Abstract
This article presents a mechanistic approach for modeling the strain hardening response of polycrystalline Ni-based superalloys such as ME3, RR 1000, Alloy 720 Li, and IN 100. The mechanistic approach considers strain hardening in Ni-based superalloys in two stages: (a) self-hardening of individual {111} slip systems in the low plastic strain regime and (2) latent hardening of multiple {111} slip systems in the high plastic strain regime. Both strain hardening regimes have been modeled on the basis of interactions of superkinks with Kear–Wilsdorf locks and related to pertinent microstructural parameters such as the volume fractions of γ′ precipitates, grain orientation, and dislocation substructure. The mechanistic strain hardening model predicts that the strain hardening exponents in both the low plastic strain (n1) and the high plastic strain (n2) regimes increase with increasing values of the sum of the squares of the volume fractions of the primary and secondary γ′ precipitates, the number of {111} and {010} slip systems activated, and the critical height of the superkinks. A comparison of model predictions against experimental strain hardening exponents indicates good agreement between model predictions and experimental data. Implications of the operative strain hardening mechanisms during low-cycle fatigue and high-cycle fatigue are elucidated.
Similar content being viewed by others
References
R.W. Kozar, A. Suzuki, W.W. Milligan, J.J. Schirra, M.F. Savage, and T.M. Pollock: Metall. Mater. Trans. A, 2009, vol. 40A (7), pp. 1588–03, https://doi.org/10.1007/s11661-009-9858-5.
T.A. Parthasarathy, S.I. Rao, and D.M. Dimiduk: Superalloys 2004, TMS (The Minerals, Metals and Materials Society), Warrendale, PA, 2004, pp. 887–96.
L. Tabourot, M. Fivel, and E. Rauch: Mater. Sci. Eng. A, 1997, vols. 234–236, pp. 639–42.
W.W. Milligan, E.L. Orth, J.J. Schirra, and M.F. Savage: Superalloys 2004, TMS (The Minerals, Metals and Materials Society), Warrendale, PA, 2004, pp. 331–39.
W. Ramberg and W.R. Osgood: Technical Note 503: Determination of Stress–Strain Curves by Three Parameters, National Advisory Committee on Aeronautics (NACA), 1941.
T.P. Gabb, J. Gayda, J. Telesman, and A. Garg: Superalloys 2008, TMS (The Minerals, Metals and Materials Society), Warrendale, PA, 2008, pp. 121–30.
B. A. Lerch and V. Gerold: Acta Metall., 1985, vol. 33, No. 9, pp. 1709–1716.
B. A. Lerch and V. Gerold: Metall. Trans. A, 1987, vol. 18A, pp. 2135–2141.
K. Gopinath, A.K. Gogia, S.V. Kamat, B. Balamuralikrishnan, and U. Ramamurty: Metall. Mater. Trans. A, 2008, vol. 39A (10), pp. 340–50.
K. S. Chan: Metall. Mater. Trans. A, 2018, 49A, p. 5353–5367.
E. Voce: J. Inst. Met., 1948, vol. 74, pp. 537–62.
H. Mecking and Y. Estrin: Microstructure-Related Constitutive Modelling of Plastic Deformation, Eighth International Symposium on Metallurgy and Material Science, Riso, Denmark, 1987.
K.S. Chan: J. Eng. Mater. Perform. https://doi.org/10.1007/s11665-020-04678-0, Published on-line, Feb 2020.
B.H. Kear and H.G.F. Wilsdorf: Trans. Metall. Soc. AIME, 1962, vol. 224, pp. 382–86.
D. Caillard and V. Paidar: Acta Mater., 1996, vol. 44 (7), pp. 2759–71.
D. Caillard: Acta Mater., 1996, vol. 44 (7), pp. 2773–85.
Caillard D (2001) Mater Sci Eng A 319–321:74–83
M. J. Mills, N. Baluc, and H. P. Karnthaler: Mater. Res. Soc. Symp. 1989, vol. 133, pp. 203–208.
M.J. Mills and D.C. Chrzan: Acta Metall. Mater., 1992, vol. 40 (11), pp. 3051–64.
K.J. Hemker, M.J. Mills, and W.D. Nix: J. Mater. Res., 1992, vol. 7 (8), pp. 2059–69.
Sun YQ, Hazzledine PM (1988) Philos Mag A, 58:603–618
Bontemps C, Veyssiere P (1990) Philos Mag Lett 61:259–267
A. Couret, Y. Sun, and P. M. Hazzledine: Mater. Res. Soc. Symp. 1991, vol. 213, pp. 317–322.
Couret A, Sun YQ, Hirsch PB (1993) Philos Mag A 67:29–50
P. B. Hirsch and Y. Q. Sun: Mat. Sci. Eng., 1993, A164, pp. 395–400.
B. Tounsi, P. Beauchamp, Y. Mishima, T. Suzuki, and P. Veyssiere: Mat. Res. Soc. Symp., 1989, vol.133, pp. 731–736.
Y. Q. Sun: Acta Mater., 1997, vol. 45, No. 9, pp. 3527–3532.
S.S. Ezz and P.B. Hirsch: Philos. Mag. A, 1994, vol. 69 (1), pp. 105–27.
