The curved interfacial crack between dissimilar isotropic solids

The paper examines analytically the role of curvature on the stress distribution of a curved interfacial crack between dissimilar isotropic solids. The crack-tip fields under in-plane and antiplane shear loading are studied, respectively. Using an asymptotic expansion of the circular interface geometry, the asymptotic solutions of the stress and displacement fields in the vicinity of the curved crack tip derived from modified stress functions is obtained. The eigenfunctions associated with the eigenvalues 2 for the curved crack consist of not only r ~ʹ terms, but also r ~+ʹ, r a+2 . . . . terms. In some cases, the terms r~+~(ln r), ra+Z(ln r), etc. may also exist. Two examples, frictionless contact near the circular crack-tip under in-plane loading and circular interfacial crack subject to antiplane shear loading, are derived in a closed-form asymptotic solution to elucidate the curvature effect. The case of fully open interfacial crack is also briefly described. Comparing the eigenfunction solutions of straight interfaces, the curvature effect enters the stress fields from the third-order term of the asymptotic solution for both cases. The condition for the existence of the r~/E(ln r) term in the circular interracial crack with frictionless contact is presented explicitly. Copyright © 1997 Elsevier Science Ltd.