Abstract
Deformation twinning was directly observed in three commercial zirconium alloy samples during split channel die plane-strain compression. One pair of samples had similar starting texture but different grain size distributions, while another pair had similar grain size distribution but different starting textures. Extension twinning was found to be more sensitive to the starting texture than to the grain size distribution. Also, regions of intense deformation near grain boundaries were observed. A hierarchical binary tree-based polycrystal plasticity model, implementing the Chin-Hosford-Mendorf twinning criterion, captured the experimentally observed twinning grains’ lattice orientation distribution, and the twin volume fraction evolution, provided the critical resolved shear stress for extension twinning, \( \tau_{0} , \) was assumed much larger than any of the values reported in the literature, based on the viscoplastic self-consistent model. A comparison of the models suggests that \( \tau_{0} \) obtained using the present model and the viscoplastic self-consistent models physically correspond to the critical stress required for twin nucleation, and twin growth, respectively.
Similar content being viewed by others
References
G.E. Dieter: Mechanical Metallurgy, 3rd ed., McGraw-Hill, New York, 1986.
A. Jain and S.R. Agnew: Mater. Sci. Eng. A, 2007, vol. 462, pp. 29–36.
R.J. McCabe, E.K. Cerreta, A. Misra, G.C. Kaschner, and C.N. Tomé: Philos. Mag., 2006, vol. 86, pp. 3595–3611.
H. Numakura and M. Koiwa: Metall. Sci. Technol., 1998, vol. 16, pp. 4–19.
S.G. Song and G.T. Gray: Metall. Mater. Trans. A, 1995, vol. 26A, pp. 2665–75.
G.C. Kaschner, C.N. Tomé, I.J. Beyerlein, S.C. Vogel, D.W. Brown, and R.J. McCabe: Acta Mater., 2006, vol. 54, pp. 2887–96.
K.L. Murty and I. Charit: Prog. Nucl. Energy, 2006, vol. 48, pp. 325–59.
E. Tenckhoff: J. ASTM Int., 2005, vol. 2, pp. 1–26.
R.J. McCabe, G. Proust, E.K. Cerreta, and A. Misra: Int. J. Plast., 2009, vol. 25, pp. 454–72.
J.W. Christian and S. Mahajan: Prog. Mater. Sci., 1995, vol. 39, pp. 1–157.
A.M. Garde, E. Aigeltinger, and R.E. Reed-Hill: Metall. Trans., 1973, vol. 4, pp. 2461–68.
S.K. Sahoo, V.D. Hiwarkar, I. Samajdar, P. Pant, G.K. Dey, D. Srivastav, R. Tewari, and S. Banerjee: Mater. Sci. Technol., 2010, vol. 26, pp. 104–14.
J.F. Bingert, T.A. Mason, G.C. Kaschner, P.J. Maudlin, and G.T. Gray III: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 955–63.
G.C. Kaschner and G.T. Gray III: Metall. Mater. Trans. A, 2000, vol. 31A, pp. 1997–2003.
S. Asgari, E. El-Danaf, S.R. Kalidindi, and R.D. Doherty: Metall. Mater. Trans. A, 1997, vol. 28A, pp. 1781–95.
E. El-danaf, S.R. Kalidindi, and R.D. Doherty: Int. J. Plast., 2001, vol. 17, pp. 1245–65.
S.R. Kalidindi: Int. J. Plast., 1998, vol. 14, pp. 1265–77.
B. Verlinden, J. Driver, I. Samajdar, and R.D. Doherty: Thermo-Mechanical Processing of Metallic Materials, Elsevier (Pergamon Materials Series), Elsevier, Amsterdam, 2007.
E. Tenckhoff: ASTM Spec. Tech. Publ., 1988, vol. 966, pp. 1–77.
A. Akhtar and A. Teghtsoonian: Acta Metall., 1971, vol. 19, pp. 655–63.
S.K. Sahoo, V.D. Hiwarkar, A. Majumdar, I. Samajdar, P. Pant, G.K. Dey, D. Srivastav, R. Tiwari, and S. Banerjee: Mater. Sci. Eng. A, 2009, vol. 518, pp. 47–55.
