Abstract
While it is useful to predict properties in metallic materials based upon the composition and microstructure, the complexity of real, multi-component, and multi-phase engineering alloys presents difficulties when attempting to determine constituent-based phenomenological equations. This paper applies an approach based upon the integration of three separate modeling approaches, specifically artificial neural networks, genetic algorithms, and Monte Carlo simulations to determine a mechanism-based equation for the yield strength of α+β processed Ti-6Al-4V (all compositions in weight percent) which consists of a complex multi-phase microstructure with varying spatial and morphological distributions of the key microstructural features. Notably, this is an industrially important alloy yet an alloy for which such an equation does not exist in the published literature. The equation ultimately derived in this work not only can accurately describe the properties of the current dataset but also is consistent with the limited and dissociated information available in the literature regarding certain parameters such as intrinsic yield strength of pure hexagonal close-packed alpha titanium. In addition, this equation suggests new interesting opportunities for controlling yield strength by controlling the relative intrinsic strengths of the two phases through solid solution strengthening.
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Allison J. JOM 2011;63:15.
Patel P. MRS bulletin 2011;36:964.
White A. MRS Bulletin 2012;37:715.
Ji S, Wang Q, Xia B, Marcotte D. Journal of Structural Geology 2004;26:1377.
Wang M, Pan N. Materials Science and Engineering: R: Reports 2008;63:1.
Allison J, Li M, Wolverton C, Su X. JOM 2006;58:28.
Kozar R, Suzuki A, Milligan W, Schirra J, Savage M, Pollock T. Metall Mater Trans A 2009;40:1588.
Collins PC, Fraser HL. ASM Handbook: Fundamentals of modeling for metals processing 2009:377.
Lütjering G, Williams JC. Titanium, 2nd edn., Springer, Berlin, 2003.
Kar S, Searles T, Lee E, Viswanathan G, Fraser H, Tiley J, Banerjee R. Metall Mater Trans A 2006;37:559.
Kapoor R, Pal D, Chakravartty J. Journal of Materials Processing Technology 2005;169:199.
Topçu İB, Sarıdemir M. Construction and Building Materials 2008;22:532.
Cai J, Cottis R, Lyon S. Corros. Sci. 1999;41:2001.
Bhadeshia H. ISIJ Int. 1999;39:966.
Bhadeshia H. Statistical Analysis and Data Mining 2009;1:296.
Bhadeshia H, MacKay D, Svensson L-E. Mater Sci Technol 1995;11:1046.
MacKay DJ. Neural. Comput. 1992;4:448.
Capdevila C, García Caballero F, García de Andrés C. ISIJ Int. 2002;42:894.
Gavard L, Bhadeshia H, MacKay D, Suzuki S. Mater Sci Technol 1996;12:453.
Collins PC, Koduri S, Welk B, Tiley J, Fraser HL. Metall Mater Trans A 2013;44:1441.
Cool T, Bhadeshia H, MacKay D. Mater. Sci. Eng. A 1997;223:186.
Pak J, Jang J, Bhadeshia H, Karlsson L. Mater. Manuf. Processes 2008;24:16.
Brun F, Yoshida T, Robson J, Narayan V, Bhadeshia H, MacKay D. Mater Sci Technol 1999;15:547.
Fujii H, Mackay D, Bhadeshia H. ISIJ Int. 1996;36:1373.
Kashyap B, Tangri K. Acta Mater. 1997;45:2383.
Tang J, Huang B, He Y, Liu W, Zhou K, Wu A. Mater. Res. Bull. 2002;37:1315.
Paradkar A, Kamat S, Gogia A, Kashyap B. Mater. Sci. Eng. A 2009;520:168.
Zhao M-C, Yin F, Hanamura T, Nagai K, Atrens A. Scripta Mater. 2007;57:857.
Tiley J, Searles T, Lee E, Kar S, Banerjee R, Russ J, Fraser H. Mater. Sci. Eng. A 2004;372:191.
Narayan V, Abad R, Lopez B. ISIJ Int. 1999;39:999.
Yoshitake S, Narayan V, Harada H. ISIJ Int. 1998;5:495.
Sourmail T, Bhadeshia H, MacKay DJ. Mater Sci Technol 2002;18:655.
Cottrell G, Kemp R, Bhadeshia H, Odette G, Yamamoto T. J. Nucl. Mater. 2007;367:603.
Sterjovski Z, Nolan D, Carpenter K, Dunne D, Norrish J. Journal of Materials Processing Technology 2005;170:536.
Malinov S, Sha W, McKeown J. Computational Materials Science 2001;21:375.
Shabani MO, Mazahery A. J. Mater. Sci. 2011;46:6700.
J.S. Tiley: Ph.D. Thesis, The Ohio State University, 2003.
P.C. Collins, S. Kar, T. Searles, S. Koduri, and G.B. Viswanathan, Frontiers in the Design of Materials (FDM-NMD-ATM), India, 2006.
Dimitriu R, Bhadeshia H, Fillon C, Poloni C. Mater. Manuf. Processes 2008;24:10.
Ono N, Nowak R, Miura S. Mater. Lett. 2004;58:39.
Gypen L, Deruyttere A. J. Mater. Sci. 1977;12:1028.
Gypen LA, Deruyttere A. J. Mater. Sci. 1977;12:1034.
Koike M, Hummel SK, Ball JD, Okabe T. The Journal of prosthetic dentistry 2012;107:393.
Morais LS, Serra GG, Muller CA, Andrade LR, Palermo EF, Elias CN, Meyers M. Acta Biomaterialia 2007;3:331.
Yapici GG, Karaman I, Maier HJ. Mater. Sci. Eng. A 2006;434:294.
Geetha M, Singh A, Asokamani R, Gogia A. Prog Mater Sci 2009;54:397.
Meyers MA, Chawla KK. Mechanical Behavior of Materials, 2nd edn., Cambridge University Press, Cambridge; 2009.
Anderson E, Jillson D, Dunbar S. Trans AIME 1953;197:1191.
S. Ankem, G. Scarr, and I. Caplan, Sixth World Conference on Titanium. I, 1988, pp. 265–68.
Williams J, Baggerly R, Paton N. Metall Mater Trans A 2002;33:837.
Hill R. Math. Proc. Cambridge Philos. Soc. 1979;85:179.
Wu HH, Trinkle DR. Phys. Rev. Lett. 2011;107:045504.
Foreman A, Makin M. Can. J. Phys. 1967;45:511.
Communications with Viswanathan and Fraser, 2008.
Savage M, Tatalovich J, Zupan M, Hemker K, Mills M. Mater. Sci. Eng. A 2001;319:398.
Savage M, Tatalovich J, Mills M. Philos Mag 2004;84:1127.
Acknowledgments
The authors gratefully acknowledge the support of the US Air Force Research Laboratory, ISES Contract No. FA 8650-08-C-5226, the encouragement to pursue this integrated approach by members of the industrial advisory board of the Center for Advanced Non-Ferrous Structural Alloys, which is a joint industry-university center between the Colorado School of Mines and the University of North Texas (NSF Award No. 1134873); and the Center for Advanced Research and Testing at the University of North Texas.
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Ghamarian, I., Samimi, P., Dixit, V. et al. A Constitutive Equation Relating Composition and Microstructure to Properties in Ti-6Al-4V: As Derived Using a Novel Integrated Computational Approach. Metall Mater Trans A 46, 5021–5037 (2015). https://doi.org/10.1007/s11661-015-3072-4
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DOI: https://doi.org/10.1007/s11661-015-3072-4