Statistical Micromechanical Analysis of the Effects of Fiber Random Distribution on the Mechanical Properties of Fibrous Composites

In this paper, a 3D micromechanical model is presented to study the effect of randomly distributed fiber within the matrix on the mechanical characterizations of unidirectional fiber reinforced composites. The Representative Volume Element (RVE) of the model consists of r×c unit cells in which fibers are distributed randomly within the matrix cells. The presented model is general and can be used to extract the stiffness properties of a fibrous composite subjected to thermal and mechanical, normal and shear loading and also to investigate the initiation of matrix plastic deformation. Different statistical distribution models including normal, uniform and beta distribution are used to study the fiber arrangement. The obtained results for the elastic properties in which fiber distributed at random show good agreement with both experimental data and available models. Statistical analysis of dependency of stiffness and strength properties with fiber array within the matrix is carried out by applying hypothesis testing based on the central limit theorem in each normal, uniform and beta distribution. According to the obtained numerical results, the necessary interpretation is done in each case. Numerical results of hypothesis testing show that fiber distribution has no effect on the stiffness properties of a fiber composite, while the strength properties of the composites are highly affected by the fiber arrangement.