Hardening non-linear behaviour in longitudinal tension of unidirectional carbon composites

Uniaxial tensile tests of unidirectional carbon-epoxy 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 by the method of the theory of non-linear 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 a simpler alternative. Averaging formulae for both types of relation are provided for a practical application. The present phenomenon includes the behaviour in a low-stress region discovered by some early work. The consideration of the present non-linear behaviour improves the correlation between theory and experiments in stress-strain relationships of fabric composites with carbon fibres.