A MACROSCOPIC PHENOMENOLOGICAL CONSTITUTIVE MODEL FOR THE UNIAXIAL TRANSFORMATION RATCHETING OF SUPER-ELASTIC NiTi SHAPE MEMORY ALLOY
-
摘要: 超弹性镍钛形状记忆合金因其良好的力学性能以及独特的超弹性和形状记忆效应已广泛应用于土木工程、航空航天和生物医疗等多个领域，在实际服役环境中超弹性镍钛合金元件不可避免地会承受不同应力水平的循环载荷作用，亟待建立描述相变棘轮行为（即峰值应变和谷值应变随着正相变和逆相变循环的进行不断累积）的循环本构模型。为此，基于已有的超弹性镍钛形状记忆合金在不同峰值应力下的单轴相变棘轮行为实验研究结果，在广义黏塑性框架下，对Graesser等提出的通过背应力非线性演化方程反映超弹性镍钛形状记忆合金超弹性行为的一维宏观唯像本构模型进行了拓展，考虑了正相变和逆相变过程中特征变量的差异及其随循环的演化，以非弹性应变的累积量为内变量引入了正相变开始应力、逆相变开始应力、相变应变和残余应变的演化方程，同时通过峰值应力与正相变完成应力的比值来确定演化方程中的相关系数，建立了描述超弹性镍钛合金单轴相变棘轮行为的本构模型。将模拟结果与对应的实验结果进行对比发现，建立的宏观唯像本构模型能够合理地描述超弹性镍钛形状记忆合金的单轴相变棘轮行为及其峰值应力依赖性，模型的预测结果和实验结果吻合得很好。Abstract: Super-elastic NiTi shape memory alloy (SMA) has been extensively used in many fields such as civil engineering, aerospace and bio-medical fields due to its good mechanical properties, including unique super-elasticity and shape memory effect. In practical applications, the SMA-based devices are unavoidable subjected to cyclic loadings at different stress levels. However, it is necessary to establish a cyclic constitutive model to describe the transformation ratcheting behavior, i.e., the peak strain and valley strain accumulate cyclically during forward transformation and reverse transformation. Based on the existing experimental results of the transformation ratchetting of the super-elastic NiTi shape memory alloy obtained under the stress-controlled cyclic tension-unloading tests with different peak stresses, the one-dimensional macroscopic phenomenological constitutive model of super-elastic NiTi shape memory alloy proposed by Graesser, where super-elastic behavior is reflected by the nonlinear evolution equation of back stress, was extended to describe the uniaxial transformation ratchetting within the framework of generalized visco-plasticity. In the extended model, the differences of characteristic variables and their evolutions between the forward transformation and reverse transformation were considered, the evolution equations of the start stress of forward transformation, the start stress of reverse transformation, maximum transformation strain and residual strain were introduced by the internal variable of relative accumulated inelastic strain. In the meantime, the correlation coefficients in these evolution equations were determined by the ratio of the peak stress and the finish stress of forward transformation. The comparison of the experiments and simulations shows that the extended model can reasonably describe the dependence of uniaxial transformation ratchetting of super-elastic NiTi shape memory alloy on the peak stress, and the simulated results are in good agreement with the experimental ones.
-
图 1 相变棘轮行为的特征变量示意图
Figure 1. Illustration of characteristic variables of transformation ratcheting
图 2 不同峰值应力下的实验和模拟应力-应变曲线
Figure 2. Experimental and simulated stress-strain curves with different peak stresses
图 4 Graesser模型描述的镍钛合金单轴应力-应变曲线
Figure 4. Stress-strain curves of NiTi shape memory alloy described by Graesser's model
图 7 残余应变、峰值应变和耗散能随循环演化的实验和模拟对比
Figure 7. The comparison of the evolution of residual strain, peak strain and dissipation energy with circulation between experiment and simulation
表 1 镍钛形状记忆合金微管的材料参数
Table 1. Material parameters used in the proposed model for NiTi shape memory micro-tube
-
[1] Buehler WJ, Gilfrich JV, Wiley RC. Effects of low-temperature phase changes on the mechanical properties of alloys near composition TiNi. Journal of Applied Physics, 1963, 34(5):1475-1477 doi: 10.1063/1.1729603 [2] Duerig TW, Pelton A, Stöckel D. An overview of nitinol medical applications. Materials Science and Engineering:A, 1999, 273-275(99):149-160 https://www.researchgate.net/publication/222484943_An_overview_of_NiTiNol_medical_applications [3] Morgan NB. Medical shape memory alloy applications-the market and its products. Materials Science and Engineering:A, 2004, 378(1):16-23 http://www.sciencedirect.com/science/article/pii/S0921509303015132 [4] 钱辉, 李宏男, 宋钢兵.形状记忆合金阻尼器消能减震体系的控制研究.