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Life prediction of thermally highly loaded components: modelling the damage process of a rocket combustion chamber hot wall

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Abstract

During their operational life-time, actively cooled liners of cryogenic combustion chambers are known to exhibit a characteristic so-called doghouse deformation, pursued by formation of axial cracks. The present work aims at developing a model that quantitatively accounts for this failure mechanism. High-temperature material behaviour is characterised in a test programme and it is shown that stress relaxation, strain rate dependence, isotropic and kinematic hardening as well as material ageing have to be taken into account in the model formulation. From fracture surface analyses of a thrust chamber it is concluded that the failure mode of the hot wall ligament at the tip of the doghouse is related to ductile rupture. A material model is proposed that captures all stated effects. Basing on the concept of continuum damage mechanics, the model is further extended to incorporate softening effects due to material degradation. The model is assessed on experimental data and quantitative agreement is established for all tests available. A 3D finite element thermo-mechanical analysis is performed on a representative thrust chamber applying the developed material-damage model. The simulation successfully captures the observed accrued thinning of the hot wall and quantitatively reproduces the doghouse deformation.

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Notes

  1. Originally Murakami expresses the effective stress in terms of the observable stress and then symmetrises the former. Here, we proceed in the opposite way, i.e. we suppose to know the effective stress and want to compute the observable stress. This is the reason for the deviating expression from the original.

References

  1. Arya, V.K., Arnold, S.M.: Viscoplastic analysis of an experimental cylindrical thrust chamber. Technical Report, NASA-TM-103287, NASA, June 1991

  2. Thomas-Ogbuji, L.: Protection of advanced copper alloys with lean Cu-Cr coatings. Technical Report, NASA-CR-2003-212548, NASA (2003)

  3. Jain, P., Raj, S.V., Hemker, H.J.: Characterization of nicraly coatings for a high strength, high conductivity grcop-84 copper alloy. Acta Mater. 55, 5103–5113 (2007)

    Article  Google Scholar 

  4. “Advanced high pressure O2/H2 technology”. Technical Report, NASA-CP-2372, NASA (1984)

  5. Hannum, N.P., Kasper, H.J., Pavli, A.J.: Experimental and theoretical investigation of fatigue life in reusable rocket thrust chambers. Technical Report, NASA TM-X-73413, NASA (1976)

  6. Quentmeyer, R.J.: Experimental fatigue life investigation of cylindrical thrust chambers. Technical Report, NASA TM-X-73665, NASA (1977)

  7. Hannum, N.P., Price, H.G. Jr.: Some effects of thermal-cycle-induced deformation in rocket thrust chambers. Technical Report, NASA-TP-1834-19810011648, NASA (1981)

  8. Kasper, H.J.: Thrust chamber life prediction. In: Morea, S.F., Wu, S.T. (eds.) Advanced High Pressure O2/H2 Technology, pp. 36–43. Technical Report, NASA-CP-2372, NASA (1984)

  9. Armstrong, W.H.: Structural analyses of cylindrical thrust chambers, final report, vol. 1. Technical Report, NASA-CR-159522, NASA (1979)

  10. Robinson, D.N., Swindeman R.W.: Unified creep-plasticity constitutive equations for 2-1/4 Cr-1 Mo steel at elevated temperature. Technical Report, ORNL-TM-8444, Oak Ridge National Laboratory, October 1982

  11. Freed, A.D.: Structure of a viscoplastic theory. Technical Report, NASA-TM-100794, NASA (1988)

  12. Arya, V.K.: Nonlinear structural analysis of cylindrical thrust chambers using viscoplastic models. J. Propuls. Power 8(3), 598–604 (1992)

    Article  MathSciNet  Google Scholar 

  13. Ray, A., Dai, X.: Damage-mitigating control of a reusable rocket engine for high performance and extended life. Technical Report, NASA-CR-4640, NASA (1995)

  14. Dai, X., Ray, A.: Life prediction of the thrust chamber wall of reusable rocket engine. J. Propuls. Power 11, 1279–1287 (1995)

    Article  Google Scholar 

  15. Lemaitre, J., Desmorat, R.: Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures. Springer, Berlin, Heidelberg, New York (2005)

