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Creep failure model of a tempered martensitic stainless steel integrating multiple deformation and damage mechanisms

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Abstract

A new model considering both deformation and damage evolution under multiple viscoplastic mechanisms is used to represent high temperature creep deformation and damage of a martensitic stainless steel in a wide range of load levels. First, an experimental database is built to characterise both creep flow and damage behaviour using tests on various kinds of specimens. The parameters of the model are fitted to the results and to literature data for long term creep exposure. An attempt is made to use the model to predict creep time to failure up to 105 h.

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References

  • P. Anderson T. Bellgardt F.L. Jones (2003) ArticleTitleCreep deformation in a modified 9Cr-1Mo steel Materials Science and Technology 19 207–213 Occurrence Handle1:CAS:528:DC%2BD3sXjtFGgu74%3D

    CAS  Google Scholar 

  • M.F. Ashby C. Gandhi D.M.R. Taplin (1979) ArticleTitleFracture mechanism maps and their construction for fcc metals and alloys Acta metallurgica 27 699–729 Occurrence Handle1:CAS:528:DyaE1MXkvFGnsr0%3D

    CAS  Google Scholar 

  • E. Bellenger P. Bussy (2001) ArticleTitlePhenomenological modeling and numerical simulation of different modes of creep damage evolution International Journal of Solids and Structures 38 577–604

    Google Scholar 

  • J. Besson C. Guillemer-Neel (2003) ArticleTitleAn extension of the Green and Gurson models to kinematic hardening Mechanics of materials 35 1–18

    Google Scholar 

  • Besson J. (2001a). Eprouvettes axisymétriques entaillées. Essais mécaniques et lois de comportement - Hermes, Paris 319–351 (in French).

  • Besson, J., Cailletaud, G., Chaboche, J.L. and Forest, S. (2001b). Mécanique non linéaire des matériaux. Hermes, Paris (in French).

  • J. Besson D. Steglich W. Brocks (2001c) ArticleTitleModeling of crack growth in round bars and plane strain specimens International Journal of Solids and Structures 38 IssueID46–47 8259–8284

    Google Scholar 

  • J. Besson L. Devillers-Guerville A. Pineau (2000) ArticleTitleModeling of scatter and size effect in ductile fracture. Application to thermal embrittlement of duplex stainless steels Engineering Fracture Mechanics 67 IssueID2 169–190

    Google Scholar 

  • J. Besson R. Foerch (1997) ArticleTitleLarge scale object-oriented finite element code design Computer Methods in Applied Mechanics and Engineering 142 165–187

    Google Scholar 

  • Brachet, J.C. (1991). Alliages martensitiques 9Cr-1Mo: effets de l’addition de l’azote, du niobium et du vanadium sur la microstructure, les transformations de phases et les propriétés mécaniques. PhD Thesis – University of Paris Sud Orsay (in French).

  • Brinkman, C.R., Gieseke, B. and Maziasz, P.J. (1993). The influence of long thermal aging on the microstructure and mechanical properties. Microstructure and Mechanical Properties of Aging Materials – The Minerals, Metals and Materials Society. 107–115

  • J. Čadek V. Šustek M. Pahutová (1997) ArticleTitleAn analysis of a set of creep data for a 9Cr–1Mo–0.2V steel Materials Science and Engineering A225 22–28

    Google Scholar 

  • E. Cerri E. Evangelista S. Spigarelli P. Bianchi (1998) ArticleTitleEvolution of microstructure in a modified 9Cr–1Mo steel during short term creep Materials Science and Engineering A 245 285–292

    Google Scholar 

  • C.C. Chu A. Needleman (1980) ArticleTitleVoids nucleation effects in biaxially stretched sheets Journal of Engineering Materials and Technology 102 249–256

    Google Scholar 

  • E. Contesti G. Cailletaud (1989) ArticleTitleDescription of creep plasticity interaction with non-unified constitutive equations: application to an austenitic stainless steel Nuclear Engineering and Design 116 265–280 Occurrence Handle1:CAS:528:DyaK3cXhtVartLc%3D

