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Capabilities of the Multi-mechanism Model in the Prediction of the Cyclic Behavior of Various Classes of Metals

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From Creep Damage Mechanics to Homogenization Methods

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 64))

Abstract

The paper deals with an evaluation of the multi-mechanism (MM) approach capabilities in the prediction of the cyclic behavior of different classes of metallic materials. For this objective, the tests detailed in (Taleb, Int J Plast 43:1–19, 2013a) have been simulated here by the MM model. In these tests, six alloys were considered: two ferritic steels (35NCD16 and XC18), two austenitic stainless steels (304L and 316L), one “extruded” aluminum alloy (2017A) and one copper-zinc alloy (CuZn27). The specimens have been subjected to proportional and non-proportional stress as well as the combination of stress and strain control at room temperature. The identification of the material parameters has been carried out using exclusively strain controlled experiments under proportional and non-proportional loading paths performed in the present study for each material. The model may describe a large number of phenomena with twenty five parameters in total but, it appears that for a given material under the adopted conditions, the activation of all parameters may be not necessary. Our attention was focused mainly on the capabilities to predict correctly the cyclic accumulation of the inelastic strain including the shape of the hysteresis loops. The comparison between test responses and their predictions by the MM model are generally satisfactory with relatively small number of material parameters (between eight and thirteen according to the material). One can also highlight the capability of the MM model to describe a transient ratcheting without activation of the dynamic recovery term in the kinematic variables. Finally, the MM model deserves improvement for a better description of the cyclic behavior of anisotropic materials.

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References

  • Abdel-Karim M (2009) Modified kinematic hardening rules for simulations of ratchetting. Int J Plast 25:1560–1587

    Article  MATH  Google Scholar 

  • Abdel-Karim M (2010) An evaluation for several kinematic hardening rules on prediction of multiaxial stress-controlled ratchetting. Int J Plast 26:711–730

    Article  MATH  Google Scholar 

  • Abdel-Karim M (2011) Effect of elastic modulus variation during plastic deformation on uniaxial and multiaxial ratchetting simulations. Eur J Mech A/Solids 30:11–21

    Article  MATH  Google Scholar 

  • Abdel-Karim M, Ohno N (2000) Kinematic hardening model suitable for ratcheting with steady-state. Int J Plast 16:225–240

    Article  MATH  Google Scholar 

  • Armstrong PJ, Frederick CO (1966) A mathematical representation of the multiaxial Bauschinger effect. CEGB Report RD/B/N 731, Berkely Nuclear Laboratories, Berkely, UK

    Google Scholar 

  • Bari S, Hassan T (2000) Anatomy of coupled constitutive models for ratchetting simulation. Int J Plast 16:381–409

    Article  MATH  Google Scholar 

  • Bari S, Hassan T (2001) Kinematic hardening rules in uncoupled modeling for multiaxial ratchetting simulation. Int J Plast 17:885–905

    Article  MATH  Google Scholar 

  • Bari S, Hassan T (2002) An advancement in cyclic plasticity modeling for multiaxial ratcheting simulation. Int J Plast 18:873–894

    Article  MATH  Google Scholar 

  • Belattar A, Taleb L, Hauet A, Taheri S (2012) Dependence of the cyclic stress-strain curve on the loading history and interaction with the fatigue of the 304L stainless steel. Mater Sci Eng A 563:170–180

    Article  Google Scholar 

  • Benallal A, Marquis D (1987) Constitutive equations for nonproportional cyclic elasto-viscoplasticity. Trans ASME J Eng Mater Tech 109:326–336

    Article  Google Scholar 

  • Besson J, Leriche R, Foerch R, Cailletaud G (1998) Object-oriented programming applied to the finite element method. Part II. Application to material behaviors. Revue Européenne des Éléments Finis 7(5):567–588

    Google Scholar 

  • Burlet H, Cailletaud G (1987) Modeling of cyclic plasticity in finite element codes. In: Desai CS (ed) 2nd International conference on constitutive laws for engineering materials: theory and applications. Elsevier, Tuscon, pp 1157–1164

