Simulation on Deformation Damage and Strain Rate Effect of Nb3Sn Composite Superconductors under Cycling Load at Extreme Low Temperature
-
摘要: Nb3Sn超导体在循环载荷下的变形损伤行为研究对揭示超导体临界性能不可逆退化背后的力学机制具有重要意义。采用分子动力学模拟方法研究了极低温条件下单晶和多晶Nb3Sn/Nb复合材料在循环载荷下的变形损伤行为，同时分析了应变率对Nb3Sn/Nb复合材料变形损伤和断裂行为的影响。结果表明：单晶Nb3Sn/Nb复合材料在循环载荷作用后，Nb3Sn层出现滑移，当滑移带交错处的局部应力大于材料强度时，在滑移带交错处微裂纹萌生，致使复合材料中Nb3Sn层断裂失效；而多晶Nb3Sn/Nb复合材料则由于晶界处应力在循环载荷下得不到松弛，当应力峰值超过晶界强度时，在晶界处萌生微裂纹，导致复合材料中Nb3Sn层发生沿晶断裂。Nb3Sn/Nb复合材料在不同应变率下表现出不同的断裂方式。随着应变率的增加，单晶Nb3Sn层中的滑移带数量增加，导致单晶Nb3Sn/Nb复合材料的韧性增强。而多晶Nb3Sn/Nb复合材料中，晶界对材料强度的影响随着应变率的增加而降低，高应变率下，复合材料在Nb3Sn层局部断裂后具有较大的剩余强度。研究结果将有助于理解Nb3Sn/Nb复合材料在循环载荷下的损伤演化过程，为材料的性能优化设计提供一定的理论指导。
-
关键词:
- Nb3Sn/Nb复合材料 /
- 分子动力学模拟 /
- 循环载荷 /
- 变形损伤 /
- 应变率效应
Abstract: The study on damage and fracture of superconducting Nb3Sn under cyclic loading is an indispensable part of understanding the origin of the irreversible strain limit in Nb3Sn. This paper uses molecular dynamics simulation to investigate the fracture and deformation damage behavior of polycrystalline and single crystal Nb3Sn/Nb composite materials under cyclic loading at extremely low temperatures. The effects of strain rate on crack initiation and growth were carefully analyzed in both polycrystalline and single crystal Nb3Sn/Nb composite materials. The results indicate that slip occurs in single crystal Nb3Sn/Nb composite materials after cyclic loading. When the local stress at the slip band intersection exceeds the material strength, microcracks initiate at the slip band intersection, leading to fracture failure of the composite material. In contrast, the failure of polycrystalline Nb3Sn/Nb composite materials is due to the inability of stress at grain boundaries to relax under cyclic loading, which leads to the initiation of microcracks at the grain boundaries and intergranular fracture of the composite material. The analysis of the different damage, fracture, and failure mechanisms of polycrystalline and single crystal Nb3Sn/Nb composite materials at different strain rates shows that the fracture is brittle at low strain rates. As the strain rate rises, the number of slip bands in the single crystal Nb3Sn layer increases, enhancing the toughness of the single crystal Nb3Sn/Nb composite material. Conversely, the influence of grain boundaries on material strength decreases in polycrystalline materials as the strain rate increases. Moreover, polycrystalline Nb3Sn/Nb composite materials exhibit significant residual strength after local fracture of Nb3Sn at high strain rates. The research results will contribute to a better understanding of the damage evolution process of Nb3Sn/Nb composite materials under cyclic loading and offer theoretical guidance for optimizing material performance. -
图 3 单晶Nb3Sn/Nb复合材料的拉伸应力-应变曲线和位错演变
Figure 3. Tensile stress-strain curves and dislocation evolution maps for single crystal Nb3Sn/Nb composite materials
图 4 4.2 K的低温环境中不同应变增幅的循环载荷作用下单晶Nb3Sn/Nb复合材料的应力-应变曲线
Figure 4. Stress-strain curves of single crystal Nb3Sn/Nb composite material under cyclic loading at different strain amplitudes in 4.2 K
图 5 循环过程中单晶和多晶Nb3Sn/Nb复合材料卸载曲线对应的模量变化
Figure 5. Modulus variation in the unloading curves ofsingle crystal and polycrystalline Nb3Sn/Nb compositematerials during the cyclic loading process
图 6 4.2 K低温环境中循环载荷作用下单晶Nb3Sn/Nb复合材料的应力-应变曲线
