近年來混合多種金屬元素而成的高熵合金、中熵合金引起了廣泛的注意，其中Ti65(AlCrNb)35組成的中熵合金具有良好的機械性質，以及低密度的特性，而且鈦含量低於傳統鈦合金(Ti-6Al-4V)，因此有潛力取鈦合金而代之。但在具體商業化之前，Ti65(AlCrNb)35的強化機制仍有許多尚待被釐清的問題。以往材料的強化機制必須經由非常精準的微觀實驗進行量測，因此很難進行大量的測試。然而近年來由於電腦的運算能力有非常顯著的提升，因此利用數值模擬來探討微觀機制的研究與實驗相輔相成，形成數位孿生(digital twin)系統，可大量減低實驗所需耗費的時間與成本，因此本研究將利用微觀力學模型探討在微觀尺度下的力學機制以提升Ti65(AlCrNb)35中熵合金的降伏強度。
本研究提出了一套經由微觀實驗到數值模擬的架構平台，結合光學顯微鏡(optical microscope, OM)所量測得到的晶體分佈、輔以開源軟體Dream.3D搭配建立符合實驗觀測的初始模型。並以此模型為代表性體積元素(representative volume element，簡記為RVE)，透過商用有限元素軟體Abaqus提供的使用者材料(user material，簡記為UMAT)副程式介面引入晶體塑性力學 (crystal plasticity)作為材料組成律，考慮微觀尺度的差排滑移系統，進行Ti65(AlCrNb)35中熵材料的分析模擬，進行介觀力學的強化機制與巨觀力學行為分析的探討。
本研究數值模擬的結果顯示：首先可以透過縮小晶粒大小來達到合金強化之目的，其提升效應與Hall-Petch理論分析相符。其次，控制應變加載速率可以影響材料的力學行為，若加載速率每提升10倍，降伏應力約提升7.4~7.8%。循環加載(2%應變) 亦可提升降伏強度，從第二圈至第三圈時，降伏應力約能夠提升4.55%，隨後降伏強度增加量逐漸減少，至第50個迴圈時降伏強度共提升130.37%。
本研究所提之流程架構將為其他中、高熵合金的模擬提供一個可供選擇的解決方案，經由適當的模擬條件可以提供材料設計者一個初步的設計準則，有效率的提升材料強度。

This research proposes an architecture platform from experimental measurement data to numerical simulation for Ti65(AlCrNb)35 medium entropy alloy, combined with the grain size and distribution measured by optical microscope (OM), and supplemented by the open source software Dream.3D to create the initial model that fits the experimental observation results. Using this model as the representative volume element (RVE), the crystal plastic mechanics introduced by the user material (UMAT) provided by the commercial finite element software Abaqus as the material constitutive equation, this model can take into account the microscopic differential slip system and simulate many Mechanical properties of crystal materials. Then the Ti65(AlCrNb)35 medium entropy alloy was simulated and analyzed to explore the strengthening mechanism and mechanical behavior of mesoscopic mechanics. In this study, the mechanical properties of the material were enhanced by reducing the grain size, adjusting the loading rate and cyclic loading (2% strain), thereby expanding the application range of the material.

[1] Abaqus., Abaqus analysis user’s manual Vol. 3 Materials. Dassault Systems Simulia., 2018.
[2] Abbaschian, R., Abbaschian, L., & Reed-Hill, R. E., Physical Metallurgy Principles (Fourth)., 2009.
[3] Asaro, R. J., Crystal plasticity. Journal of Applied Mechanics, Transactions ASME, 50(4), 921–934., 1983.
[4] Bachmann, F., Hielscher, R., & Schaeben, H., Texture analysis with MTEX- Free and open source software toolbox. Solid State Phenomena, 160, 63–68., 2010.
[5] Benedyk, J. C., Aluminum alloys for lightweight automotive structures. Materials, Design and Manufacturing for Lightweight Vehicles. Woodhead Publishing Limited., 2010.
[6] Bower, A. F., Applied mechanics of solids. CRC Press., 2009.
[7] Brandes, E. A., & Brook, G. B., Smithells Light Metals Handbook. Smithells Light Metals Handbook. Elsevier., 1998.
[8] Cantor, B., Multicomponent and high entropy alloys. Entropy, 16(9), 4749–4768., 2014.
[9] DoITPoMS - TLP Library Crystallographic Texture - Representing Texture. (n.d.)., from https://www.doitpoms.ac.uk/tlplib/crystallographic_texture/texture_representation.php, July 7, 2020.
[10] Donachie, M. J., Titanium: A Technical Guide, 2nd Edition. October, 128., 2000.
[11] Gao, M. C., Liaw, P. K., Yeh, J. W., & Zhang, Y., High-entropy alloys: Fundamentals and applications. High-Entropy Alloys: Fundamentals and Applications., 2016.
[12] Gaskell, D. R., Introduction to the thermodynamics of materials (3rd ed.)., 1995
[13] grain and particle analysis with line intersection method - File Exchange - MATLAB Central. (n.d.)., from https://www.mathworks.com/matlabcentral/fileexchange/35203-grain-and-particle-analysis-with-line-intersection-method, July 7, 2020.
