Identification of Rabotnov nonlinear constitutive relationship on the data of polyethylene and polypropylene creep tests
The paper presents calibration technique for the Rabotnov nonlinear (quasi-linear) constitutive equation is developed using a set of creep curves of the material under uni-axial loading. The constitutive equation describes rheonomic materials behavior and generalizes the linear integral relationship of viscoelasticity with an arbitrary creep function by introducing the second material function. We propose to construct isochronous creep curves by the test data, approximate them by a number of special families of functions depending on 4-7 parameters and select the most suitable family (the one yielding the smallest value of the relative quadratic deviation from the experimental points). As a rule, such families of functions could be chosen, which permit the analytic inversion of the constitutive equation, which enable not to resort to an approximate treatment procedure and reduce the identification error. Next, a “basic” isochronous curve should be selected (its selection is related to the choice of the characteristic time scale for the test under study). A nonlinearity function is being found from it. Then, with account for the specific features of the experimental data, the type of the creep function approximation is selected, and its parameters are found (using the nonlinearity function obtained before). The advantages of the identification technique were considered compared to the conventional one. In particular, the procedure for quantitative estimation of the similarity condition fulfillment for experimental isochronous creep curves (the necessary condition for the relation applicability) was proposed. The identification procedure was applied to polyethylene and polypropylene creep tests. High-density polyethylene is widely used for manufacturing of water and gas supply pipes and other products. Thus, the study of their mechanical characteristics and their behavior modeling is of great interest. Verification of the obtained material functions was performed using the creep curves, that were not used for the identification procedure, stress-strain curves with constant rate and multi-step creep tests. It was shown, that the technique developed herein describes the experimental data well.