An overview on constitutive modelling to predict elevated temperature flow behaviour of fast reactor structural materials

Abstract

This overview emphasized the aspects of formulation and application of various constitutive models developed by us in recent past viz. Johnson- Cook (JC), modified Zerilli-Armstrong (MZA), strain compensated Arrhenius type model and artificial neural network (ANN) model to predict elevated temperature flow behaviour of fast reactor structural materials. It has been shown that the JC model is not able to represent the high temperature flow behaviour of both alloy D9 and the modified 9Cr-1Mo as it does not incorporate the coupled effect of strain and temperature, and of strain rate and temperature. The new materials model based on Zerilli-Armstrong (ZA) equation considers the coupled effects of temperature and strain and of strain rate and temperature on the flow stress and hence has the capability to predict flow stress over a wider domain temperature and strain rate in comparison with JC model. The formulation and application of strain compensated Arrhenius type constitutive model to predict high temperature flow behaviour of alloy D9 and modified 9Cr-1Mo has been discussed. Development and application of a generic ANN based constitutive model to predict high temperature deformation behaviour of austenitic stainless steels has been highlighted. Finally, a comparative analysis of the merits and shortcomings of these models has been made.

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

References

  1. 1.

    Bontcheva N and Petzov G, Comput. Mater. Sci., 28 (2003) 563.

    CAS  Article  Google Scholar 

  2. 2.

    Bontcheva N, Petzov G and Parashkevova L, Comput. Mater. Sci., 38 (2006) 83.

    CAS  Article  Google Scholar 

  3. 3.

    Grass H, Krempaszky C and Werner E, Comput. Mater. Sci., 36 (2006) 480.

    CAS  Article  Google Scholar 

  4. 4.

    He Xiaoming, Yu Zhongqi and Lai Xinmin, Comput. Mater. Sci., 44 (2008) 760.

    CAS  Article  Google Scholar 

  5. 5.

    Lin Y C, Chen MS and Jun Zhang, Comput. Mater. Sci., 42 (2008) 470.

    CAS  Article  Google Scholar 

  6. 6.

    Lin Y C, Liu Ge, Comput. Mater. Sci., 48 (2010) 54.

    CAS  Article  Google Scholar 

  7. 7.

    Sung-I1 Kim and Y. Yoo, Mater. Sci. Eng. A. 311 (2001) 108.

  8. 8.

    Mecking H and Kocks U F, Acta. Metall., 29 (1981) 1865.

    CAS  Article  Google Scholar 

  9. 9.

    Estrin Y and Mecking H, Acta. Metall., 32(1) (1984) 57.

    Article  Google Scholar 

  10. 10.

    Bergstrom Y, Mater. Sci. Eng. A, 5 (1969–70) 193.

    Article  Google Scholar 

  11. 11.

    Baragar D L, J. Mech. Working Tech., 14 (1987) 295.

    CAS  Article  Google Scholar 

  12. 12.

    Davenport S B, Silk N J, Sparks C N and Sellars C M, Mater. Sci. Tech., 16 (2000) 539.

    CAS  Google Scholar 

  13. 13.

    Rao K P and Hawbolt E B, Trans. ASME J. Eng. Mater. Tech., 114 (1992) 116.

    CAS  Article  Google Scholar 

  14. 14.

    Rao K P and Prasad Y K D V, J. Mater. Process Tech., 53 (1995) 552.

    Article  Google Scholar 

  15. 15.

    Jonas J, Sellars C M and McG. Tegart W J, Int. Metall. Rev., 14 (1969) 1.

    Google Scholar 

  16. 16.

    Slooff F A, Zhou J, Duszczyk J and Katgerman L, Scripta. Materialia, 57 (2007) 759.

    CAS  Article  Google Scholar 

  17. 17.

    Lin Y C, Chen MS and Jun Zhang, Mater. Sci. Eng. A, 499 (2009) 88.

    Article  Google Scholar 

  18. 18.

    Pu Z J, Wu K H, Shai J and Zou D, Mater. Sci. Eng. A, 192–193 (1995) 780.

    Google Scholar 

  19. 19.

