Overall thermal conductivity of a fiber reinforced composite with partially debonded inhomogeneities

A homogenization problem for conductivity of a composite containing infinite fibers of circular cross-section with interface arc cracks is solved with the account of the orientation distribution of cracks. Solution for a single inhomogeneity with debonded zone is based on the known result on heat flux intensity factor and utilizes the connection between this quantity and resistivity contribution tensor. Maxwell's scheme is used for the homogenization procedure. The results are compared with exact numerical solution for the case when all the fibers are debonded and all the interfacial cracks have the same length and orientation. The application of the proposed approach is illustrated on the example of the recovery of information on damage accumulated in the process of hydrothermal aging.