Three dimensional analysis of periodic fiber-reinforced composites with randomly broken and debonded fibers

A three-dimensional analysis is presented for the prediction of the behavior of periodic fiber-reinforced composites with numerous broken fibers and debonded fiber-matrix interfaces. The locations of these defects in the composite are randomly determined. The analysis is based on the representative cell method and the higher-order theory. In the framework of the representative cell method, the problem for the representative volume element of the damaged composite that includes multiple fibers is reduced, in conjunction with the triple discrete Fourier transform, to the problem for repetitive cell of undamaged composite including just a single cell. The solution of this boundary-value problem is obtained by the higher-order theory. The inversion of the transform, in conjunction with an iterative procedure, establishes the elastic field at any point of the damaged composite. The optimal size of the representative volume element of the damaged composite within which the computations are performed is determined. The present method is capable of predicting the resulting field distributions in the composite as well as the average values of the effective moduli of the randomly damage composite and the resulting stress concentration factors. These average values and the corresponding standard deviations are determined by repeating the analysis several times (scores). A parametric study of the dependence of the effective elastic moduli and stress concentration factors upon the level of damage is performed. In addition, comparisons with a micromechanical theory predictions which are based on the analysis of a repeating unit cell, established by the assumption of spatial damage periodicity, are given.