Symmetric and skew-symmetric weight functions in perturbation models of 2D interfacial cracks

Details Symmetric and skew-symmetric weight functions in perturbation models of 2D interfacial cracks Symmetric and skew-symmetric weight functions in perturbation models of 2D interfacial cracks

2008-12-24

arxiv.org/abs/0812.4529v5

Physics

Mathematical Physics

Added new computations and figures, corrected typos

Scientific paper

In this paper we address the vector problem of a 2D half-plane interfacial crack loaded by a general asymmetric distribution of forces acting on its faces. It is shown that the general integral formula for the evaluation of stress intensity factors, as well as high-order terms, requires both symmetric and skew-symmetric weight function matrices. The symmetric weight function matrix is obtained via the solution of a Wiener-Hopf functional equation, whereas the derivation of the skew-symmetric weight function matrix requires the construction of the corresponding full field singular solution. The weight function matrices are then used in the perturbation analysis of a crack advancing quasi-statically along the interface between two dissimilar media. A general and rigorous asymptotic procedure is developed to compute the perturbations of stress intensity factors as well as high-order terms.

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