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Theory and Computation of Nonlinear Damage Accumulation for Lifetime Prediction

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New Achievements in Continuum Mechanics and Thermodynamics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 108))

Abstract

Nonlinear damage accumulation is modelled for the lifetime prediction in order to capture the loading sequence effect, which is the influence of the chronological order of the loading values on the lifetime. The prediction results from the solution of the damage evolution equation, which is defined according to the theory of continuum damage mechanics and applied together with a cohesive zone model for structural adhesive joints. The damage model consists of a creep and fatigue damage part, both taking into account the influence of the mean stress and the load multiaxiality on the predicted time to rupture. The analytical investigation of the model shows the meaning of the model parameters and propose their identification by means of tests with static and constant amplitude loading. In order to capture the loading sequence effect by nonlinear damage accumulation, the fatigue damage part is enhanced with a factor, which influences the predicted lifetime due to variable amplitude loading in the case of pure fatigue damage, while the prediction for constant amplitude loading is unaffected. The influences of the enhancement on the predicted lifetime and the damage evolution are discussed. The comparison of lifetimes with numerical predictions proves the validity of the proposed approach.

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Reference

  • Basquin OH (1910) The exponential law of endurance tests. ASTM 10:625–630

    Google Scholar 

  • Cailletaud G, Levaillant C (1984) Creep-fatigue life prediction: what about initiation? Nucl Eng Des 84:279–292

    Google Scholar 

  • Cailletaud G, Nouailhas D, Grattier J, Levaillant C, Mottot M, Tortel J, Escavarage C, Héliot J, Kang S (1984) A review of creep-fatigue life prediction methods: identification and extrapolation to long term and low strain cyclic loading. Nucl Eng Des 83:267–278

    Google Scholar 

  • Cavdar S, Meschut G (2017) Analyse der Schwingfestigkeit geklebter Stahlverbindungen unter mehrkanaliger Belastung. Tech. rep., Forschungsvereinigung Stahlanwendung e.V., number = FOSTA-Report P1028, chap 11-12, Düsseldorf

    Google Scholar 

  • Cavdar S, Kroll U, Meschut G, Matzenmiller A (2018) Experimental characterization and numerical lifetime prediction of adhesively bonded joints under multiaxial fatigue loading. In: Proc Adh Soc 2018

    Google Scholar 

  • Chaboche JL (1978) Description thermodynamique et phénoménologique de la viscoplasticité cyclique avec endommagement. Dissertation, Université Pierre et Marie Curie, Paris

    Google Scholar 

  • Chaboche JL (1981) Continuous damage mechanics—A tool to describe phenomena before crack initiation. Nucl Eng Des 64(2):233–247

    Google Scholar 

  • Chaboche JL (1987) Continuum damage mechanics: present state and future trends. Nucl Eng Des 105:19–33

    Google Scholar 

  • Chaboche JL (1988a) Continuum damage mechanics: Part I - general concepts. J Appl Mech 55:59–64

    Google Scholar 

  • Chaboche JL (1988b) Continuum damage mechanics: Part II - damage growth, crack initiation, and crack growth. J Appl Mech 55:65–72

    Google Scholar 

  • Chaboche JL (2003) Damage Mechanics. In: Karihaloo B, Knauss WG (eds) Fundamental Theories and Mechanisms of Failure, Elsevier, Comprehensive Structural Integrity, vol 2, pp 213–284

    Google Scholar 

  • Chaboche JL (2011) Cumulative Damage. In: Bathias C, Pineau A (eds) Fatigue of Materials and Structures, John Wiley & Sons

    Google Scholar 

  • Chaboche JL, Lesne PM (1988) A non-linear continous fatigue damage model. Fatigue Fract Eng Mater Struct 11(1):1–17

    Google Scholar 

  • Coleman BD, Gurtin ME (1967) Thermodynamics with internal state variables. J Chem Phys 47(2):597–613

    Google Scholar 

  • Do VNV, Lee CH, Chang KH (2015) High cycle fatigue analysis in presence of residual stresses by using a continuum damage mechanics model. Int J Fatigue 70:51–62

    Google Scholar 

  • Erpolat S, Ashcroft IA, Crocombe AD, Abdel-Wahab MM (2004) A study of adhesively bonded joints subjected to constant and variable amplitude fatigue. Int J Fatigue 26(11):1189–1196

    Google Scholar 

  • Kachanov LM (1958) On rupture time under conditions of creep. Izv Akad Nauk Sssr Otdelenie, Otd Tech 8(2631):26–31, in Russian. English translation (1999) Rupture time under creep conditions. Int J Fract 97:11–18.

