Axial shear modulus of a fiber-reinforced composite with random fiber cross-sections

Abstract

A study is made of the effective axial shear modulus of a fiber reinforced material with random fiber cross-sections so that the micromechanics is governed by stochastic differential equations. A coarse-graining procedure is adopted to investigate the macroscopic behavior of the material. This analysis leads to the formula for the effective axial shear modulus, μ^∗ = μ₁/ {1 - 2c ( μ₂ - μ₁)/(μ₂ + μ₁)}, where μ_I and μ₂ are the shear modulus of the matrix and fibers respectively and c is the concentration of the fibers less that 0.5. For c > 0.5, the fiber and matrix moduli are to be interchanged and c is to be replaced by l-c. The results of this study are compared with those of the theory of fibre reinforced materials. Finally, a numerical example is presented with graphical representation.