Neural Computing and Applications

, Volume 29, Issue 11, pp 1015–1023 | Cite as

A deep belief network to predict the hot deformation behavior of a Ni-based superalloy

  • Y. C. Lin
  • Jia Li
  • Ming-Song Chen
  • Yan-Xing Liu
  • Ying-Jie Liang
Original Article


The hot deformation behavior of a Ni-based superalloy is studied by hot compressive experiments. The true stress is found to be highly affected by the deformation parameters, including strain rate and deformation temperature. The true stress dramatically decreases with decreasing strain rate or increasing deformation temperature. A deep belief network (DBN) model is developed for predicting true stress of the studied superalloy based on the experimental data. The structure of the developed DBN model is optimized layer by layer. The high accuracy indicates that the developed DBN model is able to effectively characterize the hot deformation behavior of the studied Ni-based superalloy. Moreover, the developed DBN model also has an excellent interpolation ability.


Ni-based superalloy Hot deformation Deep belief network 



This work was supported by the National Natural Science Foundation Council of China (Grant No. 51375502), the National Key Basic Research Program (Grant No. 2013CB035801), the Project of Innovation-driven Plan in Central South University (No. 2016CX008), the Natural Science Foundation for Distinguished Young Scholars of Hunan Province (Grant No. 2016JJ1017), Program of Chang Jiang Scholars of Ministry of Education (No. Q2015140), and the Science and technology leading talent in Hunan Province (Grant No. 2016RS2006), and the Fundamental Research Funds for the Central Universities of Central South University (2016zzts311), China.


