Weight function method for interface cracks in anisotropic bimaterials

Abstract

This paper extends the Bueckner-Rice weight function method to interface crack problems in anisotropic bimaterials. This method allows one to use a known crack solution to determine any other solutions for the same geometry. It is shown that, other than a different moduli matrix, the interface weight function relation is formally identical to that in the homogeneous case, and many existing results for homogeneous crack analysis can be directly applied to the interface crack problem. For collinear cracks between two elastic half-spaces satisfying a non-oscillatory condition, a correspondence principle is established so that an anisotropic crack solution could be obtained by simply 'vectorizing' the corresponding isotropic solution.

Stroh formalism in analysis of skew-symmetric and symmetric weight functions for interfacial cracks

“…The problem is generally reduced to a functional equation of Wiener-Hopf type, and its solution gives the symmetric weight function matrix (Antipov, 1999), while the skew-symmetric component is obtained by the construction of the corresponding full-field singular solution of the elasticity boundary value problem discussed in Piccolroaz et al (2009). For interfacial cracks between anisotropic dissimilar elastic media, although weight functions have been derived by Gao (1991Gao ( , 1992 and Ma & Chen (2004), the results on skew-symmetric weight functions are not readily available.…”

Nonuniform Ferro-elastic Domain Switching for the Interfacial Crack

“…To quantify the interaction between transformation strain and interfacial crack, the weight function method is applied to evaluate the toughening effect induced by nonuniform ferro-elastic domain switching. According to the method given by Gao (1992), we calculate the weight function of a mode III semi-infinite interfacial crack between dissimilar isotropic bimaterial, to characterize the influence of switch-induced strain on the crack quantitatively, I I I II I 3/2 3/2 I I I I I I II I II I II I II I II uni uni tran t I I I A A ran sat sat 2 d 2 …”

A crack at the interface of anisotropic bodies. Singularities of the elastic fields and a criterion for fracture when the crack surfaces are in contact

“…The displacement vector u-* = (ur, u~) and the normal stress vector ~y(2)± = (cy~l, ~2) are continuous. It is well known (see [1][2][3][4][5][6][7][8][9], etc) that the power solutions (the displacement fields)…”

“…The displacement vector u-* = (ur, u~) and the normal stress vector ~y(2)± = (cy~l, ~2) are continuous. It is well known (see [1][2][3][4][5][6][7][8][9], etc) that the power solutions (the displacement fields)of the model problem of a composite plane with a semi-infinite cut, which describe the behaviour of the elastic fields close to the tip of an open crack, can have complex exponents A = +-i7 + 1/2, 7 > 0. In this case, the solution of the linear problem in the theory of elasticity is characterized by the overlapping of the crack surfaces for any sign of the stress intensity factor.…”