    Johnson G R and Cook W H, In Proc Symp seventh international Symposium on ballistics, The Hague, the Netherlands, (1983), P 541.

  20. 20.

    Johnson G R and Cook W H, Engg. Fract. Mech., 21 (1985) 31.

    Article  Google Scholar 

  21. 21.

    Zerilli F J and Armstrong R W, J. App. Phys., 61 (1987) 1816.

    CAS  Article  Google Scholar 

  22. 22.

    Rohr I, Nahme H, Thoma K and Andreson Jr C E, Int. J. Imp. Engg., 35 (2008) 811.

    Article  Google Scholar 

  23. 23.

    Khan A S, Suh Y S and Kazmi R, Int J Plast 20 (2004) 2233.

  24. 24.

    Nemat-Nasser S and Wei-Guo Guo, Mech. of Mater., 35 (2003) 1023.

    Article  Google Scholar 

  25. 25.

    Wang Y, Zhou Y and Xia Y, Mater. Sci. Eng. A, 372 (2004) 186.

    Article  Google Scholar 

  26. 26.

    Rule W K and Jones S E, Int. J. Imp. Engg., 21 (1998) 609.

    Article  Google Scholar 

  27. 27.

    Vural M, Rittel D and Ravichandran G, Metalll. and Mater. Trans. A, 34 (2003) 2873.

    Article  Google Scholar 

  28. 28.

    Su-Tang Chiou, Wei-Chun Cheng and Woei-Shyan Lee, Mater. Sci. Eng. A, 392 (2005) 156.

    Article  Google Scholar 

  29. 29.

    Woei-Shyan Lee and Chen-Yang Liu, Metalll. and Mater. Trans. A. 36 (2005) 3175.

    Article  Google Scholar 

  30. 30.

    Chen C, Yin H, Humail I S, Wang Y and Qu X, Int. J. Refr. Metals & Hard mater., 25 (2007) 411.

    Article  Google Scholar 

  31. 31.

    Woei-Shyan Lee and Chen-Yang Liu, Mater Sci Eng A 426 (2006) 101.

  32. 32.

    Johnson G R and Holmquist T J, J. App. Phys., 64 (1988) 3901.

    CAS  Article  Google Scholar 

  33. 33.

    Voyiadjis G Z and Abed F H, Mech. of Mater., 37 (2005) 355.

    Article  Google Scholar 

  34. 34.

    Dey S, Bøvik T, Hopperstad O S and Langseth M, Int. J. Imp. Engg., 34 (2007) 464.

    Article  Google Scholar 

  35. 35.

    Lennon A M and Ramesh K T, Int. J. Plast., 20 (2004) 269.

    CAS  Article  Google Scholar 

  36. 36.

    Lin Y C, Zhang J and Zhong J, Comput. Mater. Sci., 43 (2008) 752.

    CAS  Article  Google Scholar 

  37. 37.

    Kalaichelvi V, Sivakumar D, Karthikeyan R and Palanikumar K, Mater. & Dgn., 30 (2009) 1362.

    CAS  Article  Google Scholar 

  38. 38.

    Mandal S, Sivaprasad P V, Venugopal S and Murthy K P N, Appl. Soft. Comput., 9 (2009) 237.

    Article  Google Scholar 

  39. 39.

    Mandal S, Sivaprasad P V and Venugopal S, Trans. ASME J. Engg. Mater. and Tech., 129 (2007) 242.

    CAS  Article  Google Scholar 

  40. 40.

    Mandal S, Sivaprasad P V, Venugopal S and Murthy K P N, Modell and Simul Mater. Sci. Engg., 14 (2006) 1053.

    CAS  Article  Google Scholar 

  41. 41.

    Mandal S, Sivaprasad P V and Dube R K, J. Mater. Sci., 42 (2007) 2724.

    CAS  Article  Google Scholar 

  42. 42.

    Guo Z, Malinov S and Sha W, Comput. Mater. Sci., 32 (2005) 1.

    CAS  Article  Google Scholar 

  43. 43.

    Samantaray D, Mandal S, Borah U, Bhaduri A K and Sivaprasad P V, Materials Mater. Sci. Eng. A, 526 (2009) 1.

