Advertisement

Analysis of a Power Plant Rotor Made of Tempered Martensitic Steel Based on a Composite Model of Inelastic Deformation

  • Johanna EisenträgerEmail author
  • Konstantin Naumenko
  • Yevgen Kostenko
  • Holm Altenbach
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 117)

Abstract

Power plant components are subjected to high temperatures up to \(903\,\mathrm {K}\), which induce creep deformations. Furthermore, power plants are frequently started and shut-down, thus resulting in cyclic loads on the components. Since they provide adequate mechanical and thermal properties, tempered martensitic steels are ideal candidates to withstand these conditions. The contribution at hand presents a phase mixture model for simulating the mechanical behavior of tempered martensitic steels at high temperatures. To provide a unified description of the rate-dependent deformation including hardening and softening, the model makes use of an iso-strain approach including a hard and a soft constituent. The model is implemented into the finite element method, using the implicit Euler method for time integration of the evolution equations. In addition, the consistent tangent operator is derived. As a final step, the behavior of an idealized steam turbine rotor during a cold start and a subsequent hot start is simulated by means of a thermo-mechanical finite element analysis. First, the heat transfer analysis is conducted, while prescribing the instationary steam temperature and the heat transfer coefficients. The resulting temperature fields serve as input for the subsequent structural analysis, which yields the stress and strain fields in the rotor.

Notes

Acknowledgements

The financial support rendered by the German Research Foundation (DFG) in context of the research training group “Micro-Macro-Interactions in Structured Media and Particle Systems” (GRK 1554) is gratefully acknowledged.