Figure 6. Stress-strain curves of single crystal Nb3Sn/Nb composite materials under cyclic loading at 4.2 K
图 7 单次循环中单晶Nb3Sn/Nb、Nb3Sn和Nb基体的加载与卸载曲线
Figure 7. Loading and unloading curves of single crystal Nb3Sn/Nb, Nb3Sn layer and Nb matrix during a single cycle
图 8 4.2 K的低温环境中单晶Nb3Sn/Nb复合材料处于应变峰值时的损伤演化
Figure 8. Damage evolution of single crystal Nb3Sn/Nb at the peak strain under 4.2 K
图 9 单晶Nb3Sn/Nb复合材料循环过程中原子应变云图
Figure 9. Atomic strain distribution during the cyclic process of single crystal Nb3Sn/Nb
图 10 4.2 K低温环境中单晶Nb3Sn/Nb复合材料沿x轴方向拉伸时的原子应力云图
Figure 10. Atomic stress distribution of single crystal Nb3Sn/Nb under tensile loading along the x-axis at 4.2 K
图 11 4.2 K低温环境中单晶Nb3Sn/Nb材料中Nb基体部分位错密度随时间的变化
Figure 11. Variations of dislocation density in the Nb matrix of single crystal Nb3Sn/Nb material over time in a low-temperature environment of 4.2 K
图 12 循环过程中Nb基体中的位错类型
Figure 12. Types of dislocations in Nb matrix during cycling process
图 14 Nb基体中通过位错反应生成全位错
Figure 14. Generation of full dislocations through dislocation reactions in the Nb matrix
图 15 4.2 K低温环境中循环载荷下多晶Nb3Sn/Nb复合材料的应力-应变曲线
Figure 15. Stress-strain curves of polycrystalline Nb3Sn/Nb composite material under cyclic loading at 4.2 K
图 16 单次循环中多晶Nb3Sn/Nb、Nb3Sn和Nb基体的加载与卸载示意图
Figure 16. Loading and unloading curves of polycrystalline Nb3Sn/Nb, Nb3Sn layer and Nb matrix during a single cycle
图 17 4.2 K低温环境中多晶Nb3Sn/Nb复合材料在循环加载过程中的原子应变云图
Figure 17. Atomic strain distribution during the cyclic process of polycrystalline Nb3Sn/Nb during cyclic loading at a low temperature of 4.2 K
图 18 循环过程中多晶Nb3Sn层中晶界的微观原子演化
Figure 18. Microscopic atomic evolution of grain boundaries in polycrystalline Nb3Sn layer during the cyclic process
图 19 卸载过程中多晶Nb3Sn层晶界处的微裂纹扩展行为
Figure 19. Microcrack propagation behavior at grain boundaries of polycrystalline Nb3Sn layers during unloading process
图 20 4.2 K低温环境中不同应变率下单晶Nb3Sn/Nb复合材料的循环加载应力-应变曲线
Figure 20. Cyclic loading stress-strain curves of single crystal Nb3Sn/Nb under different strain rates at 4.2 K
图 21 4.2 K低温环境中不同应变率下单晶Nb3Sn/Nb复合材料极限强度下的应变
Figure 21. Strain at the ultimate strength of single crystal Nb3Sn/Nb composite materialat different strain rates at 4.2 K
图 22 4.2 K低温环境中应变峰值为0.150时不同应变率下模拟卸载过程的应力-应变曲线对比
Figure 22. Comparison of simulated stress-strain curves during the tension-unloading at different stress rates, a temperature of 4.2 K and a peak strain of 0.150
图 23 不同应变率下应变峰值为0.150时单晶Nb3Sn中原子结构演化与Nb基体中的位错分布
Figure 23. Evolution of atomic structure in single crystal Nb3Sn and distribution of dislocations in Nb matrix at different strain rates at peak strain of 0.150
图 24 不同应变率下达到极限强度时单晶Nb3Sn/Nb复合材料中Nb3Sn层的微结构
Figure 24. Microstructure of the Nb3Sn layer in single crystal Nb3Sn/Nb composite material varies with different strain rates at the ultimate strength
图 25 4.2 K低温环境中不同应变率下多晶Nb3Sn/Nb复合材料的循环加载应力-应变曲线
Figure 25. Cyclic loading stress-strain curves of polycrystalline Nb3Sn/Nb composite materials under different strain rates at 4.2 K
图 26 4.2 K的低温环境中不同应变率下多晶Nb3Sn/Nb复合材料在极限强度下的应变
Figure 26. Strain at the ultimate strength of polycrystalline Nb3Sn/Nb composite materialvaries with different strain rates at 4.2 K
图 27 不同应变率下多晶Nb3Sn/Nb复合材料在极限强度时Nb3Sn层的应变云图和微观原子结构
Figure 27. Atomic strain distribution and structure of Nb3Sn layer in polycrystalline Nb3Sn/Nb under different strain rates when ultimate strength
表 1 Nb3Sn单晶的弹性常数和晶格常数
