Phase-field simulation of microstructural dynamics in NiTi shape memory alloys and their intrinsic strain rate sensitivities
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摘要: 基于Ginzburg-Landau动力学控制方程建立了NiTi形状记忆合金非等温相场模型，实现了对NiTi合金内应力诱导马氏体相变的数值模拟。同时将晶界能密度引入系统局部自由能密度，从而考虑多晶系统中晶界的重要作用。数值计算了单晶和多晶NiTi形状记忆合金在单轴机械载荷作用下微结构的动态演化过程和宏观力学行为，并重点研究了晶粒尺寸为60 nm的NiTi纳米多晶在低应变率下（0.0005～15 s−1）力学行为的本征应变率敏感性。研究结果表明，单晶NiTi合金系统高温拉伸-卸载过程中马氏体相变均匀发生，未形成奥氏体-马氏体界面。而纳米多晶系统在加载阶段出现了马氏体带的形成-扩展现象，在卸载阶段出现了马氏体带的收缩-消失现象。相同外载作用过程中，NiTi单晶系统的宏观应力-应变曲线具有更大的滞回环面积，拥有更优的超弹性变形能力。计算结果显示，在中低应变率下纳米晶NiTi形状记忆合金应力-应变关系表现出较明显的应变率相关性，应变率升高导致材料相变应力提升。这一应变率相关性主要源于相场模型中外加载荷速率与马氏体空间演化速度的相互竞争关系。Abstract: NiTi shape memory alloy, a typical smart and functional material, has been widely applied in various engineering fields due to its excellent superelasticity and shape memory effect originated from reversible thermo-elastic martensite transformation. The phase-field method is a powerful computational approach for modeling and predicting the mesoscale morphology and microstructural evolution of materials. It is employed to describe the microstructural evolution via a set of order parameters that are continuous in both time and space. In this study, a new non-isothermal phase-field model was established based on the time-dependent Ginzburg-Landau kinetic equation. In particular, an additional grain boundary energy term was introduced into the local free energy density to consider the contribution from the grain boundary of a polycrystalline NiTi shape memory alloy system. In order to understand the underlying microscopic mechanisms for the superelastic deformation, the microstructural evolution and the overall mechanical behavior of both single-crystalline and polycrystalline NiTi shape memory alloys were numerically investigated under tensile loading and unloading at 290 K. After that, the intrinsic strain-rate sensitivity of nanocrystalline NiTi shape memory alloy was studied with the grain size of 60 nm at low strain rates (0.0005−15 s−1). The results show that the martensitic transformation in the single crystalline NiTi shape memory alloy is uniform. No austenite-martensite interface was formed during the computation. Superelastic deformation was simulated by a nanocrystalline NiTi phase-field model. Such behavior is achieved through the nucleation and expansion of martensite bands during uniaxial tensile loading as well as the disappearance of martensite bands during unloading. In comparison, the single-crystalline NiTi shape memory alloy processes larger hysteresis area and better superelastic deformation ability than the polycrystalline NiTi shape memory alloy under the same external loading condition. Noticeable strain-rate sensitivity was exhibited in stress-strain relation of the nanocrystalline NiTi shape memory alloys under low-to-medium strain-rate loadings. The phase-transformation stress increases with the rise of implemented strain rate. Such strain-rate dependence is a result of the competition in the phase-field model between the speed of martensitic domain evolution and the speed of external loading.
