Abstract
Uniaxial tensile tests of UD carbon/epoxy and carbon PEEK coupons are conducted in the longitudinal direction. It is observed that the longitudinal modulus increases with axial stress or strain up to the intermediate level of tension. A fractional constitutive relation with a quadratic denominator is derived from the manner of the theory of nonlinear elasticity. This equation adopting the estimated higher order compliance coefficients exhibits an excellent agreement with the experimental results. An empirical strain-based equation is also proposed as asimpler alternative. Averaging formulas for both types of relations are provided for a practical application. The present phenomenon includes the behavior in a lower stress region discovered by some early work. The consideration of the present nonlinear behavior fairly improves a correlation between theory and experiments in stress-strain relationships of fabric composites with carbon fibers.
