Mathematical Modeling of the Monotonic and Cyclic Loading Processes

Based on experimental studies of specimens of 12Kh18N10T stainless steel under a rigid (strain-controlled) deformation process, which includes a sequence of monotonic and cyclic loading modes, some features and differences between isotropic and anisotropic hardening under monotonic and cyclic loading are found. To describe these features in terms of the theory of plasticity (the Bondar model), the criterion of change of plastic deformation direction and a memory surface are introduced in the space of the plastic strain tensor, which allow one to separate the processes of monotonic and cyclic loading. To describe the transitional processes, evolutionary equations for isotropic and anisotropic hardening parameters are formulated. The change in the stress-strain state during monotonic and cyclic loading, obtained by calculation and experiment, is compared.