振动与冲击, 2008, 27(8):42-47 http://cdmd.cnki.com.cn/Article/CDMD-10141-2009040858.htmQian Hui, Li Hongnan, Song Gangbing. Energy dissipation system of structures with shape memory alloy damper. Journal of Vibration and Shock, 2008, 27(8):42-47 (in Chinese) http://cdmd.cnki.com.cn/Article/CDMD-10141-2009040858.htm [5] Shin M, Andrawes B. Experimental investigation of actively confined concrete using shape memory alloys. Engineering Structures, 2010, 32(3):656-664 doi: 10.1016/j.engstruct.2009.11.012 [6] 邵红红, 彭玉婷, 姜秀英等.医用镍钛合金表面多层薄膜的制备及摩擦磨损和耐腐蚀性能.功能材料, 2014, 45(4):14145-14149 http://www.cnki.com.cn/Article/CJFDTOTAL-GNCL201414028.htmShao Honghong, Peng Yuting, Xiu ying, et al. Preparation of multilayers on the surface of medical NiTi alloy and properties of friction/wear and corrosion resistance. Journal of Functional Materials, 2014, 45(4):14145-14149 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GNCL201414028.htm [7] Miyazaki S, Imai T, Igo Y, et al. Effect of cyclic deformation on the pseudoelasticity characteristics of Ti-Ni alloys. Metallurgical transactions A, 1986, 17(1):115-120 doi: 10.1007/BF02644447 [8] Lagoudas DC, Bo Z. Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part Ⅱ:Material characterization and experimental results for a stable transformation cycle. International Journal of Engineering Science, 1999, 37(9):1141-1173 doi: 10.1016/S0020-7225(98)00114-1 [9] Sehitoglu H, Anderson R, Karaman I, et al. Cyclic deformation behavior of single crystal NiTi. Materials Science and Engineering:A, 2001, 314(1):67-74 https://www.researchgate.net/publication/248469907_Cyclic_deformation_behavior_of_single_crystal_NiTi [10] Lexcellent C, Bourbon G. Thermodynamical model of cyclic behaviour of Ti-Ni and Cu-Zn-Al shape memory alloys under isothermal undulated tensile tests. Mechanics of Materials, 1996, 24(1):59-73 doi: 10.1016/0167-6636(96)00027-0 [11] Nemat-Nasser S, Guo WG. Superelastic and cyclic response of NiTi SMA at various strain rates and temperatures. Mechanics of Materials, 2006, 38(5):463-474 https://www.researchgate.net/publication/222696045_Superelastic_and_cyclic_response_of_NiTi_SMA_at_various_strain_rates_and_temperatures [12] Yu C, Kang G, Kan Q. A physical mechanism based constitutive model for temperature-dependent transformation ratchetting of NiTi shape memory alloy:One-dimensional model. Mechanics of Materials, 2014, 78(78):1-10 https://www.researchgate.net/publication/264980841_A_physical_mechanism_based_constitutive_model_for_temperature-dependent_transformation_ratchetting_of_NiTi_shape_memory_alloy_One-dimensional_model [13] Kang GH, Kan QH, Qian LM, et al. Ratchetting deformation of super-elastic and shape-memory NiTi alloys. Mechanics of Materials, 2009, 41(2):139-153 doi: 10.1016/j.mechmat.2008.09.001 [14] Song D, Kang GZ, Kan QH, et al. The effect of martensite plasticity on the cyclic deformation of super-elastic NiTi shape memory alloy. Smart Materials and Structures, 2014, 23(1):5008 https://www.researchgate.net/publication/274254958_The_effect_of_martensite_plasticity_on_the_cyclic_deformation_of_super-elastic_NiTi_shape_memory_alloy [15] Saleeb AF, Padula SA, Kumar A. A multi-axial, multimechanism based constitutive model for the comprehensive representation of the evolutionary response of SMAs under general thermomechanical loading conditions. International Journal of Plasticity, 2011, 27(5):655-687 doi: 10.1016/j.ijplas.2010.08.012 [16] Wang X, Wang Y, Lu Z, et al. An experimental study of the superelastic behavior in NiTi shape memory alloys under biaxial proportional and non-proportional cyclic loadings. Mechanics of Materials, 2010, 42(3):365-373 doi: 10.1016/j.mechmat.2009.11.010 [17] Song D, Kang GZ, Kan QH, et al. Non-proportional multiaxial transformation ratchetting of super-elastic NiTi shape memory alloy:Experimental observations. Mechanics of Materials, 2014, 70(1):94-105 https://www.researchgate.net/publication/259510553_Non-proportional_Multiaxial_Transformation_Ratchetting_of_Super-elastic_NiTi_Shape_Memory_Alloy_Experimental_Observations [18] Shaw JA, Kyriakides S. Thermomechanical aspects of NiTi. Journal of the Mechanics and Physics of Solids, 1995, 43(8):1243-1281 