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Uncertainty Quantification in the Mechanical Response of Crystal Plasticity Simulations

  • Ritwik Bandyopadhyay
  • Veerappan Prithivirajan
  • Michael D. SangidEmail author
Multiscale Computational Strategies for Heterogeneous Materials with Defects: Coupling Modeling with Experiments and Uncertainty Quantification
  • 91 Downloads

Abstract

Due to the uncertainty in calibrating the crystal plasticity (CP) model parameters, the present study quantifies the associated variability in the resulting mechanical response via a two-step process. First, a genetic algorithm framework is used to obtain the statistical distributions for the appropriate CP parameters. Second, those distributions are used in a first-order, second-moment method to compute the mean and the standard deviation for the stress along the loading direction (\( \sigma_{\text{load}} \)), plastic strain accumulation (PSA), and accumulated plastic strain energy density (Wp). The results suggest that a ~ 10% variability in \( \sigma_{\text{load}} \) and 20–25% variability in the PSA and Wp values may exist due to the uncertainty in the CP parameter estimation. Further, the contribution of a specific CP parameter to the overall uncertainty is path-dependent and varies based on the load step under consideration. The results of the present research will help practitioners to (1) identify the critical CP parameter(s) for a particular quantitative prediction of the mechanical response, (2) select appropriate experimental dataset(s) to calibrate the CP parameters, and (3) provide approximate variability in the crystal plasticity results which can propagate within a broader modeling framework.

Notes

Acknowledgements

This work was financially supported by DARPA (N66001-14-1-4041) under program managers M. Maher and J. Vandenbrande. We would like to thank the DARPA Open Manufacturing team for useful discussions: D. Schesser, J. Margiotta, D. Cheng, W. Roy, J. Williams, B. Cowles, R. Martukanitz, and K. Meinert. The authors gratefully acknowledge Dr. Todd Book for providing the characterization data for the IN718 material and Prof. Ganesh Subbarayan for interesting discussions on reliability analysis.

