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Machine Learning-Enabled Uncertainty Quantification for Modeling Structure–Property Linkages for Fatigue Critical Engineering Alloys Using an ICME Workflow

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Abstract

Integrated computational materials engineering (ICME) facilitates efficient approaches to new material discovery and design, as well as optimization of existing materials. Computational models provide a way to rapidly screen candidate material designs such that materials can be tailored for specific applications in the product design cycle. Uncertainty is ubiquitous in ICME process–structure–property workflows; it represents a major barrier to the effective use of modeling results for high-confidence decision support in materials design and development. This work addresses microstructure statistical uncertainties, and demonstrates an approach to quantify, reduce, and propagate these uncertainties through structure–property linkages to provide robust quantification of uncertainties in output properties of interest. Further, this work demonstrates the use of Gaussian process machine learning models to significantly decrease the computational cost of the aforementioned robust uncertainty quantification.

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References

  1. McDowell DL, Backman D (2011) Simulation-assisted design and accelerated insertion of materials. Comput Methods Microstruct Prop Relationsh. https://doi.org/10.1007/978-1-4419-0643-4_17

    Article  Google Scholar 

  2. White A (2012) The materials genome initiative: one year on. MRS Bull 37:715–716. https://doi.org/10.1557/mrs.2012.194

    Article  Google Scholar 

  3. McDowell DL et al (2009) Integrated design of multiscale, multifunctional materials and products. Butterworth-Heinemann, Oxford

    Google Scholar 

  4. Goulding AN, Leung JF, Neu RW (2018) Communicating materials systems knowledge through processing-structure-properties-performance (PSPP) maps. Smartech

  5. Ghanem R, Higdon D, Owhadi H (2017) Handbook of uncertainty quantification. Springer, New York

    Book  Google Scholar 

  6. Bostanabad R et al (2018) Uncertainty quantification in multiscale simulation of woven fiber composites. Comput Methods Appl Mech Eng 338:506–532. https://doi.org/10.1016/j.cma.2018.04.024

    Article  Google Scholar 

  7. Patrone P, Kearsley A, Dienstfrey A (2018) In: 2018 AIAA non-deterministic approaches conference

  8. Yeratapally SR et al (2017) Bayesian uncertainty quantification and propagation for validation of a microstructure sensitive model for prediction of fatigue crack initiation. Reliab Eng Syst Saf 164:110–123

    Article  Google Scholar 

  9. Bandyopadhyay R, Prithivirajan V, Sangid MD (2019) Uncertainty quantification in the mechanical response of crystal plasticity simulations. JOM 71:2612–2624

    Article  Google Scholar 

  10. Bandyopadhyay R et al (2020) Microstructure-sensitive critical plastic strain energy density criterion for fatigue life prediction across various loading regimes. Proc R Soc A. 476:20190766

    Article  Google Scholar 

  11. Kotha S, Ozturk D, Ghosh S (2020) Uncertainty-quantified parametrically homogenized constitutive models (UQ-PHCMs) for dual-phase α/β titanium alloys. NPJ Comput Mater 6:1–20

    Article  Google Scholar 

  12. Du X, Chen W (2002) Efficient uncertainty analysis methods for multidisciplinary robust design. AIAA J 40:545–552. https://doi.org/10.2514/2.1681

    Article  Google Scholar 

  13. McDonald M, Mahadevan S (2008) Uncertainty quantification and propagation in multidisciplinary analysis and optimization. In: 12th AIAA/ISSMO multidisciplinary analysis and optimization conference, American Institute of Aeronautics and Astronautics, p 6038

  14. Choi HJ, et al (2005) An inductive design exploration method for the integrated design of multi-scale materials and products. In: Proceedings of the ASME international design engineering technical conferences and computers and information in engineering conference, Pts A and B, vol 2, pp 859–870

  15. Hu Z, Mahadevan S (2017) Uncertainty quantification in prediction of material properties during additive manufacturing. Scripta Mater 135:135–140

    Article  CAS  Google Scholar 

  16. Cai G, Mahadevan S (2016) Uncertainty quantification of manufacturing process effects on macroscale material properties. Int J Multiscale Comput Eng 14:191

    Article  Google Scholar 

  17. Stopka KS, Whelan G, McDowell DL (2019) Microstructure-sensitive ICME workflows for fatigue critical applications

  18. Whelan G, McDowell DL (2019) Uncertainty quantification in ICME workflows for fatigue critical computational modeling. Eng Fract Mech 220:106673

