Browse > Article
http://dx.doi.org/10.3740/MRSK.2015.25.2.81

Modeling the Hall-Petch Relation of Ni-Base Polycrystalline Superalloys Using Strain-Gradient Crystal Plasticity Finite Element Method  

Choi, Yoon Suk (School of Materials Science and Engineering, Pusan National University)
Cho, Kyung-Mox (School of Materials Science and Engineering, Pusan National University)
Nam, Dae-Geun (Korea Institute of Industrial Technology)
Choi, Il-Dong (Division of Marine Equipment Engineering, Korea Maritime and Ocean University)
Publication Information
Korean Journal of Materials Research / v.25, no.2, 2015 , pp. 81-89 More about this Journal
Abstract
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;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Z. Zhao, M. Ramesh, D. Raabe, A. M. Cuitino and R. Radovitzky, Int. J. Plasticity, 24, 2278 (2008).   DOI   ScienceOn
2 E. Heripre, M. Dexet, J. Crepin, L. Gelebart, A. Roos, M. Bornert and D. Caldemaison, Int. J. Plasticity, 23, 1512 (2007).   DOI   ScienceOn
3 A. Musienko, A. Tatschl, K. Schmidegg, O. Kolednik, R. Pippan and G. Cailetaud, Acta Mater., 55, 4121 (2007).   DOI   ScienceOn
4 S. R. Kalidindi, A. Bhattacharyya and R. D. Doherty, Proc. R. Soc. Lond. A, 460, 1935 (2004).
5 C. Rehrl, B. Volker, S. Kleber, T. Antretter and R. Pippan, Acta Mater., 60, 2379 (2012).   DOI   ScienceOn
6 Y. Yang, L. Wang, T. R. Bieler, P. Eisenlohr and M. A. Crimp, Metall. Mater. Trans. A, 42, 636 (2011).   DOI   ScienceOn
7 D. Raabe, M. Sachtleber, Z. Zhao, F. Roters and S. Zaefferer, Acta Mater., 49, 3433 (2001)1.   DOI   ScienceOn
8 D. Pyle, J. Lu, D. Littlewood and A. Maniatty, Comp. Mechanics, 52, 135 (2012).
9 H. Lim, M. G. Lee, J. K. Kim, B. L. Adams and R. H. Wagoner, Int. J. Plasticity, 27, 1328 (2011).   DOI   ScienceOn
10 F. Roters, P. Eisenlohr, L. Hantcherli, D. D. Tjahjanto, T. R. Bieler and D. Raabe, Acta Mater., 58, 1152 (2011).
11 A. C. Lewis, M. A. Siddiq Qidwai and A. B. Geltmacher, Metall. Mater. Trans. A, 41, 2522 (2010).   DOI
12 M. A. Siddiq Qidwai, A. C. Lewis and A. B. Geltmacher, Acta Mater., 57, 4233 (2009).   DOI   ScienceOn
13 T. R. Bieler, P. Eisenlohr, F. Roters, D. Kumar, D. E. Mason, M. A. Crimp and D. Raabe, Int. J. Plasticity, 25, 1655 (2009).   DOI   ScienceOn
14 W. Ludwig, A. King, P. Reischig, M. Herbiga, E. M. Lauridsend, S. Schmidt, H. Proudhon, S. Forest, P. Cloetens, S. Rolland du Roscoat, J. Y. Buffière, T. J. Marrow and H. F. Poulsen, Mat. Sci. Eng. A, 524, 69 (2009).   DOI   ScienceOn
15 O. Diard, S. Leclercq, G. Rousselier and G. Cailletaud, Comp. Mat. Sci., 25, 73 (2002).   DOI   ScienceOn
16 A. Zeghadi, S. Forest, A. -F. Gourgues and O. Bouaziz, Phil. Mag., 87, 1425 (2007).   DOI   ScienceOn
17 O. Diard, S. Leclercq, G. Rousselier and G. Cailletaud, Int. J. Plasticity, 21, 691 (2005).   DOI   ScienceOn
18 D. Chandrasekaran and M. Nygards, Mat. Sci. Eng. A, 365, 191 (2004).   DOI   ScienceOn
19 F. Barbe, L. Decker, D. Jeulin and G. Cailletaud, Int. J. Plasticity, 17, 513 (2001).   DOI   ScienceOn
20 J. Harder: Int. J. Plasticity, 15, 605 (1999).   DOI   ScienceOn
21 R. Becker and O. Richmond, Modelling Simul. Mat. Sci. Eng., 2, 439 (1994).   DOI   ScienceOn
22 E. Marin and P. R. Dawson, Appl. Mech. Eng., 165, 1 (1998).   DOI   ScienceOn
23 A. Acharya and J. L. Bassani, J. Mech. Phys. Solids, 48, 1565 (2000).   DOI   ScienceOn
24 A. Acharya and A. J. Beaudoin, J. Mech. Phys. Solids, 48, 2213 (2000).   DOI   ScienceOn
25 A. J. Beaudoin, A. Acharya, S. R. Chen, D. A. Korzekwa and M. G. Stout, Acta Mater., 48, 3409 (2000).   DOI   ScienceOn
