Dynamic self-consistent analysis for elastic wave propagation in fiber reinforced composites

Abstract

A dynamic self-consistent method previously proposed and validated for composites containing spherical inclusions is applied to the simplest two-dimensional problem: SH wave propagation in unidirectional fiber reinforced composites. The self-consistent conditions for SH waves are derived and the effective wave speed and coherent attenuation are calculated numerically for five different composites. For two composites showing very different dynamic behaviors, the results of the present theory are compared with those of multiple scattering theories and another self-consistent theory. At low volume fractions the present theoretical results coincide with those of the multiple scattering theory using exact pair-correlation functions, whereas the results based on another self-consistent theory deviate markedly from the others. As the volume fraction increases, the three theories give different results although they have qualitatively similar trends. The present theoretical results for composites considered in this article exhibit less dispersion and physically realizable attenuation. An important observation is that the multiple scattering theory predicts vanishingly small attenuation at low frequency when volume fraction is high. Experiments over wide ranges of frequency and volume fraction are needed in order to assess the accuracy and validity of the present theory.