PSI - Issue 40

Artyom A. Tokarev et al. / Procedia Structural Integrity 40 (2022) 426–432 Artyom A. Tokarev, Anton Yu. Yants / Structural Integrity Procedia 00 (2022) 000 – 000

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intervals calculated using Student’s distribution) has a complex shape with a rapid damping of fluctuations and also seem to reach a constant value. 4. Summary In this work, algorithm for a series of numerical experiments to determine the representative volume of a polycrystal sample was described, the results of standard deviations, mean values of stress and an estimate of the amplitude of their fluctuations were calculated. For a polycrystal of more than 300 grains, the change rate of the mean stress is less than 1%, and the probability of deviation of the stress intensity from the mean value by more than 2% is less than 5% according to the three-sigma rule under the assumption of a normal distribution of stress intensity. Acknowledgements The work was supported by a grant from the Russian Science Foundation (Grant No. 17-19-01292). References Trusov, P.V., Shveykin, A.I., Nechaeva, E.S. et al. Multilevel models of inelastic deformation of materials and their application for description of internal structure evolution. Phys Mesomech 15, 155 – 175 (2012). Trusov, P.V., Shveykin, A.I. On motion decomposition and constitutive relations in geometrically nonlinear elastoviscoplasticity of crystallites. Phys Mesomech 20, 377 – 391 (2017). Truesdell, C. A First Course in Rational Continuum, Continuum mechanics, vols. I-IV (Gordon and Breach, New York, 1965), 304 p. Trusov, P.V., Nechaeva, E.S., Shveykin, A.I. Asymmetric stress-strain measures in construction of multilevel constitutive. Fizicheskaya mesomechanika 16, 15-31 (2013) (in Russian). Asaro, R.J., Needleman A. Texture development and strain hardening in rate dependent polycrystals. Acta Metall 33, 1985, No.6, 923 – 953. Franciosi, P. The concepts of latent hardening and strain hardening in metallic single crystals. Acta Metall 33, 1985, 1601-1612. Kondratev, N.S., Trusov, P.V., PNRPU Mechanics Bulletin 3, 78-97 (2012) (in Russian). Yants A.Yu., 2016, Two-level model for describing inelastic deformation of polycrystals: application to the analysis of complex loading in the case of large displacement gradients, PhD thesis, Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science (ICMM UB RAS), Perm. Trusov, P.V., Shveykin, A.I. Multilevel crystal plasticity models of single- and polycrystals. Direct models. Phys Mesomech 16, 99 – 124 (2013). Yants A.Yu., Trusov P.V., Teplyakova L.A. Direct Crystal Plasticity Model: Application to Investigation of Single Crystal Fragmentation under Uniaxial Loading. AIP Conference Proceedings 1909, 2017, 020231. Hirth, J.P., Lothe, J. Theory of dislocations (Krieger Publishing Company, Florida, 1982), 857 p. Honeycombe, R. The plastic deformation of metals. 2nd Edit. (London, Baltimore, Md. 1984), 483 p.