Stress Spectra and the Effective Elastic and Viscoelastic Properties of Unidirectional Composites under Transverse Loading

Abstract

The relationship between the statistical characteristics of the microstructure, the stress state in the matrix and the effective properties of unidirectional composites have been studied. A representation of the stress state in the form of stress spectra is introduced. The skewness of spectra derived for the four basic regular periodic fiber arrays reflects the degree of order in the microstructure. A hybrid array combining features of these arrays was developed to approximate a random array. All stress components in the matrix of such a pseudo-random composite under transverse load exhibit an approximately Gaussian distribution. The stress state in the matrix determines the effective elastic modulus and the viscoelastic relaxation strength. This has led to a stress-based mechanical analysis using the moments of the stress spectrum for a representative, pseudo-random fiber arrangement.