화학공학소재연구정보센터
홈 로그인 로그아웃 연락처 사이트맵
Korean Journal of Materials Research, Vol.25, No.2, 81-89, February, 2015
DOI10.3740/MRSK.2015.25.2.81  Export Citation
변형구배 결정소성 유한요소해석법을 이용한 니켈기 다결정 합금의 Hall-Petch 관계 모델링
Modeling the Hall-Petch Relation of Ni-Base Polycrystalline Superalloys Using Strain-Gradient Crystal Plasticity Finite Element Method
최윤석†, 조경목, 남대근1, 최일동2
  • 부산대학교 공과대학 재료공학부
  • 1한국생산기술연구원 동남권 지역본부
  • 2한국해양대학교 공과대학 조선기자재공학부
Yoon Suk Choi†, Kyung-Mox Cho, Dae-Geun Nam1, and Il-Dong Choi2
  • School of Materials Science and Engineering, Pusan National University, Busan 609-735, Korea
  • 1Korea Institute of Industrial Technology, Busan 618-230, Korea
  • 2Division of Marine Equipment Engineering, Korea Maritime and Ocean University, Busan 606-791, Korea
E-mail:
A strain-gradient crystal plasticity constitutive model was developed in order to predict the Hall-Petch behavior of a Ni-base polycrystalline superalloy. The constitutive model involves statistically stored dislocation and geometrically necessary dislocation densities, which were incorporated into the Bailey-Hirsch type flow stress equation with six strength interaction coefficients. A strain-gradient term (called slip-system lattice incompatibility) developed by Acharya was used to calculate the geometrically necessary dislocation density. The description of Kocks-Argon-Ashby type thermally activated strain rate was also used to represent the shear rate of an individual slip system. The constitutive model was implemented in a user material subroutine for crystal plasticity finite element method simulations. The grain size dependence of the flow stress (viz., the Hall-Petch behavior) was predicted for a Ni-base polycrystalline superalloy NIMONIC PE16. Simulation results showed that the present constitutive model fairly reasonably predicts 0.2%-offset yield stresses in a limited range of the grain size.
Keywords:crystal plasticity;strain gradient plasticity;finite element method;hall-petch relation;polycrystal
  1. Zhao Z, Ramesh M, Raabe D, Cuitino AM, Radovitzky R, Int. J. Plasticity, 24, 2278 (2008)
  2. Heripre E, Dexet M, Crepin J, Gelebart L, Roos A, Bornert M, Caldemaison D, Int. J. Plasticity, 23, 1512 (2007)
  3. Musienko A, Tatschl A, Schmidegg K, Kolednik O, Pippan R, Cailetaud G, Acta Mater., 55, 4121 (2007)
  4. Kalidindi SR, Bhattacharyya A, Doherty RD, Proc. R. Soc. Lond. A, 460, 1935 (2004)
  5. Rehrl C, Volker B, Kleber S, Antretter T, Pippan R, Acta Mater., 60, 2379 (2012)
  6. Yang Y, Wang L, Bieler TR, Eisenlohr P, Crimp MA, Metall. Mater. Trans. A-Phys. Metall. Mater. Sci., 42, 636 (2011)
  7. Raabe D, Sachtleber M, Zhao Z, Roters F, Zaefferer S, Acta Mater., 49, 3433 (2001)
  8. Pyle D, Lu J, Littlewood D, Maniatty A, Comp. Mechanics, 52, 135 (2012)
  9. Lim H, Lee MG, Kim JK, Adams BL, Wagoner RH, Int. J. Plasticity, 27, 1328 (2011)
  10. Roters F, Eisenlohr P, Hantcherli L, Tjahjanto DD, Bieler TR, Raabe D, Acta Mater., 58, 1152 (2011)
  11. Lewis AC, Siddiq Qidwai MA, Geltmacher AB, Metall. Mater. Trans. A-Phys. Metall. Mater. Sci., 41, 2522 (2010)
  12. Siddiq Qidwai MA, Lewis AC, Geltmacher AB, Acta Mater., 57, 4233 (2009)
  13. Bieler TR, Eisenlohr P, Roters F, Kumar D, Mason DE, Crimp MA, Raabe D, Int. J. Plasticity, 25, 1655 (2009)
  14. Ludwig W, King A, Reischig P, Herbiga M, Lauridsend EM, Schmidt S, Proudhon H, Forest S, Cloetens P, Rolland du Roscoat S, Buffiere JY, Marrow TJ, Poulsen HF, Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process., 524, 69 (2009)
