Antiplane interface crack in a pre-stressed fiber-reinforced elastic composite

We study the mode-III interface fracture of a fiber-reinforced elastic material, regarded as a homogeneous elastic composite, subject to initial stress and undergoing incremental displacements. We shall use the interface of zero thickness linear model, when the displacement jump across the interface is linearly related to the components of tractions by a constant k3 describing the stiffness of the interface, independent of the displacement and tractions. The incremental displacement and stress fields in the vicinity of the crack field are represented using the numerical form of the complex potential.