On the effects of fiber length and spatial distribution on the stiffness of short-fiber reinforced composites

We report on the results of a computational investigation of the effect of fiber aspect ratio (a)(r) on the stiffness of composite rods reinforced with rigid spheroidal inclusions. The reinforcing spheroids are randomly placed within the containing rod and are also perfectly aligned with the tensile axis. Attention is focused in the interesting region of low (a(r)) where the stiffness of the composite rod is known to be most sensitive on (a(r)). Use of low aspect ratio fibers makes the results of this analysis suitable for a class of processed materials, such as whisker-reinforced metal-matrix composites and extruded or molded short-fiber-reinforced polymers. We consider steady-state three-dimensional deformations of composite rods containing up to 50 individual, randomly placed aligned spheroids. The equations of elasticity for the entire multi-fiber assembly are solved using the Boundary Element Method (BEM), implemented on a four-processor server and the force needed to impose a certain tensile deformation on the composite is computed. From this, an effective tensile modulus is obtained. Statistical averages of the computed effective moduli are compared to the predictions of the Mori-Tanaka model for the stiffness of short fiber composites. We find a good agreement at low values of (a(r)). Additionally, we investigate the effect on stiffness of random perturbations in fiber length around a mean value.