Applied theory of inelasticity

We consider the main features and equations of the applied theory of inelasticity relating to the class of flow theories with combined hardening. The applied theory of inelasticity is the simplest engineering version of the theory of inelasticity; and can be used for calculations of the worked out and residual resource of high-performance structural materials under repeated and long-term thermomechanical loads. The strain rate tensor is represented as the sum of the elastic and inelastic strain tensors, i.e. here there is no conditional separation of inelastic deformation by deformation of plasticity and creep. The elastic deformation follows the generalized Hooke’s law. A loading surface is introduced that isotropically expands or reduces and displaces during loading. For the radius of the loading surface (isotropic hardening), an evolutional equation is generalized to nonisothermal loading and restoration of mechanical properties during annealing. The displacement of the loading surface (anisotropic hardening) is described through the evolution equation with a three-member structure, generalized to non-isothermal loading and the back stresses removal (displacement) during firing. To determine the rate tensor of inelastic deformation, the associated (gradient) flow law is used. For rigid (given deformations) and soft (given stresses) loading regimes, expressions are obtained to determine the rate of the accumulated inelastic deformation. Conditions of elastic and inelastic states are formulated. To describe the nonlinear processes of damage accumulation, the kinetic equation of damage accumulation is introduced, where the energy equal to the work of back stresses on the field of inelastic deformations is assumed as the energy spent on creation of damages in the material. Here this kinetic equation is generalized to nonisothermal loading and processes of embrittlement and healing of damages. The material functions closing the applied theory of inelasticity are singled out; the basic experiment and the material functions identification method are formulated. An example of determining the material functions from the basic experiment results is considered and material functions for 12Х18H9 stainless steel in the temperature range from 20 °C to 650 °C are given. Further we give a list of experiments and structural steels and alloys on which the applied inelasticity theory was verified under plastic and inelastic (viscoplastic) deformations, isothermal and nonisothermal, simple and complex loadings. In conclusion, we discuss the application of the theory of inelasticity.