An antiplane problem for a crack penetrating into an elastic inclusion provided the phase contact is imperfect

In the paper we consider an interaction of the semi-infinite crack of mode III with circular elastic inclusion. Imperfect contact at the interface is supposed. The interface conditions are described by a spring-type model assuming that the traction continuity remains intact, while the displacement experiences a jump proportional to the interfacial traction. As a result the use of the generalized integral transform of Mellin the problem reduced to hypersingular integral equation. Exact analytical solution in closed form of this equation is founded. For the stress intensity factor the simple mathematical formula is obtained. Two limiting situations are studied: the case of perfect contact and the caseof sliding contact.