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Surrogate Modeling of Viscoplasticity in Steels: Application to Thermal, Irradiation Creep and Transient Loading in HT-9 Cladding

  • Augmenting Physics-based Models in ICME with Machine Learning and Uncertainty Quantification
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Abstract

The use of structural metals in extreme environments relies both on the characterization of the mechanical response and microstructure changes in service and on modeling predictions. Data scarcity creates a need for predictive constitutive models that can be used in regimes outside calibration domains. While crystal plasticity models can be applied to non-monotonic loads and complex environments, their computational cost typically prohibits use at the level of an engineering structure. As an alternative, the present study introduces a surrogate constitutive model derived from crystal-plasticity predictions of the mechanical response of HT9 subjected to irradiation, stresses and temperatures. The surrogate law is then tested in the cases of uniaxial straining, stress cycling, thermal cycling and thermal ramping. Finally, using this constitutive relationship, finite element simulations of a pressurized tube subjected to a stress and thermal transients are performed and analyzed.

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References

  1. A.E. Waltar and A.B. Reynolds, Fast Breeder Reactors (Richland: Alan E. Waltar, 1981).

    Google Scholar 

  2. T.H. Bauer, G.R. Fenske, and J.M. Kramer, Cladding Failure Margins for Metallic Fuel in the Integral Fast Reactor (Lemont: Argonne National Lab, 1987).

    Google Scholar 

  3. C.P. Massey, K.A. Terrani, S.N. Dryepondt, and B.A. Pint, J. Nucl. Mater. 470, 128 (2016).

    Google Scholar 

  4. S. Suman, M.K. Khan, M. Pathak, R.N. Singh, and J.K. Chakravartty, Nucl. Eng. Des. 307, 319 (2016).

    Google Scholar 

  5. J.M. Kramer, Y.Y. Liu, M.C. Billone, and H.C. Tsai, J. Nucl. Mater. 204, 203 (1993).

    Google Scholar 

  6. C. Matthews, C. Unal, J. Galloway, D.D.K. Keiser Jr, and S.L. Hayes, Nucl. Technol. 198, 231 (2017).

    Google Scholar 

  7. J.C. Danko, Metals Handbook Corrosion, 9th ed., Vol. 13 (Washington, DC: ASM, 1987).

    Google Scholar 

  8. M.O. Speidel and R.M. Magdowski, Int. J. Press. Vessels Pip. 34, 119 (1988).

    Google Scholar 

  9. W. Wen, A. Kohnert, M. Arul Kumar, L. Capolungo, and C.N. Tomé, Int. J. Plast 126, 102633 (2020).

    Google Scholar 

  10. F. Garofalo, Trans. Metall. Soc. Aime 227, 351 (1963).

    Google Scholar 

  11. Y. Estrin and H. Mecking, Acta Metall. 32, 57 (1984).

    Google Scholar 

  12. H. Mecking and U.F. Kocks, Acta Metall. 29, 1865 (1981).

    Google Scholar 

  13. W. Wen, L. Capolungo, A. Patra, and C.N. Tomé, Metall. Mater. Trans. A 48, 2603 (2017).

    Google Scholar 

  14. W. Wen, L. Capolungo, and C.N. Tomé, Int. J. Plast 106, 88 (2018).

    Google Scholar 

  15. M. Basirat, T. Shrestha, L.L. Barannyk, G.P. Potirniche, and I. Charit, Metals 5, 1487 (2015).

    Google Scholar 

  16. T.O. Erinosho, K.A. Venkata, M. Mostafavi, D.M. Knowles, and C.E. Truman, Int. J. Solids Struct. 139, 129 (2018).

    Google Scholar 

  17. B. Chen, D.J. Smith, P.E.J. Flewitt, and M.W. Spindler, Mater. High Temp. 28, 155 (2011).

    Google Scholar 

  18. J. Segurado, R.A. Lebensohn, J. LLorca, and C.N. Tomé, Int. J. Plast 28, 124 (2012).

    Google Scholar 

  19. S. Ghosh, JOM 67, 129 (2015).

    Google Scholar 

  20. S. Keshavarz and S. Ghosh, Acta Mater. 61, 6549 (2013).

    Google Scholar 

  21. R.A. Lebensohn, A.D. Rollett, and P. Suquet, JOM 63, 13 (2011).

    Google Scholar 

  22. S. Ghosh, Micromechanical Analysis and Multi-Scale Modeling Using the Voronoi Cell Finite Element Method (Boca Raton: CRC Press, 2011).

