Longitudinal shear of a bi-material with fractional sliding contact in the interfacial crack

We construct an analytical solution to the anti-plane problem of an inhomogeneous bi--material medium with the interfacial crack considering sliding friction. The medium is exposed to an arbitrary normal and shear loading in the longitudinal direction. Using the jump function method, the problem is reduced to a solution to singular integral equations for the jumps of displacements and stresses in the areas with sliding friction. Explicit expressions for displacements, stress intensity factors and energy dissipation are obtained. Critical load values for determination of the onset of slippage are investigated. The effect of friction and loading parameters on the size of the slip zone, stress intensity factors and energy dissipation
is numerically analyzed.