A simplified model connecting lattice distortion with friction stress of Nb-based equiatomic high-entropy alloys

References

• Cantor B, Chang ITH, Knight P, et al. Microstructural development in equiatomic multicomponent alloys. Mater Sci Eng A. 2004;375:213–218. doi: 10.1016/j.msea.2003.10.257
   Web of Science ®Google Scholar
• Yeh JW, Chen SK, Lin SJ, et al. Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes. Adv Eng Mater. 2004;6(5):299–303. doi: 10.1002/adem.200300567
   Web of Science ®Google Scholar
• Senkov ON, Scott JM, Senkova SV, et al. Microstructure and room temperature properties of a high-entropy TaNbHfZrTi alloy. J Alloys Compd. 2011;509(20):6043–6048. doi: 10.1016/j.jallcom.2011.02.171
   Web of Science ®Google Scholar
• Ye YX, Liu CZ, Wang H, et al. Friction and wear behavior of a single-phase equiatomic TiZrHfNb high-entropy alloy studied using a nanoscratch technique. Acta Mater. 2018;147:78–89. doi: 10.1016/j.actamat.2018.01.014
   Web of Science ®Google Scholar
• Zhao YY, Chen HW, Lu ZP, et al. Thermal stability and coarsening of coherent particles in a precipitation-hardened (NiCoFeCr)94Ti2Al4 high-entropy alloy. Acta Mater. 2018;147:184–194. doi: 10.1016/j.actamat.2018.01.049
   Web of Science ®Google Scholar
• Miracle DB, Senkov ON. A critical review of high entropy alloys and related concepts. Acta Mater. 2017;122:448–511. doi: 10.1016/j.actamat.2016.08.081
   Web of Science ®Google Scholar
• Guo W, Dmowski W, Noh JY, et al. Local atomic structure of a high-entropy alloy: an X-ray and neutron scattering study. Metall Mater Trans A. 2013;44(5):1994–1997. doi: 10.1007/s11661-012-1474-0
   Google Scholar
• Owen LR, Pickering EJ, Playford HY, et al. An assessment of the lattice strain in the CrMnFeCoNi high-entropy alloy. Acta Mater. 2017;122:11–18. doi: 10.1016/j.actamat.2016.09.032
   Web of Science ®Google Scholar
• Tong Y, Jin K, Bei H, et al. Local lattice distortion in NiCoCr, FeCoNiCr and FeCoNiCrMn concentrated alloys investigated by synchrotron X-ray diffraction. Mater Des. 2018;155:1–7. doi: 10.1016/j.matdes.2018.05.056
   Web of Science ®Google Scholar
• Zou Y, Maiti S, Steurer W, et al. Size-dependent plasticity in an Nb25Mo25Ta25W25 refractory high-entropy alloy. Acta Mater. 2014;65:85–97. doi: 10.1016/j.actamat.2013.11.049
   Web of Science ®Google Scholar
• Zhang Y, Zhou YJ, Lin JP, et al. Solid-solution phase formation rules for multi-component alloys. Adv Eng Mater. 2008;10(6):534–538. doi: 10.1002/adem.200700240
   Web of Science ®Google Scholar
• Wang Z, Qiu W, Yang Y, et al. Atomic-size and lattice-distortion effects in newly developed high-entropy alloys with multiple principal elements. Intermetallics. 2015;64:63–69. doi: 10.1016/j.intermet.2015.04.014
   Web of Science ®Google Scholar
• Okamoto NL, Yuge K, Tanaka K, et al. Atomic displacement in the CrMnFeCoNi high-entropy alloy - a scaling factor to predict solid solution strengthening. AIP Adv. 2016;6(12):125008. doi: 10.1063/1.4971371
   Web of Science ®Google Scholar
• Zhao YY, Nieh TG. Correlation between lattice distortion and friction stress in Ni-based equiatomic alloys. Intermetallics. 2017;86:45–50. doi: 10.1016/j.intermet.2017.03.011
   Web of Science ®Google Scholar
• He J, Wang Q, Zhang H, et al. Dynamic deformation behavior of a face-centered cubic FeCoNiCrMn high-entropy alloy. Sci Bull. 2018;63(6):362–368. doi: 10.1016/j.scib.2018.01.022
   Web of Science ®Google Scholar
• Lei ZF, Liu XJ, Wu Y, et al. Enhanced strength and ductility in a high-entropy alloy via ordered oxygen complexes. Nature. 2018;563:546–550. doi: 10.1038/s41586-018-0685-y
   PubMed Web of Science ®Google Scholar