    MATH  Google Scholar 

  23. D.L. McDowell, Handbook of Materials Modeling: Methods: Theory, Vol. 1 (Berlin: Springer, 2018).

    Google Scholar 

  24. D.L. McDowell, Computational Materials Systems Design (Berlin: Springer, 2018), pp. 105–146.

    Google Scholar 

  25. J.E. Andrade, C.F. Avila, S.A. Hall, N. Lenoir, and G. Viggiani, J. Mech. Phys. Solids 59, 237 (2011).

    Google Scholar 

  26. F. Feyel and J.-L. Chaboche, Comput. Methods Appl. Mech. Eng. 183, 309 (2000).

    Google Scholar 

  27. I. Benedetti and F. Barbe, J. Multiscale Model. 05, 1350002 (2013).

    Google Scholar 

  28. A. Eghtesad, K. Germaschewski, R.A. Lebensohn, and R.A. Knezevic, Comput. Phys. Commun. 254, 107231 (2020).

    MathSciNet  Google Scholar 

  29. A. Eghtesad and M. Knezevic, J. Mech. Phys. Solids 134, 103750 (2020).

    MathSciNet  Google Scholar 

  30. A. Patra and C.N. Tomé, Nucl. Eng. Des. 315, 155 (2017).

    Google Scholar 

  31. S.R. Kalidindi, H.K. Duvvuru, and M. Knezevic, Acta Mater. 54, 1795 (2006).

    Google Scholar 

  32. A.E. Tallman, M. Arul Kumar, A. Castillo, W. Wen, L. Capolungo, and C.N. Tomé, Integr. Mater. Manuf. Innov. (2020). https://doi.org/10.1007/s40192-020-00181-5.

    Article  Google Scholar 

  33. C.W. Hunter, R.L. Fish, and J.J. Holmes, Nucl. Technol. 27, 376 (1975).

    Google Scholar 

  34. N. Cannon, F.-H. Huang, and M. Hamilton, in STP1046V2-EB 14th Int. Symposium on Effects of Radiation on Materials, Vol. II (ASTM International, 1990), pp. 729–738.

  35. R.A. Lebensohn, C.S. Hartley, C.N. Tomé, and O. Castelnau, Philos. Mag. 90, 567 (2010).

    Google Scholar 

  36. H. Wang, L. Capolungo, B. Clausen, and C.N. Tomé, Int. J. Plast 93, 251 (2017).

    Google Scholar 

  37. Y.Q. Wang, M.W. Spindler, C.E. Truman, and D.J. Smith, Mater. Des. 95, 656 (2016).

    Google Scholar 

  38. P. Franciosi and A. Zaoui, Acta Metall. 30, 1627 (1982).

    Google Scholar 

  39. U.F. Kocks, A.S. Argon, and M.F. Ashby, Thermodynamics and Kinetics of Slip (Oxford: Pergamon Press, 1975).

    Google Scholar 

  40. R.L. Coble, J. Appl. Phys. 34, 1679 (1963).

    Google Scholar 

  41. M.B. Toloczko, B.R. Grambau, F.A. Garner, and K. Abe, in 20th International Symposium on STP1405-EB Effects of Radiation on Materials. (2001), pp. 557–569.

  42. J.L. Deutsch and C.V. Deutsch, J. Stat. Plan. Inference 142, 763 (2012).

    Google Scholar 

  43. P. Hosemann, S. Kabra, E. Stergar, M.J. Cappillo, and S.A. Maloy, J. Nucl. Mater. 403, 7 (2010).

    Google Scholar 

  44. H.J. Frost and M.F. Ashby, Fundamental Aspects of Structure Alloy Design, ed. R.I. Jaffee and B.A. Wilcox (Boston: Springer, 1977), pp. 27–65.

    Google Scholar 

  45. Y. Chen, Nucl. Eng. Technol. 45, 311 (2013).

    Google Scholar 

  46. S.A. Maloy, T. Romero, M.R. James, and Y. Dai, J. Nucl. Mater. 356, 56 (2006).

    Google Scholar 

  47. C.J. Permann, D.R. Gaston, D. Andrš, R.W. Carlsen, F. Kong, A.D. Lindsay, J.M. Miller, J.W. Peterson, A.E. Slaughter, R.H. Stogner, and R.C. Martineau, SoftwareX 11, 100430 (2020).

    Google Scholar 

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Acknowledgements

This work was sponsored by the US Department of Energy, Office of Nuclear Energy, and Nuclear Energy Advanced Modeling and Simulations (NEAMS). This research made use of the resources of the High Performance Computing Center at Idaho National Laboratory, which is supported by the Office of Nuclear Energy of the US Department of Energy and the Nuclear Science User Facilities under Contract No. DE-AC07-05ID14517.

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Tallman, A.E., Arul Kumar, M., Matthews, C. et al. Surrogate Modeling of Viscoplasticity in Steels: Application to Thermal, Irradiation Creep and Transient Loading in HT-9 Cladding. JOM 73, 126–137 (2021). https://doi.org/10.1007/s11837-020-04402-2

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