    CAS  Google Scholar 

  • B.F. Dyson (1983) ArticleTitleContinuous cavity nucleation and creep fracture Scripta Metallurgica 17 31–37

    Google Scholar 

  • B.F. Dyson (1976) ArticleTitleConstraints on diffusional cavity growth rates Metal Science 10 349–353

    Google Scholar 

  • G. Eggeler W. Tato P. Jemmely et al. (1992) ArticleTitleCreep rupture of circular notched P91 specimens: influence of heat treatment and notch geometry Scripta Metallurgica et Materialia 27 1091–1096 Occurrence Handle1:CAS:528:DyaK38XmtlOktb4%3D

    CAS  Google Scholar 

  • G. Eggeler (1989) ArticleTitleThe effect of long term creep on particle coarsening in tempered martensite ferritic steels Acta Metallurgica 37 IssueID12 3225–3234 Occurrence Handle1:CAS:528:DyaK3cXmtVChsQ%3D%3D

    CAS  Google Scholar 

  • G. Eggeler J.C. Earthman N. Nilsvang B. Ilschner (1989b) ArticleTitleMicrostructural study of creep rupture in a 12% chromium ferritic steel Acta Metallurgica 37 IssueID1 49–60 Occurrence Handle1:CAS:528:DyaL1MXkt1OrtQ%3D%3D

    CAS  Google Scholar 

  • Engberg, G., Karlsson, S. and Von Walden, E. (1984). An interpretation of tertiary creep in 12%Cr steel at 550°C. Creep and Fracture of Engineering Materials and Structures, edited by B. Wilshire and D.R.J. Owen, Swansea 1–6 April. Pineridge Press. 697–709.

  • P.J. Ennis A. Czyrska-Filemonowicz (2002) ArticleTitleRecent advances in creep resistant steels for power plant applications OMMI 1 IssueID1 1–27

    Google Scholar 

  • J. Faleskog X. Gao C. Fong Shih (1998) ArticleTitleCell model for nonlinear fracture analysis. I. micromechanics calibration International Journal of Fracture 89 355–373

    Google Scholar 

  • H.J Frost M.F. Ashby (1982) Deformation-mechanism maps: The plasticity and creep of metals and ceramics Pergamon Press Oxford

    Google Scholar 

  • Green, R. (1972). A plasticity theory for porous solids. International Journal of Mechanical Sciences (14), 215–224

    Google Scholar 

  • Guetaz, L., Millier, J.P. and Urvoy, S. (2003). Mécanismes de déformation de l’acier martensitique Eurofer. Private communication.

  • A.S. Gullerud X. Gao R. Dodds SuffixJr. R. Haj-Ali (2000) ArticleTitleSimulation of ductile crack growth using computational cells: numerical aspects Engineering Fracture Mechanics 66 65–92

    Google Scholar 

  • A.L. Gurson (1977) ArticleTitleContinuum theory of ductile rupture by void nucleation and growth: part 1 – Yield criteria and flow rules for porous ductile media Journal of Engineering Materials and Technology 99 2–15

    Google Scholar 

  • M. Hättestrand H.O. Andrén (2001) ArticleTitleInfluence of strain on precipitation reactions during creep of an advanced 9% chromium steel Acta Materialia 49 IssueID12 2123–2128

    Google Scholar 

  • D.R. Hayhurst F.A. Leckie J.T. Henderson (1977a) ArticleTitleDesign of notched bars for creep rupture testing under tri-axial stresses International Journal of Mechanical Sciences 19 IssueID3 147–159

    Google Scholar 

  • D.R Hayhurst J.T. Henderson (1977b) ArticleTitleCreep stress redistribution in notched bars International Journal of Mechanical Sciences 19 IssueID3 133–146

    Google Scholar 

  • Hayhurst, D.R. (1995). High-temperature design and life assessment of structures using continuum damage mechanics. Creep and Fatigue: Design and Life Assessment at High Temperature in Mechanical Engineering Publications Ltd. (UK), 399–410.

