Interior cracking of a circular inclusion with imperfect interface under thermal loading

A semi-analytic solution is developed to determine the effect of an imperfe ct interface on the stress field inside a circular elastic inclusion contai ning a preexisting interior radial crack, subjected to thermal loading. The inclusion is surrounded by an infinite matrix of different elastic materia l with the inclusion-matrix interface assumed to be homogeneously imperfect . This is characterized by continuity of tractions and discontinuity of dis placements across the interface. Using complex variable methods, we derive series representations of the corresponding stress functions both inside th e circular inclusion and in the surrounding matrix. The governing boundary value problem is then formulated in such a way that these stress functions simultaneously satisfy the traction-free condition along the crack face, th e imperfect interface conditions, and the prescribed asymptotic conditions. The thermal load is modeled by a prescribed volume eigenstrain which chara cterizes the stress-free thermal strain of the inclusion. The method is ill ustrated for a number of crack-inclusion geometries and shear moduli ratios (of inclusion to matrix). We present explicit values of the stress intensi ty factor at the crack tips. These results can be used to ascertain the dir ection of initial crack propagation in, for example, fiber-reinforced compo sites or in components subjected to thermal loading in microelectronic pack aging. To demonstrate the accuracy of the results obtained in this paper, w e draw comparisons with corresponding cases documented in the literature wh ere analytical results are available.