Analysis of Branched Interface Cracks

Abstract

A solution is presented for the problem of a finite length crack branching off the interface between two bonded dissimilar isotropic materials. Results are presented in terms of the ratio of the energy release rate of a branched interface crack to the energy release rate of a straight interface crack with the same total length. It is found that this ratio reaches a maximum when the interface crack branches into the softer material. Longer branches tend to have smaller maximum energy release rate ratio angles indicating that all else being equal, a branch crack will tend to turn back parallel to the interface as it grows.

Interfacial crack kinking subjected to contact effects

“…Also, the complex z is x + i y, the prime takes derivatives in z, the overbar denotes complex conjugation, κ = 3 − 4ν for plane strain, κ = (3 − ν)/(1 + ν) for plane stress, and ν is Poisson's ratio. Mukai et al [1990] introduced two additional jump potentials S and D to solve the branching of interfacial crack of finite length within an infinite large body. Similarly to Mukai's method, Suo [1989] obtained the Muskhelishvili potentials for an infinite large body with a semiinfinite interfacial crack from…”

“…When the main crack is introduced, the stresses due to the dislocation near an interface will be removed from the crack faces by the two potentials C and C . Many investigators [Suo 1989;Mukai et al 1990;Rice et al 1990] have presented the solutions for crack problems. For a semiinfinite crack on an interface, the interface boundary conditions at y = 0 are…”

“…and P(z) is equal to zero [Suo 1989;Mukai et al 1990]. After D is obtained, the jump potentials can be inverted back to standard potentials using Equations (A.6)-(A.9).…”

A Crack Kinked at the Interface of Bonded Anisotropic Elastic Media under Longitudinal Shear Stresses

“…Later on, the cases of semi-infinite crack [7,8] and finite length crack [9] have also been studied by using the Muskhelishvili's complex potential method. As another work along the same line, a longitudinal shear problem has been analyzed in [10] by employing the Wiener-Hopf technique, which pays special attention to the kinked part of finite length approaching zero.…”

“…A main object of the problem of kinked crack problem is to calculate the stress intensity factors at the tips of the kinked cracks and to determine a criterion for describing the direction of crack initiation and propagation. Therefore, a large number of studies dealing with the problem of kinked crack problem has been made so far, especially for isotropic media [1][2][3][4][5][6][7][8][9][10] Erdogan and his coworkers [1][2][3] have studied, by using Mellin transform method, the behavior of a crack kinking on the interface at right angle. Similar problems involving penetration and deflection of a main crack terminating at the interface at right angle were also studied [4,5].…”