26 A. J. Beaudoin and A. Acharya, Mat. Sci. Eng. A, 309- 310, 411 (2001).   DOI   ScienceOn
27 A. Ma, F. Roters and D. Raabe, Acta Mater., 54, 2169 (2006).   DOI   ScienceOn
28 M. Kuroda and V. Tvergaard, J. Mech. Phys. Solids, 54, 1789 (2006).   DOI   ScienceOn
29 F. T. Meissonnier, E. P. Busso and N. P. O'Dowd, Int. J. Plasticity, 17, 601 (2001).   DOI   ScienceOn
30 U. Borg, Euro. J. Mech. A/Sol., 26, 313 (2006).
31 C. J. Bayley, W. A. Brekelmans and M. G. D. Geers, Phil. Mag., 87, 1361 (2007).   DOI   ScienceOn
32 H. Wang, K. C. Hwang, Y. Huang, P. D. Wu, B. Liu, G. Ravichandran, C. -S. Han, H. Gao, Int. J. Plasticity, 23, 1540 (2007).   DOI   ScienceOn
33 A. G. Evans and J. W. Hutchinson, Acta Mater., 57, 1675 (2007).
34 J. M. Gerken and P. R. Dawson, J. Mech. Phys. Solids, 56, 1651 (2008).   DOI   ScienceOn
35 Y. Aoyagi and K. Shizawa, Int. J. Plasticity, 23, 1022 (2007).   DOI   ScienceOn
36 K. S. Cheong, E. P. Busso and A. Arsenlis, Int. J. Plasticity, 21, 1797 (2005).   DOI   ScienceOn
37 Y. Wang, J. W. Kysar, S. Vukelic and Y. L. Yao, J. Manuf. Sci. Eng., 131, 041014-1 (2009).   DOI   ScienceOn
38 U. F. Kocks, A. S. Argon and M. F. Ashby, Prog. Mater. Sci., 19, 1 (1975).   DOI   ScienceOn
39 P. Franciosi, M. Berveiller and A. Zaoui, Acta Metall., 28, 273 (1980).   DOI   ScienceOn
40 P. Franciosi and A. Zaoui, Acta Metall., 30, 2141 (1982).   DOI   ScienceOn
41 P. Franciosi and A. Zaoui, Acta Metall., 30, 1627 (1982).   DOI   ScienceOn
42 Y. Zhou, K. W. Neale and L. S. Toth, Int. J. Plasticity, 9, 961 (1993).   DOI   ScienceOn
43 D. Peirce, R. J. Asaro and A. Needleman, Acta Metall., 31, 1951 (1983).   DOI   ScienceOn
44 D. Peirce, C. F. Shih and A. Needleman, Computers Structures, 18, 875 (1984).   DOI   ScienceOn
45 A. Arsenlis and D. M. Parks, Acta Mater., 47, 1597 (1999).   DOI   ScienceOn
46 P. M. Anderson and J. R. Rice, Acta Metall., 33, 409 (1985).   DOI   ScienceOn
47 Wigner, E., Seitz, F., 1933. On the constitution of metallic sodium. Physical Review 43, 804-810.   DOI
48 J. Harder, Int. J. Plasticity, 15, 605 (1999).   DOI   ScienceOn
49 T. Hoc, C. Rey and M. L. Giorgi, J. Phys. IV France, 11, Pr5-243 (2001).
50 L. Tabourot, M. Fivel and E. Rauch, Mater. Sci. Eng. A, 234-236, 639 (1997)   DOI   ScienceOn
51 L. Tabourot, S. Dumoulin and P. Balland, J. Phys. IV France, 11, Pr5-111 (2001).
52 R. Madec, B. Devincre, L. Kubin, T. Hoc and D. Rodney, Science, 301, 1879 (2003).   DOI   ScienceOn
53 M. Fivel, L. Tabourot, E. Rauch and G. Canova, J. Phys. IV France, 8, Pr8-151 (1998).
54 S. I. Rao, T. A. Parthasarathy, D. M. Dimiduk and P. M. Hazzledine, Phil. Mag., 84, 3195 (2004).   DOI   ScienceOn
55 W. Mangen and E. Nembach, Acta Metall., 37, 1451 (1989).   DOI   ScienceOn
56 N. Hansen, Acta Metall., 25, 863 (1977).   DOI   ScienceOn
57 N. Hansen and B. Ralph, Acta Metall., 30, 411 (1982).   DOI   ScienceOn
58 Z. Jiang, J. Lian and B. Baudelet, Acta Metall. Mater., 43, 3349 (1995).   DOI   ScienceOn
59 X. Feaugas, Acta Mater., 47, 3617 (1999).   DOI   ScienceOn
60 A. Arsenlis, D. M. Parks, R. Becker and V. V. Bulatov, J. Mech. Phys. Solids, 52, 1213 (2004).   DOI   ScienceOn
61 J. F. Nye, Acta Metall., 1, 153 (1953).   DOI   ScienceOn