Mathematical Prediction of Strength of Ablating Polymer Unidirectional Composites in Transverse Direction and in Shear Along and Across Fibers

The scope of the investigations of the paper includes the efficiency in the prediction of strength characteristics of the ablating polymer unidirectional carbon-fiber-reinforced plastics at elevated temperatures based on the properties of the unreinforced matrix and a bundle of fibers in the process of thermal oxidative breakdown at different types of stress state. The characteristics of elasticity and parameters of strength of the transverse-isotropic carbon-fiber-reinforced plastic, as well as of its components (epoxy matrix and carbon fibers of T700 type), have been determined in compliance with the regulatory documents of Ukraine at low heating rates with the subsequent exposure of the specimens at the fixed temperature, when the inertia effects can be neglected. It is illustrated that the variation in densities of the ablating unreinforced matrix and the bundle of fibers at elevated temperatures is rather well described via the models of multiphase media employing the modified integral exponential function. The authors analyze the possibility to evaluate the critical stresses of the transverse-isotropic composite at elevated temperatures based on the mechanics of multiphase media considering the thermal and mechanical characteristics of the ablating polymer matrix and the bundle of carbon fibers. It is assumed that the task of heat and mass transfer can be solved separately from the coupled tasks of thermal mechanics of the ablating materials since mechanical stresses have no effect on its parameters. It is found that the calculation of critical stresses using the hypothesis for the total hermetic sealing between the phases or in the assumption on the low pressure in pores determines the lower and upper lines of variation of the composite strength at different types of stress state. In particular, the calculated strength of the unidirectional composite under tension in the transverse direction and in shear along and across the fibers is in good correlation with the experimental data obtained by the authors and other researches.