Y.T. Zhu, X.Z. Liao, X.L. Wu, and J. Narayan: J. Mater. Sci., 2013, vol. 48, pp. 4467–75.
R.J. McCabe, I.J. Beyerlein, J.S. Carpenter, and N.A. Mara: Nat. Commun., 2014, vol. 3806, pp. 1–7.
J. Wang, R.G. Hoagland, J.P. Hirth, L. Capolungo, I.J. Beyerlein, and C.N. Tomé: Scripta Mater., 2009, vol. 61, pp. 903–6.
A. Akhtar: Metall. Trans. A, 1975, vol. 6, pp. 1217–22.
T.A. Mason, J.F. Bingert, G.C. Kaschner, S.I. Wright, and R.J. Larsen: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 949–54.
P.E. Marshall, G. Proust, J.T. Rogers, and R.J. McCabe: J. Microsc., 2010, vol. 238, pp. 218–29.
R. Kapoor, A. Sarkar, J. Singh, I. Samajdar, and D. Raabe: Scripta Mater., 2014, vol. 74, pp. 72–75.
H. Francillette, B. Bacroix, M. Gasperini, and J.L. Bechade: Acta Mater., 1998, vol. 46, pp. 4131–42.
G. Proust, C.N. Tomé, and G.C. Kaschner: Acta Mater., 2007, vol. 55, pp. 2137–48.
G.Y. Chin, W.F. Hosford, and D.R. Mendorf: Proc. R. Soc. Lond., 1969, vol. 309, pp. 433–56.
P. Van Houtte: Acta Metall., 1978, vol. 26, pp. 591–604.
C.N. Tomé, R.A. Lebensohn, and U.F. Kocks: Acta Metall. Mater., 1991, vol. 39, pp. 2667–80.
U.F. Kocks, C.N. Tomé, and H.-R. Wenk: Texture and Anisotropy, Cambridge University Press, Cambridge, U.K., 1998.
T. Leffers and R.K. Ray: Prog. Mater. Sci., 2009, vol. 54, pp. 351–96.
L. Wang, Y. Yang, P. Eisenlohr, T.R. Bieler, M.A. Crimp, and D.E. Mason: Metall. Mater. Trans. A, 2010, vol. 41A, pp. 421–30.
L. Wang, P. Eisenlohr, Y. Yang, T.R. Bieler, and M.A. Crimp: Scripta Mater., 2010, vol. 63, pp. 827–30.
T.R. Bieler, L. Wang, A.J. Beaudoin, P. Kenesei, and U. Lienert: Metall. Mater. Trans. A, 2014, vol. 45A, pp. 109–22.
J. Lind, S.F. Li, R. Pokharel, U. Lienert, A.D. Rollett, and R.M. Suter: Acta Mater., 2014, vol. 76, pp. 213–20.
S. Panchanadeeswaran, R.D. Doherty, and R. Becker: Acta Mater., 1996, vol. 44, pp. 1233–62.
N. Vanderesse, Ch. Desrayaud, S. Girard-Insardi, and M. Darrieulat: Mater. Sci. Eng. A, 2008, vol. 476, pp. 322–32.
N. Keskar, S. Mukherjee, K.V. Mani Krishna, D. Srivastava, G.K. Dey, P. Pant, R.D. Doherty, and I. Samajdar: Acta Mater., 2014, vol. 69, pp. 265–74.
H. Paul, J.H. Driver, and W. Wajda: Mater. Sci. Eng. A, 2008, vol. 477, pp. 282–94.
I. Samajdar, B. Verlinden, and P. Van Houtte: ISIJ Int., 1998, vol. 38, pp. 759–65.
D. Chapelle and M. Darrieulat: Mater. Sci. Eng. A, 2003, vol. 347, pp. 32–41.
G.I. Taylor: J. Inst. Met., 1938, vol. 62, pp. 307–24.
R.A. Lebensohn and C.N. Tomé: Acta Met. Mater., 1993, vol. 41, pp. 2611–24.
