Unknown polynomial eigenstrains reconstruction with distributed dislocation technique for crack–inclusion interaction

Abstract

The inverse formulation presents mode-I crack–inclusion interaction solution, based on Eshelby’s equivalent inclusion method (EIM) with an unknown filed of induced polynomial eigenstrains (IPE) inside an inclusion, combined with the distributed dislocations technique (DDT) to model the crack face with unknown perturbations in distributed dislocations (PDD). The expression for PDD, determined through Gauss–Chebyshev Quadrature integration of the singular integral equations, is recast in terms of the unknown coefficients of IPE, which form the only set of unknowns. The crack-face boundary condition is exactly satisfied in this step, without solving for the unknowns. The second boundary condition for continuity of stresses at the inclusion boundary is approximately satisfied through discrete-point collocation equations in a subsequent step through the inverse formation. For modest geometric and modulus ratio configurations, the method obtains the perturbed stress intensity factors with reasonable accuracy using only four terms in IPE.