E.M. Knoche: Ph.D. Thesis, University of Manchester, School of Materials, UK, 2011.
V. Singh, M. Sundararanman, W. Chen, and R. P. Wahi: Metall. Trans. A, 1991, vol. 22A, pp. 499–506.
S. Birosea: IOP Conf. Series. Mater. Sci. and Eng, 2015, vol. 82, 012033. https://doi.org/10.1088/1757-899x/82/1/012033.
T. P. Gabb, A. Garg, D. L. Ellis, and K. M O’Connor: Detailed Microstructural Characterization of the Disk Alloy ME3, NASA/TM-2004-213066, Glenn Research Center, Cleveland, OH, May 2004.
J.F.W. Bishop and R.A. Hill: Philos. Mag., 1951, vol. 42 (327), pp. 414–27.
Hertzberg RW (1976) Deformation and Fracture Mechanics of Engineering Materials. Wiley, New York
H. Mecking, U. F. Kocks, and C. Hartig: Scripta Mater., 1996, vol. 35, No. 4, pp. 465–471.
E.O. Hall: Proc. Phys. Soc. B, 1951, vol. 64 (9), pp. 742–47.
N.J. Petch: J. Iron Steel Inst., 1953, vol. 174, pp. 25–28.
L.A. Gypen and A. Deruyttere: J. Mater. Sci., 1977, vol. 12,pp. 1028–33.
W. Huther and B. Reppich: Z. Metallkd., 1978, vol. 69, pp. 628–34, 1114
D.M. Collins and H.J. Stone: Int. J. Plast., 2014, vol. 54, pp. 96–112.
Brown LM, Ham RK (1971) In: Kelly A, Nicholson RB (eds) Strengthening Methods in Crystals. Elsevier Publishing Co. Ltd., Essex, pp 9–135
M. H. Yoo: Acta Metall., 1987, vol. 35, No. 7, pp. 1559–1569.
C. L. Fu and M. H. Yoo: Mat. Res. Symp. Proc., 1989, vol. 133, pp. 81–86.
Scheunemann-Frerker G, Gabrisch H, Feller-Kniepmeier M (1992) Philos Mag A 65:1353–1368
C. Zener: Elasticity and Anelasticity of Metals, University of Chicago, Chicago, 1948.
F.C. Frank and W.T. Read: Phys. Rev., 1950, vol. 79, pp. 722–23.
Y. Ru, S. Li, J. Zhou, Y. Pei, H. Wang, S. Gong, and H. Xu: Sci Rep, 2016, vol. 6, 29941. https://doi.org/10.1038/srep29941.
W. M. Lomer: Phil. Mag., 1951, vol. 42, pp. 1327 - 1331.
A. H. Cotterell: Dislocation and Plastic Flow in Crystals, Oxford University, UK, 1953.
N. Thompson: Proc. Phys. Soc. B, 1953, vol. 66, No. 6, pp. 481 - 492.
H. Yang, Z. Li, and M. Huang: Computational Mater. Sci., 2013, vol. 75, pp. 52–59.
B. H. Kear, J. M. Oblak, and A. F. Giamei: Metall. Trans., 1970, vol. 1, pp. 2477–2486.
H. R. Pak, T. Saburi, and S. Nenno: Scripta Metall., 1976, vol. 10, pp. 1081–1085.
K. Suzuki, M. Ichihara, and S. Takeuchi: Acta Metall., 1979, vol. 27, pp. 193–200.
I. Baker and E. M. Schulson: Phys. Stat. Sol. A, 1985, vol. 89, pp. 163–172.
A. Chiba and S. Hanada; Philos. Mag., A, 1994, vol. 69, pp. 751–65.
M. F. Ashby: Phil. Mag., 1970, vol. 21, pp. 399–424.
K. U. Snowden: Acta Metall., 1963, vol. 11, pp. 675–684.
M. F. Kanninen and C. H. Popelar: Advanced Fracture Mechanics, 1st Edition, Oxford University Press, Oxford, UK, 1985, pp. 126 -128.
Southwest Research Institute: DARWIN User’s Manual, Southwest Research Institute, San Antonio, TX, 2008.
A. Staroselsky and B. N. Cassenti: Mech. Mater., 2010, vol. 42, pp. 945–959.
Z.-L. Zhan and J. Tong: Mech. Mater., 2007, vol. 39, pp. 64–72.
Z.-L. Zhan and J. Tong: Mech. Mater., 2007, vol. 39, pp. 73–80.
Lin YC, Chen X-M, Wen D-X, Chen M-S (2014) Comput Mater Sci 83:282–289
X. Tang, B. Wang, Y. Huo, W. Ma, J. Zhou, H. Ji, and X. Fu: Mat. Sci. Eng. A, 2016, vol. 662, pp. 54–64.
W. Ren and T. Nicholas: Mater. Sci. Eng., 2002, vol. A332, pp. 236–248.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Manuscript submitted April 6, 2020.
Rights and permissions
About this article
Cite this article
Chan, K.S. Mechanistic Modeling of Strain Hardening in Ni-Based Superalloys. Metall Mater Trans A 51, 5653–5666 (2020). https://doi.org/10.1007/s11661-020-05965-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11661-020-05965-0