  1. 1.
    Lin YC, Chen XM (2011) A critical review of experimental results and constitutive descriptions for metals and alloys in hot working. Mater Des 32:1733–1759CrossRefGoogle Scholar
  2. 2.
    Wen DX, Lin YC, Chen J, Chen XM, Zhang JL, Liang YJ, Li LT (2015) Work-hardening behaviors of typical solution-treated and aged Ni-based superalloys during hot deformation. J Alloys Compd 617:372–379CrossRefGoogle Scholar
  3. 3.
    Ashtiani HRR, Bisadi H, Parsa MH (2013) Influence of thermomechanical parameters on the hot deformation behavior of AA1070. J Eng Mater Technol 136:011004CrossRefGoogle Scholar
  4. 4.
    Nan Y, Ning YQ, Liang HQ, Guo HZ, Yao ZK, Fu MW (2015) Work-hardening effect and strain-rate sensitivity behavior during hot deformation of Ti–5Al–5Mo–5V–1Cr–1Fe alloy. Mater Des 82:84–90CrossRefGoogle Scholar
  5. 5.
    Montheillet F, Piot D, Matougui N, Fares ML (2014) A critical assessment of three usual equations for strain hardening and dynamic recovery. Metall Mater Trans A 45(10):4324–4332CrossRefGoogle Scholar
  6. 6.
    Serajzadeh S, Motlagh SR, Mirbagheri SMH, Akhgar JM (2015) Deformation behavior of AA2017-SiCp in warm and hot deformation regions. Mater Des 67:318–323CrossRefGoogle Scholar
  7. 7.
    Samantaray D, Mandal S, Jayalakshmi M, Athreya CN, Bhaduri AK, Sarma VS (2014) New insights into the relationship between dynamic softening phenomena and efficiency of hot working domains of a nitrogen enhanced 316L(N) stainless steel. Mater Sci Eng, A 598:368–375CrossRefGoogle Scholar
  8. 8.
    Babu KA, Mandal S, Kumar A, Athreya CN, Boer BD, Sarma VS (2016) Characterization of hot deformation behaviour of alloy 617 through kinetic analysis, dynamic material modeling and microstructural studies. Mater Sci Eng A 664:177–187CrossRefGoogle Scholar
  9. 9.
    Chen MS, Lin YC, Ma XS (2012) The kinetics of dynamic recrystallization of 42CrMo Steel. Mater Sci Eng A 556:260–266CrossRefGoogle Scholar
  10. 10.
    Zhu FJ, Wu HY, Lee S, Lin MC, Chen D (2015) Dynamic behavior of a 6069 Al alloy under hot compression. Mater Sci Eng A 640:385–393CrossRefGoogle Scholar
  11. 11.
    Dong YY, Zhang CS, Zhao GQ, Guan YJ, Gao AJ, Sun WC (2016) Constitutive equation and processing maps of an Al–Mg–Si aluminum alloy: determination and application in simulating extrusion process of complex profiles. Mater Des 92:983–997CrossRefGoogle Scholar
  12. 12.
    Trimble D, O’Donnell GE (2015) Constitutive modelling for elevated temperature flow behaviour of AA7075. Mater Des 76:150–168CrossRefGoogle Scholar
  13. 13.
    Liao HC, Wu YN, Zhou KX, Yang J (2015) Hot deformation behavior and processing map of Al-Si-Mg alloys containing different amount of silicon based on Gleebe-3500 hot compression simulation. Mater Des 65:1091–1099CrossRefGoogle Scholar
  14. 14.
    Lin YC, Chen MS, Zhong J (2008) Constitutive modeling for elevated temperature flow behavior of 42CrMo Steel. Comput Mater Sci 42:470–477CrossRefGoogle Scholar
  15. 15.
    Li YY, Zhao SD, Fan SQ, Zhong B (2014) Plastic properties and constitutive equations of 42CrMo steel during warm forming process. Mater Sci Technol 30(6):645–652CrossRefGoogle Scholar
  16. 16.
    Samantaray D, Phaniraj C, Mandal S, Bhaduri AK (2011) Strain dependent rate equation to predict elevated temperature flow behavior of modified 9Cr–1Mo (P91) steel. Mater Sci Eng A 528(3):1071–1077CrossRefGoogle Scholar
  17. 17.
    Yang LC, Pan YT, Chen IG, Lin DY (2015) Constitutive relationship modeling and characterization of flow behavior under hot working for Fe–Cr–Ni–W–Cu–Co super-austenitic stainless steel. Metals 5(3):1717–1731CrossRefGoogle Scholar
  18. 18.
    Li JP, Xia XS (2015) Modeling high temperature deformation behavior of large-scaled Mg–Al–Zn magnesium alloy fabricated by semi-continuous casting. J Mater Eng Perform 24:3539–3548CrossRefGoogle Scholar
  19. 19.
    Zhang C, Zhang LW, Shen WF, Li MF, Gu SD (2015) Characterization of hot deformation behavior of Hastelloy C-276 using constitutive equation and processing map. J Mater Eng Perform 24:149–157CrossRefGoogle Scholar
  20. 20.
    Fan QC, Jiang XQ, Zhou ZH, Ji W, Chao HQ (2015) Constitutive relationship and hot deformation behavior of Armco-type pure iron for a wide range of temperature. Mater Des 65:193–203CrossRefGoogle Scholar
  21. 21.
    Lin YC, Li LT, Jiang YQ (2012) A phenomenological constitutive model for describing thermo-viscoplastic behavior of Al–Zn–Mg–Cu alloy under hot working condition. Exp Mech 52:993–1002CrossRefGoogle Scholar