    Article  Google Scholar 

  44. 44.

    Samantaray D, Mandal S and Bhaduri A K, Comput. Mater. Sci., 47 (2009) 568.

    CAS  Article  Google Scholar 

  45. 45.

    Zener C, Hollomon H, J. App. Phys., 15 (1944) 22.

    Article  Google Scholar 

  46. 46.

    Sellars C M, McTegart W J, Acta Metall., 14 (1966) 1136.

    CAS  Article  Google Scholar 

  47. 47.

    Mandal S, Rakesh V, Sivaprasad PV, Venugopal S and Kasiviswanathan K V, Mater. Sci. Eng. A, 500 (2009) 114.

    Article  Google Scholar 

  48. 48.

    Samantaray D, Mandal S and Bhaduri A K, Mater. & Dgn., 31 (2010) 981.

    CAS  Article  Google Scholar 

  49. 49.

    McQueen H J and Ryan N D, Mater. Sci. Eng. A, 322 (2002) 43.

    Article  Google Scholar 

  50. 50.

    McQueen H J, Metall. Trans. A, 33 (2002) 345.

    Article  Google Scholar 

  51. 51.

    Haykin S, Neural Networks: A Comprehensive Foundation, Prentice Hall, New Jersey (1999)

    Google Scholar 

  52. 52.

    Kosko B, Neural Networks and fuzzy systems, Prentice Hall, New Jersey, (1992).

    Google Scholar 

  53. 53.

    Sivaprasad P V, Mandal S, Venugopal S, Narayanan C, Shanmugam V and Raj B, Trans. Ind. Inst. Met., 59 (2006) 437.

    Google Scholar 

  54. 54.

    Chuan M S, Biglou J, Lenard J G and Kim J G, J. Mater. Process Tech., 86 (1999) 245.

    Article  Google Scholar 

  55. 55.

    Hornik K, Stinchcombe M and White H, Neur. Net., 2 (1989) 359.

    Article  Google Scholar 

  56. 56.

    Mandal S, Sivaprasad P V, Murthy K P N and Raj B, Metals Mater. and Process, 18 (2006) 159.

    CAS  Google Scholar 

  57. 57.

    Venugopal S, Optimization of workability and control of microstructure in deformation processing of austenitic stainless steels; Development and application of processing maps for stainless steels type AISI 304 and 316L, PhD thesis, University of Madras, Madras, (1993)

    Google Scholar 

  58. 58.

    Sivaprasad P V, Mannan S L, Prasad Y V R K and Chaturvedi R C, Mater. Sci. Tech., 17 (2002) 545.

    Google Scholar 

  59. 59.

    Sivaprasad PV, Hot deformation behaviour of 15Cr-15Ni-2.2 Mo-Timodified stainless steels and 9Cr-1MofFerritic Steels: A study using processing maps and process modelling, PhD thesis, Indian Institute of Technology, Bombay, (1997)

    Google Scholar 

  60. 60.

    Guo Z and Sha W, Comput. Mater. Sci., 29 (2004) 12.

    CAS  Article  Google Scholar 

  61. 61.

    Mandal S, Sivaprasad P V, Venugopal S, Murthy K P N and Raj B, Mater. Sci. Eng. A, 485 (2008) 571.

    Article  Google Scholar 

  62. 62.

    Mandal S, Sivaprasad P V, Barat P and Raj B, Mater. Manuf. Process, 24 (2009) 219.

    CAS  Article  Google Scholar 

  63. 63.

    Dulieu D and Nutting J, ISI Spec. Rep., 86 (1964) 140.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Sumantra Mandal.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Samantaray, D., Mandal, S., Bhaduri, A.K. et al. An overview on constitutive modelling to predict elevated temperature flow behaviour of fast reactor structural materials. Trans Indian Inst Met 63, 823–831 (2010). https://doi.org/10.1007/s12666-010-0126-6

Download citation

Keywords

  • constitutive modelling
  • structural materials
  • johnson-cook, modified zerilli-armstrong
  • strain compensated arrhenius type model
  • artificial neural network