[14] Groeber, M. A., & Jackson, M. A., DREAM.3D: A Digital Representation Environment for the Analysis of Microstructure in 3D. Integrating Materials and Manufacturing Innovation, 3., 2014.
[15] He, Q., & Yang, Y., On lattice distortion in high entropy alloys. Frontiers in Materials, 5(July), 1–8., 2018.
[16] Hielscher, R., & Schaeben, H., A novel pole figure inversion method: Specification of the MTEX algorithm. Journal of Applied Crystallography, 41(6), 1024–1037., 2008.
[17] Hill, R., & Rice, J. R., Constitutive analysis of elastic-plastic crystals at arbitrary strain. Journal of the Mechanics and Physics of Solids, 20(6), 401–413., 1972.
[18] Huang, P. K., Yeh, J. W., Shun, T.-T., &Chen, S.-K. Multi-Principal-Element Alloys with Improved Oxidation and Wear Resistance for Thermal Spray Coating. Advanced Engineering Materials, 6(12), 74–78., 2004.
[19] Huang, Y., a user-material subroutine incorporating single crystal plasticity in the Abaqus finite element program a user-material subroutine incorporating single crystal plasticity in the Abaqus finite element program., 1991.
[20] Lee, E. H., Elastic-plastic deformation at finite strains. Journal of Applied Mechanics, Transactions ASME, 36(1), 1–6., 1964.
[21] Li, S., VanHoutte, P., & Kalidindi, S. R., A quantitative evaluation of the deformation texture predictions for aluminium alloys from crystal plasticity finite element method. Modelling and Simulation in Materials Science and Engineering, 12(5), 845–870., 2004.
[22] Liao, Y. C., Li, T. H., Tsai, P. H., Jang, J. S. C., Hsieh, K. C., Chen, C. Y., Huang, J. C., Wu, H. J., Lo, Y. C., Huang, C. W., Tsao, I. Y., Designing novel lightweight, high-strength and high-plasticity Tix(AlCrNb)100-x medium-entropy alloys. Intermetallics, 117, November 2019.
[23] Ling, X., Horstemeyer, M. F., & Potirniche, G. P., On the numerical implementation of 3D rate-dependent single crystal plasticity formulations. International Journal for Numerical Methods in Engineering, 63(4), 548–568., 2005.
[24] Macdonald, B. E., Fu, Z., Zheng, B., Chen, W., Lin, Y., Chen, F, Zhang, L., Ivanisenko, J., Zhou, Y., ,Hahn, H., Lavernia, E. J., Recent Progress in High Entropy Alloy Research. Jom (Vol. 69)., 2017.
[25] Marin, E. B. On the formulation of a crystal plasticity model., 1–62., 2006.
[26] Mechanics, A., Latent hardening in single crystals - I. Theory and experiments., Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 435., 1–19., 1991.
[27] Miracle, D. B., Miller, J. D., Senkov, O. N., Woodward, C., Uchic, M. D., & Tiley, J. Exploration and development of high entropy alloys for structural applications. Entropy, 16(1), 494–525., 2014.
[28] Peirce, D., Asaro, R. J., & Needleman, A., An analysis of nonuniform and localized deformation in ductile single crystals. Acta Metallurgica, 30(6), 1087–1119., 1982.
[29] R. E. Smallman., Modern Physical Metallurgy (Fourth)., 1962.
[30] Ranganathan, S., Alloyed pleasures: Multimetallic cocktails. CURRENT SCIENCE -BANGALORE-, 85, 1404–1406., 2003.
[31] Richard A. Swalin., Thermodynamics of solids (2nd ed.)., 1972.
[32] Roters, F., Eisenlohr, P., Hantcherli, L., Tjahjanto, D. D., Bieler, T. R., & Raabe, D., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications. Acta Materialia, 58(4), 1152–1211., 2010.
[33] Samaei, A. T., Mirsayar, M. M., & Aliha, M. R. M., The microstructure and mechanical behavior of modern high temperature alloys. Engineering Solid Mechanics, 3(1), 1–20. , 2015.
[34] Tsai, M. H., & Yeh, J. W., High-entropy alloys: A critical review. Materials Research Letters, 2(3), 107–123., 2014.
[35] Wu, W., Owino, J., Al-Ostaz, A., & Cai, L., Applying Periodic Boundary Conditions in Finite Element Analysis, SIMULIA Community Conference, 1–13., 2014.
[36] Yeh, J. W., Alloy design strategies and future trends in high-entropy alloys. JOM, 65(12), 1759–1771., 2013.
[37] Yeh, J. W., Physical Metallurgy of High-Entropy Alloys. JOM. Minerals, Metals and Materials Society., October 23, 2015.
[38] Yeh, J. W., Chen, S. K., Lin, S. J., Gan, J. Y., Chin, T. S., Shun, T. T., Tsau, C. H., Chang, S. Y., Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes. Advanced Engineering Materials, 6(5), 299–303., 2004.
[39] Zhang, Y., Zuo, T. T., Tang, Z., Gao, M. C., Dahmen, K. A., Liaw, P. K., & Lu, Z. P. Microstructures and properties of high-entropy alloys. Progress in Materials Science, 61, 1–93., September 2013