  22. 22.
    Chen L, Zhao GQ, Yu JQ (2015) Hot deformation behavior and constitutive modeling of homogenized 6026 auminum alloy. Mater Des 75:57–64CrossRefGoogle Scholar
  23. 23.
    He A, Xie GL, Zhang HL, Wang XT (2013) A comparative study on Johnson–Cook, modified Johnson–Cook and Arrhenius-Type constitutive models to predict the high temperature flow stress in 20CrMo alloy steel. Mater Des 52:677–685CrossRefGoogle Scholar
  24. 24.
    Bobbili R, Madhu V, Gogia AK (2016) Tensile behaviour of aluminium 7017 alloy at various temperatures and strain rates. J Mater Res Technol 5(2):190–197CrossRefGoogle Scholar
  25. 25.
    Bobbili R, Madhu V (2016) Constitutive modeling of hot deformation behavior of high-strength armor steel. J Mater Eng Perform 25(5):1829–1838CrossRefGoogle Scholar
  26. 26.
    Sajadifar SV, Yapici GG (2015) High temperature flow response modeling of ultra-fine grained titanium. Metals 5(3):1315–1327CrossRefGoogle Scholar
  27. 27.
    Sajadifar SV, Yapici GG (2014) Elevated temperature mechanical behavior of severely deformed titanium. J Mater Eng Perform 23(5):1834–1844CrossRefGoogle Scholar
  28. 28.
    Lin YC, Wen DX, Chen MS, Chen XM (2016) A novel unified dislocation density-based model for hot deformation behavior of a nickel-based superalloy under dynamic recrystallization conditions. Appl Phys A 112:805CrossRefGoogle Scholar
  29. 29.
    Lin YC, Wen DX, Huang YC, Chen XM, Chen XW (2015) A unified physically-based constitutive model for describing strain hardening effect and dynamic recovery behavior of a Ni-based superalloy. J Mater Res 30:3784–3794CrossRefGoogle Scholar
  30. 30.
    Lin YC, Chen XM, Wen DX, Chen MS (2014) A physically-based constitutive model for a typical nickel-based superalloy. Comput Mater Sci 83:282–289CrossRefGoogle Scholar
  31. 31.
    Dong DQ, Chen F, Cui ZS (2015) A physically-based constitutive model for SA508-III steel: modeling and experimental verification. Mater Sci Eng A 634:103–115CrossRefGoogle Scholar
  32. 32.
    Chen F, Ren FC, Cui ZS, Lai XM (2014) Constitutive modeling for elevated temperature flow behavior of 30Cr2Ni4MoV ultra-super-critical rotor steel. J Iron Steel Res Int 21(5):521–526CrossRefGoogle Scholar
  33. 33.
    Mejía I, Reyes-Calderón F, Cabrera JM (2015) Modeling the hot flow behavior of a Fe–22Mn–0.41C–1.6Al–1.4Si TWIP steel microalloyed with Ti, V and Nb. Mater Sci Eng A 644:374–385CrossRefGoogle Scholar
  34. 34.
    Lin YC, Chen MS, Zhong J (2008) Prediction of 42CrMo steel flow stress at high temperature and strain rate. Mech Res Commun 35:142–150CrossRefGoogle Scholar
  35. 35.
    Zhu RH, Liu Q, Li JF, Xiang S, Chen YL, Zhang XH (2015) Dynamic restoration mechanism and physically based constitutive model of 2050 Al–Li alloy during hot compression. J Alloys Compd 650:75–85CrossRefGoogle Scholar
  36. 36.
    Lin YC, Zhang J, Zhong J (2008) Application of neural networks to predict the elevated temperature flow behavior of a low alloy steel. Comput Mater Sci 43:752–758CrossRefGoogle Scholar
  37. 37.
    Yao GG, Wang B, Yi DQ, Wang B, Ding XF (2014) Artificial neural network modelling to predict hot deformation behaviour of as HIPed FGH4169 superalloy. J Mater Sci Technol 30:1170–1176CrossRefGoogle Scholar
  38. 38.
    Yang XW, Li WY (2015) Flow behavior and processing maps of a low-carbon steel during hot deformation. Metall Mater Trans A46:6052–6064CrossRefGoogle Scholar
  39. 39.
    Quan GZ, Liang JT, Lv WQ, Wu DS, Liu YY, Luo GC, Zhou J (2014) A characterization for the constitutive relationships of 42CrMo high strength steel by artificial neural network and its application in isothermal deformation. Mater Res 17:1102–1114CrossRefGoogle Scholar
  40. 40.
    Zuo Q, Liu F, Wang L, Chen CF, Zhang ZH (2015) Prediction of hot deformation behavior in Ni-based alloy considering the effect of initial microstructure. Prog Nat Sci Mater Int 25(1):66–77CrossRefGoogle Scholar
  41. 41.
    Kuremoto T, Kimura S, Kobayashi K, Obayashi M (2014) Time series forecasting using a deep belief network with restricted Boltzmann machine. Neuro Comput 137:47–56Google Scholar
  42. 42.
    Hinton GE, Osindero S, Teh YW (2006) A fast learning algorithm for deep belief nets. Neural Comput 18:1527–1554MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Chen K, Salman A (2011) Learning speaker-specific characteristics with a deep neural architecture. IEEE Trans Neural Netw Learn 22:1744–1756CrossRefGoogle Scholar