Table 1. Elastic constant and lattice constant of Nb3Sn single crystal
Method C11/GPa C12/GPa C44/GPa Lattice constants/Å MD simulations (300 K) 284.11 95.84 53.76 5.21 Experimental results (300 K) 253.85 112.44 39.62 5.29 MD simulations (4.2 K) 333.18 127.09 53.71 5.17 Ab initio simulations (0 K) 284.83 107.73 67.07 5.32 
下载: 导出CSV
-
[1] ZHANG R, GAO P F, WANG X Z. Strain dependence of critical superconducting properties of Nb3Sn with different intrinsic strains based on a semi-phenomenological approach [J]. Cryogenics, 2017, 86: 30–37. doi: 10.1016/j.cryogenics.2017.07.007 [2] DEVRED A, BACKBIER I, BESSETTE D, et al. Status of ITER conductor development and production [J]. IEEE Transactions on Applied Superconductivity, 2012, 22(3): 4804909. doi: 10.1109/TASC.2012.2182980 [3] KIYOSHI T, MATSUMOTO S, KOSUGE M, et al. Superconducting inserts in high-field solenoids [J]. IEEE Transactions on Applied Superconductivity, 2002, 12(1): 470–475. doi: 10.1109/TASC.2002.1018445 [4] DEVRED A, BACKBIER I, BESSETTE D, et al. Challenges and status of ITER conductor production [J]. Superconductor Science and Technology, 2014, 27(4): 044001. doi: 10.1088/0953-2048/27/4/044001 [5] BOTTURA L, DE RIJK G, ROSSI L, et al. Advanced accelerator magnets for upgrading the LHC [J]. IEEE Transactions on Applied Superconductivity, 2012, 22(3): 4002008. doi: 10.1109/TASC.2012.2186109 [6] EISENSTATT L R, WRIGHT R N. Plastic deformation in polycrystalline Nb3Sn [J]. Metallurgical Transactions A, 1980, 11(7): 1131–1138. doi: 10.1007/BF02668137 [7] CLARK J B, WRIGHT R N. Laboratory extrusion of Nb3Sn [J]. Metallurgical Transactions A, 1983, 14(11): 2295–2299. doi: 10.1007/BF02663304 [8] OCHIAI S, OSAMURA K. Influence of cyclic loading at room temperature on the critical current at 4.2 K of Nb3Sn superconducting composite wire [J]. Cryogenics, 1992, 32(6): 584–590. doi: 10.1016/0011-2275(92)90045-C [9] WESSEL W A J, NIJHUIS A, ILYIN Y, et al. A novel “test arrangement for strain influence on strands” (TARSIS): mechanical and electrical testing of ITER Nb3Sn strands [J]. AIP Conference Proceedings, 2004, 711(1): 466–473. [10] NIJHUIS A, VAN DEN EIJNDEN N C, ILYIN Y, et al. Impact of spatial periodic bending and load cycling on the critical current of a Nb3Sn strand [J]. Superconductor Science and Technology, 2005, 18(12): S273–S283. doi: 10.1088/0953-2048/18/12/009 [11] VAN DEN EIJNDEN N C, NIJHUIS A, ILYIN Y, et al. Axial tensile stress-strain characterization of ITER model coil type Nb3Sn strands in TARSIS [J]. Superconductor Science and Technology, 2005, 18(11): 1523–1532. doi: 10.1088/0953-2048/18/11/020 [12] NIJHUIS A, MIYOSHI Y, JEWELL M C, et al. Systematic study on filament fracture distribution in ITER Nb3Sn strands [J]. IEEE Transactions on Applied Superconductivity, 2009, 19(3): 2628–2632. doi: 10.1109/TASC.2009.2018082 [13] MITCHELL N. Analysis of the effect of Nb3Sn strand bending on CICC superconductor performance [J]. Cryogenics, 2002, 42(5): 311–325. doi: 10.1016/S0011-2275(02)00041-3 [14] SHETH M K, LEE P, MCRAE D M, et al. Procedures for evaluating filament cracking during fatigue testing of Nb3Sn strand [J]. AIP Conference Proceedings, 2012, 1435(1): 201–208. [15] SHEN F Z, ZHANG H C, HUANG C J, et al. Experimental study on strain sensitivity of internal-tin Nb3Sn superconducting strand based on non-destructive technology [J]. Physica C: Superconductivity