Longitudinal deformation of fibre reinforced metals: influence of fibre distribution on stiffness and flow stress

A computational analysis of the longitudinal deformation of continuous fibre reinforced metals is presented. Elastic and elastic–plastic matrix behaviour are considered. Analytical approaches are confronted with finite element analyses (FEA) for varying fibre distributions, ranging from single fibre unit cells to complex cells. Analysis of microfields shows that the main cause for deviation from the equistrain rule of mixtures is a stiffening effect of matrix confinement when surrounded by touching fibres arranged as “rings”. Comparison with FEA shows that Hill's [J. Mech. Phys. Solids 12 (1964) 199, 213] bounds, although best possible in terms of volume fraction, are of limited value in so far as Hill's upper bound lies far above any practical limit for a fibre reinforced material, whereas Hill's lower bound loses its bounding property when extended to non-linear behaviour via an incremental scheme. This latter effect can be corrected by changing slightly Hill's derivation in a way that preserves the bounding property. Finally, implications are given for the derivation of in situ matrix flow stress curves from experimental tensile curves on fibre reinforced composites. It is suggested that linear three-point bounds can in practice be used for this purpose.