Multi-faceted Uncertainty Quantification for Structure-Property Relationship with Crystal Plasticity Finite Element

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TMS 2023 152nd Annual Meeting & Exhibition Supplemental Proceedings (TMS 2023)

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Abstract

The structure-property linkage is one of the two most important relationships in materials science besides the process-structure linkage, especially for metals and polycrystalline alloys. The stochastic nature of microstructures begs for a robust approach to reliably address the linkage. As such, uncertainty quantification (UQ) plays an important role in this regard and cannot be ignored. To probe the structure-property linkage, many multi-scale integrated computational materials engineering (ICME) tools have been proposed and developed over the last decade to accelerate the material design process in the spirit of Material Genome Initiative (MGI), notably crystal plasticity finite element model (CPFEM) and phase-field simulations. Machine learning (ML) methods, including deep learning and physics-informed/-constrained approaches, can also be conveniently applied to approximate the computationally expensive ICME models, allowing one to efficiently navigate in both structure and property spaces effortlessly. Since UQ also plays a crucial role in verification and validation for both ICME and ML models, it is important to include UQ in the picture. In this paper, we summarize a few of our recent research efforts addressing UQ aspects of homogenized properties using CPFEM in a big picture context.

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References

  1. Acar P (2021) Recent progress of uncertainty quantification in small-scale materials science. Progress Mater Sci 117:100723

    Google Scholar 

  2. Agnew S, Brown D, Tomé C (2006) Validating a polycrystal model for the elastoplastic response of magnesium alloy AZ31 using in situ neutron diffraction. Acta Mater 54(18):4841–4852

    Article  CAS  Google Scholar 

  3. Arróyave R, McDowell DL (2019) Systems approaches to materials design: past, present, and future. Ann Rev Mater Res 49(1):103–126

    Article  Google Scholar 

  4. Balay S, Abhyankar S, Adams M, Brown J, Brune P, Buschelman K, Dalcin L, Dener A, Eijkhout V, Gropp W et al. (2019) PETSc users manual

    Google Scholar 

  5. Couperthwaite R, Khatamsaz D, Molkeri A, James J, Srivastava A, Allaire D, Arróyave R (2021) The BAREFOOT optimization framework. Integr Mater Manufact Innov 10(4):644–660

    Article  Google Scholar 

  6. Dalbey K, Eldred M, Geraci G, Jakeman J, Maupin K, Monschke JA, Seidl D, Tran A, Menhorn F, Zeng X (2021) Dakota a multilevel parallel object-oriented framework for design optimization parameter estimation uncertainty quantification and sensitivity analysis: version 6.14 theory manual. Technical report, Sandia National Lab.(SNL-NM), Albuquerque, NM (United States) (2021)

    Google Scholar 

  7. Diehl M, Groeber M, Haase C, Molodov DA, Roters F, Raabe D (2017) Identifying structure–property relationships through DREAM.3D representative volume elements and DAMASK crystal plasticity simulations: an integrated computational materials engineering approach. JOM 69(5):848–855

    Google Scholar 

  8. Giles MB (2008) Multilevel Monte Carlo path simulation. Oper Res 56(3):607–617

    Article  Google Scholar 

  9. Giles MB (2015) Multilevel Monte Carlo methods. Acta Numer 24:259–328

    Article  Google Scholar 

  10. Groeber MA, Jackson MA (2014) DREAM. 3D: a digital representation environment for the analysis of microstructure in 3D. Integr Mater Manufact Innov 3(1):5

    Google Scholar 

  11. Haario H, Laine M, Mira A, Saksman E (2006) DRAM: efficient adaptive MCMC. Stat Comput 16(4):339–354

    Article  Google Scholar 

  12. Haji-Ali AL, Nobile F, Tamellini L, Tempone R (2016) Multi-index stochastic collocation for random PDEs. Comput Methods Appl Mech Eng 306:95–122

    Article  Google Scholar 

  13. Haji-Ali AL, Nobile F, Tempone R (2016) Multi-index Monte Carlo: when sparsity meets sampling. Numer Math 132(4):767–806

    Article  Google Scholar 

  14. Honarmandi P, Arróyave R (2020) Uncertainty quantification and propagation in computational materials science and simulation-assisted materials design. Integr Mater Manufact Innov 1–41 (2020)

    Google Scholar 

  15. Kalidindi SR, Medford AJ, McDowell DL (2016) Vision for data and informatics in the future materials innovation ecosystem. JOM 68(8):2126–2137

    Article  Google Scholar 

  16. Khatamsaz D, Molkeri A, Couperthwaite R, James J, Arróyave R, Allaire D, Srivastava A (2021) Efficiently exploiting process-structure-property relationships in material design by multi-information source fusion. Acta Mater 206:116619

    Google Scholar 

  17. McDowell DL (2007) Simulation-assisted materials design for the concurrent design of materials and products. JOM 59(9):21–25

    Article  Google Scholar 

  18. Panchal JH, Kalidindi SR, McDowell DL (2013) Key computational modeling issues in integrated computational materials engineering. Comput Aided Des 45(1):4–25

