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, lambda, is defined as a ratio of the root-mean-square strain of the reinforcers identically oriented to the macro-linear strain along the same direction. The quantitative relation between lambda and microstructure parameters of composites is obtained. By using lambda, 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 basis for the present commonly-used empirical formulas. Compared with the microscopic mechanical theories, the present theory is of utility for stiffness modulus prediction of practical engineering composites in terms of accuracy and simplicity.