References

  1. 1.
    Masuyama, F.: Advances in physical metallurgy and processing of steels. History of power plants and progress in heat resistant steels. Iron Steel Inst. Jpn. Int. 41(6), 612–625 (2001)CrossRefGoogle Scholar
  2. 2.
    Breeze, P.A.: Power Generation Technologies. Newnes (2014)Google Scholar
  3. 3.
    Fournier, B., Dalle, F., Sauzay, M., Longour, J., Salvi, M., Caës, C., Tournié, I., Giroux, P.-F., Kim, S.-H.: Comparison of various 9–12%Cr steels under fatigue and creep-fatigue loadings at high temperature. Mater. Sci. Eng. A 528(22–23), 6934–6945 (2011)CrossRefGoogle Scholar
  4. 4.
    Hosseini, E., Kalyanasundaram, V., Li, X., Holdsworth, S.R.: Effect of prior deformation on the subsequent creep and anelastic recovery behaviour of an advanced martensitic steel. Mater. Sci. Eng. A 717, 68–77 (2018)CrossRefGoogle Scholar
  5. 5.
    Fournier, B., Sauzay, M., Mottot, M., Brillet, H., Monnet, I., Pineau, A.: Experimentally based modelling of cyclically induced softening in a martensitic steel at high temperature. In: Shibli, I.A., Holdsworth, S.R., Merckling, G. (eds.) ECCC Creep Conference, pp. 649–661. DEStech Publications, Lancaster, PA, USA (2005)Google Scholar
  6. 6.
    Fournier, B., Sauzay, M., Renault, A., Barcelo, F., Pineau, A.: Microstructural evolutions and cyclic softening of 9%Cr martensitic steels. J. Nucl. Mater. 386388, 71–74 (2009)Google Scholar
  7. 7.
    Fournier, B., Salvi, M., Dalle, F., de Carlan, Y., Caës, C., Sauzay, M., Pineau, A.: Lifetime prediction of 9–12% Cr martensitic steels subjected to creep-fatigue at high temperature. Int. J. Fatigue 32(6), 971–978 (2010)CrossRefGoogle Scholar
  8. 8.
    Röttger, D.R.: Untersuchungen zum Wechselverformungs- und Zeitstandverhalten der Stähle X20CrMoV121 und X10CrMoVNb91. Ph.D. Thesis, Universität GH Essen, Essen (1997)Google Scholar
  9. 9.
    Straub, S.: Verformungsverhalten und Mikrostruktur warmfester martensitischer 12%-Chromstähle. Ph.D. Thesis, Friedrich-Alexander-Universität, Erlangen-Nürnberg (1995)Google Scholar
  10. 10.
    Fournier, B., Sauzay, M., Pineau, A.: Micromechanical model of the high temperature cyclic behavior of 9–12%Cr martensitic steels. Int. J. Plast. 27(11), 1803–1816 (2011)CrossRefGoogle Scholar
  11. 11.
    Pétry, C., Lindet, G.: Modelling creep behaviour and failure of 9Cr–0.5Mo–1.8W–VNb steel. Int. J. Press. Vessel. Pip. 86(8), 486–494 (2009)CrossRefGoogle Scholar
  12. 12.
    Naumenko, K., Kutschke, A., Kostenko, Y., Rudolf, T.: Multi-axial thermo-mechanical analysis of power plant components from 9–12%Cr steels at high temperature. Eng. Fract. Mech. 78(8), 1657–1668 (2011)CrossRefGoogle Scholar
  13. 13.
    Götz, G.: Langzeitentwicklung der Mikrostruktur neuer 9–12% Chromstähle für den Einsatz in Kraftwerken. Ph.D. Thesis, Friedrich-Alexander-Universität, Erlangen-Nürnberg (2004)Google Scholar
  14. 14.
    Giroux, P.F., Dalle, F., Sauzay, M., Malaplate, J., Fournier, B., Gourgues-Lorenzon, A.F.: Mechanical and microstructural stability of P92 steel under uniaxial tension at high temperature. Mater. Sci. Eng. A 527(16–17), 3984–3993 (2010)CrossRefGoogle Scholar
  15. 15.
    Wang, L., Li, M., Almer, J.: In situ characterization of grade 92 steel during tensile deformation using concurrent high energy x-ray diffraction and small angle x-ray scattering. J. Nucl. Mater. 440(1–3), 81–90 (2013)CrossRefGoogle Scholar
  16. 16.
    Alsagabi, S., Shrestha, T., Charit, I.: High temperature tensile deformation behavior of grade 92 steel. J. Nucl. Mater. 453(1–3), 151–157 (2014)CrossRefGoogle Scholar
  17. 17.
    Kostenko, Y., Almstedt, H., Naumenko, K., Linn, S., Scholz, A.: Robust methods for creep fatigue analysis of power plant components under cyclic transient thermal loading. In: ASME Turbo Expo 2013: Turbine Technical Conference and Exposition, pp. V05BT25A040. American Society of Mechanical Engineers, New York (2013)Google Scholar
  18. 18.