and Its Applications, 2021, 584: 1353784. doi: 10.1016/j.physc.2020.1353784 [16] JIANG L, SU X Y, SHEN L Y, et al. Damage behavior of Nb3Sn/Cu superconducting strand at room temperature under asymmetric strain cycling [J]. Fusion Engineering and Design, 2021, 172: 112869. doi: 10.1016/j.fusengdes.2021.112869 [17] TABIN J, SKOCZEŃ B, BIELSKI J. Discontinuous plastic flow in superconducting multifilament composites [J]. International Journal of Solids and Structures, 2020, 202: 12–27. doi: 10.1016/j.ijsolstr.2020.05.033 [18] QIULI SUN E. Multi-scale nonlinear stress analysis of Nb3Sn superconducting accelerator magnets [J]. Superconductor Science and Technology, 2022, 35(4): 045019. doi: 10.1088/1361-6668/ac5a11 [19] MITCHELL N. Finite element simulations of elasto-plastic processes in Nb3Sn strands [J]. Cryogenics, 2005, 45(7): 501–515. doi: 10.1016/j.cryogenics.2005.06.003 [20] WANG X, LI Y X, GAO Y W. Mechanical behaviors of multi-filament twist superconducting strand under tensile and cyclic loading [J]. Cryogenics, 2016, 73: 14–24. doi: 10.1016/j.cryogenics.2015.11.002 [21] JIANG L, ZHANG X Y, ZHOU Y H. Nonlinear static and dynamic mechanical behaviors of Nb3Sn superconducting composite wire: experiment and analysis [J]. Acta Mechanica Sinica, 2023, 39(3): 122322. doi: 10.1007/s10409-022-22322-x [22] LEE J, POSEN S, MAO Z G, et al. Atomic-scale analyses of Nb3Sn on Nb prepared by vapor diffusion for superconducting radiofrequency cavity applications: a correlative study [J]. Superconductor Science and Technology, 2019, 32(2): 024001. doi: 10.1088/1361-6668/aaf268 [23] ZHANG Y, ASHCRAFT R, MENDELEV M I, et al. Experimental and molecular dynamics simulation study of structure of liquid and amorphous Ni62Nb38 alloy [J]. The Journal of Chemical Physics, 2016, 145(20): 204505. doi: 10.1063/1.4968212 [24] KO W S, KIM D H, KWON Y J, et al. Atomistic simulations of pure tin based on a new modified embedded-atom method interatomic potential [J]. Metals, 2018, 8(11): 900. doi: 10.3390/met8110900 [25] CHUDINOV V G, GOGOLIN V P, GOSHCHITSKII B N, et al. Simulation of collision cascades in intermetallic Nb3Sn compounds [J]. Physica Status Solidi (A), 1981, 67(1): 61–67. doi: 10.1002/pssa.2210670103 [26] LUTSKO J F. Stress and elastic constants in anisotropic solids: molecular dynamics techniques [J]. Journal of Applied Physics, 1988, 64(3): 1152–1154. doi: 10.1063/1.341877 [27] PENG Y X, KNIGHT C, BLOOD P, et al. Extending parallel scalability of LAMMPS and multiscale reactive molecular simulations [C]//Proceedings of the 1st Conference of the Extreme Science and Engineering Discovery Environment: Bridging from the eXtreme to the Campus and Beyond. Chicago: ACM, 2012: 37. [28] PAPADIMITRIOU I, UTTON C, TSAKIROPOULOS P. Ab initio investigation of the intermetallics in the Nb-Sn binary system [J]. Acta Materialia, 2015, 86: 23–33. doi: 10.1016/j.actamat.2014.12.017 [29] SUNDARESWARI M, RAMASUBRAMANIAN S, RAJAGOPALAN M. Elastic and thermodynamical properties of A15 Nb3X (X = Al, Ga, In, Sn and Sb) compounds-first principles DFT study [J]. Solid State Communications, 2010, 150(41/42): 2057–2060. [30] ZHANG R, GAO P F, WANG X Z, et al. First-principles study on elastic and superconducting properties of Nb3Sn and Nb3Al under hydrostatic pressure [J]. AIP Advances, 2015, 5(10): 107233. doi: 10.1063/1.4935099 [31] DE MARZI G, MORICI L, MUZZI L, et al. Strain sensitivity and superconducting properties of Nb3Sn from first principles calculations [J]. Journal of Physics: Condensed Matter, 2013, 25(13): 135702. doi: 10.1088/0953-8984/25/13/135702 [32] ESHELBY J D. Dynamical theory of crystal lattices: Max Born and Kun Huang: Oxford University Press, 1954, pp. xii+420. 