Modified Theory of Inelasticity

The main provisions and equations of the modified theory of inelasticity, which belongs to the class of theories of flow during combined hardening, are considered. The modified theory of inelasticity is the simplest version of the theory of inelasticity, which is integrated into a finite element complex for calculations of the exhausted and residual life of structural materials under conditions of repetition and duration of the thermomechanical loads. The strain tensor is represented as the sum of elastic and inelastic strain tensors, i.e. there is no conventional division of irreversible (inelastic) deformation into plasticity and creep deformation. Elastic deformation follows Hooke's law which is generalized to non-isothermal loading. In the space of stress tensor components, a loading surface is introduced, which expands or contracts isotropically and shifts during loading. For the radius of the loading surface (isotropic hardening), an evolutionary equation is formulated, generalized to non-isothermal loading and recovery of mechanical properties during annealing. The displacement of the loading surface (anisotropic hardening) is described on the basis of an evolutionary equation with a three-term structure, generalized to non-isothermal loading and microstress relief (displacement) during annealing. To separate the monotonic and cyclic deformation in the space of the inelastic deformation tensor, a memory surface is introduced that limits the region of cyclic deformation. To describe placing and ratcheting of an inelastic deformation loop under asymmetrical cyclic loading, a modification of the theory of inelasticity is introduced. The modification of the theory of inelasticity comes down to the fact that when formulating the evolutionary equation for microstresses, the constitutive (material) parameter of the equation for microstresses of the first type is taken to depend on the accumulated inelastic deformation based on different relations for both cyclic and monotonic deformation. To determine the inelastic deformation rate tensor, the associated (gradient) flow law is used. Conditions for elastic and inelastic states are formulated. To describe nonlinear processes of damage accumulation, a kinetic equation of damage accumulation is introduced, based on the work of microstresses of the second type on the field of inelastic deformations. The kinetic equation is generalized to non-isothermal loading and embrittlement and healing processes. The material parameters and functions that close the theory are identified; the basic experiment and the method for their determination are formulated. The material parameters and functions of the bronze alloy BrKh08-Sh at temperatures of 20, 400, 500, 600 °C are given. The theory is verified under cyclic isothermal deformation and fracture (low-cycle strength) under high temperature conditions. Creep and long-term strength under isothermal and non-isothermal loads are also considered. The calculation results are compared with the experimental results.