Non-Hookean Elastic Behavior and Crystallite Orientation in Carbon Fibers

Abstract

Four different PAN-based carbon fibers (high strength, high modulus, and two enhanced strain fibers) were investigated in the standard single filament tensile tests. Nonlinear response was observed in all tested carbon fibers, but the nonlinearity in these fibers was not of the same extent. The tangential fiber modulus values for successive strain intervals (from zero up to failure strain) were fitted by linear as well as the second-order polynomial regression method. The coefficients of linear and square regression as well as the mean square deviation of experimental points from the points on a fitted curve were equal in all tested groups of fibers. The fitted square regression curve has a theoretical foundation, but the empirical expression is obtained by linear regression of modulus-strain data in carbon fibers. However, since the obtained linear relations include the coefficient gamma, which can be a measure of elastic nonlinearity, deduced gamma coefficient values were correlated to the parameters of carbon fiber crystallite structure as well as crystallites orientation.