50s. net. [J]. Journal of the Mechanics and Physics of Solids, 1955, 3(3): 231. [33] SCHEUERLEIN C, DI MICHIEL M, BUTA F, et al. Stress distribution and lattice distortions in Nb3Sn multifilament wires under uniaxial tensile loading at 4.2 K [J]. Superconductor Science and Technology, 2014, 27(4): 044021. doi: 10.1088/0953-2048/27/4/044021 [34] 时海芳, 任鑫. 材料力学性能 [M]. 2版. 北京: 北京大学出版社, 2015: 181–183.SHI H F, REN X. Mechanical properties of materials [M]. 2nd ed. Beijing: Peking University Press, 2015: 181–183. [35] LIANG L W, WANG Y J, CHEN Y, et al. Dislocation nucleation and evolution at the ferrite-cementite interface under cyclic loadings [J]. Acta Materialia, 2020, 186: 267–277. doi: 10.1016/j.actamat.2019.12.052 [36] ESSMANN U, MUGHRABI H. Annihilation of dislocations during tensile and cyclic deformation and limits of dislocation densities [J]. Philosophical Magazine A, 1979, 40(6): 731–756. doi: 10.1080/01418617908234871 [37] ZOTOV N, GRABOWSKI B. Molecular dynamics simulations of screw dislocation mobility in bcc Nb [J]. Modelling and Simulation in Materials Science and Engineering, 2021, 29(8): 085007. doi: 10.1088/1361-651X/ac2b02 [38] SPARKS G, MAAß R. Shapes and velocity relaxation of dislocation avalanches in Au and Nb microcrystals [J]. Acta Materialia, 2018, 152: 86–95. doi: 10.1016/j.actamat.2018.04.007 [39] PADILLA II H A, BOYCE B L. A review of fatigue behavior in nanocrystalline metals [J]. Experimental Mechanics, 2010, 50(1): 5–23. doi: 10.1007/s11340-009-9301-2 [40] KUMAR K S, SURESH S, CHISHOLM M F, et al. Deformation of electrodeposited nanocrystalline nickel [J]. Acta Materialia, 2003, 51(2): 387–405. doi: 10.1016/S1359-6454(02)00421-4 [41] OVID’KO I A, SHEINERMAN A G. Triple junction nanocracks in fatigued nanocrystalline materials [J]. Reviews on Advanced Materials Science, 2004, 7(1): 61–66. [42] OVID’KO I A, SHEINERMAN A G. Grain size effect on crack blunting in nanocrystalline materials [J]. Scripta Materialia, 2009, 60(8): 627–630. doi: 10.1016/j.scriptamat.2008.12.028 [43] SUENAGA M, JANSEN W. Chemical compositions at and near the grain boundaries in bronze-processed superconducting Nb3Sn [J]. Applied Physics Letters, 1983, 43(8): 791–793. doi: 10.1063/1.94457 [44] OCHIAI S, OSAMURA K, UEHARA T. Grain size and its relation to tensile strength of Nb3Sn compound in bronze-processed multi-filamentary superconducting materials [J]. Journal of Materials Science, 1987, 22(6): 2163–2168. doi: 10.1007/BF01132954 [45] OH S H, JEONG Y J, NA S H, et al. Atomic behavior of Ti in A15 Nb3Sn and its effects on diffusional growth of Nb3Sn layer [J]. Journal of Alloys and Compounds, 2023, 957: 170438. doi: 10.1016/j.jallcom.2023.170438 [46] OCHIAI S, OSAMURA K, MAEKAWA M. Comparison of mechanical and superconducting properties of titanium-added Nb3Sn composite wire with those of non-added ones [J]. Superconductor Science and Technology, 1991, 4(6): 262–269. doi: 10.1088/0953-2048/4/6/009 -
下载:
点击查看大图
计量
- 文章访问数: 46
- HTML全文浏览量: 16
- PDF下载量: 12