  • D.R. Hayhurst W.A. Trampczynski F.A. Leckie (1983) ArticleTitleOn the role of cavity nucleation in creep deformation and fracture Acta Metallurgica 31 IssueID10 1537–1542

    Google Scholar 

  • U. Herding G. Kuhn (1996) ArticleTitleA field boundary element formulation of damage mechanics Engineering Analysis with Boundary Elements 18 IssueID2 137–147

    Google Scholar 

  • Hourlier, F. (1982). Propagation de fissures de fatigue sous sollicitations polymodales. PhD Thesis – Ecole Nationale Supérieure des Mines de Paris, Paris, France (in French).

  • D. Hull D.E. Rimmer (1959) ArticleTitleThe growth of grain boundary voids under stress Philosophical Magazine 4 IssueID42 673–687 Occurrence Handle1:CAS:528:DyaF3cXms1aitg%3D%3D

    CAS  Google Scholar 

  • K. Iwanaga T. Tsuchiyama S. Takaki (1998) ArticleTitleRelationship between creep behavior and microstructure in martensitic heat resistant steel Tetsu-to-Hagané (Journal of the Iron and Steel Institute of Japan) 84 IssueID12 896–901

    Google Scholar 

  • L.M. Kachanov (1958) ArticleTitleTime of the rupture process under creep conditions Isv. Akad. Nauk. SSR. Otd Tekh. Nauk 8 26–31

    Google Scholar 

  • Y. Kadoya N. Nishimura B.F. Dyson M. McLean (1997) Origins of tertiary creep in high chromium steels J.C. Earthman F.A. Mohamed (Eds) Creep and Fracture of Engineering Materials and Structures The Minerals, Metals, and Materials Society Warrendale, PA 343–352

    Google Scholar 

  • M.E. Kassner T.A. Hayes (2003) ArticleTitleCreep cavitation in metals International Journal of Plasticity 19 IssueID10 1715–1748

    Google Scholar 

  • K. Kimura H. Kushima F. Abe (2000) ArticleTitleHeterogeneous changes in microstructure and degradation behaviour of 9Cr-1Mo-V-Nb steel during long term creep Key Engineering Materials 171 IssueID174 483–490

    Google Scholar 

  • Kimura, K., Suzuki, K., Toda, Y., Kushima, H. and Abe, F. (2002) Precipitation of a Z-Phase and degradation behaviour of modified 9Cr-1Mo steel, Materials for Advanced Power Engineering. Proc. of the 7th Liège conf., Forschungszentrum Julich, Lecomte-Beckers, Carton, Schuber and Ennis, ed. Vol. II(21), 1171–1180

  • L. Kloc V. Sklenička (1997) ArticleTitleTransition from power-law to viscous creep behaviour of P-91 type heat resistant steel Materials Science and Engineering A234-236 962–965 Occurrence Handle1:CAS:528:DyaK2sXlsVWmtL8%3D

    CAS  Google Scholar 

  • Klueh, R.L. and Harries, D.R. (2001). High-chromium ferritic and martensitic steels for nuclear applications. Book – American Society for Testing Materials.

  • J. Koplik A. Needleman (1988) ArticleTitleVoid growth and coalescence in porous plastic solids International Journal of Solids and Structures 24 IssueID8 835–853

    Google Scholar 

  • Kushima, H., Kimura, K., Abe, F. (2002) Long term creep strength prediction of high Cr ferritic resistant steels. Materials for advanced power engineering. Proc. of the 7th Liège conf., Forschungszentrum Julich, Lecomte-Beckers, Carton, Schuber and Ennis, Eds. vol III(21), 1581–1590.

