Using a scale-bridging technique to determine the effect of elastic properties on stress distribution around the femoral stem of an artificial hip joint with a simplified geometry
Tóm tắt
A scale-bridging technique was used to investigate the effect of the elastic properties of β-Ti alloys on the stress distribution around the femoral stem of an artificial hip joint with a simplified geometry when under an external loading. The anisotropic elastic constants of single-crystalline β-Ti alloys (TN1: Ti-18.75 at% Nb, TN2: Ti-37.5 at% Nb, and TN3: Ti-43.75 at% Nb) were calculated using an ab-initio technique that was based on density functional theory calculation. The single-crystalline elastic constants calculated via the ab-initio technique were used to calculate the elastic constants of polycrystal β-Ti alloys using an elastic selfconsistent scheme. Finite element analysis based on the elastic constants of polycrystalline β-Ti alloys for a femoral stem was conducted to calculate the above-mentioned stress distribution. The model system consisting of a TN1 alloy exhibited a relatively high level of von Mises stress on the surface of cancellous and cortical bones compared to model systems consisting of TN2, TN3 alloys and commercial biomaterials (Ti-6Al-4V alloy and 316STS). The thickness of the cancellous bone between the femoral stem and the cortical bone affected the stress concentration on the surface of the cortical bone.
Tài liệu tham khảo
M. Niinomi, Mater. Sci. Eng. A. 243, 231 (1998).
S. Gross and E. W. Abel, J. Biomech. 34, 995 (2001).
J. Park and R. S. Lakes, Biomaterials: An Introduction, 3rd ed., p.392, Springer, New York, London (2007).
S.-H. Park, K.-D. Woo, J.-Y. Kim, and S.-H. Kim, Korean. J. Met. Mater, 50, 469 (2012).
A. M. Omran, K. D. Woo, D. K. Kim, S. W. Kim, M. S. Moon, N. A. Barakat, and D. L. Zhang, Met. Mater. Int. 14, 321 (2008).
M. Popa, E. Vasilescu, P. Drob, D. Raducanu, J. M. C. Moreno, S. Ivanescu, C. Vasilescu, and S. I. Drob, Met. Mater. Int. 18, 639 (2012).
U. Simon, P. Augat, A. Ignatius, and L. Claes, J. Biomech. 36, 1079 (2003).
S. J. Shefelbine, U. Simon, L. Claes, A. Gold, Y. Gabet, I. Bab, R. Müller, and P. Augat, Bone. 36, 480 (2005).
S. Benli, S. Aksoy, H. Havltclolu, and M. Kucuk, J. Biomech. 41, 3229 (2008).
S. H. Pettersen, T. S. Wik, and B. Skallerud, Clin. Biomech. 24, 196 (2009).
D. Ma, M. Friák, J. Neugebauer, D. Raabe, and F. Roters, Phys. Stat. Sol(b). 245, 2642 (2008).
G. Ghosh, S. Delsante, G. Borzone, M. Asta, and R. Ferro, Acta Mater. 54, 4977 (2006).
G. Ghosh, S. Vaynman, M. Asta, and M. E. Fine, Intermetallics. 15, 44 (2007).
B.-Y. Tang, N. Wang, W.-Y. Yu, X.-Q. Zeng, and W.-J. Ding, Acta Mater. 56, 3353 (2008).
M. Friák, T. Hickel, B. Grabowski, L. Lymperakis, A. Udyansky, A. Dick, D. Ma, F. Roters, L.-F. Zhu, A. Schlieter, U. Kühn, Z. Ebrahimi, R. A. Lebensohn, D. Holec, J. Eckert, H. Emmerich, D. Raabe, and J. Neugebauer, Eur. Phys. J. Plus. 126, 101 (2011).
D. Raabe, B. Sander, M. Friák, D. Ma, and J. Neugebauer, Acta Mater. 55, 4475 (2007).
G. Kresse and J. Furthmuller, Comput. Mater. Sci. 6, 15 (1996).
G. Kresse and J. Furthmuller, Phys. Rev. B. 54, 11169 (1996).
U. F. Kocks, C. N. Tome and H. R. Wenk, Textures and Anisotropy: Preferred Orientations in Polycrystals and Their Effect on Materials Properties, Cambridge University Press, New York (1998).
http://cmp.univie.ac.at/research/vasp/(2013).
P. E. Blöchl, Phys. Rev. B. 50, 17953 (1994).
G. Kresse and D. Joubert, Phys. Rev. B. 59, 1758 (1999).
J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
H. J. Monkhorst and J. D. Pack, Phys. Rev. B. 13, 5188 (1976).
J. F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices, Oxford University Press, New York (1985).
K. B. Panda and K. S. Ravi, Chandran, Acta Mater. 54, 1641 (2006).
W. Voigt, Lehrbuch der Kristallpysik, Leipzig Taubner, Germany (1928).
A. Reuss and Z. Angnew, Math. Mech. 9, 49 (1929).
G. Denoziere and D. N. Ku, J. Biomech. 39, 766 (2006).
D. L. Kopperdahl and T. M. Keaveny, J. Biomech. 31, 601 (1998).
A. Herreraa, E. Ibarzb, J. Cegoñino, A. Lobo-Escolar, S. Puértolas, E. López, J. Mateo and L. Gracia, World. J. Orthop. 3(4), 25 (2012).
Y. Noyama, T. Nakano, T. Ishimoto, T. Sakai, and H. Yoshikawa, Bone. 52, 659 (2013).
C. Zener, Elasticity and an Elasticity of Metals, University of Chicago Press, Chicago (1948).
W. F. Hosford, The Mechanics of Crystals and Textured Polycrytstals, 19, Oxford University Press, New York (1993).
R. Hill, Proc. Phys. Soc. A. 65, 349 (1952).
A. V. Hershey, J. Appl. Mech. 21, 236 (1954).
W. A. Counts, M. Friak, C. C. Battaile, D. Raabe, and J. Neugebauer, Phys. Stat. Sol(b). 245, 2630 (2008).
C.-H. Goh, R. W. Neu, and D. L. McDowell, Int. J. Plasticity. 19, 1627 (2003).
J. Chen and F. Y. Yan, Trans. Nonferr. Met. Soc. China. 22, 1356 (2012).