    Polcik, P.: Modellierung des Verformungsverhaltens der warmfesten 9–12% Chromstähle im Temperaturbereich von 550–650\(^{\circ }\)C. Ph.D. Thesis, Friedrich-Alexander-Universität, Erlangen-Nürnberg (1998)Google Scholar
  19. 19.
    Eisenträger, J.: A framework for modeling the mechanical behavior of tempered martensitic steels at high temperatures. Ph.D. Thesis, Otto von Guericke University Magdeburg (2018)Google Scholar
  20. 20.
    stern.de. Turbine - Technik VIEW Fotocommunity (2016)Google Scholar
  21. 21.
    Eisenträger, J., Naumenko, K., Altenbach, H., Gariboldi, E.: Analysis of temperature and strain rate dependencies of softening regime for tempered martensitic steel. J. Strain Anal. Eng. Des. 52, 226–238 (2017)CrossRefGoogle Scholar
  22. 22.
    Chilukuru, H., Durst, K., Wadekar, S., Schwienheer, M., Scholz, A., Berger, C., Mayer, K.H., Blum, W.: Coarsening of precipitates and degradation of creep resistance in tempered martensite steels. Mater. Sci. Eng. A 510–511, 81–87 (2009)CrossRefGoogle Scholar
  23. 23.
    Agamennone, R., Blum, W., Gupta, C., Chakravartty, J.K.: Evolution of microstructure and deformation resistance in creep of tempered martensitic 9–12%Cr-2%W-5%Co steels. Acta Mater. 54(11), 3003–3014 (2006)CrossRefGoogle Scholar
  24. 24.
    Orlová, A., Buršík, J., Kuchřoavá, K., Sklenička, V.: Microstructural development during high temperature creep of 9% Cr steel. Mater. Sci. Eng. A 245, 39–48 (1998)CrossRefGoogle Scholar
  25. 25.
    Fournier, B., Sauzay, M., Barcelo, F., Rauch, E., Renault, A., Cozzika, T., Dupuy, L., Pineau, A.: Creep-fatigue interactions in a 9 Pct Cr-1 Pct mo martensitic steel: Part II. Microstructural evolutions. Metall. Mater. Trans. A 40(2), 330–341 (2009)CrossRefGoogle Scholar
  26. 26.
    Blum, W.: Mechanisms of creep deformation in steel. In: Abe, F., Kern, T.-U., Viswanathan, R. (eds.) Creep-Resistant Steels, pp. 365–402. Woodhead Publishing Limited, Sawston (2008)CrossRefGoogle Scholar
  27. 27.
    Verma, P., Srinivasa, N.S.C., Singha, V.: Low cycle fatigue behavior of modified 9Cr-1Mo steel at 300\({\,}^\circ \)C. Mater. Sci. Eng. A 715, 17–24 (2018)Google Scholar
  28. 28.
    Giroux, P.-F.: Experimental study and simulation of cyclic softening of tempered martensite ferritic steels. Ph.D. Thesis, École Nationale Supérieure des Mines de Paris (2011)Google Scholar
  29. 29.
    Chaboche, J.L., Rousselier, G.: On the plastic and viscoplastic constitutive equations: Part II: application of internal variable concepts to the 316 stainless steel. J. Press. Vessel. Technol. 105(2), 159 (1983)CrossRefGoogle Scholar
  30. 30.
    Wang, J., Steinmann, P., Rudolph, J., Willuweit, A.: Simulation of creep and cyclic viscoplastic strains in high-Cr steel components based on a modified Becker–Hackenberg model. Int. J. Press. Vessel. Pip. 128, 36–47 (2015)CrossRefGoogle Scholar
  31. 31.
    Velay, V., Bernhart, G., Penazzi, L.: Cyclic behavior modeling of a tempered martensitic hot work tool steel. Int. J. Plast. 22(3), 459–496 (2006)CrossRefGoogle Scholar
  32. 32.
    Farragher, T.P., Scully, S., O’Dowd, N.P., Leen, S.B.: Thermomechanical analysis of a pressurized pipe under plant conditions. J. Press. Vessel. Technol. 135, 011204–1–011204–9 (2013)CrossRefGoogle Scholar
  33. 33.
    Farragher, T.P., Scully, S., O’Dowd, N.P., Hyde, C.J., Leen, S.B.: High temperature, low cycle fatigue characterization of P91 weld and heat affected zone material. J. Press. Vessel. Technol. 136(2), 021403–1–021403–10 (2014)CrossRefGoogle Scholar
  34. 34.
    Armstrong, P.J., Frederick, C.O.: A mathematical representation of the multiaxial bauschinger effect. Technical report, Berkeley Nuclear Laboratories (1966)Google Scholar
  35. 35.
    Chaboche, J.L.: Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int. J. Plast. 5(3), 247–302 (1989)CrossRefGoogle Scholar
  36. 36.
    Koo, G.-H., Kwon, J.-H.: Identification of inelastic material parameters for modified 9Cr-1Mo steel applicable to the plastic and viscoplastic constitutive equations. Int. J. Press. Vessel. Pip. 88, 26–33 (2011)CrossRefGoogle Scholar
