Thermal stress problem for a partly debonded rigid circular-arc fiber inclusion in an infinite matrix

The heat conduction and thermoelastic problem of a circular-arc fiber bonded along one of its faces to an elastic plate while the other face forms an interfacial crack, is examined. Explicit solutions in the form of the complex potentials are provided, when a uniform heat flow is applied at infinity and the interface crack is an insulated and an “open” crack. It is shown that the stress field at the crack tip exhibits two singularities of orders 0.75 and 0.25 and the well known logarithmic oscillation of the interface crack. Generalized stress intensity factors of the stress singularities are defined and analytical and numerical results of these are provided.