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Mathematical Modeling of the Monotonic and Cyclic Loading Processes

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Based on experimental studies of specimens of 12Kh18N10T stainless steel under a rigid (strain-controlled) deformation process, which includes a sequence of monotonic and cyclic loading modes, some features and differences between isotropic and anisotropic hardening under monotonic and cyclic loading are found. To describe these features in terms of the theory of plasticity (the Bondar model), the criterion of change of plastic deformation direction and a memory surface are introduced in the space of the plastic strain tensor, which allow one to separate the processes of monotonic and cyclic loading. To describe the transitional processes, evolutionary equations for isotropic and anisotropic hardening parameters are formulated. The change in the stress-strain state during monotonic and cyclic loading, obtained by calculation and experiment, is compared.

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References

  1. V. S. Bondar, Inelastic Behavior and Fracture of Materials and Structures under Complex Nonisothermal Loading [in Russian], Doctoral Dissertation (Phys.-Math. Sci.), MAMI, Moscow (1990).

  2. V. S. Bondar, Inelasticity. Variants of the Theory [in Russian], Fizmatlit, Moscow (2004).

  3. V. S. Bondar, Inelasticity. Variants of the Theory, Begell House, New York (2013).

    Google Scholar 

  4. I. A. Volkov and Yu. G. Korotkikh, Equations of State of Damaged Viscoelastoplastic Media [in Russian], Fizmatlit, Moscow, (2008).

  5. S. A. Kapustin, Yu. A. Churilov, and V. A. Gorokhov, Modeling of Nonlinear Deformation and Fracture of Structures under Conditions of Multifactorial Effects Based on the FEM [in Russian], NNGU, Nizhny Novgorod (2015).

  6. J. Besson, G. Cailletaud, J.-L. Chaboche, and S. Forest, Non-Linear Mechanics of Materials, Springer (2010).

  7. J.-L. Chaboche, “A review of some plasticity and viscoplasticity constitutive theories,” Int. J. Plasticity, 24, 1642–1692 (2008).

    Article  CAS  Google Scholar 

  8. J.-L. Chaboche, P. Kanouté, and F. Azzouz, “Cyclic inelastic constitutive equations and their impact on the fatigue life predictions,” Int. J. Plasticity, 35, 44–66 (2012).

    Article  CAS  Google Scholar 

  9. V. S. Bondar, V. V. Danshin, and D. A. Makarov, “Mathematical modeling of deformation and damage accumulation under cyclic loading,” PNRPU Mech. Bull., No. 2, 125–152 (2014).

  10. V. S. Bondar, D. R. Abashev, and V. K. Petrov, “Comparative analysis of variants of plasticity theories under cyclic loading,” PNRPU Mech. Bull., No. 2, 23–44 (2017).

  11. Yu. G. Korotkikh, “A description of the processes of accumulation of damages of a material in nonisothermal viscoplastic deformation,” Strength Mater., 17, No. 1, 21–26 (1985).

    Article  Google Scholar 

  12. I. L. Volkov, L. A. Igumnov, I. S. Tarasov, et al., “Modeling fatigue life for polycrystalline structural alloys under block-type nonsymmetrical low-cycle loading,” Probl. Prochn. Plast., No. 1, 15–30 (2018).

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Authors and Affiliations

  1. Moscow Polytechnic University, Moscow, Russia

    V. S. Bondar & D. R. Abashev

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  1. V. S. Bondar
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  2. D. R. Abashev
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Correspondence to V. S. Bondar.

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Translated from Problemy Prochnosti, No. 3, pp. 36 – 45, May – June, 2020.

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Bondar, V.S., Abashev, D.R. Mathematical Modeling of the Monotonic and Cyclic Loading Processes. Strength Mater 52, 366–373 (2020). https://doi.org/10.1007/s11223-020-00186-7

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  • DOI: https://doi.org/10.1007/s11223-020-00186-7

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