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
A.E. Waltar and A.B. Reynolds, Fast Breeder Reactors (Richland: Alan E. Waltar, 1981).
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).
C.P. Massey, K.A. Terrani, S.N. Dryepondt, and B.A. Pint, J. Nucl. Mater. 470, 128 (2016).
S. Suman, M.K. Khan, M. Pathak, R.N. Singh, and J.K. Chakravartty, Nucl. Eng. Des. 307, 319 (2016).
J.M. Kramer, Y.Y. Liu, M.C. Billone, and H.C. Tsai, J. Nucl. Mater. 204, 203 (1993).
C. Matthews, C. Unal, J. Galloway, D.D.K. Keiser Jr, and S.L. Hayes, Nucl. Technol. 198, 231 (2017).
J.C. Danko, Metals Handbook Corrosion, 9th ed., Vol. 13 (Washington, DC: ASM, 1987).
M.O. Speidel and R.M. Magdowski, Int. J. Press. Vessels Pip. 34, 119 (1988).
W. Wen, A. Kohnert, M. Arul Kumar, L. Capolungo, and C.N. Tomé, Int. J. Plast 126, 102633 (2020).
F. Garofalo, Trans. Metall. Soc. Aime 227, 351 (1963).
Y. Estrin and H. Mecking, Acta Metall. 32, 57 (1984).
H. Mecking and U.F. Kocks, Acta Metall. 29, 1865 (1981).
W. Wen, L. Capolungo, A. Patra, and C.N. Tomé, Metall. Mater. Trans. A 48, 2603 (2017).
W. Wen, L. Capolungo, and C.N. Tomé, Int. J. Plast 106, 88 (2018).
M. Basirat, T. Shrestha, L.L. Barannyk, G.P. Potirniche, and I. Charit, Metals 5, 1487 (2015).
T.O. Erinosho, K.A. Venkata, M. Mostafavi, D.M. Knowles, and C.E. Truman, Int. J. Solids Struct. 139, 129 (2018).
B. Chen, D.J. Smith, P.E.J. Flewitt, and M.W. Spindler, Mater. High Temp. 28, 155 (2011).
J. Segurado, R.A. Lebensohn, J. LLorca, and C.N. Tomé, Int. J. Plast 28, 124 (2012).
S. Ghosh, JOM 67, 129 (2015).
S. Keshavarz and S. Ghosh, Acta Mater. 61, 6549 (2013).
R.A. Lebensohn, A.D. Rollett, and P. Suquet, JOM 63, 13 (2011).
S. Ghosh, Micromechanical Analysis and Multi-Scale Modeling Using the Voronoi Cell Finite Element Method (Boca Raton: CRC Press, 2011).
D.L. McDowell, Handbook of Materials Modeling: Methods: Theory, Vol. 1 (Berlin: Springer, 2018).
D.L. McDowell, Computational Materials Systems Design (Berlin: Springer, 2018), pp. 105–146.
J.E. Andrade, C.F. Avila, S.A. Hall, N. Lenoir, and G. Viggiani, J. Mech. Phys. Solids 59, 237 (2011).
F. Feyel and J.-L. Chaboche, Comput. Methods Appl. Mech. Eng. 183, 309 (2000).
I. Benedetti and F. Barbe, J. Multiscale Model. 05, 1350002 (2013).
A. Eghtesad, K. Germaschewski, R.A. Lebensohn, and R.A. Knezevic, Comput. Phys. Commun. 254, 107231 (2020).
A. Eghtesad and M. Knezevic, J. Mech. Phys. Solids 134, 103750 (2020).
A. Patra and C.N. Tomé, Nucl. Eng. Des. 315, 155 (2017).
S.R. Kalidindi, H.K. Duvvuru, and M. Knezevic, Acta Mater. 54, 1795 (2006).
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.
C.W. Hunter, R.L. Fish, and J.J. Holmes, Nucl. Technol. 27, 376 (1975).
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.
R.A. Lebensohn, C.S. Hartley, C.N. Tomé, and O. Castelnau, Philos. Mag. 90, 567 (2010).
H. Wang, L. Capolungo, B. Clausen, and C.N. Tomé, Int. J. Plast 93, 251 (2017).
Y.Q. Wang, M.W. Spindler, C.E. Truman, and D.J. Smith, Mater. Des. 95, 656 (2016).
P. Franciosi and A. Zaoui, Acta Metall. 30, 1627 (1982).
U.F. Kocks, A.S. Argon, and M.F. Ashby, Thermodynamics and Kinetics of Slip (Oxford: Pergamon Press, 1975).
R.L. Coble, J. Appl. Phys. 34, 1679 (1963).
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.
J.L. Deutsch and C.V. Deutsch, J. Stat. Plan. Inference 142, 763 (2012).
P. Hosemann, S. Kabra, E. Stergar, M.J. Cappillo, and S.A. Maloy, J. Nucl. Mater. 403, 7 (2010).
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.
Y. Chen, Nucl. Eng. Technol. 45, 311 (2013).
S.A. Maloy, T. Romero, M.R. James, and Y. Dai, J. Nucl. Mater. 356, 56 (2006).
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).
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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DOI: https://doi.org/10.1007/s11837-020-04402-2