  • F.R. Larson J. Miller (1952) ArticleTitleA time–temperature relationship for rupture and creep stresses Transactions of the ASME 74 765–775

    Google Scholar 

  • J.B. Leblond G. Perrin P. Suquet (1994) ArticleTitleExact results and approximate models for porous viscoplastic solids International Journal of Plasticity 10 IssueID3 213–235

    Google Scholar 

  • J. Lemaitre (1985) ArticleTitleA continuum damage mechanics model for ductile fracture Journal of Engineering Materials and Technology 107 83–89

    Google Scholar 

  • Y. Liu S. Murakami Y. Kanagawa (1994) ArticleTitleMesh dependence and stress singularity in finite element analysis of creep crack growth by continuum damage mechanics approach European Journal of Mechanics 13A IssueID3 395–417

    Google Scholar 

  • D. McLean (1981) ArticleTitleDamage accumulation in creep Annales de chimie 6 124–139 Occurrence Handle1:CAS:528:DyaL3MXhvFKjsrc%3D

    CAS  Google Scholar 

  • B. Michel (2004) ArticleTitleFormulation of a new intergranular creep damage model for austenitic stainless steels Nuclear Engineering and Design 227 IssueID2 161–174 Occurrence Handle1:CAS:528:DC%2BD2cXitlyksg%3D%3D

    CAS  Google Scholar 

  • F.C. Monkman N.J. Grant (1956) ArticleTitleAn empirical relationship between rupture life and minimum creep rate in creep-rupture tests Proceedings of the ASTM 56 593–620

    Google Scholar 

  • M.R. Myers R. Pilkington N.G. Needham (1987) ArticleTitleCavity nucleation and growth in a 1%Cr-0.5%Mo steel Materials Science and Engineering 95 IssueID2 81–91 Occurrence Handle1:CAS:528:DyaL2sXmsVSmtLw%3D

    CAS  Google Scholar 

  • T. Nakajima S. Spigarelli E. Evangelista T. Endo (2003) ArticleTitleStrain enhanced growth of precipitates during creep of T91 Materials Transactions JIM 44 IssueID9 1802–1808 Occurrence Handle1:CAS:528:DC%2BD3sXos1Gltrk%3D

    CAS  Google Scholar 

  • A. Needleman V. Tvergaard (1991) ArticleTitleAn analysis of dynamic, ductile crack growth in a double edge cracked specimen International Journal of Fracture 49 41–67

    Google Scholar 

  • A. Needleman J.R. Rice (1980) ArticleTitleOverview n°9 – Plastic creep flow effects in the diffusive cavitation of grain boundaries Acta Metallurgica 28 IssueID10 1315–1332 Occurrence Handle1:CAS:528:DyaL3MXltFCqtA%3D%3D

    CAS  Google Scholar 

  • P. Onck E. Giessen ParticleVan der (1997) ArticleTitleMicrostructurally based modelling of intergranular creep fracture using grain elements Mechanics of Materials 26 IssueID2 109–126

    Google Scholar 

  • A. Orlová J. Bursik K. Kucharova V. Sklenička (1998) ArticleTitleMicrostructural development during high temperature creep of 9%Cr steel Materials Science and Engineering A 245 39–48

    Google Scholar 

  • A.M. Othman B.F. Dyson D.R. Hayhurst J. Lin (1994) ArticleTitleContinuum damage mechanics modelling of circumferentially notched tension bars undergoing tertiary creep with physically based constitutive equations Acta Metallurgica et Materialia 42 IssueID3 597–611

    Google Scholar 

  • T. Pardoen I. Doghri F. Delannay (1998) ArticleTitleExperimental and numerical comparison of void growth models and void coalescence criteria for the prediction of ductile fracture in copper bars Acta Materialia 46 IssueID2 541–552 Occurrence Handle1:CAS:528:DyaK1cXnsVKmug%3D%3D

    CAS  Google Scholar 

  • R. Piques E. Molinié A. Pineau (1991) ArticleTitleComparison between two assessment methods for defects in the creep range Fatigue and Fracture of Engineering Materials and Structures 14 IssueID9 871–885

    Google Scholar 

  • Piques, R. (1989). Mécanique et mécanismes de l’amorçage et de la propagation de fissures en viscoplasticité dans un acier austénitique inoxydable. PhD Thesis, Ecole Nationale Supérieure des Mines de Paris, Paris, France (in French).

