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

Jan Vorel , Michal Sejnoha

Abstract

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 Sko ek (1998). The analysis shows that a reasonable agreement of the numerical predictions with experimental measurements can be achieved.

Key Words

carbon-carbon composites; multi-scale analysis; Mori-Tanaka method; optimization; porous materials.

Address

Jan Vorel — Dept. of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Thakurova 7, 166 29 Prague 6, Czech Republic
Michal Sejnoha — Dept. of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Thakurova 7, 166 29 Prague 6, Czech Republic Centre for Integrated Design of Advances Structures, Thakurova 7, 166 29 Prague 6, Czech Republic

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