Evaluation of homogenized thermal conductivities of imperfect carbon-carbon textile composites using the Mori-Tanaka method

Three-scale homogenization procedure is proposed in this paper to provide estimates of the effective thermal conductivities of porous carbon-carbon textile composites. On each scale the level of fiber tow (micro-scale), the level of yarns (meso-scale) and the level of laminate (macro-scale) a two step homogenization procedure based on the Mori-Tanaka averaging scheme is adopted. This involves evaluation of the effective properties first in the absence of pores. In the next step, an ellipsoidal pore is introduced into a new, generally orthotropic, matrix to make provision for the presence of crimp voids and transverse and delamination cracks resulting from the thermal transformation of a polymeric precursor into the carbon matrix. Other sources of imperfections also attributed to the manufacturing processes, including non-uniform texture of the reinforcements, are taken into consideration through the histograms of inclination angles measured along the fiber tow path together with a particular shape of the equivalent ellipsoidal inclusion proposed already in (Skoček et al., 2008). The analysis shows that a reasonable agreement of the numerical predictions with experimental measurements can be achieved.