Issue 49

Yu. Bayandin et alii, Frattura ed Integrità Strutturale, 49 (2019) 243-256; DOI: 10.3221/IGF-ESIS.49.24 245 this case, both the processes of defect accumulation and plasticity contribute to stress relaxation. Stress relaxation is determined by the nucleation and growth of defects in the shock front and should depend on the effective viscosity, which is the main stress relaxation factor that needs to be identified from experimental data. In the present paper, these parameters depend in general on many thermodynamic variables and can be represented by following the approach of the kinetic theory [29] as 0 0 exp i i U              (1) where  is the temperature factor, 0 U is the characteristic value of the energy of the interatomic bond rupture, 0 i  is the characteristic relaxation times,  is the generalized thermodynamic force, which in the Zhurkov model coincides with the applied stresses [12, 14]. In the works of the authors [6, 18], the dependence of the relaxation times on the accumulated strain in the form 2 0 exp H h                t (2) where  ,  – the intensity of strains and stresses, respectively, t  – yield stress, H , h – the hardening and depletion coefficients, respectively. The generalized thermodynamic force depends on both stress and strain. It is necessary to assume the influence on the relaxation times of only the structural (inelastic) component, for example, in polymers practically coincides with the total strain [18]. The relaxation times for inelastic strain can depend on the accumulated structural strain due to defects [6]. In this case, the energy factor in Eqn. (1) is the thermodynamic force, which tends to return the system to the equilibrium state. Therefore, the relaxation times will be less than the system is further from the equilibrium state. Then Eqn. (1) for the model of solid with mesoscopic defects can be represented by 0 0 exp p i i U J E                             Σ (3) where ( ) J  is the intensity of the tensor argument, Σ is the stress tensor,  is the specific free energy,   p is the nonlinear component of the thermodynamic force, which depends only on the inelastic strain p due to the defects. Comparison of Eqs. (2) and (3) shows that the energy contribution to the relaxation processes is divided into the effect of applied stresses and the structural component, expressed in nonlinear dependence on the characteristic deformations, as a polynomial for the model presented in [1, 9, 18] or as nonlinear dependence of the component of the thermodynamic force due to defects [6]. S TRUCTURAL - STATISTICAL MODEL OF ELASTOVISCOPLASTIC DEFORMATION AND FAILURE OF SOLID WITH MESOSCOPIC DEFECTS he approach developed by the authors is based on the description of the collective behavior of an ensemble of mesoscopic defects using the effective field theory for multiscale interaction between defects [5, 30]. Based on the geometric features of defects as a local changing in the symmetry of the distortion field (deformation) the nucleation and the growth of defects are associated with the contribution of induced by defects strain that is introduced as an additional structural variable. Taking into account the interaction of defects within the framework of the developed statistical-thermodynamic model it was possible to propose a continual description of solid with defects to formulate a system of constitutive equations linking the mechanisms of structural relaxation caused by the nucleation and growth of defects with the kinetics of elastic-plastic transitions and the stages of failure. An important point in the describing of mechanical properties of elastoplastic material is the established relationship between the formation of collective modes of defects ensembles related to the kinetics of plastic strain and damage localization. Variables for characterizing of defects T