  • P. Polcik T. Sailer W. Blum S. Straub J. Buršik A. Orlová (1999) ArticleTitleOn the microstructural development of the tempered martensitic Cr-steel P91 during long term creep – a comparison of data Materials Science and Engineering A260 252–259 Occurrence Handle1:CAS:528:DyaK1MXhsVems78%3D

    CAS  Google Scholar 

  • V. Prunier U. Gampe K. Nikbin I.A. Shibli (1998) HIDA activity on P91 steel. Creep and Fatigue Crack Growth in High Temperature Plant HIDA Conference CEA Saclay France

    Google Scholar 

  • C.E. Pugh (1978) ArticleTitleOn establishing constitutive equations for use in design of high temperature fast reactor structure Nuclear Engineering and Design 51 23–27

    Google Scholar 

  • Y.N. Rabotnov (1969) Creep problems in structural members North-Holland Amsterdam

    Google Scholar 

  • J.R Rice D.R. Tracey (1969) ArticleTitleOn the ductile enlargement of voids in triaxial stress fields Journal of the Mechanics and Physics of Solids 17 IssueID3 201–217

    Google Scholar 

  • G. Rousselier (1987) ArticleTitleDuctile fracture models and their potential in local approach of fracture Nuclear Engineering and Design 105 97–111 Occurrence Handle1:CAS:528:DyaL1cXhtVamsLg%3D

    CAS  Google Scholar 

  • K. Sawada M. Taneike K Kimura F. Abe (2003) ArticleTitleIn situ observation of recovery of lath structure in 9% chromium creep resistant steel Materials Science and Technology 19 IssueID6 739–742 Occurrence Handle1:CAS:528:DC%2BD3sXlsFant70%3D

    CAS  Google Scholar 

  • K. Sawada M. Takeda K. Maruyama R. Ishii M. Yamada Y. Nagae R. Komine (1999) ArticleTitleEffect of W recovery of lath structure during creep of high chromium martensitic steels Materials Science and Engineering A267 19–25 Occurrence Handle1:CAS:528:DyaK1MXjt1Kmurw%3D

    CAS  Google Scholar 

  • B.A. Senior (1989) ArticleTitleThe precipitation of Laves phase in 9Cr – 1Mo steels Materials Science and Engineering A 119 L5–L9

    Google Scholar 

  • T.L. Sham A. Needleman (1983) ArticleTitleEffects of triaxial stressing on creep cavitation of grain boundaries Acta Metallurgica 31 IssueID6 919–926

    Google Scholar 

  • J.C Simo R.L. Taylor (1985) ArticleTitleConsistent tangent operators for rate-independent elastoplasticity Computer Methods in Applied Mechanics Engineering 48 IssueID1 101–118

    Google Scholar 

  • V. Sklenička K. Kucharova M. Svoboda L. Kloc J. Buršik A. Kroupa (2003) ArticleTitleLong term creep behavior of 9–12% Cr power plant steels Materials characterization 51 IssueID1 35–48

    Google Scholar 

  • S. Spigarelli L. Kloc P. Bontempi (1997) ArticleTitleAnalysis of creep curves in a 9Cr-1Mo modified steel by means of simple constitutive equations Scripta Materialia 37 IssueID4 399–404 Occurrence Handle1:CAS:528:DyaK2sXkvFOgtbg%3D

    CAS  Google Scholar 

  • Ch. Stocker K. Spiradek G. Zeiler (2002) ArticleTitleMicrostructural features influencing the creep properties of 9–12% Cr steels focusing on Laves phase precipitation Materials for Advanced Power Engineering III IssueID21 1459–1469

    Google Scholar 

  • K. Suzuki S. Kumai H. Kushima et al. (2003) ArticleTitlePrecipitation of Z-phase and precipitation sequence during creep deformation of modified 9Cr-1Mo Steel Tetsu-to-Hagané (Journal of the Iron and Steel Institute of Japan) 89 IssueID6 691–698 Occurrence Handle1:CAS:528:DC%2BD3sXktlajurg%3D

