Plasticity of materials under proportional and nonproportional cyclic loading

The mathematical modeling of elastoplastic deformation of materials under proportional (simple) and nonproportional (complex) cyclic loading is considered. In this paper we consider a very simple version of the theory of plasticity, which is a particular version of the theory of inelasticity. The version of the theory of plasticity refers to the class of single-reversed flow theories with a combined hardening. The applicability range of the version of the theory of plasticity is limited to small deformations of initially isotropic metals at the temperatures without phase transformations and strain rates, when dynamic and rheological effects can be neglected. Materials with the additional isotropic hardening effect under nonproportional cyclic loading are considered. The results of computational and experimental studies of the elastoplastic deformation and fatigue destruction of materials are presented for various nonproportional cyclic loadings. Based on the analysis of the experimental results related to the material deformation under rigid asymmetrical cyclic loading, the principle of the symmetry of cyclic properties is formulated. Corollaries are given from the principle of symmetry for soft asymmetric cyclic loads. The calculated and experimental results of investigating the asymmetric cyclic loading are given. An adequate description of the processes of complex loading, the effects of the additional isotropic hardening and ratcheting, as well as the destruction processes within the framework of a single, rather simple version of the theory of plasticity are the obvious advantages of the mathematical modeling under consideration. Meanwhile the number of the material functions (in this case 14 parameters and 1 function) is much less than the number of the material functions and parameters that finalize modern theories. In addition, the basic experiment and the method of identifying the material functions of the considered version of the theory of plasticity are clearly defined and are fairly simple and easily implemented. The comparison of the calculation and experimental results indicate the adequacy of the proposed mathematical modeling.