Antiplane shear crack terminating at and going through a bimaterial interface

Abstract

going through aA B S T R A C T The antiplane shear problem of two bonded elastic half planes containing a crack perpendicular to the interface is considered. The cases of a semi-infinite crack terminating at the interface, a finite crack away from and terminating at the interface, two cracks one on each side of the interface,, and a finite crack crossing the interface are separately investigated. The nature of the stress singularity for the crack terminating at and going through the interface is studied, and it is shown that at the irregular point on the interface, for the former the power of singularity is not -½ and for the latter the stresses are bounded. For a material pair of aluminum-epoxy some numerical results giving the stress intensity factors, the density functidlls, and the crack opening displacements are presented.

On the solution of integral equations with a generalized Cauchy kernel

“…and the stress intensity factors or the parameters giving the strength of the flux singularity at the end points r = a and r = b may be defined and evaluated from k3(a) = lim \/2(a -r) ol6:(r,ir) (r < a) For a material pair corresponding to aluminum and epoxy and for a uniform shear stress q(r) = qQ applied to the crack surface some results are given in Table 1, where the previous results, calculated by using a Gauss-Chebyshev quadrature technique [6], are also displayed. From the table it may be observed that the method seems to give rather good results even with a relatively small number of terms used for approximating the unknown function h, the convergence improves as the crack moves away from the interface, and at the crack tip near the interface the convergence for \x2 > Hi appears to be slower than the case for which /u, > /u2.…”

“…In the terminology of elasticity the problem is one of antiplane shear loading of a nonhomogeneous medium which consists of two bonded half spaces with shear moduli /xj and n2■ The medium contains a crack along 6 = it, a < r < b and, in the perturbation problem considered, the crack surface traction al9z(r,-n) = q(r) is the only nonzero external load. If wl and w2 are the z-component of the displacement vector in materials 1 and 2, respectively, it was shown that (see, for example, [6,7]) the differential equations and boundary conditions…”

“…The integral equation can also be obtained by using w(t) rather than ip(t) as the unknown function and, for example, following the procedure outlined in [6], It may be noted that in terms of w some of the stress components of physical interest may be expressed aŝ…”

Mixed Boundary-value Problems in Mechanics

“…In addition to [28, 29, 35, 361,, further app lications of the singular integral equations with generalr ized Cauchy kernels may be found in [37][38][39].…”

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

“…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].…”