Stiffness and thermal expansion predictions for hybrid short fiber composites

A model is developed to predict thermal expansion coefficients and elastic moduli of multi‐component (hybrid) composites. The model includes the influences of fiber aspect ratio; isotropic and anisotropic fiber materials; planar, three‐dimensional or arbitrary fiber orientation; hollow and solid spherical reinforcements; and voids. The first step in the procedure is to predict the properties of an aligned‐fiber single‐reinforcement composite for each reinforcement type. Various micro‐mechanics approaches are used, depending on the type of reinforcement. A simplified version of Lee and Westmann's theory is found to work well for hollow spherical reinforcements. Performing an orientation average accounts for the spatial orientation of each reinforcement, then an aggregate averaging procedure combines the single‐reinforcement properties to model the hybrid. Predictions of the model compare favorably to experimental elastic and thermal properties of short fiber/hollow sphere composites designed for very high speed integrated circuit (VHSIC) board applications.