Abstract
Processes of plastic deformation and damage accumulation in polycrystalline structural alloys are investigated under block-type, nonstationary, non-symmetric cyclic loading. In the framework of damage mechanics, a mathematical model is proposed that effectively describes elastoplastic deformation and fatigue related damage accumulation processes under low-cycle loading. This model can be subsumed under three main parts: the relations defining elastoplastic behavior of the material; the equations describing damage accumulation kinetics; the strength criterion of the damaged material. For validating the model, we perform a numerical analysis and a comparison with the data from full-scale experiments.We demonstrate that the proposed model qualitatively and quantitatively describes the main effects of plastic deformation and damage accumulation processes in structural alloys under complex loading scenarios. Moreover, fatigue related lifetime of the structure is accurately captured by this model as well.
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Abali BE (2017a) Computational Reality, Solving Nonlinear and Coupled Problems in Continuum Mechanics, Advanced Structured Materials, vol 55. Springer Nature, Singapore
Abali BE (2017b) Computational study for reliability improvement of a circuit board. Mechanics of Advanced Materials and Modern Processes 3(1):1–11
Altenbach H, Eremeyev V (2014a) Strain rate tensors and constitutive equations of inelastic micropolar materials. International Journal of Plasticity 63:3–17
Altenbach H, Eremeyev VA (2014b) Basic equations of continuum mechanics. In: Plasticity of Pressure-Sensitive Materials, Springer, pp 1–47
Bodner SR, Lindholm US (1976) Kriteriy prirasheniya povrezhdeniya dlya zavisyashego ot vremeni razrusheniya materialov (in Russian). Trudy Amer Ob-va inzh-meh Ser D Teoret Osnovy inzh Raschetov 100(2):51–58
Bondar VS, Danshin VV (2008) Plastichnost. proportsyonalnye i neproportsyonalalnye nagruzheniya (in Russian). M: Fizmatlit p 176
Chaboche JL (1989) Constitutive equations for cyclic plasticity and cyclic viscoplasticity. International journal of plasticity 5(3):247–302
Collins J (1984) Povrezhdeniye materialov v konstruktziyah. Analiz. Predskazaniye. Predotvrasheniye (in Russian). M: Mir
Eremeyev VA, Skrzat A, Stachowicz F (2016) On FEM evaluation of stress concentration in micropolar elastic materials. Nanoscience and Technology: An International Journal 7(4)
Giorgio I, Andreaus U, Scerrato D, dell’Isola F (2016) A visco-poroelastic model of functional adaptation in bones reconstructed with bio-resorbable materials. Biomechanics and modeling in mechanobiology 15(5):1325–1343
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(10):1863–1889
Huang ZY, Chaboche JL, Wang QY, 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: A 589:34–40
Jiang Y, Zhang J (2008) Benchmark experiments and characteristic cyclic plasticity deformation. International Journal of Plasticity 24(9):1481–1515
Korotkikh YG (1985) Opisaniye protsessov nakopleniya povrezhdeniy materiala pri neizotermicheskom vyazkoplasticheskom deformirovanii (in Russian). Problemy prochnosti 1:18–23
Lemaitre J (1985) Kontinualnaya model povrezhdeniya, ispolzuemaya dlya rascheta razrusheniya plastichnykh materialov (in Russian). Trudy Amer Ob-va inzh-meh Ser D Teoret Osnovy inzh Raschetov 107(1):90–98
Lemba (1978) Sisebottom plastichnost pri cyklicheskim nagruzhenii po neproportsionalnym traektoriyam (in Russian). Teoreticheskiye osnovy inzhenernykh raschetov 100(1):108–126
Mackenzie J (1950) The elastic constants of a solid containing spherical holes. Proceedings of the Physical Society Section B 63(1):2