    Google Scholar 

  16. Saarivirta, M.J.: High conductivity copper-rich Cu-Zr alloys. Trans. Metall. Soc. AIME 218, 431–437 (1960)

    Google Scholar 

  17. Singh, J., Jerman, G., Poorman, R., Bhat, B.N., Kuruvilla, A.K.: Mechanical properties and microstructural stability of wrought, laser, and electron beam glazed NARloy-Z alloy at elevated temperatures. J. Mater. Sci. 32(14), 3891–3903 (1997)

    Article  Google Scholar 

  18. Zhou, Y., Zhao, H., Zhang, K.: Investigation of the AgCuZr ternary system. J. Less-Common Metals 138(1), 7–10 (1988)

    Article  Google Scholar 

  19. Schwarz, W., Schwub, S., Höppel, H.W., Göken, M.: Modelling viscoplastic material behaviour comprising ageing: constitutive equations and numerical implementation in ANSYS-usermat. In: ANSYS Conference & 27th CADFEM Users’ Meeting 2009, Conference Proceedings, chap. 2.7.5 (2009)

  20. Germain, P.: Cours de Mecanique des Milieux Continus, vol. 1. Masson (1973)

  21. Chaboche, J.L.: Viscoplastic constitutive equations for the description of cyclic anisotropic behaviour of metals. Bulletin de l’Academie Polonaise des Sciences XXV(XXV(1), 33–41 (1977)

    Google Scholar 

  22. Chaboche, J.-L.: Cyclic viscoplastic constitutive equations. Part I: a thermodynamically consistent formulation. J. Appl. Mech. 60, 813–821 (1993)

    Article  MATH  Google Scholar 

  23. Chaboche, J.L.: Unified cyclic viscoplastic constitutive equations: development, capabilities and thermodynamic framework. In: Krausz, A.S., Krausz, K. (eds.) Unified Constitutive Laws of Plastic Deformation. pp. 1–68. Academic Press (1996)

  24. Chaboche, J.-L.: Thermodynamic formulation of constitutive equations and application to the viscoplasticity and viscoelasticity of methals and polymers. Int. J. Solids Struct. 34(18), 2239–2254 (1997)

    Article  MATH  Google Scholar 

  25. Chaboche, J.-L., Jung, O.: Application of a kinematic hardening viscoplasticity model with thesholds to the residual stress relaxation. Int. J. Plasticity 13(10), 785–807 (1998)

    Article  Google Scholar 

  26. Lemaitre, J., Chaboche, J.-L.: Mechanics of Solid Materials. Cambridge University Press (2000)

  27. Chaboche, J.-L.: A review of some plasticity and viscoplasticity constiutive theories. Int. J. Plasticity 24, 1642–1693 (2008)

    Article  MATH  Google Scholar 

  28. Chaboche, J.-L.: Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int. J. Plasticity 5, 247–302 (1989)

    Article  MATH  Google Scholar 

  29. Brocks, W., Lin, R.: An extended chaboche viscoplastic law at finite strains and its numerical implementation. Technical Report, GKSS-Forschungszentrum Geesthacht GmbH (2003)

  30. Orowan, E.: Symposium on Internal Stress in Metals and Alloys. The Institute of Metals, London (1948)

  31. Yao, J.H., Elder, K.R., Guo, H., Grant, M.: Ostwald ripening in two and three dimensions. Phys. Rev. B 45(14), 8173–8176 (1992)

    Article  Google Scholar 

  32. Ardell, A.J.: Temporal behavior of the number density of particles during Ostwald ripening. Mater. Sci. Eng. A 238, 108–120 (1997)

    Article  Google Scholar 

  33. Guyot, P., Cottignies, L.: Precipitation kinetics, mechanical strength and electrical conductivity of AlZnMgCu alloys. Acta Mater. 44(10), 4161–4167 (1996)

    Article  Google Scholar 

  34. Wang, K.G., Guo, Z., Sha, W., Glicksman, M.E., Rajan, K.: Property predictions using microstructural modeling. Acta Mater. 53, 3395–3402 (2005)

    Article  Google Scholar 

  35. Cailletaud, G., Depoid, C., Massinon D., Nicouleau-Bourles, E.: Elastoviscoplasticity with aging in aluminium alloys. In: Maugin, G.A., Drouot, R., Sidoroff, F. (eds.) Continuum Thermomechanics, pp. 75–86. Kluwer, Dordrecht (2000)

  36. Lemaitre, J., Chaboche, J.-L., A nonlinear model of creep-fatigue damage cumulation and interaction. Technical Report, T.P. 1934, Office National D’Etudes et de Recherches Aerospatiales (1974)

