Multiple-scale analysis and its applications on interface crack problems

The present work studies the stress fields surrounding an interface crack and obtains the asymptotic and intermediate solutions of bi-material crack fields by applying perturbation method--the multiple scale method. The motivation of the work is to understand the modes of failure of many advanced materials, including debonding and delamination. Unlike numerical studies of these problems, the analytical results obtained via the perturbation method shed light on the parametric dependences of the fields on material mismatch, and provide useful approximations for the stress and displacement fields.;The current study brings a small parameter into the interface crack problem which represents the difference between the properties of two materials. By perturbing the homogeneous crack field, the behavior of bimaterial crack fields is found. We consider a plane strain problem of a crack lying along the interface of two elasto-plastic power-law materials which possess a small difference in material properties. The difference comes from either the hardening parameters or material moduli. In applying the multiple scale method, we identify problems to be solved in succession. In doing so, we obtain long-range asymptotic solutions to the problems in question.;The results of our study show that for the non-linear interface crack problem the near crack tip singularity is non-oscillatory. The near-tip singularity is completely determined by the asymptotic solution in terms of the larger hardening exponent of the two power-law hardening materials. The fields in the material with the lower hardening behaves, asymptotically, as if the other material is rigid. The near-tip mode mixity is determined by the hardening parameters of both materials. When the remote loading is pure shear mode, the near-tip mode mixity deviates from the pure shear mode towards the opening mode as the two materials become less hardening or as the disparity between the hardening parameters of the two materials grows.