Abstract
The processes of plastic deformation and damage accumulation of polycrystalline structural alloys under block-type non-stationary asymmetric cyclic loading are considered. A mathematical model describing the processes of thermoplastic deformation and fatigue damage accumulation under low-cycle loading has been developed, based on the viewpoint of mechanics of damaged media (MDM). The MDM model consists of three interrelated parts: governing equations defining the cyclic thermoplastic behavior of the material, taking into account its dependence on the failure process; equations describing the kinetics of damage accumulation; a strength criterion of the damaged material. A version of the constitutive equations of elastoplasticity is based on the concept of the yield surface and the gradient principle of the plastic strain rate vector to the yield surface in the loading point. This version of equations of state reflects the main effects of the cyclic thermoplastic material deformation process for arbitrary complex deformation trajectories. A version of the kinetic equations of damage accumulation based on the introduction of a scalar damage parameter has been proposed. Based on the energy principles, it accounts for the main effects of nucleation, growth and merging of microdefects under random complex regimes of low-cycle loading. The condition for achieving the critical damage value is used as the strength criterion of a damaged material. To assess the reliability and determine the scope of applicability of the constitutive equations of MDM, the processes of plastic deformation and damage accumulation in a number of structural steels in low-cycle tests have been numerically analyzed, and the obtained numerical results have been compared with the data of full-scale experiments. It is shown that the proposed model of damaged media qualitatively and quantitatively, with the accuracy required for practical calculations, describes the main effects of plastic deformation processes and fatigue damage accumulation in structural alloys under block non-stationary asymmetric low-cycle loading.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abali, B. E., Muller, W., & dell’Isola, F. (2017). Theory and computation of higher gradient elasticity theories based on action principles. Archive of Applied Mechanics, 87, 1495–1510.
Alibert, J. J., Seppecher, P., & dell’Isola, F. (2003). Truss modular beams with deformation energy depending on higher displacement gradients. Mathematics and Mechanics of Solids, 8, 51–73.
Auffray, N., dell’Isola, F., Eremeyev, V., Madeo, A., & Rosi, G. (2013). Analytical continuum mechanics à la Hamilton-Piola: Least action principle for second gradient continua and capillary fluids. Mathematics and Mechanics of Solids.
Barchiesi, E., Spagnuolo, M., & Placidi L. (2018). Mechanical metamaterials: A state of the art. Mathematics and Mechanics of Solids.
Bodner S. R., & Lindholm, U. S. (1976). Kriterii prirashcheniia povrezhdeniia dlia zavisiashchego ot vremeni razrusheniia materialov. Trudy Amer. ob-va inzh.-mekh. Ser. D. Teoret. osnovy inzh. Raschetov, 100(2), 51–58.
Bondar, V. S., & Danshin V. V. (2008) Plastichnost. Proportsionalnye i neproportsionalnye nagruzheniya. (in Rus.) M.: Fizmatlit. – 176 s.
Chaboche, J. L. (1989). Constitutive equation for cyclic plasticity and cyclic viscoplasticity. International Journal of Plasticity, 5(3), 247–302.
Del Vescovo, D., & Giorgio, I. (2014). Dynamic problems for metamaterials: Review of existing models and ideas for further research. International Journal of Engineering Science, 80, 153–172.
dell’Isola, F., Della, C. A., & Giorgio, I. (2017). Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives. Mathematics and Mechanics of Solids, 22, 852–872.
dell’Isola, F., Seppecher, P., Alibert, J. J., Lekszycki, T., Grygoruk, R., Pawlikowski, M., et al. (2019). Pantographic metamaterials: An example of mathematically driven design and of its technological challenges. Continuum Mechanics and Thermodynamics, 31(4), 851–884.
dell’Isola, F., Seppecher, P., & Madeo, A. (2012). How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: Approach “à la D’Alembert.” Zeitschrift für Angewandte Mathematik und Physik, 63, 1119–1141.
dell’Isola, F., Andreaus, U., & Placidi, L. (2015). At the origins and in the vanguard of peri-dynamics, non-local and higher gradient continuum mechanics. An underestimated and still topical contribution of Gabrio Piola. Mathematics and Mechanics of Solids, 20, 887–928.
