Formulation of a macroscopic strength criterion for tridirectional fiber composites

The theory of homogenization applied to limit analysis allows to rigorously define the macroscopic strength properties of periodic multi-phase materials, such as composite materials reinforced by arrays of equally spaced fibers, embedded in a matrix. By means of this approach, the strength properties of composite laminae reinforced by long and parallel fibers have already been obtained by various authors. The theoretical results established for these materials showed excellent agreement with experimental findings. The aim of the present work is to extend the same procedure to composites reinforced by a tridirectional array of mutually orthogonal fibers, which are materials of recent development. Through a static approach of limit analysis applied to a representative volume element, lower bounds to the actual failure domain of the material is obtained. This a1lows the numerical computation of strength domains for the material subjected to complex states of stress. Furthermore, if the material is subjected to uniaxial tension at any orientation to the fibers, analytical equations for the macroscopic strength are derived and discussed as well. Finally, mention is made to the influence of the limited strength properties of the fiber-matrix interface upon the macroscopic strength of the composite