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Origin of the ω-Strengthening and Embrittlement in β-Titanium Alloys: Insight from First Principles

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Abstract

The ω-phase precipitates in β-Ti alloys increase the strength but significantly degrade the ductility of the alloys. In the present work, the mechanism of ω-strengthening and embrittlement is investigated by using a first principles method based on density functional theory. The generalized stacking fault energies of various slip systems in both the β and ω phases are calculated. The strengthening and embrittlement effects of the ω phase are discussed by comparing the slip energy barriers of slip systems in the β and ω phases with different orientation relationships. It is found that the slip energy barriers of slip systems in the ω phase, except for \((\bar 2020){[0001]_\omega },\) are much higher than those of slip systems in the β phase, which explains the ω-strengthening and embrittlement effects. The slip energy barrier of the most active slip system in the phase, \((\bar 2020){[0001]_\omega },\) increases with the depletion of Mo and increasing extent of structure collapse, suggesting that aging treatment enhances the -strengthening and embrittlement effects.

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REFERENCES

  1. Lütjering, G. and Williams, J.C., Titanium, Berlin, Heidelberg: Springer, 2007. https://doi.org/10.1007/978-3-540-73036-1

  2. Banerjee, D. and Williams, J.C., Perspectives on Titanium Science and Technology, Acta Mater., 2013, vol. 61, pp. 844–879. https://doi.org/10.1016/j.actamat.2012.10.043

    Article  ADS  Google Scholar 

  3. Silcock, J.M., An X-Ray Examination of the to Phase in TiV, TiMo and TiCr Alloys, Acta Metall., 1958, vol. 6, pp. 481–493. https://doi.org/10.1016/0001-6160(58)90111-1

    Article  Google Scholar 

  4. Brammer, W.G. and Rhodes, C.G., Determination of Omega Phase Morphology in Ti–35% Nb by Transmission Electron Microscopy, Philos. Mag., 1967, vol. 16, pp. 477–486. https://doi.org/10.1080/14786436708220858

    Article  ADS  Google Scholar 

  5. Devaraj, A., Williams, R.E.A., Nag, S., Srinivasan, R., Fraser, H.L., and Banerjee, R., Three-Dimensional Morphology and Composition of Omega Precipitates in a Binary Titanium–Molybdenum Alloy, Scripta Mater., 2009, vol. 61, pp. 701–704. https://doi.org/10.1016/j.scriptamat.2009.06.006

    Article  Google Scholar 

  6. Williams, J.C., Hickman, B.S., and Leslie, D.H., The Effect of Ternary Additions on the Decomposition of Metastable Beta-Phase Titanium Alloys, Metall. Transact., 1971, vol. 2, pp. 477–484. https://doi.org/10.1007/bf02663337

    Article  ADS  Google Scholar 

  7. De Fontaine, D., Paton, N.E., and Williams, J.C., The Omega Phase Transformation in Titanium Alloys as an Example of Displacement Controlled Reactions, Acta Metallurg., 1971, vol. 19, pp. 1153–1162. https://doi.org/10.1016/0001-6160(71)90047-2

    Article  Google Scholar 

  8. Duerig, T.W., Terlinde, G.T., and Williams, J.C., Phase Transformations and Tensile Properties of Ti-10V-2Fe-3Al, Metall. Transact. A, 1980, vol. 11, pp. 1987–1998. https://doi.org/10.1007/bf02655118

    Article  ADS  Google Scholar 

  9. Williams, J.C., Fontaine, D., and Paton, N.E., The ω-Phase as an Example of an Unusual Shear Transformation, Metall. Transact., 1973, vol. 4, pp. 2701–2708. https://doi.org/10.1007/bf02644570

    Article  ADS  Google Scholar 

  10. Choudhuri, D., Zheng, Y., Alam, T., Shi, R., Hendrickson, M., Banerjee, S., Wang, Y., Srinivasan, S.G., Fraser, H., and Banerjee, R., Coupled Experimental and Computational Investigation of Omega Phase Evolution in a High Misfit Titanium-Vanadium Alloy, Acta Mater., 2017, vol. 130, pp. 215–228. https://doi.org/10.1016/j.actamat.2017.03.047

    Article  ADS  Google Scholar 

  11. Zhu, J.-L., Cao, S., Wang, Y., Yang, R., and Hu, Q.-M., First-Principles Investigations of ω Variant Selection during Athermal β→ω Transformation of Binary Ti-xMo Alloy, Comput. Mater. Sci., 2018, vol. 155, pp. 524–533. https://doi.org/10.1016/j.commatsci.2018.09.028

    Article  Google Scholar 

  12. Devaraj, A., Nag, S., Srinivasan, R., Williams, R.E.A., Banerjee, S., Banerjee, R., and Fraser, H.L., Experimental Evidence of Concurrent Compositional and Structural Instabilities Leading to ω Precipitation in Titanium–Molybdenum Alloys, Acta Mater., 2012, vol. 60, pp. 596–609. https://doi.org/10.1016/j.actamat.2011.10.008

    Article  ADS  Google Scholar 

  13. Tane, M., Okuda, Y., Todaka, Y., Ogi, H., and Nagakubo, A., Elastic Properties of Single-Crystalline ω Phase in Titanium, Acta Mater., 2013, vol. 61, pp. 7543–7554. https://doi.org/10.1016/j.actamat.2013.08.036

    Article  ADS  Google Scholar 

  14. Chen, W., Cao, S., Kou, W., Zhang, J., Wang, Y., Zha, Y., Pan, Y., Hu, Q., Sun, Q., and Sun, J., Origin of the Ductile-to-Brittle Transition of Metastable β-Titanium Alloys: Self-Hardening of ω-Precipitates, Acta Mater., 2019, vol. 170, pp. 187–204. https://doi.org/10.1016/j.actamat.2019.03.034