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图 1 NiTi 形状记忆合金局部自由能密度与序参量的关系
Figure 1. Relationship between local free energy density and order parameter of NiTi shape memory alloy
图 2 数值计算边界条件及外加载荷历程
Figure 2. Boundary conditions and applied load history of the simulations
图 3 单晶NiTi合金290 K环境温度下单轴拉伸-卸载过程的应力-应变曲线
Figure 3. Stress-strain curve of monocrystal NiTi shape memory alloy during tension-unloading at 290 K
图 4 对应于图3中应力-应变曲线上关键点处的微结构，图中不同颜色代表不同的微结构形态
Figure 4. Microstructures corresponding to the representative points of the stress-strain curve in Fig. 3, and different colors represent different microstructural morphologies
图 5 晶粒尺寸为60 nm的多晶NiTi形状记忆合金有限元模型
Figure 5. A finite element model of the polycrystalline NiTi shape memory alloy with the grain size of 60 nm
图 6 晶粒尺寸为60 nm的NiTi多晶形状记忆合金290 K环境温度下单轴拉伸-卸载过程的应力-应变响应
Figure 6. Stress-strain response of the NiTi polycrystalline shape memory alloy with the grain size of 60 nm during tension-unloading at 290 K
图 7 对应于图6中应力-应变曲线上关键点处的微结构云图
Figure 7. Microstructural morphologies corresponding to the representative points of the stress-strain curve in Fig.6
图 8 NiTi单晶、多晶系统在20 s−1应变率下的应力-应变响应
Figure 8. Stress-strain curves of NiTi monocrystalline and polycrystalline at the strain rate of 20 s−1
图 9 纳米晶NiTi多晶系统在不同应变率下的应力-应变曲线
Figure 9. Stress-strain curves of NiTi polycrystalline system at different strain rates
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[1] BIL C, MASSEY K, ABDULLAH E J. Wing morphing control with shape memory alloy actuators [J]. Journal of Intelligent Material Systems and Structures, 2013, 24(7): 879–898. DOI: 10.1177/1045389X12471866. [2] HARTL D J, LAGOUDAS D C. Aerospace applications of shape memory alloys [J]. Proceedings of the Institution of Mechanical Engineers: Journal of Aerospace Engineering, 2007, 221(4): 535–552. DOI: 10.1243/09544100JAERO211. [3] KAHN H, HUFF M A, HEUER A H. The TiNi shape-memory alloy and its applications for MEMS [J]. Journal of Micromechanics and Microengineering, 1998, 8(3): 213–221. DOI: 10.1088/0960-1317/8/3/007. [4] PETRINI L, MIGLIAVACCA F. Biomedical applications of shape memory alloys [J]. Journal of Metallurgy, 2011, 2011: 501483. DOI: 10.1155/2011/501483. [5] MACHADO L G, SAVI M A. Medical applications of shape memory alloys [J]. Brazilian Journal of Medical and Biological Research, 2003, 36(6): 683–691. DOI: 10.1590/s0100-879x2003000600001. [6] STOECKEL D, YU W. Superelastic Ni-Ti wire [J]. Wire Journal International, 1991, 24(3): 45–50. [7] CHEN W W, WU Q P, KANG J H, et al. Compressive superelastic behavior of a NiTi shape memory alloy at strain rates of 0.001–750 s−1 [J]. International Journal of Solids and Structures, 2001, 38(50/51): 8989–8998. DOI: 10.1016/S0020-7683(01)00165-2. [8] DAYANANDA G N, RAO M S. Effect of strain rate on properties of superelastic NiTi thin wires [J]. Materials Science and Engineering: A, 2008, 486(1/2): 96–103. DOI: 10.1016/j.msea.2007.09.006. [9] AHADI A, SUN Q P. Effects of grain size on the rate-dependent thermomechanical responses of nanostructured superelastic NiTi [J]. Acta Materialia, 2014, 76: 186–197. DOI: 10.1016/j.actamat.2014.05.007. [10] KIM S, CHO M. A strain rate effect of Ni-Ti shape memory alloy wire [J]. Japanese Journal of Applied Physics, 2010, 49(11R): 115801. DOI: 10.1143/JJAP.49.115801. [11] 王礼立. 高应变率下材料动态力学性能 [J]. 