Model of Inelasticity, a Method for Identification of Material Functions and Model Verification

The presented study formulates the equations of the inelasticity model. The strain rate is defined as the sum of elastic and inelastic strain rates. Elastic deformations are calculated based on the generalized Hooke's law. In the space of stress tensor components, the concept of a loading surface is introduced, which can change its dimensions (both isotropically expanding and contracting) and move during the loading process. An evolutionary equation for the radius of this surface is proposed, accounting for the effects of non-isothermal loading and the recovery of the material's mechanical properties after annealing. The displacement of the loading surface is represented as the sum of displacements (microstresses) of two types. To differentiate between monotonic and cyclic deformation processes, a memory surface is introduced in the space of the inelastic deformation tensor components, which characterizes both types of loading. For ratcheting processes of inelastic deformation under asymmetric cyclic loading, additional evolutionary equations for microstresses of the first type are proposed, covering both monotonic and cyclic deformations. The rates of inelastic deformations are calculated based on the associated (gradient) flow law. A kinetic equation is used to model the accumulation of damage, considering the work of microstresses of the second type on the inelastic deformation field, with generalization to non-isothermal loading, as well as processes of embrittlement and self-healing of the material. The necessary material functions are defined, and basic experimental data and their identification methods are provided. In particular, material parameters for 12X18H10T stainless steel are presented. The proposed model is verified for cyclic and monotonic tension-compression tests of 12X18H10T stainless steel samples up to failure. Creep phenomena at various stress levels up to failure are also considered. To compare theoretical and experimental results, tension-compression diagrams, dependencies of amplitude and mean stress on the number of cycles, the number of cycles to failure, as well as creep and long-term strength diagrams of the material are used.