Abstract
Heterogeneous internal elastic strain in polycrystalline hexagonal close-packed materials is found to originate from the intrinsic anisotropy in thermal expansivity. As most noncubic metals have anisotropic thermal expansivity, cooling from elevated temperature leads to internal stresses. To simulate the internal stresses present in a polycrystal prior to plastic deformation, the anisotropic coefficients of thermal expansion over a wide range of temperatures need to be known. One sample of strongly textured commercial purity titanium was probed using high-energy x-ray diffraction microscopy during in situ heating. From averages of the directional lattice strain as a function of temperature, the directional expansion of the material showed a crossover where the incremental \( c \)-axis expansion exceeded the \( a \)-axis expansion between 700°C and 800°C. Applying a three-dimensional crystal thermoelasticity model using a realistic microstructure based upon the experimental data, the anisotropic coefficients of thermal expansion were extracted by fitting to the average strain evolution identified from experiments.
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References
F. Roters, P. Eisenlohr, T.R. Bieler, and D. Raabe, Crystal Plasticity Finite Element Methods: In Materials Science and Engineering (New York: Wiley, 2011).
T.R. Bieler, P. Eisenlohr, F. Roters, D. Kumar, D.E. Mason, M.A. Crimp, and D. Raabe, Int. J. Plast. 25, 1655 (2009).
P. Zhang, D.S. Balint, and J. Lin, Philos. Mag. 91, 4555 (2011).
Z. Zheng, D.S. Balint, and F.P.E. Dunne, Int. J. Plast. 87, 15 (2016).
B. Chen, J. Jiang, and F.P.E. Dunne, Int. J. Plast. 101, 213 (2018).
D. Ozturk, A. Shahba, and S. Ghosh, Fatigue Fract. Eng. Mater. Struct. 39, 752 (2016).
M.A. Groeber and M.A. Jackson, Integr. Mater. Manuf. Innov. 3, 5 (2014).
R. Quey and L. Renversade, Comput. Methods Appl. Mech. Eng. 330, 308 (2018).
V. Tari, R.A. Lebensohn, R. Pokharel, T.J. Turner, P.A. Shade, J.V. Bernier, and A.D. Rollett, Acta Mater. 154, 273 (2018).
W. Xu, M. Ferry, N. Mateescu, J.M. Cairney, and F.J. Humphreys, Mater. Charact. 58, 961 (2007).
C. Zhang, H. Li, P. Eisenlohr, W. Liu, C.J. Boehlert, M.A. Crimp, and T.R. Bieler, Int. J. Plast. 69, 21 (2015).
H.F. Poulsen, S. Garbe, T. Lorentzen, D. Juul Jensen, F.W. Poulsen, N.H. Andersen, T. Frello, R. Feidenhans’l, and H. Graafsma, J. Synchrotron Radiat. 4, 147 (1997).
H. Abdolvand, J. Wright, and A.J. Wilkinson, Nat. Commun. 9, 171 (2018).
J.A. Moore, S.F. Li, M. Rhee, and N.R. Barton, J. Dyn. Behav. Mater. 4, 464 (2018).
K. Chatterjee, J.Y.P. Ko, J.T. Weiss, H.T. Philipp, J. Becker, P. Purohit, S.M. Gruner, and A.J. Beaudoin, J. Mech. Phys. Solids 109, 95 (2017).
T.J. Turner, P.A. Shade, J.V. Bernier, S.F. Li, J.C. Schuren, P. Kenesei, R.M. Suter, and J. Almer, Metall. Mater. Trans. A 48, 627 (2017).
T.R. Bieler, L. Wang, A.J. Beaudoin, P. Kenesei, and U. Lienert, Metall. Mater. Trans. A 45, 109 (2014).
L. Wang, Z. Zheng, H. Phukan, P. Kenesei, J.-S. Park, J. Lind, R.M. Suter, and T.R. Bieler, Acta Mater. 132, 598 (2017).
U. Lienert, M.C. Brandes, J.V. Bernier, J. Weiss, S.D. Shastri, M.J. Mills, and M.P. Miller, Mater. Sci. Eng. A 524, 46 (2009).
E.S. Greiner and W.C. Ellis, Met. Technol. 180, 657 (1949).
S. Zinelis, A. Tsetsekou, and T. Papadopoulos, J. Prosthet. Dent. 90, 332 (2003).
P. Hidnert, J. Res. Natl. Bur. Stand. 30, 101 (1943).
R.L.P. Berry and G.V. Raynor, Research 6, 21s (1953).
R.R. Pawar and V.T. Deshpande, Acta Crystallogr. Sect. A 24, 316 (1968).
P.A. Shade, B. Blank, J.C. Schuren, T.J. Turner, P. Kenesei, K. Goetze, R.M. Suter, J.V. Bernier, S.F. Li, J. Lind, U. Lienert, and J. Almer, Rev. Sci. Instrum. 86, 93902 (2015).
L. Wang, J. Lind, H. Phukan, P. Kenesei, J.-S. Park, R.M. Suter, A.J. Beaudoin, and T.R. Bieler, Scr. Mater. 92, 35 (2014).
L. Wang, R.I. Barabash, Y. Yang, T.R. Bieler, M.A. Crimp, P. Eisenlohr, W. Liu, and G.E. Ice, Metall. Mater. Trans. A 42, 626 (2011).
L. Wang, P. Eisenlohr, Y. Yang, T.R. Bieler, and M.A. Crimp, Scr. Mater. 63, 827 (2010).
L. Wang, Y. Yang, P. Eisenlohr, T.R. Bieler, M.A. Crimp, and D.E. Mason, Metall. Mater. Trans. A 41, 421 (2009).
N.Y. Juul, G. Winther, D. Dale, M.K.A. Koker, P. Shade, and J. Oddershede, Scr. Mater. 120, 1 (2016).
D.C. Pagan, J.V. Bernier, D. Dale, J.Y.P. Ko, T.J. Turner, B. Blank, and P.A. Shade, Scr. Mater. 142, 96 (2018).
J.V. Bernier, N.R. Barton, U. Lienert, and M.P. Miller, J. Strain Anal. Eng. Des. 46, 527 (2011).
Z. Zheng, A. Stapleton, K. Fox, and F.P.E. Dunne, Int. J. Plast. 111, 234 (2018).
Acknowledgements
This work is based upon research conducted at the Cornell High Energy Synchrotron Source (CHESS), which is supported by the National Science Foundation under award DMR-1332208. Z.Z. and F.P.E.D. would like to acknowledge support from the Engineering and Physical Sciences Research Council through HexMat programme grant EP/K034332/1. T.R.B. and P.E. acknowledge support from the Department of Energy Office of Basic Science via grant DE-FG02-09ER46637. F.P.E.D. wishes to acknowledge gratefully the provision of funding for his Royal Academy of Engineering/Rolls-Royce research chair.
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Zheng, Z., Eisenlohr, P., Bieler, T.R. et al. Heterogeneous Internal Strain Evolution in Commercial Purity Titanium Due to Anisotropic Coefficients of Thermal Expansion. JOM 72, 39–47 (2020). https://doi.org/10.1007/s11837-019-03743-x
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DOI: https://doi.org/10.1007/s11837-019-03743-x