Probabilistic Micromechanics/Macromechanics for Ceramic Matrix Composites

Abstract

Ceramic matrix composites (CMCs) are known to display a considerable amount of scatter in their properties due to variations involved in fiber/matrix properties, interphase properties, interphase bonding, amount of matrix voids, and many geometric or fabrication process related parameters such as ply thickness and ply orientation. This paper summarizes the preliminary studies related to the incorporation of formal probabilistic descriptions of the material behavior and fabrication related parameters into micromechanics and macromechanics for CMCs. This process involves a synergistic coupling of two existing methodologies: namely ceramic matrix composite micro- and macromechanics analysis, and a fast probability integration (FPI) technique to obtain probabilistic composite behavior/response. Preliminary results in the form of cumulative probability distributions and information on the response probability sensitivities to primitive variables for a unidirectional SiC/RBSN ceramic matrix composite are presented. The cumulative distribution functions are computed for composite moduli, thermal expansion coefficients, thermal conductivities and longitudinal tensile strength at room temperature. Variations in the constituent properties that directly affect the above mentioned composite properties are accounted for via assumed probabilistic distributions. Collectively the results show that the present technique provides valuable information on the composite properties and sensitivity factors which are useful to the design/test engineers. Furthermore, the present methodology is computationally more efficient than a standard Monte-Carlo simulation technique and the agreement between the two is excellent as shown via select examples.