetric and skew-symmetric weight functions associate with plane crack problems at the interface between dissimilar anisotropic piezoelectric media. The effect of the coupled electrical fields is incorporated in the derived original expressions for the weight function matrices. These matrices are used together with Betti's reciprocity identity in order to obtain singular integral equations relating the extended displacement and traction fields to the loading acting on the crack faces. In order to study the variation of the piezoelectric effect, two different poling directions are considered. Examples are shown for both poling directions with a number of mechanical and electrical loadings applied to the crack faces.
We study a crack lying along an imperfect interface in an anisotropic bimaterial. A method is devised where known weight functions for the perfect interface problem are used to obtain singular integral equations relating the tractions and displacements for both the in-plane and out-of-plane fields. The problem can be considered as modelling bimaterial ceramics which are joined with a thin soft adhesive substance. The integral equations for the out-of-plane problem are solved numerically for orthotropic bimaterials with differing orientations of anisotropy and for different extents of interfacial imperfection. These results are then compared with finite element computations.authorsversionPeer reviewe
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