PSI - Issue 23

I.A. Volkov et al. / Procedia Structural Integrity 23 (2019) 316–321 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

317

2

evaluation of life of structural elements, using finite-element analysis of inelastic strains in hazardous zones of structural elements, requires formulation of defining relations of thermo-plasticity, accounting for realistic material properties by М itenkov et al (2007). Currently, special attention is paid to experimental studies of laws of cyclic deformation processes. It has been found that stationary cyclic deformation (if there is any) is preceded by a transition stage determined by cyclic hardening, softening or relaxation of the memory of the material about the previous cyclic deformation history. The parameters of the stabilized plastic hysteresis loop do not depend on the stabilization point of the loop. When a material undergoes nonsymmetrical cyclic deformation, unidirectional (creep) accumulation of plastic deformation can be observed. When a material undergoes hard cyclic loading with initial anisotropy of the stress amplitudes in half-cycles of tension and compression, relaxation of the average stresses of the cycle to zero is observed in a finite number of loading cycles. When a material suffers from combined mechanical and thermal loads, which vary out of phase, the processes of cyclic change of stresses and total and plastic strains are multiaxial and non-proportional, leading to additional effects of cyclic behavior of the material. The results of experimental investigations of such processes indicate that behavior of structural materials under cyclic proportional loading substantially differs from that under monotone deformation processes (the laws of cyclic hardening differ considerably from those of monotone deformation). In turn, multiaxial non-proportional cyclic processes substantially differ from proportional cyclic processes considered by Lemba (1978) or McDowell (1985) or О hasi (1985). State equations based on monotone loading processes and not accounting for specific features of cyclic deformation under proportional and non-proportional loading, can lead to gross errors in determining the main parameters of the stressed-strained state, which will later be used for evaluating service life characteristics of the material. Formulation of reliable defining relations of thermo-plasticity for the above processes requires, in the first place, experimentally studying effects of cyclic behavior of structural materials under proportional and non proportional loading by Volkov, Коrotkikh (2008) and Chaboche (1989). Classical methods of predicting fatigue life of materials, using semi-empirical formulas (rules), based on a stabilized analysis of the deformation process and correlating the parameters of plastic hysteresis loops with number of cycles to failure, require ample experimental information and are valid only for a limited class of loading regimes within the limits of the available basic experimental information by Volkov, Коrotkikh (2008) . In the recent years, a new scientific direction, mechanics of damaged media (MDM) by Volkov, Коrotkikh (2008) , Chaboche (1989) or Bodner, Lindholm (1976), Lemaitre (1985), Collins (1984) or Мurakami (1983) or Volkov, Igumnov (2017), has been successfully developed for analyzing such problems. The current practice of using equations of MDM for various life exhausting mechanisms makes it possible to claim that such an approach is sufficiently effective for practical applications for evaluating service life characteristics of materials and can be used to evaluate the process of service life exhaustion of structural elements and units of bearing structures accurately enough by М itenkov et al (2007). In the present paper, a model of MDM by Volkov, Коrotkikh (2008) or Volkov, Igumnov (2017) or Volkov et al (2016) is developed for describing processes of plastic deformation and fatigue damage accumulation in the 12 Х 18 Н 9 stainless steel in the conditions of block-type nonstationary nonsymmetrical low-cycle loading. The obtained numerical results are compared with the data of full-scale experiments by Kazakov et al (1999). 2. Defining relations of mechanics of damaged media The model of damaged media developed by Volkov, Коrotkikh (2008) or Volkov, Igumnov (2017) consists of three interconnected parts: relations defining thermoplastic behavior of the material, accounting for its dependence on the failure process; evolutionary equations describing damage accumulation kinetics; a strength criterion of the damaged material. 2.1. Defining relations of plasticity In the elastic region, the relation between spherical and deviatoric components of stress and strain tensors and their rates is described by Hooke’s law:

' К е Т Т К K Gе G G             ' 3 ( ) / , 2 / е 

3 [ ( К е Т Т 

' 2 , e ij Gе

)],

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ij 

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,

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