Construction of the Theory of Plasticity Irrelative of the Loading Surface and Associated Flow Law

The experimental uniaxial cyclic loading diagram for a 40Kh16N9G2S steel specimen was analyzed to define the three sections representing different stress behavior, i.e., three different stress modes. For each stress mode, the corresponding evolutionary equations governing anisotropic hardening were formulated. For describing the isotropic hardening, the evolutionary equation for the second-mode saturation parameter is introduced. The stress deviator is defined as the sum of stress deviators of the three modes. The nonlinear damage accumulation is represented by the kinetic equation based on the energy principle, where the energy equal to the work of second-mode stresses within the strain field is taken as the energy spent for damaging of the material. The material functions governing the theory are defined, the basic experiment and the identification method of the material functions are formulated. The material functions of 40Kh16N9G2S steel and theory verification results under proportional strain-controlled cyclic loading and nonproportional loading along the strain path in the form of concentric circles with the common center in the origin of coordinates are presented. Five path turns are examined, starting from the large-curvature path to the mean-curvature one. Computational and experimental results are in close agreement.