Analysis of the Strong Plastic Evolution of TiVNbMo High Solid Solution Alloy Based on Grey System Theory

doi:10.3901/JME.2024.18.173

Abstract

Abstract: According to the maximum entropy principle, a series of TiVNbMo alloys were prepared based on the design under the valence electron concentration (VEC) constraint. After homogenization at 1 200 ℃/24 h, the alloys showed a microstructure of BCC single solid solution phase with uniform composition. The relationships of yield strength and ductility, respectively, to the mean atomic mean radius r^*, VEC, electron bonding order (Bo), d electron transfer energy Md, atomic mismatch δ and shear modulus G were analyzed based on the correlation method and the GM(1, N) model of the grey system theory, and the yield strength of the alloys was well predicted based on the physical parameters. For a comparison, the tensile strength of the alloys was also calculated using the solid solution strengthening model. The results showed that the correlation between the yield strength and the physical parameters is ordered by G>δ>VEC>Bo>r^*>Md; the correlation between the ductility and the physical parameters is ordered by Md>r^*>Bo>VEC>δ>G. The shear modulus G and the atomic mismatch δ are the physical parameters that have the greatest influence on the strength and ductility. By selecting the physical parameters G, δ, VEC and Bo which have the higher correlation order, the yield strength predicted based on the GM(1, 5) model has a smaller error respect to the experimental results and is more convenient to be used than the conventional solid solution strengthening model.

Key words: TiVNbMo high solid-solution alloys, GM(1,N) model of grey system theory, physical parameters, grey correlation

CLC Number:

TG146

LI Zhou, XU Zaidong, WU Baolin, FU Xiaoyun, WAN Gang, ZHANG Lu. Analysis of the Strong Plastic Evolution of TiVNbMo High Solid Solution Alloy Based on Grey System Theory[J]. Journal of Mechanical Engineering, 2024, 60(18): 173-182.