    Google Scholar 

  • Krajcinovic D, Lemaitre J (1987) Continuum Damage Mechanics: Theory and Applications. Springer

    Google Scholar 

  • Kroll U (2018) Modellierung der Schädigungsentwicklung und Lebensdauerprognose für Stahlklebverbindungen unter hochzyklischer Ermüdungsbelastung. Dissertation, Fachbereich Maschinenbau, Universität Kassel

    Google Scholar 

  • Kroll U, Matzenmiller A (2015) Parameter identification of a damage model for the lifetime prediction of adhesively bonded joints. In: Saanouni K (ed) Damage Mechanics: Theory, Computation and Practice, Trans Tech Publications, Appl Mech Mater, vol 784, pp 300–307

    Google Scholar 

  • Kroll U, Matzenmiller A (2016) On nonlinear damage accumulation and creep-fatigue interaction of a damage model for the lifetime prediction of adhesively bonded joints. PAMM 16(1):151–152

    Google Scholar 

  • Kroll U, Matzenmiller A (2017) Analyse der Schwingfestigkeit geklebter Stahlverbindungen unter mehrkanaliger Belastung. Tech. Rep. FOSTA-Report P1028, chap 13-15, Forschungsvereinigung Stahlanwendung e.V., Düsseldorf

    Google Scholar 

  • Lemaitre J (1979) Damage Modeling for Prediction of Plastic or Creep Fatigue Failure in Structures. In: Proc IASMiRT 1979 (Trans. 5th Intl. Conf. Struct. Mech. React. Tech.)

    Google Scholar 

  • Lemaitre J (1984) How to use damage mechanics. Nucl Eng Des 80:233–245

    Google Scholar 

  • Lemaitre J (1996) A Course on Damage Mechanics. Springer

    Google Scholar 

  • Lemaitre J, Chaboche JL (1975) A Non-Linear Model of Creep-Fatigue Damage Cumulation and Interaction. In: Hult J (ed) Mechanics of Visco-Elastic Media and Bodies, Springer, pp 291–301

    Google Scholar 

  • Lemaitre J, Chaboche JL (1990) Mechanics of Solid Materials. Cambridge University Press

    Google Scholar 

  • Lemaitre J, Desmorat R (2005) Engineering Damage Mechanics. Springer

    Google Scholar 

  • Lemaitre J, Doghri I (1994) Damage 90: a post processor for crack initiation. Comput Methods Appl Mech Eng 115(3–4):197–232

    Google Scholar 

  • Lemaitre J, Dufailly J (1987) Damage measurements. Eng Fract Mech 28(5–6):643–661

    Google Scholar 

  • Lemaitre J, Plumtree A (1979) Application of damage concepts to predict creep-fatigue failures. J Eng Mater Technol 101(3):284–292

    Google Scholar 

  • Matzenmiller A, Kurnatowski B (2012) Schwingfestigkeitsauslegung von geklebten Stahlbauteilen des Fahrzeugbaus unter Belastung mit variablen Amplituden. Tech. Rep. FOSTA-Report P796, pp. 51–101, 133–138, 210–215, Forschungsvereinigung Stahlanwendung e.V., Verlag und Vertriebsgesellschaft mbH, Düsseldorf

    Google Scholar 

  • Miner MA (1945) Cumulative damage in fatigue. J Appl Mech 67:A159–A164

    Google Scholar 

  • Murakami S, Ohno N (1981) A Continuum Theory of Creep and Creep Damage. In: Ponter ARS, Hayhurst DR (eds) Creep in Structures, Springer, pp 422–444

    Google Scholar 

  • Normenausschuss Bauwesen (NABau) im DIN (2010) Eurocode 3: Bemessung und Konstruktion von Stahlbauten - Teil 1-8: Bemessung von Anschlüssen. DIN Deutsches Institut für Normung e. V.

    Google Scholar 

  • Normenausschuss Bauwesen (NABau) im DIN (2011) Eurocode 9: Bemessung und Konstruktion von Aluminiumtragwerken - Teil 1-3: Ermüdungsbeanspruchte Tragwerke. DIN Deutsches Institut für Normung e. V.

