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It is well known that carbon fibers exhibit nonlinear stress-strain behavior with their axial modulus increasing as they are strained. An empirical model is proposed to take into account this nonlinearity by adding a second-order term to Hooke's Law. This modified Hooke's law has the form σ = E0ε + Fε2. The tangent modulus is found by differentiating with respect to strain, giving Etangent = E0 + 2Fε. The tangent modulus increases linearly with strain.
Data are presented on three material forms—composite, impregnated strand, and single filament—to validate the empirical model. The E0 and F elastic coefficients are determined by performing a least-squares fit to the quadratic model. Data are generated for T-700 and T-40 high-strength polyacrylonitrile (PAN)-based carbon fibers. The nonlinearity of the fiber is shown to be comparable in single filaments, impregnated strands, and uniaxial composites.
The experimental results show that the empirical model provides an excellent fit to the stress-strain behavior of the carbon fiber. The E0 and F elastic coefficients are repeatable in various resin systems and differ for each fiber type. The elastic coefficients determined by this method should be used in the design of composite parts that see high loading in the fiber direction. As an example, the initial modulus of a T-40 fiber is 263 GPa (38.1 Msi) and increases to a secant modulus at failure of 308 GPa (44.7 Msi), and increase of 17%.
graphite/epoxy, fiber-reinforced composite, tensile modulus, mechanical properties, composite materials, test methods, stiffness change
Development scientist, Amoco Performance Products, Inc., Parma Technical Center, Parma, OH