Probabilistic micromechanics and macromechanics for ceramic matrix composites

The properties of ceramic matrix composites (CMC's) are known to display a considerable amount of scatter due to variations in fiber/matrix properties, interphase properties, interphase bonding, amount of matrix voids, and many geometry-or fabrication-related parameters, such as ply thickness and ply orientation. This paper summarizes preliminary studies in which formal probabilistic descriptions of the material-behavior-and fabrication-related parameters were incorporated into micromechanics and macromechanics for CMC's. In this process two existing methodologies, namely CMC micromechanics and macromechanics analysis and a fast probability integration (FPI) technique are synergistically coupled to obtain the probabilistic composite behavior or response. Preliminary results in the form of cumulative probability distributions and information on the probability sensitivities of the response to primitive variables for a unidirectional silicon carbide/reaction-bonded silicon nitride (SiC/RBSN) CMC are presented. The cumulative distribution functions are computed for composite moduli, thermal expansion coefficients , thermal conductivities, and longitudinal tensile strength at room temperature. The variations in the constituent properties that directly affect these composite properties are accounted for via assumed probabilistic distributions. Collectively, the results show that the present technique provides valuable information about the composite properties and sensitivity factors, which is useful to design or test engineers. Furthermore , the present methodology is computationally more efficient than a standard Monte-Carlo simulation technique; and the agreement between the two solutions is excellent, as shown via select examples.