力学与实践, 1982, 4(1): 9–19, 26. DOI: 10.6052/1000-0879-1982-002.WANG L L. Dynamic mechanical properties of materials at high strain rates [J]. Mechanics in Engineering, 1982, 4(1): 9–19, 26. DOI: 10.6052/1000-0879-1982-002. [12] YANG Z L, WANG H, HUANG Y L, et al. Strain rate dependent mechanical response for monoclinic NiTi shape memory alloy: micromechanical decomposition and model validation via neutron diffraction [J]. Materials & Design, 2020, 191: 108656. DOI: 10.1016/j.matdes.2020.108656. [13] LIU S, LIN Y, HAN L Y, et al. Atomistic simulation of microstructure evolution of NiTi single crystals in bending deformation [J]. Computational Materials Science, 2021, 199: 110733. DOI: 10.1016/j.commatsci.2021.110733. [14] SUN Y Z, LUO J, ZHU J M. Phase field study of the microstructure evolution and thermomechanical properties of polycrystalline shape memory alloys: grain size effect and rate effect [J]. Computational Materials Science, 2018, 145: 252–262. DOI: 10.1016/j.commatsci.2018.01.014. [15] NEMAT-NASSER S, CHOI J Y, GUO W G, et al. High strain-rate, small strain response of a NiTi shape-memory alloy [J]. Journal of Engineering Materials and Technology, 2005, 127(1): 83–89. DOI: 10.1115/1.1839215. [16] JIANG D J, XIAO Y. Modelling on grain size dependent thermomechanical response of superelastic NiTi shape memory alloy [J]. International Journal of Solids and Structures, 2021, 210/211: 170–182. DOI: 10.1016/j.ijsolstr.2020.11.036. [17] AHLUWALIA R, QUEK S S, WU D T. Simulation of grain size effects in nanocrystalline shape memory alloys [J]. Journal of Applied Physics, 2015, 117(24): 244305. DOI: 10.1063/1.4923044. [18] XU B, KANG G Z, KAN Q H, et al. Phase field simulation on the cyclic degeneration of one-way shape memory effect of NiTi shape memory alloy single crystal [J]. International Journal of Mechanical Sciences, 2020, 168: 105303. DOI: 10.1016/j.ijmecsci.2019.105303. [19] CISSÉ C, ZAEEM M A. A phase-field model for non-isothermal phase transformation and plasticity in polycrystalline yttria-stabilized tetragonal zirconia [J]. Acta Materialia, 2020, 191: 111–123. DOI: 10.1016/j.actamat.2020.03.025. [20] ARTEMEV A, JIN Y, KHACHATURYAN A G. Three-dimensional phase field model of proper martensitic transformation [J]. Acta Materialia, 2001, 49(7): 1165–1177. DOI: 10.1016/S1359-6454(01)00021-0. [21] WANG Y U, JIN Y M, KHACHATURYAN A G. The effects of free surfaces on martensite microstructures: 3D phase field microelasticity simulation study [J]. Acta Materialia, 2004, 52(4): 1039–1050. DOI: 10.1016/j.actamat.2003.10.037. [22] ZHONG Y, ZHU T. Phase-field modeling of martensitic microstructure in NiTi shape memory alloys [J]. Acta Materialia, 2014, 75: 337–347. DOI: 10.1016/j.actamat.2014.04.013. [23] YEDDU H K, MALIK A, ÅGREN J, et al. Three-dimensional phase-field modeling of martensitic microstructure evolution in steels [J]. Acta Materialia, 2012, 60(4): 1538–1547. DOI: 10.1016/j.actamat.2011.11.039. [24] CUI S S, WAN J F, RONG Y H, et al. Phase-field simulations of thermomechanical behavior of MnNi shape memory alloys using finite element method [J]. Computational Materials Science, 2017, 139: 285–294. DOI: 10.1016/j.commatsci.2017.08.010. [25] CUI S S, WAN J F, ZUO X W, et al. Three-dimensional, non-isothermal phase-field modeling of thermally and stress-induced martensitic transformations in shape memory alloys [J]. International Journal of Solids and Structures, 2017, 109: 1–11. DOI: 10.1016/j.ijsolstr.2017.01.001. [26] MALIK A, YEDDU H K, AMBERG G, et al. Three dimensional elasto-plastic phase field simulation of martensitic transformation in polycrystal [J]. Materials Science and Engineering: A, 2012, 556: 221–232. DOI: 