    Google Scholar 

  • Cailletaud G, Saï K (1995) Study of plastic/viscoplastic models with various inelastic mechanisms. Int J Plast 11:991–1005

    Article  MATH  Google Scholar 

  • Chaboche JL (1986) Time-independent constitutive theories for cyclic plasticity. Int J Plast 2:149–188

    Article  MATH  Google Scholar 

  • Chaboche JL (1989) Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int J Plast 5:247–302

    Article  MATH  Google Scholar 

  • Chaboche JL (1991) On some modifications of kinematic hardening to improve the description of ratcheting effects. Int J Plast 7:661–678

    Article  Google Scholar 

  • Chaboche JL (1994) Modeling of ratcheting: evaluation of various approaches. Eur J Mech A/Solids 13(4):501–518

    Google Scholar 

  • Chaboche JL (2008) A review of some plasticity and viscoplasticity constitutive theories. Int J Plast 24:1642–1693

    Article  MATH  Google Scholar 

  • Chaboche JL, Dang-Van K, Cordier G (1979) Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel. In: Proceedings of the 5th International conference on SMiRT, Berlin, Paper L 11/3

    Google Scholar 

  • Chaboche JL, Kanouté P, Azzouz F (2012) Cyclic inelastic constitutive equations and their impact in the fatigue life predictions. Int J Plast 35:44–66

    Article  Google Scholar 

  • Chen X, Jiao R (2004) Modified kinematic hardening rule for multiaxial ratchetting prediction. Int J Plast 20:871–898

    Article  Google Scholar 

  • Chen X, Kim KS (2003) Modeling of ratcheting behavior under multiaxial cyclic loading. Acta Mech 163:9–23

    MATH  Google Scholar 

  • Chen X, Jiao R, Kim KS (2003) Simulation of ratcheting strain to a high number of cycles under biaxial loading. Int J Solids Struct 40:7449–7461

    Article  Google Scholar 

  • Contesti E, Cailletaud G (1989) Description of creep-plasticity interaction with non-unified constitutive equations: application to an austenitic stainless steel. Nucl Eng Des 116(3):265–280

    Article  Google Scholar 

  • Dafalias YF, Feigenbaum HP (2011) Biaxial ratchetting with novel variations of kinematic hardening. Int J Plast 27:479–491

    Article  MATH  Google Scholar 

  • Feigenbaum H, Dugdale J, Dafalias YF, Kourousis K, Plesek J (2012) Multiaxial ratcheting with advanced kinematic and directional distortional hardening rules. Int J Sol Struct 49:3063–3076

    Article  Google Scholar 

  • Hassan T, Taleb L, Krishna S (2008) Influences of non proportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int J Plast 24:1863–1889

    Article  MATH  Google Scholar 

  • Jiang Y, Zhang J (2008) Benchmark experiments and characteristic cyclic plasticity deformation. Int J Plast 24:1481–1515

    Article  MATH  Google Scholar 

  • Kang GZ (2008) Ratchetting: recent progresses in phenomenon observation, constitutive modeling and application. Int J Fatigue 30:1448–1472

    Article  Google Scholar 

  • Kang GZ, Gao Q (2002) Uniaxial and non-proportionally multiaxial ratcheting of U71Mn rail steel: experiments and simulations. Mech Mater 34:809–820

    Article  Google Scholar 

  • Kang GZ, Gao Q (2004) Temperature-dependent cyclic deformation of S304 stainless steel under non-proportionally multiaxial load and its constitutive modeling. Key Eng Mater 274:247–252

    Article  Google Scholar 

  • Kang GZ, Kan Q (2007) Constitutive modeling for uniaxial time-dependent ratcheting of SS304 stainless steel. Mech Mater 39:488–497

