MICROBIFURCATION AND MACROBIFURCATION OF FIBROUS METAL MATRIX COMPOSITES UNDER UNIAXIAL COMPRESSION

THE AIM of this paper is to investigate the relation between macrobifurcation and microbifurcation of dilute fibrous metal-matrix composites under uniaxial compression. The microbifurcation analysis involves examining the possibility for the existence of shear bands, or formation of either diffuse axisymmetric or asymmetric geometric modes in the representative volume element, which in the present analysis is considered to be the composite cylinder model. The results indicate that for small slenderness ratios (long wavelengths) [slenderness ratio = kR(m)/L, with R(m) = outer radius of the composite cylinder, L = fiber length, and k = wave number (for a fixed R(m), this quantity is inversely proportional to the wavelength, 2L/k)], the diffuse asymmetric mode is always the critical mode for microbifurcation. For small to moderate fiber volume fractions, we found a specific slenderness ratio (wavelength) above (below) which the diffuse axisymmetric mode becomes the critical microbifurcation mode. Due to the criticality of the asymmetric mode in the microbifurcation, only this mode has been considered in the macro analysis. The overall incremental moduli in the macrobifurcation study are obtained by using the Voigt approximation. For realistic dimensions of the composite cylinder, the critical strain for asymmetric microbifurcation will be always lower than the critical strain for the macrobifurcation of the same type in a solid cylinder with effective properties and a radius which is larger than that of the composite cylinder. An important aspect of the analysis is that it provides exact solutions to the three-dimensional diffuse bifurcation of the representative volume element under consideration.