Physics-Informed Network Models: a Data Science Approach to Metal Design

Abstract

Functional graded materials (FGM) allow for reconciliation of conflicting design constraints at different locations in the material. This optimization requires a priori knowledge of how different architectural measures are interdependent and combine to control material performance. In this work, an aluminum FGM was used as a model system to present a new network modeling approach that captures the relationship between design parameters and allows an easy interpretation. The approach, in an un-biased manner, successfully captured the expected relationships and was capable of predicting the hardness as a function of composition.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

References

  1. 1.

    (2011) Materials genome initiative for global competitiveness. Tech. rep. https://www.mgi.gov/about

  2. 2.

    Arnold SM, Holland F, Gabb TP, Nathal M, Wong TT (2013) American institute of aeronautics and astronautics. https://doi.org/10.2514/6.2013-1850

  3. 3.

    Arnold SM, Holland F, Bednarcyk BA (2014) American institute of aeronautics and astronautics. https://doi.org/10.2514/6.2014-0460

  4. 4.

    Miracle D, Majumdar B, Wertz K, Gorsse S (2017) Scr Mater 127(Supplement C):195. https://doi.org/10.1016/j.scriptamat.2016.08.001. http://www.sciencedirect.com/science/article/pii/S1359646216303657

    Article  Google Scholar 

  5. 5.

    Lingerfelt EJ, Belianinov A, Endeve E, Ovchinnikov O, Somnath S, Borreguero JM, Grodowitz N, Park B, Archibald RK, Symons CT, Kalinin SV, Messer OEB, Shankar M, Jesse S (2016) Procedia computer science 80(Supplement C):2276. https://doi.org/10.1016/j.procs.2016.05.410. http://www.sciencedirect.com/science/article/pii/S1877050916308869

  6. 6.

    Kalidindi SR, De Graef M (2015) Materials Data Science: Current Status and Future Outlook. Annu Rev Mater Res 45(1):171–193. https://doi.org/10.1146/annurev-matsci-070214-020844

    Article  Google Scholar 

  7. 7.

    Jacobsen MD, Benedict MD, Foster BJ, Ward CH, Foster BJ, Jacobsen MD, Benedict MD (2015). In: Proceedings of the 3rd world congress on integrated computational materials engineering (ICME 2015). Springer, Cham, pp 285–292. https://doi.org/10.1007/978-3-319-48170-8_34. https://link.springer.com/chapter/10.1007/978-3-319-48170-8_34

  8. 8.

    Jacobsen MD, Fourman JR, Porter KM, Wirrig EA, Benedict MD, Foster BJ, Ward CH, Jacobsen MD, Foster BJ, Fourman JR, Benedict MD, Porter KM, Wirrig EA (2016) Creating an integrated collaborative environment for materials research. Integr Mater Manuf Innov 5(1):12. https://doi.org/10.1186/s40192-016-0055-2. https://link.springer.com/article/10.1186/s40192-016-0055-2

    Article  Google Scholar 

  9. 9.

    Havlin S, Kenett DY, Ben-Jacob E, Bunde A, Cohen R, Hermann H, Kantelhardt JW, Kertész J, Kirkpatrick S, Kurths J, Portugali J, Solomon S (2012) The European Physical Journal Special Topics 214(1):273. https://doi.org/10.1140/epjst/e2012-01695-x. http://link.springer.com/article/10.1140/epjst/e2012-01695-x

    Article  Google Scholar 

  10. 10.

    Nibbe RK, Koyutürk M, Chance MR (2010) PLOs Comput Biol 6(1):e1000639. https://doi.org/10.1371/journal.pcbi.1000639

    Article  Google Scholar 

  11. 11.

    Steinhaeuser K, Chawla NV, Ganguly AR (2011) Statistical Analysis and Data Mining 4(5):497. https://doi.org/10.1002/sam.10100. http://onlinelibrary.wiley.com/doi/10.1002/sam.10100/abstract

  12. 12.

    Bhadeshia HKDH (1999) ISIJ Int 39(10):966. https://doi.org/10.2355/isijinternational.39.966

  13. 13.

    Bhadeshia HKDH (2009) Neural Networks and Information in Materials Science. Statistical Analy Data Mining 1(5):296–305. https://doi.org/10.1002/sam.10018. http://onlinelibrary.wiley.com/doi/10.1002/sam.10018/abstract

    Article  Google Scholar 

  14. 14.

    Sha W, Edwards KL (2007) Mater Des 28(6):1747. https://doi.org/10.1016/j.matdes.2007.02.009. http://www.sciencedirect.com/science/article/pii/S0261306907000520

    Article  Google Scholar 

  15. 15.

    Hoyle RH (2012) Handbook of structural equation modeling, 1st edn. The Guilford Press, New York

    Google Scholar 

  16. 16.

    French RH, Podgornik R, Peshek TJ, Bruckman LS, Xu Y, Wheeler NR, Gok A, Hu Y, Hossain MA, Gordon DA, Zhao P, Sun J, Zhang G-Q (2015) Curr Opinion Solid State Mater Sci 19(4):212. https://doi.org/10.1016/j.cossms.2014.12.008. http://www.sciencedirect.com/science/article/pii/S1359028614000989

    Article  Google Scholar 

  17. 17.

    Faraway JJ (2004) Linear models with R, 1st edn. Chapman and Hall/CRC, Boca Raton

    Google Scholar 

  18. 18.