    Google Scholar 

  • Ostergren WJ, Krempl E (1979) A uniaxial damage accumulation law for time-varying loading including creep-fatigue interaction. J Press Vessel Technol 101:118–124

    Google Scholar 

  • Paas M, Schreurs P, Brekelmans W (1993) A continuum approach to brittle and fatigue damage: theory and numerical procedures. Int J Solids Struct 30(4):579–599

    Google Scholar 

  • Palmgren A (1924) Die Lebensdauer von Kugellagern. Zeitschrift des Vereines Deutscher Ingenieure (VDI Zeitschrift) 68(14):339–341

    Google Scholar 

  • Pavlou D (2001) Creep life prediction under stepwise constant uniaxial stress and temperature conditions. Eng Struct 23(6):656–662

    Google Scholar 

  • Rabotnov YN (1963) On the Equation of State of Creep. Proc IMechE 1963 (Joint Intl Conf Creep) 178(68):2–117–2–122

    Google Scholar 

  • Rabotnov YN (1969) Creep rupture. In: Hetenyi M, Vincenti M (eds) Applied Mechanics – Proceedings of the XII International Congress on Applied Mechanics, Springer, pp 342–349

    Google Scholar 

  • Rennert R, Kullig E, Vormwald M, Esderts A, Siegele D (2012) Rechnerischer Festigkeitsnachweis für Maschinenbauteile aus Stahl, Eisenguss und Aluminiumwerkstoffen: FKM-Richtlinie, 6th edn. Forschungskuratorium Maschinenbau e. V. (FKM), VDMA Verlag

    Google Scholar 

  • Robinson E (1938) Effect of temperature variation on the creep strength of steels. Trans ASME 160:253–259

    Google Scholar 

  • Schlimmer M, Hahn O, Hennemann OD, Mihm KM, Jendrny J, Teutenberg D, Brede M, Nagel C (2012) Methodenentwicklung zur Berechnung und Auslegung geklebter Stahlbauteile im Fahrzeugbau bei schwingender Beanspruchung. Tech. Rep. FOSTA-Report P653, Forschungsvereinigung Stahlanwendung e.V., Düsseldorf

    Google Scholar 

  • Schneider B, Kehlenbeck H, Nagel C (2012) Schwingfestigkeitsauslegung von geklebten Stahlbauteilen des Fahrzeugbaus unter Belastung mit variablen Amplituden. Tech. Rep. FOSTA-Report P796, chap 2, Forschungsvereinigung Stahlanwendung e.V., Düsseldorf

    Google Scholar 

  • Su C, Wei YJ, Anand L (2004) An elastic–plastic interface constitutive model: application to adhesive joints. Int J Plast 20(12):2063–2081

    Google Scholar 

  • Todinov M (2001) Necessary and suffcient condition for additivity in the sense of the Palmgren–Miner rule. Comput Mater Sci 21(1):101–110

    Google Scholar 

  • Truesdell C, Toupin RA (1960) The Classical Field Theories. In: Flügge S (ed) Principles of Classical Mechanics and Field Theory, Handbuch der Physik, vol 3/I, Springer

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mechanics, Department of Mechanical Engineering, University of Kassel, Mönchebergstraße 7, 34125, Kassel, Germany

    Anton Matzenmiller & Ulrich Kroll

Authors
  1. Anton Matzenmiller
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  2. Ulrich Kroll
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Correspondence to Anton Matzenmiller .

Editor information

Editors and Affiliations

  1. Institute of Mechanics, Technische Universität Berlin, Berlin, Germany

    Bilen Emek Abali

  2. Institut für Mechanik, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany

    Holm Altenbach

  3. Dipartimento di Ingegneria Strutturale e Geotecnica, Università degli Studi di Roma “La Sapienza”, Roma, Italy

    Francesco dell'Isola

  4. Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Gdansk, Poland

    Victor A. Eremeyev

  5. Fakultät Maschinenbau, Esslingen University of Applied Sciences, Esslingen, Germany

    Andreas Öchsner

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Matzenmiller, A., Kroll, U. (2019). Theory and Computation of Nonlinear Damage Accumulation for Lifetime Prediction. 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_22

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  • DOI: https://doi.org/10.1007/978-3-030-13307-8_22

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