Stress-Strain Relations of a Viscoelastic Composite Reinforced with Elliptic Cylinders

Abstract

The stress-strain behaviors of a two-phase composite comprising a viscoelastic matrix and elastic elliptic cylinders are examined by means of a micromechanical theory. The reinforcing cylinders are taken to be aligned along direction 1 but randomly oriented in the 2-3 plane, with a common aspect ratio a (the thickness-to-width ratio). The strain-rate sensitivity of the stress-strain curves of the transversely isotropic composite is investigated as a function of the cross-sectional aspect ratio of the elliptic cylinders, and it is found that when the aspect ratio is one-corresponding to the traditional aligned fibers -the reinforcement is the poorest and that when the aspect ratio approaches zero corresponding to long, thin ribbons it is the most effective. Other types of crosssectional aspect ratios all give rise to a stress-strain curve lying between these two. Except for the thin ribbon with a and axial tension for all, other types of reinforcement all exhibit a saturation stress under a constant strain rate and result in strong strain-rate sensitivity for the overall response of the system.