Guozheng, K., Qing, G., Lixun, C., & Yafang, S. (2002). Experimental study on uniaxial and nonproportionally multiaxial ratcheting of SS304 stainless steel at room and high temperatures. Nuclear Engineering and Design, 216, 13–26.
Hassan, T., Taleb, L., & Krishna, S. (2008). Influence of non-proportional loading on ratcheting responses and simulations by two recent cyclic plasticity models. International Journal of Plasticity, 24, 1863–1889.
Huang, Z. Y., Chaboche, J. L., Wang, Q. Y., Wagner, D., & Bathias C. (2014). Effect of dynamic strain aging on isotropic hardening in low cycle fatigue for carbon manganese steel. Materials Science and Engineering, A589, 34–40.
Jiang, Y., & Zhang, J. (2008). Benchmark experiments and characteristic cyclic plasticity deformation. International Journal of Plasticity, 24, 1481–1515.
Kollinz, G. (1984). Povrezhdeniye materialov v konstructsiyakh. Analiz. Predskazaniye. Predotvrashcheniye. M.: Mir.
Korotkikh, Yu. G., Volkov, I. A., Igumnov, L. A., Shishulin, D. N., & Guseva, M. A. (2016). Modelirovanie slozhnogo plasticheskogo deformirovaniya i nakopleniya ustalostnyh povrezhdenij v zharoprochnyh splavah pri kombinirovannom termomekhanicheskom nagruzhenii (in Rus). Vol. 78. No. 1. P. 45–59.
Korotkikh, Yu. G., Volkov, I. A., Igumnov, L. A., Shishulin, D. N., & Tarasov, I. S. (2015). Modelirovanie processov neuprugogo deformirovaniya i razrusheniya zharoprochnyh splavov pri ciklicheskom termomekhanicheskom nagruzhenii (in Rus). Vol. 77. No.4. P. 329–343.
Lamba, S. (1978). Plastichnost pri tsiklicheskom nagruzhenii po neproportsionalnym traektoriyam (in Rus.). Teoreticheskiye osnovy inzhenernyh raschetov, 100(1), 108–126.
Lemaitre, G. (1985) Kontinualnaya model povrezhdeniya, ispolzuemaya dlya rascheta razrusheniya plastichnykh materialov. Trudy Amer. ob-va inzh.-mekh. Ser. D. Teoret. osnovy inzh. Raschetov, 107(1), 90–98.
Macdowell. (1985). Eksperimentalnoye izucheniye struktury opredelyayushih uravneniy dlya neproportsionalnoy tsiklicheskoy plastichnosti (in Rus.). Teoreticheskiye osnovy inzhenernyh raschetov (4), 98–111.
Mackenzie, J. K. (1950). The elastic constants of a solid containing spherical holes. Proceedings of the Physical Society. Section B, 63(2).
Misra, A., & Poorsolhjouy, P. (2015). Granular micromechanics model for damage and plasticity of cementitious materials based upon thermomechanics. Mathematics and Mechanics of Solids.
Misra, A., & Singh, V. (2015). Thermomechanics-based nonlinear rate-dependent coupled damage-plasticity granular micromechanics model. Continuum Mechanics and Thermodynamics, 27, 787–817.
Mitenkov, F. M., Kaydalov, V. B., & Korotkikh, Yu. G. i dr. (2007). Metody obosnovaniya resursa YaEU.(in Rus.) – M.: Mashinostroyeniye, 2007. – 445s.