  37. 37.
    Wang, P., Cui, L., Lyschik, M., Scholz, A., Berger, C., Oechsner, M.: A local extrapolation based calculation reduction method for the application of constitutive material models for creep fatigue assessment. Int. J. Fatigue 44, 253–259 (2012)CrossRefGoogle Scholar
  38. 38.
    Saad, A.A., Sun, W., Hyde, T.H., Tanner, D.W.J.: Cyclic softening behaviour of a P91 steel under low cycle fatigue at high temperature. Procedia Eng. 10, 1103–1108 (2011)CrossRefGoogle Scholar
  39. 39.
    Saad, A.A.: Cyclic plasticity and creep of power plant materials. Ph.D. Thesis, University of Nottingham, Nottingham (2012)Google Scholar
  40. 40.
    Barrett, R.A., O’Donoghue, P.E., Leen, S.B.: An improved unified viscoplastic constitutive model for strain-rate sensitivity in high temperature fatigue. Int. J. Fatigue 48, 192–204 (2013)CrossRefGoogle Scholar
  41. 41.
    Zhang, S.-L., Xuan, F.-Z.: Interaction of cyclic softening and stress relaxation of 9–12% Cr steel under strain-controlled fatigue-creep condition: experimental and modeling. Int. J. Plast. 1–20 (2017)Google Scholar
  42. 42.
    Benaarbia, A., Rae, Y., Sun, W.: Unified viscoplasticity modelling and its application to fatigue-creep behaviour of gas turbine rotor. Int. J. Mech. Sci. 136, 36–49 (2018)CrossRefGoogle Scholar
  43. 43.
    Estrin, Y., Braasch, H., Brechet, Y.: A dislocation density based constitutive model for cyclic deformation. J. Eng. Mater. Technol. 118(4), 441–447 (1996)CrossRefGoogle Scholar
  44. 44.
    Sauzay, M., Brillet, H., Monneta, I., Mottot, M., Barcelo, F., Fournier, B., Pineau, A.: Cyclically induced softening due to low-angle boundary annihilation in a martensitic steel. Mater. Sci. Eng. A 400401, 241–244 (2005)CrossRefGoogle Scholar
  45. 45.
    Sauzay, M., Fournier, B., Mottot, M., Pineau, A., Monnet, I.: Cyclic softening of martensitic steels at high temperature: experiments and physically based modelling. Mater. Sci. Eng. A 483484, 410–414 (2008)CrossRefGoogle Scholar
  46. 46.
    Barrett, R.A., O’Donoghue, P.E., Leen, S.B.: A dislocation-based model for high temperature cyclic viscoplasticity of 9–12Cr steels. Comput. Mater. Sci. 92, 286–297 (2014)CrossRefGoogle Scholar
  47. 47.
    Barrett, R.A., O’Donoghue, P.E., Leen, S.B.: A physically-based constitutive model for high temperature microstructural degradation under cyclic deformation. Int. J. Fatigue 100, 388–406 (2017)CrossRefGoogle Scholar
  48. 48.
    Barkar, T., Ågren, J.: Creep simulation of 9–12% Cr steels using the composite model with thermodynamically calculated input. Mater. Sci. Eng. A 395(1–2), 110–115 (2005)CrossRefGoogle Scholar
  49. 49.
    Voigt, W.: Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper. Ann. Phys. 274(12), 573–587 (1889)CrossRefGoogle Scholar
  50. 50.
    Naumenko, K., Altenbach, H., Kutschke, A.: A combined model for hardening, softening, and damage processes in advanced heat resistant steels at elevated temperature. Int. J. Damage Mech. 20(4), 578–597 (2011)CrossRefGoogle Scholar
  51. 51.
    Naumenko, K., Gariboldi, E.: A phase mixture model for anisotropic creep of forged Al–Cu–Mg–Si alloy. Mater. Sci. Eng. A 618, 368–376 (2014)CrossRefGoogle Scholar
  52. 52.
    Raj, S.V., Iskovitz, I.S., Freed, A.D.: Modeling the role of dislocation substructure during class M and exponential creep. In: Krausz, A.S., Krausz, K. (eds.) Unified Constitutive Laws of Plastic Deformation, pp. 343–439. Academic Press Inc., Cambridge (1996)CrossRefGoogle Scholar
  53. 53.
    Eisenträger, J., Naumenko, K., Altenbach, H.: Numerical implementation of a phase mixture model for rate-dependent inelasticity of tempered martensitic steels. Acta Mech. 229, 3051–3068 (2018)MathSciNetCrossRefGoogle Scholar
  54. 54.
    Zhu, Y., Kang, G., Kan, Q., Bruhns, O.T.: Logarithmic stress rate based constitutive model for cyclic loading in finite plasticity. Int. J. Plast. 54, 34–55 (2014)CrossRefGoogle Scholar
  55. 55.