• Wu YD, Cai YH, Wang T, et al. A refractory Hf25Nb25Ti25Zr25 high-entropy alloy with excellent structural stability and tensile properties. Mater Lett. 2014;130:277–280. doi: 10.1016/j.matlet.2014.05.134
   Web of Science ®Google Scholar
• Schuh B, Völker B, Todt J, et al. Thermodynamic instability of a nanocrystalline, single-phase TiZrNbHfTa alloy and its impact on the mechanical properties. Acta Mater. 2018;142:201–212. doi: 10.1016/j.actamat.2017.09.035
   Web of Science ®Google Scholar
• Senkov ON, Semiatin SL. Microstructure and properties of a refractory high-entropy alloy after cold working. J Alloys Compd. 2015;649:1110–1123. doi: 10.1016/j.jallcom.2015.07.209
   Web of Science ®Google Scholar
• Senkov ON, Pilchak AL, Semiatin SL. Effect of cold deformation and annealing on the microstructure and tensile properties of a HfNbTaTiZr refractory high entropy alloy. Metall Mater Trans A. 2018;49(7):2876–2892. doi: 10.1007/s11661-018-4646-8
   Google Scholar
• Juan CC, Tsai MH, Tsai CW, et al. Simultaneously increasing the strength and ductility of a refractory high-entropy alloy via grain refining. Mater Lett. 2016;184:200–203. doi: 10.1016/j.matlet.2016.08.060
   Web of Science ®Google Scholar
• Nelson JB, Riley DP. An experimental investigation of extrapolation methods in the derivation of accurate unit-cell dimensions of crystals. Proc Phys Soc. 1945;57(3):160–177. doi: 10.1088/0959-5309/57/3/302
   Google Scholar
• ASM Handbook Committee. ASM handbook. Vol. 2, Properties and selection: nonferrous alloys and special-purpose materials. Materials Park (OH): ASM International; 1990.
   Google Scholar
• Wu Z. Temperature and alloying effects on the mechanical properties of equiatomic fcc solid solution alloys [dissertation]. Knoxville (TN): University of Tennessee; 2014.
   Google Scholar
• Song H, Tian F, Hu QM, et al. Local lattice distortion in high-entropy alloys. Phy Rev Mater. 2017;1(2):023404. doi: 10.1103/PhysRevMaterials.1.023404
   Web of Science ®Google Scholar
• Bailey JE, Hirsch PB. The dislocation distribution, flow stress, and stored energy in cold-worked polycrystalline silver. Philos Mag. 1960;5(53):485–497. doi: 10.1080/14786436008238300
   Web of Science ®Google Scholar
• Hall EO. The deformation and ageing of mild steel: III discussion of results. Proc Phys Soc Sect B. 1951;64(9):747–753. doi: 10.1088/0370-1301/64/9/303
   Google Scholar
• Courtney TH. Mechanical behavior of materials. Long Grove (IL): Waveland Press; 2000.
   Google Scholar
• Ledbetter HM. Ratio of the shear and Young’s moduli for polycrystalline metallic elements. Mater Sci Eng. 1977;27(2):133–135. doi: 10.1016/0025-5416(77)90165-3
   Google Scholar
• Conrad H, Feuerstein S, Rice L. Effects of grain size on the dislocation density and flow stress of niobium. Mater Sci Eng. 1967;2(3):157–168. doi: 10.1016/0025-5416(67)90032-8
   Google Scholar
• Cordero ZC, Knight BE, Schuh CA. Six decades of the Hall-Petch effect - a survey of grain-size strengthening studies on pure metals. Int Mater Rev. 2016;61(8):495–512. doi: 10.1080/09506608.2016.1191808
   Web of Science ®Google Scholar
• Laurent-Brocq M, Akhatova A, Perrière L, et al. Insights into the phase diagram of the CrMnFeCoNi high entropy alloy. Acta Mater. 2015;88:355–365. doi: 10.1016/j.actamat.2015.01.068
   Web of Science ®Google Scholar
• Lee C, Song G, Gao MC, et al. Lattice distortion in a strong and ductile refractory high-entropy alloy. Acta Mater. 2018;160:158–172. doi: 10.1016/j.actamat.2018.08.053
   Web of Science ®Google Scholar
• Greer JR, De Hosson JTM. Plasticity in small-sized metallic systems: intrinsic versus extrinsic size effect. Prog Mater Sci. 2011;56(6):654–724. doi: 10.1016/j.pmatsci.2011.01.005
   Web of Science ®Google Scholar
• Dieter GE. Mechanical metallurgy. New York: McGraw-Hill; 1961.