    Wheeler N, Xu Y, Du W, Gok A, Ma J, Bruckman L, Elsaeiti M, Sun J, French R (2013) Semi-supervised generalized structural equation modeling. https://github.com/vuvlab/sgsem

  19. 19.

    Mitchell TM (1997) Machine learning, 1st edn. McGraw-Hill Education, New York

    Google Scholar 

  20. 20.

    White H, Gallant AR, Hornik K, Stinchcombe M, Wooldridge J (1992) Artificial neural networks: approximation and learning theory, illustrated edition edition edn. Blackwell Pub, Oxford

    Google Scholar 

  21. 21.

    Skinner AJ, Broughton JQ (1995) Model Simul Mater Sci Eng 3(3):371. https://doi.org/10.1088/0965-0393/3/3/006. http://stacks.iop.org/0965-0393/3/i=3/a=006

    Article  Google Scholar 

  22. 22.

    Rioja RJ, Sawtell RR, Chu MG, Karabin M, Cassada WA, Karabin M (2012) Functional Gradient Products Enabled by Planar Solidification Technologies. Springer, Pittsburgh, pp 1383–1388. https://link.springer.com/chapter/10.1007/978-3-319-48761-8_211. https://doi.org/10.1007/978-3-319-48761-8_211

    Google Scholar 

  23. 23.

    Chu M, Giron A, Cassada W (2012) The Minerals, Metals and Materials Society, Pittsburgh, pp 1367–1375

  24. 24.

    Chu MG, Yu H, Giron A, Kallaher K (2007) Method of unidirectional solidification of castings and associated apparatus. http://www.google.com/patents/US7264038. U.S. Classification 164/122.1, 164/133, 164/337; International Classification B22D35/04, B22D27/04, B22D37/00, B22D35/00; Cooperative Classification B22D27/045, B22D7/00; European Classification B22D27/04A

  25. 25.

    (2015) International alloy designations and chemical composition limits for wrought aluminum and wrought aluminum alloys. The Alumninum Association, Arlington, pp 38. http://www.aluminum.org/sites/default/files/TEAL_1_OL_2015.pdf

  26. 26.

    Deshpande NU, Ray KK, Mallik AK (1986) 2:108. http://mio.asminternational.org/apd/viewPicture.aspx?dbKey=grantami_apd&id=10757508&revision=421381

  27. 27.

    Balderach DC, Hamilton JA, Leung E, Cristina Tejeda M, Qiao J, Taleff EM (2003) Mater Sci Eng A 339(1–2):194. https://doi.org/10.1016/S0921-5093(02)00158-2. http://www.sciencedirect.com/science/article/pii/S0921509302001582

    Article  Google Scholar 

  28. 28.

    Fleischer RL (1963) Acta Metallurgica 11(3):203. https://doi.org/10.1016/0001-6160(63)90213-X. http://www.sciencedirect.com/science/article/pii/000161606390213X

    Article  Google Scholar 

  29. 29.

    Labusch R (1970) Phys Stat Sol (b) 41(2):659. https://doi.org/10.1002/pssb.19700410221. http://onlinelibrary.wiley.com/doi/10.1002/pssb.19700410221/abstract

    Article  Google Scholar 

  30. 30.

    Orowan E (1948) Institute of metals, London, pp 451–453

  31. 31.

    Guo Z, Sha W (2002) Mater Trans 43(No. 6):1273

    Article  Google Scholar 

  32. 32.

    Hall EO (1951) Proc Phys Soc B 64(9):747. https://doi.org/10.1088/0370-1301/64/9/303. http://stacks.iop.org/0370-1301/64/i=9/a=303

    Article  Google Scholar 

  33. 33.

    Petch NJ (1953) J Iron Steel Inst Jpn 174:25

    Google Scholar 

  34. 34.

    Tiryakioğlu M (2015) Materials science and engineering: A 633:17. https://doi.org/10.1016/j.msea.2015.02.073. http://www.sciencedirect.com/science/article/pii/S0921509315002014

    Article  Google Scholar 

  35. 35.

    R Core Team (2015) R: a language and environment for statistical computing, R Foundation for Statistical Computin, Vienna. https://www.R-project.org/

  36. 36.

    RPubs - Predictive R-squared according to Tom Hopper. https://rpubs.com/RatherBit/102428

  37. 37.

    Bunge H (1970) Krist Techn 5:145. https://doi.org/10.1002/crat.19700050112

    Article  Google Scholar 

  38. 38.

    Schmid E, Boas W (1968) Plasticity of crystals with special reference to metals. Chapman & Hall, London

    Google Scholar 

  39. 39.

    Bruckman LS, Wheeler NR, Ma J, Wang E, Wang CK, Chou I, Sun J, French RH (2013) IEEE Access 1:384. https://doi.org/10.1109/ACCESS.2013.2267611. http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6527980

    Article  Google Scholar 

Download references

Acknowledgments

The material for this study was provided by the Alcoa/Arconic Alloy Technology Division. This work was funded by the Army Research Office Short Term Innovative Research program: W911NF-14-0549. The data and R-analytics code utilized for the paper can be found at https://cwru-msl.github.io/MRL17/.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jennifer L. W. Carter.

Rights and permissions

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Verma, A.K., French, R.H. & Carter, J.L.W. Physics-Informed Network Models: a Data Science Approach to Metal Design. Integr Mater Manuf Innov 6, 279–287 (2017). https://doi.org/10.1007/s40192-017-0104-5

Download citation

Keywords

  • Metal design
  • Network models
  • Optimization
  • Functional gradient materials