    Article  ADS  Google Scholar 

  15. Gysler, A., Lütjering, G., and Gerold, V., Deformation Behavior of Age-Hardened Ti-Mo Alloys, Acta Metallurg, 1974, vol. 22, pp. 901–909. https://doi.org/10.1016/0001-6160(74)90057-1

    Article  Google Scholar 

  16. Lai, M.J., Tasan, C.C., and Raabe, D., Deformation Mechanism of ω-Enriched Ti–Nb-Based Gum Metal: Dislocation Channeling and Deformation Induced ω–β Transformation, Acta Mater., 2015, vol. 100, pp. 290–300. https://doi.org/10.1016/j.actamat.2015.08.047

    Article  ADS  Google Scholar 

  17. Liu, H., Niinomi, M., Nakai, M., Cho, K., and Fujii, H., Deformation-Induced ω-Phase Transformation in a β-Type Titanium Alloy during Tensile Deformation, Scripta Mater., 2017, vol. 130, pp. 27–31. https://doi.org/10.1016/j.scriptamat.2016.10.036

    Article  Google Scholar 

  18. Vítek, V., Intrinsic Stacking Faults in Body-Centred Cubic Crystals, Philos. Mag., 1968, vol. 18, pp. 773–786. https://doi.org/10.1080/14786436808227500

    Article  ADS  Google Scholar 

  19. Zunger, A., Wei, S.H., Ferreira, L.G., and Bernard, J.E., Special Quasirandom Structures, Phys. Rev. Lett., 1990, vol. 65, pp. 353–356. https://doi.org/10.1103/physrevlett.65.353

    Article  ADS  Google Scholar 

  20. van de Walle, A., Multicomponent Multisublattice Alloys, Nonconfigurational Entropy and Other Additions to the Alloy Theoretic Automated Toolkit, Calphad, 2009, vol. 33, pp. 266–278. https://doi.org/10.1016/j.calphad.2008.12.005

    Article  Google Scholar 

  21. Walle, A. and Ceder, G., Automating First-Principles Phase Diagram Calculations, J. Phase Equilib., 2002, vol. 23, pp. 348–359. https://doi.org/10.1361/105497102770331596

    Article  Google Scholar 

  22. van de Walle, A., Asta, M., and Ceder, G., The Alloy Theoretic Automated Toolkit: A User Guide, Calphad, 2002, vol. 26, pp. 539–553. https://doi.org/10.1016/s0364-5916(02)80006-2

    Article  Google Scholar 

  23. Blöchl, P.E., Projector Augmented-Wave Method, Phys. Rev. B, 1994, vol. 50, pp. 17953–17979. https://doi.org/10.1103/physrevb.50.17953

    Article  ADS  Google Scholar 

  24. Kresse, G. and Hafner, J., Ab Initio Molecular Dynamics for Liquid Metals, Phys. Rev. B, 1993, vol. 47, pp. 558–561. https://doi.org/10.1103/physrevb.47.558

    Article  ADS  Google Scholar 

  25. Kresse, G. and Furthmüller, J., Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set, Phys. Rev. B, 1996, vol. 54, pp. 11169–11186. https://doi.org/10.1103/physrevb.54.11169

    Article  ADS  Google Scholar 

  26. Kresse, G. and Joubert, D., From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method, Phys. Rev. B, 1999, vol. 59, pp. 1758–1775. https://doi.org/10.1103/physrevb.59.1758

    Article  ADS  Google Scholar 

  27. Perdew, J.P., Burke, K., and Ernzerhof, M., Generalized Gradient Approximation Made Simple, Phys. Rev. Lett., 1996, vol. 77, pp. 3865–3868. https://doi.org/10.1103/physrevlett.77.3865

    Article  ADS  Google Scholar 

  28. Cao, S., Jiang, Y., Yang, R., and Hu, Q.-M. Properties of β/ω Phase Interfaces in Ti and Their Implications on Mechanical Properties and ω Morphology, Comput. Mater. Sci., 2019, vol. 158, pp. 49–57. https://doi.org/10.1016/j.commatsci.2018.10.042

    Article  Google Scholar 

  29. Chen, W., Zhang, J., Cao, S., Pan, Y., Huang, M., Hu, Q., Sun, Q., Xiao, L., and Sun, J., Strong Deformation Anisotropies of ω-Precipitates and Strengthening Mechanisms in Ti-10V-2Fe-3Al Alloy Micropillars: Precipitates Shearing Versus Precipitates Disordering, Acta Mater., 2016, vol. 117, pp. 68–80. https://doi.org/10.1016/j.actamat.2016.06.065

    Article  ADS  Google Scholar 

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Funding

This work is financially supported by Natural Science Foundation of China under grant Nos. 91860107, 52071315, and 52001307, National Science and Technology Major Project under grant No. J2019-VI-0012-0126, and China Postdoctoral Science Foundation under grant No. 2019M661149.

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Authors and Affiliations

  1. Institute of Metal Research, Chinese Academy of Sciences, 110016, Shenyang, China

    Sh. Cao, R. Yang & Q.-M. Hu

  2. State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, 710049, Xi’an, China

    W. Chen

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  1. Sh. Cao
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  2. W. Chen
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  3. R. Yang
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  4. Q.-M. Hu
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Correspondence to Sh. Cao or W. Chen.

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Translated from Fizicheskaya Mezomekhanika, 2021, Vol. 24, No. 5, pp. 16–25.

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Cao, S., Chen, W., Yang, R. et al. Origin of the ω-Strengthening and Embrittlement in β-Titanium Alloys: Insight from First Principles. Phys Mesomech 24, 513–522 (2021). https://doi.org/10.1134/S1029959921050027

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