   Google Scholar
• Wu Z, Bei H, Pharr GM, et al. Temperature dependence of the mechanical properties of equiatomic solid solution alloys with face-centered cubic crystal structures. Acta Mater. 2014;81:428–441. doi: 10.1016/j.actamat.2014.08.026
   Web of Science ®Google Scholar
• Salishchev G, Tikhonovsky M, Shaysultanov D, et al. Effect of Mn and V on structure and mechanical properties of high-entropy alloys based on CoCrFeNi system. J Alloys Compd. 2014;591:11–21. doi: 10.1016/j.jallcom.2013.12.210
   Web of Science ®Google Scholar
• He J, Wang H, Huang H, et al. A precipitation-hardened high-entropy alloy with outstanding tensile properties. Acta Mater. 2016;102:187–196. doi: 10.1016/j.actamat.2015.08.076
   Web of Science ®Google Scholar
• Fleischer RL. Substitutional solution hardening. Acta Metall. 1963;11(3):203–209. doi: 10.1016/0001-6160(63)90213-X
   Google Scholar
• Varvenne C, Luque A, Curtin WA. Theory of strengthening in fcc high entropy alloys. Acta Mater. 2016;118:164–176. doi: 10.1016/j.actamat.2016.07.040
   Web of Science ®Google Scholar
• Wu Z, Gao Y, Bei H. Single crystal plastic behavior of a single-phase, face-center-cubic-structured, equiatomic FeNiCrCo alloy. Scr Mater. 2015;109:108–112. doi: 10.1016/j.scriptamat.2015.07.031
   Web of Science ®Google Scholar
• Patriarca L, Ojha A, Sehitoglu H, et al. Slip nucleation in single crystal FeNiCoCrMn high entropy alloy. Scr Mater. 2016;112:54–57. doi: 10.1016/j.scriptamat.2015.09.009
   Web of Science ®Google Scholar
• Dao M, Asaro RJ. Localized deformation modes and non-Schmid effects in crystalline solids. Part I. Critical conditions of localization. Mech Mater. 1996;23(2):71–102. doi: 10.1016/0167-6636(96)00012-9
   Web of Science ®Google Scholar
• Patra A, Zhu T, McDowell DL. Constitutive equations for modeling non-Schmid effects in single crystal bcc-Fe at low and ambient temperatures. Int J Plast. 2014;59:1–14. doi: 10.1016/j.ijplas.2014.03.016
   Web of Science ®Google Scholar
• Gröger R, Bailey A, Vitek V. Multiscale modeling of plastic deformation of molybdenum and tungsten: I. Atomistic studies of the core structure and glide of 1/2 <1 1 1> screw dislocations at 0 K. Acta Mater. 2008;56(19):5401–5411. doi: 10.1016/j.actamat.2008.07.018
   Web of Science ®Google Scholar
• Nabarro FRN. Dislocations in a simple cubic lattice. Proc Phys Soc. 1947;59(2):256–272. doi: 10.1088/0959-5309/59/2/309
   Google Scholar
• Yang M, Yan D, Yuan F, et al. Dynamically reinforced heterogeneous grain structure prolongs ductility in a medium-entropy alloy with gigapascal yield strength. PNAS. 2018;115(28):7224–7229. doi: 10.1073/pnas.1807817115
   PubMed Web of Science ®Google Scholar
• Sohn SS, da Silva A K, Ikeda Y, et al. Ultrastrong medium-entropy single-phase alloys designed via severe lattice distortion. Adv Mater. 2019;31(8):1807142. doi: 10.1002/adma.201807142
   Web of Science ®Google Scholar