Micromechanics model for predicting effective elastic moduli of porous ceramic matrices with randomly oriented carbon nanotube reinforcements

Multi-step micromechanics-based models are developed to predict the overall effective elastic moduli of porous ceramic with randomly oriented carbon nanotube (CNT) reinforcements. The presence of porosity in the ceramic matrix that has been previously neglected in the literature is considered in present analysis. The ceramic matrix with porosity is first homogenized using a classical Mori-Tanaka model. Then, the homogenized porous ceramic matrix with randomly oriented CNTs is analysed using two micromechanics models. The results predicted by the present models are compared with experimental and analytical results that have been reported in literature. The comparison shows that the discrepancies between the present analytical results and experimental data are about 10% for 4 wt% of CNTs and about 0.5% for 8 wt% CNTs, both substantially lower than the discrepancies currently reported in the literature.