Mitenkov, F. M., Volkov, I. A., Igumnov, L. A., & Korotkikh, Yu. G. i dr. (2015). Prikladnaya teoriya plastichnosti. (in Rus.) – M.: Fizmatlit, 2015. – 284 s.
Murakami, E. (1983). Sushchnost mehaniki povrezhdennoi sredy I eye prilozheniye k teorii anizotropnykh povrezhdeniy pri polzuchesti. TOIR, 2, 44–50.
Ohasi, Kavan, Kaito. (1985). Neuprugoye povedeniye stali 316 pri mnogoosnyh neproportsionalnyh tsiklicheskih nagruzheniyah pri povyshennoy temperature (in Rus.). Teoreticheskiye osnovy inzhenernyh raschetov. 107(2), 6–15.
Placidi, L. (2015). A variational approach for a nonlinear one-dimensional damage-elasto-plastic second-gradient continuum model. Continuum Mechanics and Thermodynamics, 28, 119–137.
Placidi, L., Barchiesi, E., & Misra, A. (2018). A strain gradient variational approach to damage: A comparison with damage gradient models and numerical results. Mathematics and Mechanics of Complex Systems, 6, 77–100.
Placidi, L., Barchiesi, E., Turco, E., & Rizzi, N. L. (2016). A review on 2D models for the description of pantographic fabrics. Zeitschrift für angewandte Mathematik und Physik, 67.
Placidi, L., Misra, A., & Barchiesi, E. (2019). Simulation results for damage with evolving microstructure and growing strain gradient moduli. Continuum Mechanics and Thermodynamics, 31, 1143–1163.
Taleb, L., Cailletaud, G., & Sa’i, K. (2014). Experimental and numerical analysis about the cyclic behavior of the 304L and 316L stainless steels at 350 °C. International Journal of Plasticity, 61, 32–48.
Tanaka, E., Murakami, S., & Ooka, M. (1985a). Effects of strain path shapes on nonproportional cyclic plasticity. Journal of the Mechanics and Physics of Solids, 33(6), 559–575.
Tanaka, E., Murakami, S., & Ooka, M. (1985b). Effects of plastic strain amplitudes on non-proportional cyclic plasticity. ActaMechanica, 57, 167–182.
Volkov, I. A., & Igumnov, L. A. (2017). Vvedeniye v kontinualnyyu mekhaniku povrezhdennoy sredy (in Rus). M.: Fizmatlit. P. 304.
Volkov, I. A., Igumnov, L. A., Korotkih, Yu. G., Kazakov, D. A., Emel’yanov, A. A., Tarasov, I. S., et al. (2016). Programmnaya realizatsiya protsessov vyazkoplasticheskogo deformirovaniya i nakopleniya povrezhdeniy v konstrukcionnyh splavah pri termomekhanicheskom nagruzhenii (in Rus). Vol. 78. No. 2. P. 188–207.
Volkov I.A., Korotkikh Yu.G., 2008, Uravneniya sostoyaniya vyazkouprugoplasticheskih sred s povrezhdeniyami. (in Rus). M.: Fizmatlit. P. 424.
Zhao, C.-F., Yin, Z.-Y., Misra, A., & Hicher, P.-Y. (2018). Thermomechanical formulation for micromechanical elasto-plasticity in granular materials. International Journal of Solids and Structures, 138, 64–75.
Acknowledgements
The reported study was funded by RFBR, project numbers 18-08-00881, 20-08-00450.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Volkov, I.A., Igumnov, L., Tarasov, I.S., Shishulin, D.N., Kapitanov, D.V. (2021). Modeling Fatigue Life of Structural Alloys Under Block Asymmetric Loading. In: dell'Isola, F., Igumnov, L. (eds) Dynamics, Strength of Materials and Durability in Multiscale Mechanics. Advanced Structured Materials, vol 137. Springer, Cham. https://doi.org/10.1007/978-3-030-53755-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-53755-5_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-53754-8
Online ISBN: 978-3-030-53755-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)