Tensile elongation of unidirectional or laminated composites combining a brittle reinforcement with a ductile strain and strain-rate hardening matrix

Abstract

We use the long-wavelength model of Hutchinson and Neale (1977) and Ghosh (1977) to estimate the uniform tensile elongation of two-phase composites deforming quasistatically according to the equistrain rule of mixtures, in which one phase is ductile while the other fractures progressively according to two-parameter Weibull statistics. We use shear-lag models in the literature to quantify load transfer from the ductile phase to the fractured brittle phase, and to estimate the influence of matrix strain and strain-rate hardening, of brittle phase fracture characteristics, and of phase volume and strength ratios, on the composite strain to failure as dictated by the onset of unstable necking. Calculations show that strain and strain-rate hardening of the ductile phase do relatively little to increase the ductility of the composite. Two parameters play a dominant role, namely the brittle-phase Weibull modulus and a dimensionless parameter describing load transfer across the two phases. The main practical implication of this analysis is that, to produce reasonably ductile two-phase composites, the best strategy is to aim for small layer thicknesses.