Applied and engineering versions of the theory of elastoplastic processes of active complex loading part 2: Identification and verification

Abstract

The deviator constitutive relation of the proposed theory of plasticity has a three-term form (the stress, stress rate, and strain rate vectors formed from the deviators are collinear) and, in the specialized (applied) version, in addition to the simple loading function, contains four dimensionless constants of the material determined from experiments along a two-link strain trajectory with an orthogonal break. The proposed simple mechanism is used to calculate the constants of the model for four metallic materials that significantly differ in the composition and in the mechanical properties; the obtained constants do not deviate much from their average values (over the four materials). The latter are taken as universal constants in the engineering version of the model, which thus requires only one basic experiment, i.e., a simple loading test. If the material exhibits the strengthening property in cyclic circular deformation, then the model contains an additional constant determined from the experiment along a strain trajectory of this type. (In the engineering version of the model, the cyclic strengthening effect is not taken into account, which imposes a certain upper bound on the difference between the length of the strain trajectory arc and the module of the strain vector.) We present the results of model verification using the experimental data available in the literature about the combined loading along two-and multi-link strain trajectories with various lengths of links and angles of breaks, with plane curvilinear segments of various constant and variable curvature, and with three-dimensional helical segments of various curvature and twist. (All in all, we use more than 80 strain programs; the materials are low-and medium-carbon steels, brass, and stainless steel.) These results prove that the model can be used to describe the process of arbitrary active (in the sense of nonnegative capacity of the shear) combine loading and final unloading of originally quasi-isotropic elastoplastic materials. In practical calculations, in the absence of experimental data about the properties of a material under combined loading, the use of the engineering version of the model is quite acceptable. The simple identification, wide verifiability, and the availability of a software implementation of the method for solving initial-boundary value problems permit treating the proposed theory as an applied theory.