“…Several works have been done to determine the effect of short fibers on the properties of polymer composites [41][42][43][44][45][46][47][48][49][50][51][52] . Here, we investigated the elastic modulus of short fiber composites and comparison is made with well known models for randomly oriented short fiber composites 53 , such as Halpin-Tsai for 2D and 3D randomly oriented short fiber composites 51,52 , numerical integration of angular dependence of the modulus of 2D randomly oriented short fiber composites based on the model of Tsai-Hill [42][43] , and the model of Berlin et al 46 for Young's modulus of 3D randomly oriented short fiber composites including the fiber critical aspect ratio determined by three methods [47][48][49][50] . Of all the models tested, it was found that Berlin's approach for 3D randomly oriented short fiber composites in combination with the critical fiber aspect ratio given by Rosen's model produce reasonable prediction for PFC composites using: where E comp is the modulus of 3D randomly oriented short fiber composite, E fiber is the fiber modulus, E m is the matrix modulus, ϕ fiber is fiber volume fraction of unfoamed composites, l is fiber length, l c is the critical fiber length, l max is the maximum fiber For our composites foams, the Kevlar is dispersed in the solid phases of the foam.…”