References

  1. 1.
    M.D. Sangid, Int. J. Fatigue 57, 58 (2013).CrossRefGoogle Scholar
  2. 2.
    F.P.E. Dunne, A. Walker, and D. Rugg, Proc. R. Soc. Lond. A 463, 1467 (2007).CrossRefGoogle Scholar
  3. 3.
    F.P.E. Dunne and D. Rugg, Fatigue Fract. Eng. Mater. Struct. 31, 949 (2008).CrossRefGoogle Scholar
  4. 4.
    K. Kirane and S. Ghosh, Int. J. Fatigue 30, 2127 (2008).CrossRefGoogle Scholar
  5. 5.
    K. Kirane, S. Ghosh, M. Groeber, and A. Bhattacharjee, J. Eng. Mater. Technol. 131, 21003 (2009).CrossRefGoogle Scholar
  6. 6.
    M. Anahid, M.K. Samal, and S. Ghosh, J. Mech. Phys. Solids 59, 2157 (2011).CrossRefGoogle Scholar
  7. 7.
    C.P. Przybyla and D.L. McDowell, Int. J. Plast. 26, 372 (2010).CrossRefGoogle Scholar
  8. 8.
    C.P. Przybyla and D.L. McDowell, Int. J. Plast. 27, 1871 (2011).CrossRefGoogle Scholar
  9. 9.
    J.D. Hochhalter, D.J. Littlewood, R.J. Christ, M.G. Veilleux, J.E. Bozek, A.R. Ingraffea, and A.M. Maniatty, Model. Simul. Mater. Sci. Eng. 18, 045004 (2010).CrossRefGoogle Scholar
  10. 10.
    J. Jiang, J. Yang, T. Zhang, J. Zou, Y. Wang, F.P.E. Dunne, and T.B. Britton, Acta Mater. 117, 333 (2016).CrossRefGoogle Scholar
  11. 11.
    B. Chen, J. Jiang, and F.P.E. Dunne, Int. J. Plast 101, 213 (2018).CrossRefGoogle Scholar
  12. 12.
    A. Cruzado, S. Lucarini, J. LLorca, and J. Segurado, Int. J. Fatigue 107, 40 (2018).CrossRefGoogle Scholar
  13. 13.
    V. Prithivirajan and M.D. Sangid, Mater. Des. 15, 139 (2018).CrossRefGoogle Scholar
  14. 14.
    E.H. Lee, J. Appl. Mech. 36, 1 (1969).CrossRefGoogle Scholar
  15. 15.
    I. Karaman, H. Sehitoglu, A.J. Beaudoin, Y.I. Chumlyakov, H.J. Maier, and C.N. Tome, Acta Mater. 48, 2031 (2000).CrossRefGoogle Scholar
  16. 16.
    S. Balasubramanian and L. Anand, Acta Mater. 50, 133 (2002).CrossRefGoogle Scholar
  17. 17.
    M.M. Shenoy, A.P. Gordon, D.L. McDowell, and R.W. Neu, J. Eng. Mater. Technol. 127, 325 (2005).CrossRefGoogle Scholar
  18. 18.
    A. Guery, F. Hild, F. Latourte, and S. Roux, Mech. Mater. 100, 55 (2016).CrossRefGoogle Scholar
  19. 19.
    P. Dawson, D. Boyce, S. MacEwen, and R. Rogge, Metall. Mater. Trans. A 31, 1543 (2000).CrossRefGoogle Scholar
  20. 20.
    D.C. Pagan, P.A. Shade, N.R. Barton, J.S. Park, P. Kenesei, D.B. Menasche, and J.V. Bernier, Acta Mater. 128, 406 (2017).CrossRefGoogle Scholar
  21. 21.
    S.R. Yeratapally, M.G. Glavicic, M. Hardy, and M.D. Sangid, Acta Mater. 107, 152 (2016).CrossRefGoogle Scholar
  22. 22.
    S.R. Yeratapally, M.G. Glavicic, C. Argyrakis, and M.D. Sangid, Reliab. Eng. Syst. Saf. 164, 110 (2017).CrossRefGoogle Scholar
  23. 23.
    R.C. Smith, Uncertainty Quantification: Theory, Implementation, and Applications (Philadelphia: SIAM, 2013).Google Scholar
  24. 24.
    A. Haldar and S. Mahadevan, Probability, Reliability, and Statistical Methods in Engineering Design (London: Wiley, 2000).Google Scholar
  25. 25.
    M.D. Sangid, T.A. Book, D. Naragani, J. Rotella, P. Ravi, A. Finch, P. Kenesei, J.-S. Park, H. Sharma, J. Almer, and X. Xiao, Addit. Manuf. 22, 479 (2018).CrossRefGoogle Scholar
  26. 26.
    M.A. Groeber and M.A. Jackson, Integr. Mater. Manuf. Innov. 3, 1 (2014).CrossRefGoogle Scholar
  27. 27.
  28. 28.
    M. Groeber, Development of an Automated Characterization—Representation Framework for the Modeling of Polycrystalline Materials in 3D (Columbus: The Ohio State University, 2007).Google Scholar
  29. 29.
    M.D. Sangid, H. Sehitoglu, H.J. Maier, and T. Niendorf, Mater. Sci. Eng. A 527, 7115 (2010).CrossRefGoogle Scholar
  30. 30.
    L.H. Chan, Synthetic Three-Dimensional Voxel-Based Microstructures That Contain Annealing Twins (Pittsburgh: Carnegie Mellon University, 2010).Google Scholar
  31. 31.
    G. Taylor, J. Inst. Met. 62, 307 (1938).Google Scholar
  32. 32.
    J. Bishop and R. Hill, Philos. Mag. 42, 1298 (1951).MathSciNetCrossRefGoogle Scholar
  33. 33.
    H.J. Bunge, Krist. Tech. 5, 145 (1970).CrossRefGoogle Scholar
  34. 34.
    C. Geuzaine and J.-F. Remacle, Int. J. Numer. Methods Eng. 79, 1309 (2009).CrossRefGoogle Scholar
  35. 35.
    R.J. Asaro, J. Appl. Mech. 50, 921 (1983).CrossRefGoogle Scholar
  36. 36.
    L. Anand and M. Kothari, J. Mech. Phys. Solid 44, 525 (1996).CrossRefGoogle Scholar
  37. 37.
    F. Roters, P. Eisenlohr, L. Hantcherli, D.D. Tjahjanto, T.R. Bieler, and D. Raabe, Acta Mater. 58, 1152 (2010).CrossRefGoogle Scholar
  38. 38.
    J.W. Hutchinson, Metall. Trans. A 8, 1465 (1977).CrossRefGoogle Scholar
  39. 39.
    C.O. Frederick and P.J. Armstrong, Mater High Temp. 24, 1 (2007).CrossRefGoogle Scholar
  40. 40.
    M.F. Horstemeyer, D.L. McDowell, and R.D. McGinty, Model. Simul. Mater. Sci. Eng. 7, 253 (1999).CrossRefGoogle Scholar
  41. 41.
    U.F. Kocks, Metall. Mater. Trans. B 1, 1121 (1970).CrossRefGoogle Scholar
  42. 42.
    A. Manonukul and F.P.E. Dunne, Proc. R. Soc. Lond. A 460, 1881 (2004).CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society 2019

Authors and Affiliations

  1. 1.School of Aeronautics and AstronauticsPurdue UniversityWest LafayetteUSA

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