Mathematical modelling of deformation and damage accumulation under cyclic loading

In order to construct a theory that adequately describes the effects of cyclic loadings, it is initially necessary to analyze the experimental plastic loop of a hysteresis stainless steel SS304; and three types of backstresses responsible for the displacement of the center of the surface of loading are specified on this steel. For each type of backstresses we have formulated evolutionary equations on basis of the equations of the theory of plastic flow in the combined hardening. We have allocated the material functions which close the theory,. We have also formulated the basic experiment and method of the material functions identification. Evaluating the work of different types of backstresses on the field of plastic deformations under cyclic loadings with various magnitude of the deformation up to the experimental values of the number of cycles before failure, it has been obtained that the work of backstresses second type is a universal characteristic of the material. This result made it possible to formulate the kinetic equation of damage accumulation, based on which we have considered the nonlinear processes of damage accumulation. To determine the material functions responsible for the destruction, we have formulated the basic experiment and identification method. The authors have given material functions for stainless steel SS304. We have investigated the processes of elastic-plastic deformation of stainless steel SS304 with non-stationary hard cyclic loading under block changes of amplitude and mean deformation of the cycle. Also the processes of soft non-stationary and non-symmetric cyclic loading (ratcheting) under block changes of amplitude and mean stress cycle have been examined. The results of calculations are compared with the experimental results. Computational research of nonlinear processes of damage accumulation and low cycle fatigue of stainless steel SS304 are conducted under symmetric hard cyclic loading both at the constant amplitude of strain and block change of the amplitude of strain. The calculation results show that the scope of deformation reduction leads to increase of the nonlinearity of damage accumulation, while the increase of the deformation scale results in the fact that the accumulation of damages tends to be linear. There is a significant deviation from the rule of linear summation of damages under a satisfactory conformity of calculation results with the experiments. The paper presents such new results as: - specifying three types of backstresses responsible for kinematic hardening analyzing the experimental loops of plastic hysteresis; - establishing the work universality of the second type backstresses under low-cycle and high-cycle fatigue on basis of experimental results analysis; - constructing the theory of plastic flow under combined hardening and kinetic equations of damage accumulation on the basis of the evolution equations for three types of backstresses; - identifying the material parameters and verifying the proposed theory.