Influence of Random Fiber Length on Macroscopic Properties of Short Fiber Reinforced Composites Due to Microscopic Physical Uncertainty

For the multiscale simulation of advanced materials with hierarchical, heterogeneous, and random microstructures such as fibrous composites by finite element method, mathematical homogenization method has been extended to the stochastic multiscale method. In this paper, a stochastic perturbation-based homogenization method was used to predict homogenized properties of short fiber reinforced composites with random fiber length, random orientation, and random mechanical properties of fiber and matrix resin. For demonstration, a random short fiber reinforced plastic was investigated considering thirteen random physical parameters and two ways of approximation of statistically measured fiber length distributions. The influences of each uncertainty factor on the homogenized properties of the material were observed. The results show that the homogenization properties are likely orthotropic even though the fiber and matrix are considered as isotropic materials. The material is stronger in the direction where the fibers are mostly longitudinal. Each component of the homogenized properties is resulted in a probability density function under the influence of the random physical parameters. Besides, the scatter of the properties was predicted due to very slight difference between two fiber length distributions.