    Article  Google Scholar 

  • Kang GZ, Gao Q, Yang XJ (2002) A visco-plastic constitutive model incorporated with cyclic hardening for uniaxial/multiaxial ratchetting of SS304 stainless steel at room temperature. Mech Mater 34:521–531

    Article  Google Scholar 

  • Kang GZ, Gao Q, Yang XJ (2004) Uniaxial and nonproportional multiaxial ratchetting of SS304 stainless steel at room temperature: experiments and simulations. Int J Non-linear Mech 39:843–857

    Article  MATH  Google Scholar 

  • Kang GZ, Li YG, Gao Q (2005) Non-proportionally multiaxial ratcheting of cyclic hardening materials at elevated temperatures and its constitutive modeling. Mech Mater 37:1101–1118

    Google Scholar 

  • Kobayashi M, Ohno N (2002) Implementation of cyclic plasticity models based on a general form of kinematic hardening. Int J Numer Meth Eng 53:2217–2238

    Article  MATH  Google Scholar 

  • Krishna S, Hassan T, Ben Naceur I, Saï K, Cailletaud G (2009) Macro versus micro-scale constitutive models in simulating proportional and non proportional cyclic and ratcheting responses of stainless steel 304. Int J Plast 25:1910–1949

    Article  Google Scholar 

  • May A, Taleb L, Belouchrani M (2013) Analysis of the cyclic behavior and fatigue damage of extruded 2017 aluminum alloy. Mater Sci Eng A 571:123–136

    Article  Google Scholar 

  • Murakami S, Kawai M, Ohmi YJ (1989) Effects of amplitude-history and temperature-history on multiaxial cyclic behavior of type 316 stainless steel. Trans ASME J Eng Mater Tech 111:278–285

    Google Scholar 

  • Nouailhas D, Cailletaud G, Policella H, Marquis D, Dufailly J, Lieurade HP, Ribes A, Bollinger E (1985) On the description of cyclic hardening and initial cold working. Eng Fract Mech 21:887–895

    Article  Google Scholar 

  • Ohno N (1982) A constitutive model of cyclic plasticity with a nonhardening strain region. Trans ASME J Appl Mech 49:721–727

    Article  Google Scholar 

  • Ohno N (1990) Recent topics in constitutive modeling of cyclic plasticity and viscoplasticity. Appl Mech Rev 43:283–295

    Article  Google Scholar 

  • Ohno N, Abdel-Karim M (2000) Uniaxial ratcheting of 316FR steel at room temperature. Part II: Constitutive modeling and simulation. Trans ASME J Eng Mater Tech 122:35–41

    Article  Google Scholar 

  • Ohno N, Wang JD (1991) Transformation of a nonlinear kinematic hardening rule to a multisurface form under isothermal and nonisothermal conditions. Int J Plast 7:879–891

    Article  MATH  Google Scholar 

  • Ohno N, Wang JD (1993) Kinematic hardening rules with critical state of dynamic recovery. Part I: Formulations and basic features for ratcheting behavior. Int J Plast 9:375–403

    Article  MATH  Google Scholar 

  • Ohno N, Wang JD (1994) Kinematic hardening rules for simulation of ratchetting behavior. Eur J Mech A/Solids 13:519–531

    MATH  Google Scholar 

  • Portier L, Calloch S, Marquis D, Geyer P (2000) Ratchetting under tension-torsion loadings: experiments and modelling. Int J Plast 16:303–335

    Article  MATH  Google Scholar 

  • Pugh CE (1978) On establishing constitutive equations for use in design of high temperature fast-reactor structure. Nucl Eng Des 51(1):23–27

    Article  Google Scholar 

  • Saï K (2011) Multi-mechanism models: present state and future trends. Int J Plast 27:250–281

    Article  Google Scholar 

  • Saï K, Cailletaud G (2007) Multi-mechanism models for the description of ratchetting: effect of the scale transition rule and of the coupling between hardening variables. Int J Plast 23:1589–1617

    Article  MATH  Google Scholar 

  • Saï K, Taleb L, Cailletaud G (2012) Numerical simulation of an anisotropic behavior of 2017 aluminum alloy. Comput Mater Sci 65:48–57