  44. 44.
    Kuremoto T, Kimura S, Kobayashi K, Obayashi M (2014) Time series forecasting using a deep belief network with restricted boltzmann machines. Neurocomputing 137:47–56CrossRefGoogle Scholar
  45. 45.
    Ahmed A, Yu K, Xu W, Gong Y, Xing E (2008) Training hierarchical feed-forward visual recognition models using transfer learning from pseudo-tasks. Comput Vis ECCV 5304:69–82Google Scholar
  46. 46.
    Lin YC, Wu XY, Chen XM, Chen J, Wen DX, Zhang JL, Li LT (2015) EBSD study of a hot deformed nickel-based superalloy. J Alloys Compd 640:101–113CrossRefGoogle Scholar
  47. 47.
    Tehovnik F, Burja J, Podgornik B, Godec M, Vode F (2015) Microstructural evolution of inconel 625 during hot rolling. Mater Technol 49(5):801–806Google Scholar
  48. 48.
    Zhang HB, Zhang KF, Jiang SS, Lu Z (2015) The dynamic recrystallization evolution and kinetics of Ni–18.3Cr–6.4Co–5.9 W–4Mo–2.19Al–1.16Ti superalloy during hot deformation. Int. J Mater Res 30(7):1029–1041CrossRefGoogle Scholar
  49. 49.
    Ning YQ, Xie BC, Li H, Fu MW (2015) Dynamic recrystallization of wrought–solidified–wrought complex structure in Ni-based superalloys. Adv Eng Mater 17(5):648–655CrossRefGoogle Scholar
  50. 50.
    Lin YC, Wu XY, Chen XM, Chen J, Wen DX, Zhang JL, Li LT (2015) EBSD study of a hot deformed nickel-based superalloy. J Alloys Compd 640:101–113CrossRefGoogle Scholar
  51. 51.
    Satheesh Kumar SS, Raghu T, Bhattacharjee PP, Rao GA, Borah U (2016) Strain rate dependent microstructural evolution during hot deformation of a hot isostatically processed nickel base superalloy. J Alloys Compd 681:28–42CrossRefGoogle Scholar
  52. 52.
    Satheesh Kumar SS, Raghu T, Bhattacharjee PP, Rao GA, Borah U (2015) Constitutive modeling for predicting peak stress characteristics during hot deformation of hot isostatically processed nickel-base superalloy. J Mater Sci 50(19):6444–6456CrossRefGoogle Scholar
  53. 53.
    Chen F, Liu J, Ou HG, Lu B, Cui ZS, Long H (2015) Flow characteristics and intrinsic workability of IN718 superalloy. Mater Sci Eng A 642:279–287CrossRefGoogle Scholar
  54. 54.
    Lin YC, Wen DX, Deng J, Liu G, Chen J (2014) Constitutive models for high-temperature flow behaviors of a Ni-based superalloy. Mater Des 59:115–123CrossRefGoogle Scholar
  55. 55.
    Etaati A, Dehghani K, Ebrahimi GR, Wang H (2013) Predicting the flow stress behavior of Ni–42.5Ti–3Cu during hot deformation using constitutive equations. Met Mater Int 19:5–9CrossRefGoogle Scholar
  56. 56.
    Lin YC, Li KK, Li HB, Chen J, Chen XM, Wen DX (2015) New constitutive model for high-temperature deformation behavior of Inconel 718 Superalloy. Mater Des 74:108–118CrossRefGoogle Scholar
  57. 57.
    Chen XM, Lin YC, Chen MS, Li HB, Wen DX, Zhang JL, He M (2015) Microstructural evolution of a nickel-based superalloy during hot deformation. Mater Des 77:41–49CrossRefGoogle Scholar
  58. 58.
    Chen XM, Lin YC, Wen DX, Zhang JL, He M (2014) Dynamic recrystallization behavior of a typical nickel-based superalloy during hot-forming. Mater Des 57:568–577CrossRefGoogle Scholar
  59. 59.
    Shen FR, Chao J, Zhao JX (2015) Forecasting exchange rate using deep belief networks and conjugate gradient method. Neurocomputing 167:243–253CrossRefGoogle Scholar
  60. 60.
    Fischer A, Igel C (2014) Training restricted Boltzmann machines: an introduction. Pattern Recognit 47(1):25–39CrossRefzbMATHGoogle Scholar
  61. 61.
    Roux NL, Bengio Y (2008) Representational power of restricted boltzmann machines and deep belief networks. Neural Comput 20:1631–1649MathSciNetCrossRefzbMATHGoogle Scholar
  62. 62.
    Kuremoto T, Kimura S, Kobayashi K, Obayashi M (2014) Time series forecasting using a deep belief network with restricted boltzmann machine. Neurocomputing 137:47–56CrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2016

Authors and Affiliations

  • Y. C. Lin
    • 1
    • 2
    • 3
  • Jia Li
    • 1
    • 3
  • Ming-Song Chen
    • 1
    • 3
  • Yan-Xing Liu
    • 1
    • 3
  • Ying-Jie Liang
    • 1
    • 3
  1. 1.School of Mechanical and Electrical EngineeringCentral South UniversityChangshaChina
  2. 2.Light Alloy Research InstituteCentral South UniversityChangshaChina
  3. 3.State Key Laboratory of High Performance Complex ManufacturingChangshaChina

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