    Article  Google Scholar 

  19. Swiler LP, Eldred MS, Adams BM (2017) Dakota: bridging advanced scalable uncertainty quantification algorithms with production deployment. Handbook of Uncertainty Quantification. Springer, Berlin, pp 1651–1693

    Chapter  Google Scholar 

  20. Bessa MA et al (2017) A framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionality. Comput Methods Appl Mech Eng 320:633–667. https://doi.org/10.1016/j.cma.2017.03.037

    Article  Google Scholar 

  21. Martin JD, Simpson TW (2005) Use of Kriging models to approximate deterministic computer models. AIAA J 43:853–863. https://doi.org/10.2514/1.8650

    Article  Google Scholar 

  22. Hombal V, Mahadevan S (2011) Bias minimization in gaussian process surrogate modeling for uncertainty quantification. Int J Uncertain Quantif 1:321–349. https://doi.org/10.1615/Int.J.UncertaintyQuantification.2011003343

    Article  Google Scholar 

  23. Bilionis I, Zabaras N (2016) Bayesian uncertainty propagation using Gaussian processes. Handbook of uncertainty quantification. Springer, Cham, pp 1–45

    Google Scholar 

  24. Le Maı̂tre OP et al (2004) Uncertainty propagation using Wiener-Haar expansions. J Comput Phys 197:28–57. https://doi.org/10.1016/j.jcp.2003.11.033

    Article  Google Scholar 

  25. Karniadakis GE (2011) Uncertainty quantification (UQ)

  26. Venturi D, Cho H, Karniadakis GE (2016) Mori-Zwanzig approach to uncertainty quantification. Handbook of uncertainty quantification. Springer, Cham, pp 1–36

    Google Scholar 

  27. Owen N et al (2017) Comparison of surrogate-based uncertainty quantification methods for computationally expensive simulators. SIAM/ASA J Uncertain Quantif 5:403–435

    Article  Google Scholar 

  28. Pedregosa F et al (2011) Scikit-learn: machine learning in Python. J Mach Learn Res 12:2825–2830

    Google Scholar 

  29. Smith M (2009) Simulia: Providence

  30. Groeber MA, Jackson MA (2014) DREAM.3D: a digital representation environment for the analysis of microstructure in 3D. Integr Mater Manuf Innov 3:5. https://doi.org/10.1186/2193-9772-3-5

    Article  Google Scholar 

  31. Kern PC (2016) Georgia Institute of Technology

  32. Smith B, Shih D, McDowell D (2018) Cyclic plasticity experiments and polycrystal plasticity modeling of three distinct Ti alloy microstructures. Int J Plast 101:1–23

    Article  CAS  Google Scholar 

  33. Kanit T et al (2003) Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int J Solids Struct 40:3647–3679. https://doi.org/10.1016/S0020-7683(03)00143-4

    Article  Google Scholar 

  34. McDowell DL (1999) Damage mechanics and metal fatigue: a discriminating perspective. Int J Damage Mech 8:376–403. https://doi.org/10.1177/105678959900800406

    Article  Google Scholar 

  35. McDowell D, Dunne F (2010) Microstructure-sensitive computational modeling of fatigue crack formation. Int J Fatigue 32:1521–1542

    Article  CAS  Google Scholar 

  36. Mayeur J, McDowell D (2007) A three-dimensional crystal plasticity model for duplex Ti–6Al–4V. Int J Plast 23:1457–1485

    Article  CAS  Google Scholar 

  37. Zhang M, Zhang J, McDowell DL (2007) Microstructure-based crystal plasticity modeling of cyclic deformation of Ti–6Al–4V. Int J Plast 23:1328–1348. https://doi.org/10.1016/j.ijplas.2006.11.009

    Article  CAS  Google Scholar 

  38. Przybyla CP et al (2013) Microstructure-sensitive HCF and VHCF simulations. Int J Fatigue 57:9–27. https://doi.org/10.1016/j.ijfatigue.2012.09.014

    Article  CAS  Google Scholar 

  39. McDowell DL (2007) Simulation-based strategies for microstructure-sensitive fatigue modeling. Mater Sci Eng, A 468:4–14

    Article  Google Scholar 

  40. Castelluccio GM, McDowell DL (2012) Assessment of small fatigue crack growth driving forces in single crystals with and without slip bands. Int J Fract 176:49–64

    Article  CAS  Google Scholar 

  41. Fatemi A, Socie DF (1988) A critical plane approach to multiaxial fatigue damage including out-of-phase loading. Fatigue Fract Eng Mater Struct 11:149–165

