Modeling the kinetics of stress-strain state and damage accumulation in structural alloys under the mutual influence of fatigue and creep

The corresponding mathematical model of cyclic viscoplastic deformation of damaged material, a structural element counteracting multiaxial disproportionate modes of hybrid thermomechanical loading, is considered. The model is determined by the relations between viscoplastic deformation and failure, as well as the evolution equations of damage accumulation kinetics and the material strength criterion. The description of viscoplastic deformation is based on the existence of plasticity and creep surfaces in the stress space and the principle of gradient of the velocity vectors of the corresponding deformations at the loading point. Such a description distinguishes the main effects of the cyclic behaviour of the material for complex loading trajectories. The description of kinetic damage accumulation is based on the scalar damage parameter. The formation, growth and coalescence of micro-defects are considered. A coupled formulation of the evolution equations for low-cycle fatigue and long-term strength is proposed. The condition that the damage value reaches a critical value is taken as the strength criterion. In the work, material parameters and scalar functions of the mathematical model are obtained. Based on the model, the results of the numerical simulation of the behaviour of the alloys are presented. It is shown that the model describes the durability of the materials with practical reliability.