Makdauel (1985) Eksperimentalnoye izuchenie struktury opredelyayushih uravneniy dlya neproportsionalnoy cyklicheskoy plastichnosti (in Russian). Teoreticheskiye osnovy inzhenernykh raschetov 107(4):98–111
Mazière M, Forest S (2015) Strain gradient plasticity modeling and finite element simulation of lüders band formation and propagation. Continuum Mechanics and Thermodynamics 27(1-2):83–104
Miehe C, Göktepe S, Diez JM (2009) Finite viscoplasticity of amorphous glassy polymers in the logarithmic strain space. International Journal of Solids and Structures 46(1):181–202
Misra A, Poorsolhjouy P (2015) Granular micromechanics model for damage and plasticity of cementitious materials based upon thermomechanics. Mathematics and Mechanics of Solids p 1081286515576821
Mitenkov AM, Kaydalov VB, Korotkikh YG (2007) Metody obosnovaniya resursa yaeu (in Russian). Mashinostroyeniye p 445
Mitenkov FM, Volkov IA, Igumnov LA (2015) Prikladnaya teoriya plastichnosti (in Russian). Fizmatlit p 284
Montáns FJ, Bathe KJ (2005) Computational issues in large strain elasto-plasticity: an algorithm for mixed hardening and plastic spin. International Journal for Numerical Methods in Engineering 63(2):159–196
Murakami S (1983) Sushnost mehaniki povrezhdennoy sredy i eyo prilozheniye k teorii anizotropnykh povrerzhdeniy pri polzuchesti (in Russian). TOIR 2:44–50
Ohasi, Kavai, Kaito (1985) Neuprugoye povedeniye stali 316 pri mnogoosnykh neproportsionalnykh zyklicheskikh nagruzheniyakh pri povyshennoy temperature (in Russian). Teoreticheskiye osnovy inzhenernykh raschetov 107(2):6–15
Papadopoulos P, Lu J (1998) A general framework for the numerical solution of problems in finite elasto-plasticity. Computer Methods in Applied Mechanics and Engineering 159(1-2):1–18
Papadopoulos P, Lu J (2001) On the formulation and numerical solution of problems in anisotropic finite plasticity. Computer Methods in Applied Mechanics and Engineering 190(37-38):4889–4910
Placidi L (2016) A variational approach for a nonlinear one-dimensional damage-elasto-plastic second-gradient continuum model. Continuum Mechanics and Thermodynamics 28(1-2):119–137
Schröder J, Gruttmann F, Löblein J (2002) A simple orthotropic finite elasto–plasticity model based on generalized stress–strain measures. Computational Mechanics 30(1):48–64
Soyarslan C, Tekkaya A (2010) A damage coupled orthotropic finite plasticity model for sheet metal forming: Cdm approach. Computational Materials Science 48(1):150–165
Taleb L, Cailletaud G, Saï K (2014) Experimental and numerical analysis about the cyclic behavior of the 304L and 316L stainless steels at 350℃. International Journal of Plasticity 61:32–48
Tanaka E, Murakami S, Ōoka M (1985a) Effects of plastic strain amplitudes on non-proportional cyclic plasticity. Acta Mechanica 57(3-4):167–182
Tanaka E, Murakami S, Ōoka M (1985b) Effects of strain path shapes on non-proportional cyclic plasticity. Journal of the Mechanics and Physics of Solids 33(6):559–575
Volkov IA, Igumnov LA (2017) Vvedenie v kontinualnuyu mehaniku povrezhdennoy sredy (in Russian). M: Fizmatlit p 304
Volkov IA, Korotkikh YG (2008) Uravneniya sostoyaniya vyazkouprugoplasticheskikh sred s povrezhdeniyami (in Russian). Fizmatlit p 424
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dell’Isola, F. et al. (2019). Estimating Fatigue Related Damage in Alloys under Block-type Non-symmetrical Low-cycle Loading. In: Abali, B., Altenbach, H., dell'Isola, F., Eremeyev, V., Öchsner, A. (eds) New Achievements in Continuum Mechanics and Thermodynamics. Advanced Structured Materials, vol 108. Springer, Cham. https://doi.org/10.1007/978-3-030-13307-8_6
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