A method for constructing a nonlinear constitutive relation at the low number of the tensile cycles for the unidirectional CFRP with a thermoplastic matrix

Elements of most structures are usually operated under the time-varying loads; therefor, the material behavior models under such types of loading are acquiring utmost importance. The paper considers main types of the constitutive relations used to describe nonlinear behavior of the composite materials. It analyzes regularities in the anisotropy of mechanical behavior of the unidirectional carbon fiber reinforced plastic (CFRP) with a thermoplastic matrix under a small number of the loading cycles. Rheological behavior and physical nonlinearity under the intralayer shear are caused by the polymer matrix properties and its adhesion to the fiber. To study this behavior, the paper proposes a method for constructing a hereditary constitutive relation based on results of the tensile testing the unidirectional specimens at different angles to the reinforcement direction. The model applicability is tested on AS4/PEEK CFRP with a thermoplastic matrix; the hereditary relation parameters are obtained using the Levenberg-Marquardt gradient method by minimizing discrepancy between the calculated and experimental values of deformations. Results of comparing the experimental curves and the calculated ones demonstrate the model’s ability to describe main characteristics of the hysteresis loops under several loading cycles, as well as deformation at the constant rate.
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