S. Mahesh: Int. J. Plast., 2009, vol. 25, pp. 752–67.
I.J. Beyerlein and C.N. Tomé: Int. J. Plast., 2008, vol. 24, pp. 867–95.
M. Darrieulat, J.-Y. Poussardin, R.-Y. Fillit, and Ch. Desrayaud: Mater. Sci. Eng. A, 2007, vol. 445–446, pp. 641–51.
M.M. Nowell and S.I. Wright: Ultramicroscopy, 2005, vol. 103, pp. 41–58.
T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein: Introduction to Algorithms, 3rd ed., MIT press, Cambridge, 2009.
P.Van Houtte, S. Li, M. Seefeldt, and L. Delannay: Int. J. Plast., 2005, vol. 21, pp. 589–624.
C.N. Tomé, P.J. Maudlin, R.A. Lebensohn, and G.C. Kaschner: Acta Mater., 2001, vol. 49, pp. 3085–96.
C. Tomé, G.R. Canova, U.F. Kocks, N. Christodoulou, and J.J. Jonas: Acta Metall., 1984, vol. 32, pp. 1637–53.
H. Honneff and H. Mecking: in Proc. 5th Int. Conf. Textures Mater., Springer, Berlin, 1978, pp. 265–75.
G.Y. Chin, E.A. Nesbitt, and A.J. Williams: Acta Metall., 1966, vol. 14, pp. 467–76.
S. Raveendra, A.K. Kanjarla, H. Paranjape, S.K. Mishra, S. Mishra, L. Delannay, I. Samajdar, and P. Houtte: Metall. Mater. Trans. A, 2011, vol. 42A, pp. 2113–24.
S.R. Kalidindi, C.A. Bronkhorst, and L. Anand: J. Mech. Phys. Solids, 1992, vol. 40, pp. 537–69.
F. Roters, P. Eisenlohr, L. Hantcherli, D.D. Tjahjanto, T.R. Bieler, and D. Raabe: Acta Mater., 2010, vol. 58, pp. 1152–1211.
A. Zeghadi, S. Forest, A.-F. Gourgues, and O. Bouaziz: Philos. Mag., 2007, vol. 87, pp. 1425–46.
W.J. McG Tegart: Philos. Mag., 1964, vol. 9, pp. 339–41.
P.G. Partridge: Met. Rev., 1967, vol. 12, pp. 169–94.
M.L. Picklesimer: J. Electrochem. Soc., 1966, vol. 4, pp. 289–300.
J.L. Martin and R.E. Reed-Hill: Trans. Met. Soc. AIME, 1964, vol. 230, pp. 780–85.
E.J. Rapperport: Acta Metall., 1959, vol. 7, pp. 254–60.
R.A. Lebensohn, M.I. Gonzalez, C.N. Tomé, and A.A. Pochettino: J. Nucl. Mater., 1996, vol. 229, pp. 57–64.
E. Girard, R. Guillen, P. Weisbecker, and M. Francois: J. Nucl. Mater., 2001, vol. 294, pp. 330–38.
D. Gloaguen, T. Berchi, E. Girard, and R. Guillén: Acta Mater., 2007, vol. 55, pp. 4369–79.
L. Capolungo, I.J. Beyerlein, G.C. Kaschner, and C.N. Tomé: Mater. Sci. Eng. A, 2009, vol. 513–514, pp. 42–51.
M. Barnett, M. Setty, and F. Siska: Metall. Mater. Trans. A, 2013, vol. 44A, pp. 2962–69.
Acknowledgments
This research is supported by the Board of Research in Nuclear Science (BRNS) and by the National Facility of Texture and OIM, a DST-IRPHA facility at IIT Bombay.
Author information
Authors and Affiliations
Corresponding author
Additional information
Manuscript submitted March 7, 2015.
Rights and permissions
About this article
Cite this article
Singh, J., Mahesh, S., Kumar, G. et al. Deformation Twinning in Zirconium: Direct Experimental Observations and Polycrystal Plasticity Predictions. Metall Mater Trans A 46, 5058–5071 (2015). https://doi.org/10.1007/s11661-015-3085-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11661-015-3085-z