    Article  Google Scholar 

  • Saï K, Taleb L, Guesmi F, Cailletaud G (2014) Multi-mechanism modeling of proportional and non-proportional ratchetting of stainless steel 304. Acta Mech 225:3265–3283

    Article  MATH  Google Scholar 

  • Taheri S, Hauet A, Taleb L, Kpodekon C (2011) Micro-macro investigations about the fatigue behaviour of pre-hardened 304L steel. Int J Plast 27:1981–2004

    Article  MATH  Google Scholar 

  • Taleb L (2013a) About the cyclic accumulation of the inelastic strain observed in metals subjected to cyclic stress control. Int J Plast 43:1–19

    Article  Google Scholar 

  • Taleb L (2013b) On the cyclic behavior of 304L and 316L stainless steels. Key Eng Mater 535–536:201–204

    Article  Google Scholar 

  • Taleb L, Cailletaud G (2010) An updated version of the multimechanism model for cyclic plasticity. Int J Plast 26:859–874

    Article  MATH  Google Scholar 

  • Taleb L, Cailletaud G (2011) Cyclic accumulation of the inelastic strain in the 304L SS under stress control at room temperature: ratcheting or creep? Int J Plast 27:1936–1958

    Article  MATH  Google Scholar 

  • Taleb L, Cailletaud G, Blaj L (2006) Numerical simulation of complex ratcheting tests with a multi-mechanism model type. Int J Plast 22:724–753

    Article  MATH  Google Scholar 

  • Taleb L, Cailletaud G, Saï K (2014) Experimental and numerical analysis about the cyclic behavior of the 304L and 316L stainless steels at 350\(^\circ \)c. Int J Plast 61:32–48

    Article  Google Scholar 

  • Vincent L, Calloch S, Kurtyka T, Marquis D (2002) An improvement of multiaxial ratcheting modeling via yield surface distortion. J Eng Mater Technol 124:402–411

    Article  Google Scholar 

  • Vincent L, Calloch S, Marquis D (2004) A general cyclic plasticity model taking into account yield surface distortion for multiaxial ratcheting. Int J Plast 20:1817–1850

    Article  MATH  Google Scholar 

  • Wolff M, Taleb L (2008) Consistency of two multi-mechanism models in isothermal plasticity. Int J Plast 24:2059–2083

    Article  MATH  Google Scholar 

  • Yaguchi M, Takahashi Y (2005) Ratchetting of viscoplastic material with cyclic softening: II. Application of constitutive models. Int J Plast 21:835–860

    Article  MATH  Google Scholar 

  • Yoshida F (2000) A constitutive model of cyclic plasticity. Int J Plast 16:359–380

    Article  MATH  Google Scholar 

  • Yoshida F, Uemori T (2002) A model for large strain cyclic plasticity describing the bauschinger effect and work hardening stagnation. Int J Plast 18:661–686

    Article  MATH  Google Scholar 

  • Yu D, Chen X, Yu W, Chen G (2012) Thermo-viscoplastic modeling incorporating dyamic strain aging effect on the uniaxial behavior of Z2CND18.12N stainless steel. Int J Plast 37:119–139

    Article  Google Scholar 

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Acknowledgments

The authors acknowledge the “Région Haute Normandie” and the European Community, through the FEDER program for their grateful financial support.

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Correspondence to Lakhdar Taleb .

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Taleb, L., Saï, K., Cailletaud, G. (2015). Capabilities of the Multi-mechanism Model in the Prediction of the Cyclic Behavior of Various Classes of Metals. In: Altenbach, H., Matsuda, T., Okumura, D. (eds) From Creep Damage Mechanics to Homogenization Methods. Advanced Structured Materials, vol 64. Springer, Cham. https://doi.org/10.1007/978-3-319-19440-0_19

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  • DOI: https://doi.org/10.1007/978-3-319-19440-0_19

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