  37. Chaboche, J.L.: Continuum damage mechanics. Part I: general concepts. J. Appl. Mech. 55, 59–63 (1988)

    Article  Google Scholar 

  38. Chaboche, J.L.: Continuum damage mechanics. Part II: damage growth, crack initiation, and crack growth. J. Appl. Mech. 55, 65–72 (1988)

    Article  Google Scholar 

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

    Article  Google Scholar 

  40. Kattan, P.I., Voyiadjis, G.Z.: Damage Mechanics with Finite Elements: Practical Applications with Computer Tools. Springer, Berlin, Heidelbeg, New York (2002)

    Google Scholar 

  41. Voyiadjis, G.Z., Kattan, P.I.: Damage Mechanics. Taylor & Francis (2005)

  42. Landgraf, R.W., Morrow, J., Endo, T.: Determination of the cyclic stress-strain curve. J. Mater. JMLSA 4, 176–188 (1969)

    Google Scholar 

  43. Murakami, S., Ohno, N.: A continuum theory of creep and creep damage. In: Ponter, A.R.S., Hayhurst, D.R. (eds.) Creep in Structures, pp. 422–444. Springer, New York (1981)

  44. Murakami, S.: Model of anisotropic creep damage. In: Lemaitre, J. (ed.) Handbook of Materials Behavior Models, vol. 2. Failures of Materials, pp. 446–452. Academic Press (2001)

  45. Harth, T., Lehn, J.: Identification of material parameters for inelastic constitutive models using stochastic methods. GAMM-Mitt 30(2), 409–429 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  46. Preclik, D., Knab, O., Görgen, J., Hagemann, G.: Simulation and analysis of thrust chamber flowfields: cryogenic propellant rockets, liquid rocket thrust chambers: aspects of modeling, analysis, and design. In: Progress in Aeronautics and Astronautics, vol. 200. AIAA (2004)

  47. Knab, O., Frey, M., Görgen, J., Maeding, C., Quering, K., Wiedmann, D.: Progress in combustion and heat transfer modelling in rocket thrust chamber applied engineering. In: American Institute of Aeronautics and Astronautics, 45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Denver, Colorado, number AIAA-2009-5477 (2009)

  48. Gurson, A.L.: Continuum theory of ductile rupture by void nucleation and growth. Part I: yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. 99, 2–15 (1977)

    Article  Google Scholar 

  49. Hao, S., Brocks, W.: The Gurson-Tvergaard-Needleman-model for rate and temperature-dependent materials with isotropic and kinematic hardening. Comput. Mech. 20, 30–40 (1997)

    Article  Google Scholar 

  50. Rousselier, G.: The rousselier model for porous metal plasticity and ductile fracture. In: Lemaitre, J. (ed.) Handbook of Materials Behavior Models vol. 2: Failures of Materials, pp. 436–444. Academic Press (2001)

  51. Ding, H.Z., Mughrabi, H., Höppel, H.W.: A low-cycle fatigue life prediction model of ultrafine-grained metals. Fatigue Fract. Eng. Mater. Struct. 25, 975–984 (2002)

    Article  Google Scholar 

  52. Gernoth, A., Riccius, J.R., Haidn, O.J, Brummer, L., Mewes, B., Quering, K.: TMF panel tests: close-to-reality simulation of thermomechanical fatigue processes in heat-loaded walls. In: 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 21–23 July 2008, Hartford, CT (2008)

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Acknowledgments

This work was carried out in the project “Life prediction of thermally highly loaded components” co-funded by the Bavarian Research Foundation. The authors express their gratitude to the Bavarian Research Foundation for the financial support.

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Authors and Affiliations

  1. Astrium GmbH Space Transportation, 81663, Munich, Germany

    W. Schwarz, K. Quering & D. Wiedmann

  2. Department of Materials Science and Engineering, Institute I: General Materials Properties, Friedrich-Alexander-University Erlangen-Nürnberg, Martensstr. 5, 91058, Erlangen, Germany

    S. Schwub, H. W. Höppel & M. Göken

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  1. W. Schwarz
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  2. S. Schwub
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Correspondence to W. Schwarz.

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Schwarz, W., Schwub, S., Quering, K. et al. Life prediction of thermally highly loaded components: modelling the damage process of a rocket combustion chamber hot wall. CEAS Space J 1, 83–97 (2011). https://doi.org/10.1007/s12567-011-0007-9

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