Elastostatic problems of curvilinear cracks in bonded dissimilar materials

Abstract Boundary problems for a circular elastic insert bonded partially to the interior of an infinite medium of another material are formulated and solved in closed form. The unbonded portions of the interface may be regarded as circular arcs of discontinuities or curved cracks. By application of the complex function theory dealing with sectionally holomorphic functions, the present problem is reduced to the solution of the problem of linear relationship or Hilbert problem. Exact solutions to several examples of theoretical and practical importance are obtained. They include the cases of uni-axial tension applied at infinity and concentrated forces located in the insert and/or the surrounding material. Contact stresses are computed and compared to those for perfect bonding. It is found that the stresses near the tips of a curved crack possess the same trig-log character of singularity as those obtained for a straight crack between dissimilar media. Formulas for finding the crack-tip stress-intensity factors, employed m the Griffith-Irwin theory of fracture, are also derived.