    Shutov, A.V., Kreißig, R.: Finite strain viscoplasticity with nonlinear kinematic hardening: phenomenological modeling and time integration. Comput. Methods Appl. Mech. Eng. 197(21–24), 2015–2029 (2008)MathSciNetCrossRefGoogle Scholar
  56. 56.
    Naumenko, K., Altenbach, H.: Modeling High Temperature Materials Behavior for Structural Analysis. Part I: Continuum Mechanics Foundations and Constitutive Models. Advanced Structured Materials, vol. 28. Springer International Publishing, Berlin (2016)Google Scholar
  57. 57.
    Eisenträger, J., Naumenko, K., Altenbach, H.: Calibration of a phase mixture model for hardening and softening regimes in tempered martensitic steel over wide stress and temperature ranges. J. Strain Anal. Eng. Des. 53, 156–177 (2018)CrossRefGoogle Scholar
  58. 58.
    Silbermann, C.B., Shutov, A.V., Ihlemann, J.: Modeling the evolution of dislocation populations under non-proportional loading. Int. J. Plast. 55, 58–79 (2014)CrossRefGoogle Scholar
  59. 59.
    Belytschko, T., Liu, W.K., Moran, B.: Nonlinear Finite Elements for Continua and Structures. Wiley, New York (2000)Google Scholar
  60. 60.
    Wriggers, P.: Nonlinear Finite Element Methods. Springer, Berlin (2008)Google Scholar
  61. 61.
    Luccioni, L.X., Pestana, J.M., Taylor, R.L.: Finite element implementation of non-linear elastoplastic constitutive laws using local and global explicit algorithms with automatic error control. Int. J. Numer. Methods Eng. 50(5), 1191–1212 (2001)CrossRefGoogle Scholar
  62. 62.
    Courant, R., Friedrichs, K., Lewy, H.: Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann. 100, 32–74 (1928)MathSciNetCrossRefGoogle Scholar
  63. 63.
    Hartmann, S., Haupt, P.: Stress computation and consistent tangent operator using non-linear kinematic hardening models. Int. J. Numer. Methods Eng. 36(22), 3801–3814 (1993)CrossRefGoogle Scholar
  64. 64.
    Hartmann, S., Lührs, G., Haupt, P.: An efficient stress algorithm with applications in viscoplasticity and plasticity. Int. J. Numer. Methods Eng. 40(6), 991–1013 (1997)CrossRefGoogle Scholar
  65. 65.
    Kobayashi, M., Mukai, M., Takahashi, H., Ohno, N., Kawakami, T., Ishikawa, T.: Implicit integration and consistent tangent modulus of a time-dependent non-unified constitutive model. Int. J. Numer. Methods Eng. 58(10), 1523–1543 (2003)CrossRefGoogle Scholar
  66. 66.
    Harville, D.A.: Matrix Algebra From a Statistician’s Perspective. Springer, New York (1997)CrossRefGoogle Scholar
  67. 67.
    Ghorpade, S.R., Limaye, B.V.: A Course in Multivariable Calculus and Analysis. Springer, New York (2010)CrossRefGoogle Scholar
  68. 68.
    Zhu, X., Chen, H., Xuan, F., Chen, X.: Cyclic plasticity behaviors of steam turbine rotor subjected to cyclic thermal and mechanical loads. Eur. J. Mech. A/Solids 66, 243–255 (2017)CrossRefGoogle Scholar
  69. 69.
    Stephan, P., Kabelac, S., Kind, M., Martin, H., Mewes, D., Schaber, K.: VDI Heat Atlas. Springer, Berlin (2010)Google Scholar
  70. 70.
    Leyzerovich, A.S.: Steam Turbines for Modern Fossil-fuel Power Plants. Fairmont Press, Lilburn, GA, USA (2008)Google Scholar
  71. 71.
    Strauß, K.: Kraftwerkstechnik zur Nutzung fossiler, nuklearer und regenerativer Energiequellen. Springer, Berlin (2009)Google Scholar
  72. 72.
    Suresh, S.: Fatigue of Materials. Cambridge University Press, Cambridge (2006)Google Scholar
  73. 73.
    Meng, Q., Wang, Z.: Creep damage models and their applications for crack growth analysis in pipes: a review. Eng. Fract. Mech. 205, 547–576 (2019)CrossRefGoogle Scholar
  74. 74.
    Sloan, S.W.: Substepping schemes for the numerical integration of elastoplastic stress-strain relations. Int. J. Numer. Methods Eng. 24(5), 893–911 (1987)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Johanna Eisenträger
    • 1
    Email author
  • Konstantin Naumenko
    • 1
  • Yevgen Kostenko
    • 2
  • Holm Altenbach
    • 1
  1. 1.Otto von Guericke University MagdeburgMagdeburgGermany
  2. 2.Siemens AG, Power and Gas DivisionMülheim an der RuhrGermany

Personalised recommendations