  15. Zeghadi A, Forest S, Gourgues AF, Bouaziz O, Phil. Mag., 87, 1425 (2007)
  16. Diard O, Leclercq S, Rousselier G, Cailletaud G, Int. J. Plasticity, 21, 691 (2005)
  17. Chandrasekaran D, Nygards M, Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process., 365, 191 (2004)
  18. Diard O, Leclercq S, Rousselier G, Cailletaud G, Comput. Mater. Sci., 25, 73 (2002)
  19. Barbe F, Decker L, Jeulin D, Cailletaud G, Int. J. Plasticity, 17, 513 (2001)
  20. Harder J, Int. J. Plasticity, 15, 605 (1999)
  21. Becker R, Richmond O, Model. Simul. Mater. Sci. Eng., 2, 439 (1994)
  22. Marin E, Dawson PR, Appl. Mech. Eng., 165, 1 (1998)
  23. Acharya A, Bassani JL, J. Mech. Phys. Solids, 48, 1565 (2000)
  24. Acharya A, Beaudoin AJ, J. Mech. Phys. Solids, 48, 2213 (2000)
  25. Beaudoin AJ, Acharya A, Chen SR, Korzekwa DA, Stout MG, Acta Mater., 48, 3409 (2000)
  26. Beaudoin AJ, Acharya A, Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process., 309-310, 411 (2001)
  27. Ma A, Roters F, Raabe D, Acta Mater., 54, 2169 (2006)
  28. Kuroda M, Tvergaard V, J. Mech. Phys. Solids, 54, 1789 (2006)
  29. Meissonnier FT, Busso EP, O’Dowd NP, Int. J. Plasticity, 17, 601 (2001)
  30. Arsenlis A, Parks DM, Becker R, Bulatov VV, J. Mech. Phys. Solids, 52, 1213 (2004)
  31. Borg U, Eur. J. Mech. A/Sol., 26, 313 (2006)
  32. Bayley CJ, Brekelmans WA, Geers MGD, Phil. Mag., 87, 1361 (2007)
  33. Wang H, Hwang KC, Huang Y, Wu PD, Liu B, Ravichandran G, Han CS, Gao H, Int. J. Plasticity, 23, 1540 (2007)
  34. Evans AG, Hutchinson JW, Acta Mater., 57, 1675 (2007)
  35. Gerken JM, Dawson PR, J. Mech. Phys. Solids, 56, 1651 (2008)
  36. Aoyagi Y, Shizawa K, Int. J. Plasticity, 23, 1022 (2007)
  37. Cheong KS, Busso EP, Arsenlis A, Int. J. Plasticity, 21, 1797 (2005)
  38. Wang Y, Kysar JW, Vukelic S, Yao YL, J. Manuf. Sci. Eng., 131, 041014 (2009)
  39. Nye JF, Acta Metall., 1, 153 (1953)
  40. KOCKS UF, ARGON AS, ASHBY MF, Prog. Mater. Sci., 19, 1 (1975)
  41. Franciosi P, Berveiller M, Zaoui A, Acta Metall., 28, 273 (1980)
  42. Franciosi P, Zaoui A, Acta Metall., 30, 2141 (1982)
  43. Franciosi P, Zaoui A, Acta Metall., 30, 1627 (1982)
  44. Zhou Y, Neale KW, Toth LS, Int. J. Plasticity, 9, 961 (1993)
  45. Peirce D, Asaro RJ, Needleman A, Acta Metall., 31, 1951 (1983)
  46. Peirce D, Shih CF, Needleman A, Compos. Struct., 18, 875 (1984)
  47. Anderson PM, Rice JR, Acta Metall., 33, 409 (1985)
  48. Wigner E, Seitz F, 1933. On the constitution of metallic sodium. Physical Review 43, 804-810.
  49. Harder J, Int. J. Plasticity, 15, 605 (1999)
  50. Arsenlis A, Parks DM, Acta Mater., 47, 1597 (1999)
  51. Hoc T, Rey C, Giorgi ML, J. Phys. IV France, 11, Pr5 (2001)
  52. Tabourot L, Fivel M, Rauch E, Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process., 234-236, 639 (1997)
  53. Tabourot L, Dumoulin S, Balland P, J. Phys. IV France, 11, Pr5 (2001)
  54. Madec R, Devincre B, Kubin L, Hoc T, Rodney D, Science, 301, 1879 (2003)
  55. Fivel M, Tabourot L, Rauch E, Canova G, J. Phys. IV France, 8, Pr8 (1998)
  56. Rao SI, Parthasarathy TA, Dimiduk DM, Hazzledine PM, Phil. Mag., 84, 3195 (2004)
  57. Mangen W, Nembach E, Acta Metall., 37, 1451 (1989)
  58. Hansen N, Acta Metall., 25, 863 (1977)
  59. Hansen N, Ralph B, Acta Metall., 30, 411 (1982)
  60. Jiang Z, Lian J, Baudelet B, Acta Metall. Mater., 43, 3349 (1995)
  61. Feaugas X, Acta Mater., 47, 3617 (1999)