References

[1] 王姝予，宋世杰，陆晓翀，等. CrMnFeCoNi高熵合金拉伸断裂的晶体塑性有限元模拟[J]. 机械工程学报，2021，57(22)：43-51. WANG Shuyu，SONG Shijie，LU Xiaochong，et al. Crystal plastic finite element simulation of tensile fracture of CrMnFeCoNi high entropy alloy[J]. Journal of Mechanical Engineering，2021，57(22)：43-51.
[2] MIRACLE D B，SENKOV O N. A critical review of high entropy alloys and related concepts[J]. Acta Mater. 2017，122：448-511.
[3] SENKOV O N，MIRACLE D B，CHAPUT K J，et al. Development and exploration of refractory high entropy alloys - a review[J]. Journal of Materials Research，2018：1-37.
[4] DIAO H Y，FENG R.，DAHMEN K A，et al. Fundamental deformation behavior in high-entropy alloys：An overview[J]. Current Opinion in Solid State & Materials Science，2017，21(5)：252-266.
[5] FAZAKAS E，ZADOROZHNYY V，VARGA L K，et al. Experimental and theoretical study of Ti20Zr20Hf20Nb20X20(X=V or Cr) refractory high-entropy alloys[J]. International Journal of Refractory Metals & Hard Materials，2014(47) 131-138.
[6] SENKOV O N，WILKS G B，SCOTT J M，et al. Mechanical properties of Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys[J]. Intermetallics，2011，19(5)：698-706.
[7] ZHANG Y，ZHOU Y J，LIN J P，et al．Solid-solution phase formation rules for multi-component alloys[J]. Advanced Engineering Materials，2008，10(6)：534-538.
[8] RAO S I，WOODWARD C，AKDIM B，et al. Theory of solid solution strengthening of BCC chemically complex alloys[J]. Acta Materialia，2021，209(C3)：116758.
[9] STEPANOV D N，SHAYSULTANOV G A，TIKHONOVSKY M A，et al. Tensile properties of the Cr-Fe-Ni-Mn non-equiatomic multicomponent alloys with different Cr contents[J]. Materials & Design，2015，87：60-65.
[10] CHEN Y，XU Z，WANG M，et al. A single-phase V0.5Nb0.5ZrTi refractory high-entropy alloy with outstanding tensile properties[J]. Materials Science and Engineering A，2020，792：139774.
[11] SHEIKH S，SHAFEIE S，HU Q，et al. Alloy design for intrinsically ductile refractory high-entropy alloys[J]. J. Appl. Phys.，2016，120(16)：164902.
[12] WANG Jie，BAI Shuxin，TANG Yu，et al. Effect of the valence electron concentration on the yield strength of Ti-Zr-Nb-V high-entropy alloys[J]. Journal of Alloys and Compounds，2021，868：159190.
[13] 张济山，崔华. d电子合金理论及其在合金设计中的应用[J]. 材料科学与工程，1993(10)：1-10. ZHANG Jishan，CUI Hua. The d-electron alloy theory and its application in alloy design[J]. Materials Science and Engineering，1993(10)：1-10.
[14] 邓聚龙. 灰色系统理论教程[M]. 上海：华中理工大学出版社，1990. DENG Julong. Grey system theory tutorial[M]. Shanghai：Huazhong University of Science and Technology Press，1990.
[15] 刘思峰. 灰色系统理论的产生与发展[J]. 南京航空航天大学学报，2004(2)：131-136. LU Sifeng. The emergence and development of grey system theory[J]. Journal of Nanjing University of Aeronautics and Astronautics，2004(2)：131-136.
[16] 陈吉平，丁智平，曾军，等. 基于灰色理论镍基单晶合金多轴非比例加载低周疲劳研究[J]. 机械工程学报，2014，50(24)：66-72 CHEN Jiping，DING Zhiping，ZENG Jun，et al. Study on low cycle fatigue of nickel base single crystal alloy under multi-axial non-proportional loading based on grey theory[J]. Journal of Mechanical Engineering，2014，50(24)：66-77.
[17] 詹棠森，汪子婷，汤可宗，等. 改进GM(1，N)模型全局优化算法及应用[J]. 数理统计与管理，2021，40(5)：851-858. ZHAN Tangsen，WANG Ziting，TANG Kezong，et al. Improved GM(1，N) model global optimization algorithm and its application[J]. Mathematical Statistics and Management，2021，40(5)：851-858.
[18] 沈艳，余冬华，韩凯歌. 基于自相关的GM(1，1)与GM(1，N)联合模型优化及应用[J]. 应用科技，2014，41(6)：62-66. SHEN Yan，YU Donghua，HAN Kaige. Optimization and application of GM(1，1) and GM(1，N) joint model based on autocorrelation[J]. Applied Technology，2014，41(6)：62-66.
[19] 罗智辉，张新明，叶凌英. 时效1420铝锂合金第二相粒子灰色关联分析[J]. 兵器材料科学与工程，2009(2)：15-17. LUO Zhihui，ZHANG Xinming，YE Lingying. Grey correlation analysis of second phase particles in aged 1420 Al-Li alloy [J]. Weapon material Science and Engineering，2009(2)：15-17.
[20] 陈部湘，张新明，邓运来. Mg-9Gd-4Y-0.6Zr合金过时效硬度变化的灰色预测[J]. 矿冶工程，2008，28(1)：81-83. CHEN Buxiang，ZHANG Xinming，DENG Yunlai. Grey prediction of hardness change of Mg-9Gd-4Y-0.6Zr alloy after aging[J]. Metal Materials and Metallurgy Engineering，2008，28(1)：81-83.
[21] SENKOV O N，SCOTT J M，SENKOVA S V，et al. Microstructure and room temperature properties of a high-entropy TaNbHfZrTi alloy[J]. Journal of Alloys and Compounds，2011，509(20)：6043-6048.
[22] LUGOVY M，SLYUNYAYEV V，BRODNIKOVSKYY M. Solid solution strengthening in multicomponent fcc and bcc alloys：Analytical approach[J]. Progress in Natural Science，2021，509(20)：6043-6048.
[23] SALISHCHEV G A，TIKHONOVSKY M A，SHAYSULTANOV D G，et al. Effect of Mn and V on structure and mechanical properties of high-entropy alloys based on CoCrFeNi system[J]. Journal of Alloys & Compounds，2014，591：11-21.
[24] DEZERALD L，PROVILLE L，VENTELON L，et al. First-principles prediction of kink-pair activation enthalpy on screw dislocations in bcc transition metals：V，Nb，Ta，Mo，W，and Fe[J]. Physical Review B，2015，91(9)：268-272.
[25] SMALLMAN R E，NGAN A. Introduction to dislocations[J]. Modern Physical Metallurgy(Eighth Edition)，2014，13(2)：121-158.
[26] LIAO M，LIU Y，CUI P，et al. Modeling of alloying effect on elastic properties in BCC Nb-Ti-V-Zr solid solution：From unary to quaternary[J]. Computational Materials Science，2019，172：109289.
[27] YANG X，ZHANG Y. Prediction of high-entropy stabilized solid-solution in multi-component alloys[J]. Materials Chemistry & Physics，2012，132(2-3)：233-238.
[28] 李武会，任凤章，马战红，等. 电子理论在材料科学中的应用[J]. 中国有色金属学报，2008，18(3)：494-504. LI Wuhui，REN Fengzhang，MA Zhanhong，et al. Application of electron theory to materials science[J]. Chinese Journal of Nonferrous Metals，2008，18(3)：494-504.
[29] NGUYEN V T，QIAN M，SHI Z，et al. Compositional design of strong and ductile (tensile) Ti-Zr-Nb-Ta medium entropy alloys (MEAs) using the atomic mismatch approach[J]. Materials Science & Engineering A，2019(742)：762-772.
[30] MARESCA F，CURTIN W A . Theory of screw dislocation strengthening in random BCC alloys from dilute to “High-Entropy” alloys[J]. Acta Materialia，2020，182：144-162.
[31] AKDIM B，WOODWARD C，RAO S，et al. Predicting core structure variations and spontaneous partial kink formation for 1/2<111> screw dislocations in three BCC NbTiZr alloys[J]. Scripta Materialia，2021(199)：113834.