Overall Temperature-Dependent Elastic Properties of Carbon Fiber Polymer Matrix Composites at High Temperatures

The objective of this work is prediction of the effective elastic properties of carbon fiber reinforced polymer matrix composites undergoing volumetric ablation due to pyrolytic thermal decomposition. The assumption of volumetric ablation states the overall volume of the material remains constant, during the loss of mass in the presence of thermal pyrolytic decomposition of the polymer matrix. Thermal decomposition caused by heating, leads to formation of solid pyrolytic (char) and gaseous phases (pore) in the composite material. The volume fractions of the gas, and polymer phases are temperature-dependent and are obtained in the present work from a first order Arrhenius-type equation describing decomposition of the polymer matrix at a constant heating rate. Microstructure generation algorithms are developed to create densely packed randomized particle filled microstructures consisting of circular (representing fibers) and elliptical (representing pores) inclusions and to accommodate the growth of pores with temperature. The randomized particle filled microstructures are shown to be statistically isotropic. Temperature dependent microstructures are generated using this algorithm by creating different Representative Volume Element (RVE) for different temperatures to model the growth of pores with temperature. Temperature dependent elastic properties of the constituent phases (polymer, fiber, pores) is considered.

Numerical homogenization technique is used to compute the effective elastic modulus and Poisson’s ratio of the material. The calculations are performed using Finite Element Analysis (FEA), and a commercial FEA package ABAQUS is used in this study. A 2-step numerical homogenization technique is used in this work. The first step consists of homogenization of temperature dependent RVE which includes polymer and gaseous pore phase. Second step includes the homogenization of the fiber phase with the calculated “lumped” matrix phase. The effect of pressure generated by pyrolysis gases trapped inside the pores of the degrading material is studied. The concentrations of the different pyrolysis gases during heating is obtained from experiments. The gas pressure is incorporated in the RVE as pressure applied on the polymer-pore boundary. The pore pressure created due to the pyrolysis gas is observed to not have a significant effect on the overall elastic properties for the type of material studied. The computational results for the overall elastic properties (transverse and longitudinal) are obtained for the AS4/3501-6 composite in a temperature range up to 700 K. The transverse elastic modulus decreases in value with increasing temperature, while the Poisson’s ratio remained relatively unchanged.  The results are compared with available experimental results and a good agreement between the two values are observed. The char phase is not considered in this study but a discussion about including the char phase in the current model is included.