Thermal Conductivity and Expansion of Cross- Ply Composites with Matrix Cracks

Theoretical models are developed for heat conduction and thermal expansion in a fiber-reinforced ceramic cross-ply laminate containing an array of parallel transverse matrix cracks. Two stages of the transverse matrix cracks are considered : Stage-I with tunnel cracks in the 90” plies aligned parallel to the fibers, and Stage-II with cracks extended across both the 90 and 0” plies with intact fibers bridging the matrix in the 0” plies. The effect of debonded fiber-matrix interfaces in the 0” plies is also considered in Stage-II. Approximate closed form solutions for the overall in-plane thermal conductivities and coefficients of thermal expansion (CTEs) as functions of matrix crack spacing and constituent properties are obtained using an approach which combines an analysis akin to a shear-lag analysis with finite element results. Emphasis is placed on the important class of composites whose fiber expansivity is smaller than that of the matrix. For this class, matrix cracking and interfacial debonding results in reduced thermal expansivity. Interfacial debonding has a significant effect on both longitudinal conductivity and thermal expansivity, especially the latter. Comparisons between the present model predictions and numerical and experimental results are provided where these are available.