    Article  Google Scholar 

  42. McDowell DL, Berard J-Y (1992) A δJ-based approach to biaxial fatigue. Fatigue Fract Eng Mater Struct 15:719–741. https://doi.org/10.1111/j.1460-2695.1992.tb00053.x

    Article  CAS  Google Scholar 

  43. Pineau A et al (2016) Failure of metals II: fatigue. Acta Mater 107:484–507. https://doi.org/10.1016/j.actamat.2015.05.050

    Article  CAS  Google Scholar 

  44. Rovinelli A et al (2017) Assessing reliability of fatigue indicator parameters for small crack growth via a probabilistic framework. Modell Simul Mater Sci Eng 25:045010

    Article  Google Scholar 

  45. Rovinelli A et al (2018) Predicting the 3D fatigue crack growth rate of small cracks using multimodal data via Bayesian networks: in-situ experiments and crystal plasticity simulations. J Mech Phys Solids 115:208–229

    Article  CAS  Google Scholar 

  46. Nicolas A et al (2019) Predicting fatigue crack initiation from coupled microstructure and corrosion morphology effects. Eng Fract Mech 220:106661

    Article  Google Scholar 

  47. Przybyla CP, McDowell DL (2011) Simulated microstructure-sensitive extreme value probabilities for high cycle fatigue of duplex Ti–6Al–4V. Int J Plast 27:1871–1895

    Article  CAS  Google Scholar 

  48. Castelluccio GM, McDowell DL (2014) Mesoscale modeling of microstructurally small fatigue cracks in metallic polycrystals. Mater Sci Eng, A 598:34–55

    Article  CAS  Google Scholar 

  49. Castelluccio GM, McDowell DL (2015) Microstructure and mesh sensitivities of mesoscale surrogate driving force measures for transgranular fatigue cracks in polycrystals. Mater Sci Eng, A 639:626–639

    Article  CAS  Google Scholar 

  50. Stopka KS, McDowell DL (2020) Microstructure-sensitive computational estimates of driving forces for surface versus subsurface fatigue crack formation in Duplex Ti–6Al–4V and Al 7075-T6. JOM 72:28–38

    Article  CAS  Google Scholar 

  51. Möller B, Beer M (2008) Engineering computation under uncertainty–capabilities of non-traditional models. Comput Struct 86:1024–1041

    Article  Google Scholar 

  52. Rasmussen CE (2004) Gaussian processes in machine learning. Advanced lectures on machine learning. Springer, Berlin, pp 63–71

    Chapter  Google Scholar 

  53. Sen I et al (2007) Microstructural effects on the mechanical behavior of B-modified Ti–6Al–4V alloys. Acta Mater 55:4983–4993

    Article  CAS  Google Scholar 

  54. Roy S et al (2011) Development of solidification microstructure in boron-modified alloy Ti–6Al–4V–0.1B. Acta Mater 59:5494–5510

    Article  CAS  Google Scholar 

  55. Attallah M et al (2009) Comparative determination of the α/β phase fraction in α + β-titanium alloys using X-ray diffraction and electron microscopy. Mater Charact 60:1248–1256

    Article  CAS  Google Scholar 

  56. Collins PC et al (2009) Development of methods for the quantification of microstructural features in α + β-processed α/β titanium alloys. Mater Sci Eng, A 508:174–182

    Article  Google Scholar 

  57. Lütjering G (1998) Influence of processing on microstructure and mechanical properties of (α + β) titanium alloys. Mater Sci Eng, A 243:32–45

    Article  Google Scholar 

  58. Wang YC, Langdon TG (2013) Influence of phase volume fractions on the processing of a Ti–6Al–4V alloy by high-pressure torsion. Mater Sci Eng, A 559:861–867

    Article  CAS  Google Scholar 

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Acknowledgements

This work was sponsored in part by the Office of Naval Research (ONR), under Grant Number N00014-17-1-2036. The views and conclusions contained herein are those of the authors only and should not be interpreted as representing those of ONR, the U.S. Navy or the U.S. Government. In addition, the authors are grateful for the support of the Carter N. Paden, Jr. Distinguished Chair in Metals Processing.

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Correspondence to Gary Whelan.

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Whelan, G., McDowell, D.L. Machine Learning-Enabled Uncertainty Quantification for Modeling Structure–Property Linkages for Fatigue Critical Engineering Alloys Using an ICME Workflow. Integr Mater Manuf Innov 9, 376–393 (2020). https://doi.org/10.1007/s40192-020-00192-2

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