    Article  Google Scholar 

  19. Peherstorfer B (2019) Multifidelity Monte Carlo estimation with adaptive low-fidelity models. SIAM/ASA J Uncertainty Quantif 7(2):579–603

    Article  Google Scholar 

  20. Peherstorfer B, Willcox K, Gunzburger M (2016) Optimal model management for multifidelity Monte Carlo estimation. SIAM J Sci Comput 38(5):A3163–A3194

    Article  Google Scholar 

  21. Roters F, Diehl M, Shanthraj P, Eisenlohr P, Reuber C, Wong SL, Maiti T, Ebrahimi A, Hochrainer T, Fabritius HO et al (2019) DAMASK-The Düsseldorf advanced material simulation kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale. Comput Mater Sci 158:420–478

    Article  CAS  Google Scholar 

  22. Sedighiani K, Diehl M, Traka K, Roters F, Sietsma J, Raabe D (2020) An efficient and robust approach to determine material parameters of crystal plasticity constitutive laws from macro-scale stress-strain curves. Int J Plast 134:102779

    Google Scholar 

  23. Sedighiani K, Traka K, Roters F, Raabe D, Sietsma J, Diehl M (2022) Determination and analysis of the constitutive parameters of temperature-dependent dislocation-density-based crystal plasticity models. Mech Mater 164:104117

    Google Scholar 

  24. Tran A, Eldred M, Wildey T, McCann S, Sun J, Visintainer RJ (2022) aphBO-2GP-3B: a budgeted asynchronous parallel multi-acquisition functions for constrained Bayesian optimization on high-performing computing architecture. Struct Multidiscip Optim 65(4):1–45

    Article  Google Scholar 

  25. Tran A., Maupin K., Rodgers T (2022) Monotonic Gaussian process for physics-constrained machine learning with materials science applications. J Comput Inf Sci Eng (2022)

    Google Scholar 

  26. Tran A, Mitchell JA, Swiler LP, Wildey T (2020) An active-learning high-throughput microstructure calibration framework for process-structure linkage in materials informatics. Acta Mater 194:80–92

    Article  CAS  Google Scholar 

  27. Tran A, Tran H (2019) Data-driven high-fidelity 2D microstructure reconstruction via non-local patch-based image inpainting. Acta Mater 178:207–218

    Article  CAS  Google Scholar 

  28. Tran A, Wildey T (2020) Solving stochastic inverse problems for property-structure linkages using data-consistent inversion and machine learning. JOM 73:72–89

    Article  Google Scholar 

  29. Tran A, Wildey T, Lim H (2022) Microstructure-sensitive uncertainty quantification for crystal plasticity finite element constitutive models using stochastic collocation method. Front Mater (2022)

    Google Scholar 

  30. Tran A, Wildey T, McCann S (2020) sMF-BO-2CoGP: A sequential multi-fidelity constrained Bayesian optimization for design applications. J Comput Inf Sci Eng 20(3):1–15

    Article  Google Scholar 

  31. Tromans D (2011) Elastic anisotropy of HCP metal crystals and polycrystals. Int J Res Rev Appl Sci 6(4):462–483

    Google Scholar 

  32. Wang F, Sandlöbes S, Diehl M, Sharma L, Roters F, Raabe D (2014) In situ observation of collective grain-scale mechanics in Mg and Mg-rare earth alloys. Acta Mater 80:77–93

    Article  CAS  Google Scholar 

  33. Wang L, Zheng Z, Phukan H, Kenesei P, Park JS, Lind J, Suter R, Bieler TR (2017) Direct measurement of critical resolved shear stress of prismatic and basal slip in polycrystalline Ti using high energy x-ray diffraction microscopy. Acta Mater 132:598–610

    Article  CAS  Google Scholar 

  34. Zambaldi C, Yang Y, Bieler TR, Raabe D (2012) Orientation informed nanoindentation of \(\alpha \)-Titanium: indentation pileup in hexagonal metals deforming by prismatic slip. J Mater Res 27(1):356–367

    Article  CAS  Google Scholar 

  35. Zhang C, Bütepage J, Kjellström H, Mandt S (2018) Advances in variational inference. IEEE Trans Pattern Anal Mach Intell 41(8):2008–2026

    Article  Google Scholar 

  36. Zhang Y, Apley DW, Chen W (2020) Bayesian optimization for materials design with mixed quantitative and qualitative variables. Sci Rep 10(1):1–13

    Google Scholar 

Download references

Acknowledgements

This article has been authored by an employee of National Technology and Engineering Solutions of Sandia, LLC under Contract No. DE-NA0003525 with the U.S. Department of Energy (DOE). The employee owns all right, title and interest in and to the article and is solely responsible for its contents. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this article or allow others to do so, for United States Government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan https://www.energy.gov/downloads/doe-public-access-plan. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

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Correspondence to Anh Tran .

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Tran, A., Robbe, P., Lim, H. (2023). Multi-faceted Uncertainty Quantification for Structure-Property Relationship with Crystal Plasticity Finite Element. In: TMS 2023 152nd Annual Meeting & Exhibition Supplemental Proceedings. TMS 2023. The Minerals, Metals & Materials Series. Springer, Cham. https://doi.org/10.1007/978-3-031-22524-6_53

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