    CAS  Google Scholar 

  • T. Tsuchiyama T. Miyamoto S. Takaki (2001) ArticleTitleRecrystallisation of lath martensite with bulge nucleation and growth mechanism ISIJ International 41 IssueID9 1047–1052 Occurrence Handle1:CAS:528:DC%2BD3MXotlajt7Y%3D

    CAS  Google Scholar 

  • V. Tvergaard A. Needleman (1984a) ArticleTitleOn the creep constrained diffusive cavitation of grain boundary facets Journal of the Mechanics and Physics of Solids 32 IssueID5 373–393

    Google Scholar 

  • V. Tvergaard A. Needleman (1984b) ArticleTitleAnalysis of the cup cone fracture in a round tensile bar Acta Metallurgica 32 IssueID1 157–169

    Google Scholar 

  • V. Tvergaard (1989) ArticleTitleMaterial failure by void growth to coalescence Advances in Applied Mechanics 27 83–151

    Google Scholar 

  • V. Tvergaard (1982) ArticleTitleDuctile fracture by nucleation between larger voids Journal of the Mechanics and Physics of Solids 30 265–286

    Google Scholar 

  • E. Giessen ParticleVan der M.W.D. Van der Burg A. Needleman V. Tvergaard (1995) ArticleTitleVoid growth due to creep and grain boundary diffusion at high triaxialities Journal of the Mechanics and Physics of Solids 43 IssueID1 123–165

    Google Scholar 

  • Vilhemsen T. (1996). Creep failure of modified 9Cr steel weldments. PhD Thesis of the University of London and for the Imperial College, London.

  • Wasmer, K., Biglari, F. and Nikbin, K.M. (2002). Multiaxial failure behaviour in advanced steels at elevated temperatures. Proceedings of the ECF 14 Conference, Krakow, 553–562.

  • Weinert P. (2002). Microstructural physically based creep modelling of 9–12% Cr steels. Materials for Advanced Power Engineering, Proc of the 7th Liège con,, Forschungszentrum Julich, Lecomte-Beckers, Carton, Schuber and Ennis, Eds. vol. II, 1211–1221.

  • R. Wu R. Sandström (1996) ArticleTitleStrain dependence of creep cavity nucleation in low alloy and 12% Cr steels Materials Science and Technology 12 IssueID5 405–415 Occurrence Handle1:CAS:528:DyaK28Xlt12is7s%3D

    CAS  Google Scholar 

  • R. Wu R. Sandström (1995) ArticleTitleCreep cavity nucleation and growth in 12Cr-Mo-V steel Materials Science and Technology 11 IssueID6 579–588 Occurrence Handle1:CAS:528:DyaK2MXnvFOjtbg%3D

    CAS  Google Scholar 

  • L. Xia C.F. Shih J.W. Hutchinson (1995) ArticleTitleA computational approach to ductile crack growth under large scale yielding conditions Journal of the Mechanics and Physics of Solids 43 IssueID3 389–413 Occurrence Handle1:CAS:528:DyaK2MXlsFyhsrY%3D

    CAS  Google Scholar 

  • M. Yaguchi Y. Takahashi (2000) ArticleTitleA viscoplastic constitutive model incorporating dynamic strain aging effect during cyclic deformation conditions International Journal of Plasticity 16 241–262 Occurrence Handle1:CAS:528:DC%2BD3cXis1Ghu70%3D

    CAS  Google Scholar 

  • Yoshida, M. (1985). Endommagement intergranulaire de fluage dans un acier inoxydable 17Cr–12Ni – Etude quantitative – Rôle de la multiaxialité des contraintes. PhD Thesis, Ecole Nationale Supérieure des Mines de Paris, Paris, France (in French).

  • Z.F. Yue Z.Z. Lu X.M. Wang (2002) ArticleTitleA numerical study of damage development and creep life in circular notched specimens during creep Materials at high temperature 19 IssueID3 147–152

    Google Scholar 

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Gaffard, V., Besson, J. & Gourgues-Lorenzon, A.F. Creep failure model of a tempered martensitic stainless steel integrating multiple deformation and damage mechanisms. Int J Fract 133, 139–166 (2005). https://doi.org/10.1007/s10704-005-2528-8

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