Regularity of Strain Distribution in Short-Fiber/Whisker Reinforced Composites

Based on studies on the strain distribution in short-fiber/whisker reinforced metal matrix composites, a deformation characteristic parameter, λ is defined as a ratio of root-mean-square strain of the reinforcers identically oriented to the macro-linear strain along the same direction. Quantitative relation between X and microstructure parameters of composites is obtained. By using X, the stiffness moduli of composites with arbitrary reinforcer orientation density function and under arbitrary loading condition are derived. The upper-bound and lower-bound of the present prediction are the same as those from the equal-strain theory and equal-stress theory, respectively. The present theory provides a physical explanation and theoretical base for the present commonly-used empirical formulae. Compared with the microscopic mechanical theories, the present theory is competent for stiffness modulus prediction of practical engineering composites in accuracy and simplicity.