10.1016/j.msea.2012.06.080. [27] MIKULA J, QUEK S S, JOSHI S P, et al. The role of bimodal grain size distribution in nanocrystalline shape memory alloys [J]. Smart Materials and Structures, 2018, 27(10): 105004. DOI: 10.1088/1361-665X/aada30. [28] ZHANG W, JIN Y M, KHACHATURYAN A G. Phase field microelasticity modeling of heterogeneous nucleation and growth in martensitic alloys [J]. Acta Materialia, 2007, 55(2): 565–574. DOI: 10.1016/j.actamat.2006.08.050. [29] ZHU J M, LUO J, SUN Y Z. Phase field study of the grain size and temperature dependent mechanical responses of tetragonal zirconia polycrystals: a discussion of tension-compression asymmetry [J]. Computational Materials Science, 2020, 172: 109326. DOI: 10.1016/j.commatsci.2019.109326. [30] HEO T W, CHEN L Q. Phase-field modeling of displacive phase transformations in elastically anisotropic and inhomogeneous polycrystals [J]. Acta Materialia, 2014, 76: 68–81. DOI: 10.1016/j.actamat.2014.05.014. [31] CHEN L Q, WANG Y Z. The continuum field approach to modeling microstructural evolution [J]. JOM, 1996, 48(12): 13–18. DOI: 10.1007/BF03223259. [32] JIN Y M, ARTEMEV A, KHACHATURYAN A G. Three-dimensional phase field model of low-symmetry martensitic transformation in polycrystal: simulation of ζ′2 martensite in AuCd alloys [J]. Acta Materialia, 2001, 49(12): 2309–2320. DOI: 10.1016/S1359-6454(01)00108-2. [33] YAMANAKA A, TAKAKI T, TOMITA Y. Elastoplastic phase-field simulation of martensitic transformation with plastic deformation in polycrystal [J]. International Journal of Mechanical Sciences, 2010, 52(2): 245–250. DOI: 10.1016/j.ijmecsci.2009.09.020. [34] MAMIVAND M, ZAEEM M A, EL KADIRI H. Shape memory effect and pseudoelasticity behavior in tetragonal zirconia polycrystals: a phase field study [J]. International Journal of Plasticity, 2014, 60: 71–86. DOI: 10.1016/j.ijplas.2014.03.018. [35] THAMBURAJA P, ANAND L. Polycrystalline shape-memory materials: effect of crystallographic texture [J]. Journal of the Mechanics and Physics of Solids, 2001, 49(4): 709–737. DOI: 10.1016/S0022-5096(00)00061-2. [36] HATCHER N, KONTSEVOI O Y, FREEMAN A J. Role of elastic and shear stabilities in the martensitic transformation path of NiTi [J]. Physical Review B, 2009, 80(14): 144203. DOI: 10.1103/PhysRevB.80.144203. [37] XIE X, KANG G Z, KAN Q H, et al. Phase field modeling for cyclic phase transition of NiTi shape memory alloy single crystal with super-elasticity [J]. Computational Materials Science, 2018, 143: 212–224. DOI: 10.1016/j.commatsci.2017.11.017. [38] XI S B, SU Y. Phase field study of the microstructural dynamic evolution and mechanical response of NiTi shape memory alloy under mechanical loading [J]. Materials, 2021, 14(1): 183. DOI: 10.3390/MA14010183. [39] LIU Y, LI Y L, RAMESH K T, et al. High strain rate deformation of martensitic NiTi shape memory alloy [J]. Scripta Materialia, 1999, 41(1): 89–95. DOI: 10.1016/S1359-6462(99)00058-5. [40] ELIBOL C, WAGNER M F X. Strain rate effects on the localization of the stress-induced martensitic transformation in pseudoelastic NiTi under uniaxial tension, compression and compression-shear [J]. Materials Science and Engineering: A, 2015, 643: 194–202. DOI: 10.1016/j.msea.2015.07.039. [41] XIAO Y, ZENG P, LEI L P, et al. Experimental investigation on rate dependence of thermomechanical response in superelastic NiTi shape memory alloy [J]. Journal of Materials Engineering and Performance, 2015, 24(10): 3755–3760. DOI: 10.1007/s11665-015-1688-6. -
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