doi: 10.1016/0022-5096(95)00024-D [19] Morin C, Moumni Z, Zaki W. Thermomechanical coupling in shape memory alloys under cyclic loadings:Experimental analysis and constitutive modeling. International Journal of Plasticity, 2011, 27(12):1959-1980 doi: 10.1016/j.ijplas.2011.05.005 [20] Strnadel B, Ohashi S, Ohtsuka H, et al. Cyclic stress-strain characteristics of Ti-Ni and Ti-Ni-Cu shape memory alloys. Materials Science and Engineering:A, 1995, 202(1):148-156 http://www.sciencedirect.com/science/article/pii/0921509395098011 [21] Strnadel B, Ohashi S, Ohtsuka H, et al. Effect of mechanical cycling on the pseudoelasticity characteristics of Ti-Ni and Ti-Ni-Cu alloys. Materials Science and Engineering:A, 1995, 203(1):187-196 https://www.researchgate.net/publication/256627507_Effect_of_mechanical_cycling_on_the_pseudoelasticity_characteristics_of_TiNi_and_TiNiCu_alloys [22] 万征, 姚仰平, 孟达.复杂加载下混凝土的弹塑性本构模型.力学学报, 2016, 48(5):1159-1171 http://lxxb.cstam.org.cn/CN/abstract/abstract146013.shtmlWan Zheng, Yao Yangping, Meng Da. An elastoplastic constitutive model of concrete under complicated load. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(5):1159-1171 (in Chinese) http://lxxb.cstam.org.cn/CN/abstract/abstract146013.shtml [23] 陈庆, 朱合华, 闫治国等.基于自洽法的电化学沉积修复饱和混凝土细观描述.力学学报, 2015, 47(2):367-371 doi: 10.6052/0459-1879-14-147Chen Qing, Zhu Hehua, Yan Zhiguo, et al. Micro-scale description of the saturated concrete repaired by electrochemical deposition method based on self-consistent method. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(2):367-371 (in Chinese) doi: 10.6052/0459-1879-14-147 [24] 谈炳东, 许进升, 贾云飞等.短纤维增强EPDM包覆薄膜超弹性本构模型.力学学报, 2017, 49(2):317-323 http://lxxb.cstam.org.cn/CN/abstract/abstract146320.shtmlTan Bingdong, Xu Jinsheng, Jia Yunfei, et al. Hyperelastic constitutive model for short fiber reinforced EPDM inhibitor film. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2):317-323 (in Chinese) http://lxxb.cstam.org.cn/CN/abstract/abstract146320.shtml [25] 黄小双, 彭雄奇, 张必超.帘线/橡胶复合材料各向异性黏-超弹性本构模型.力学学报, 2016, 48(1):140-145 doi: 10.6052/0459-1879-15-189Huang Xiaoshuang, Peng Xiongqi, Zhang Bichao. An anisotropic visco-hyperelastic constitutive model for cord-rubber composites. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1):140-145 (in Chinese) doi: 10.6052/0459-1879-15-189 [26] Lagoudas DC, Entchev PB. Modeling of transformation-induced plasticity and its effect on the behavior of porous shape memory alloys. Part Ⅰ:constitutive model for fully dense SMAs. Mechanics of Materials, 2004, 36(9):865-892 doi: 10.1016/j.mechmat.2003.08.006 [27] Yu C, Kang GZ, Kan QH, et al. Rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy:thermo-mechanical coupled and physical mechanism-based constitutive model. International Journal of Plasticity, 2015, 72:60-90 doi: 10.1016/j.ijplas.2015.05.011 [28] Manchiraju S, Anderson PM. Coupling between martensitic phase transformations and plasticity:a microstructure-based finite element model. International Journal of Plasticity, 2010, 26(10):1508-1526 doi: 10.1016/j.ijplas.2010.01.009 [29] Yu C, Kang GZ, Kan QH, et al. A micromechanical constitutive model based on crystal plasticity for thermo-mechanical cyclic deformation of NiTi shape memory alloys. International Journal of Plasticity, 2013, 44(9):161-191 https://www.researchgate.net/publication/271560243_A_micromechanical_constitutive_model_based_on_crystal_plasticity_for_thermo-mechanical_cyclic_deformation_of_NiTi_shape_memory_alloys [30] Graesser E, Cozzarelli F. A proposed three-dimensional constitutive model for shape memory alloys. Journal of Intelligent Material Systems and Structures, 1994, 5(5):78-89 http://jim.sagepub.com/content/5/1/78.short [31] Özdemir H. Nonlinear transient dynamic analysis of yielding struc-tures.[PhD Thesis]. University of Califormia Berkeley, 1976 [32] Ren WJ, Li HN, Song GB. A one-dimensional strain-rate-dependent constitutive model for superelastic shape memory alloys. Smart Materials and Structures, 2007, 16(1):191-197 doi: 10.1088/0964-1726/16/1/023 [33] 钱辉, 李宏男, 宋钢兵等.基于塑性理论的形状记忆合金本构模型、试验和数值模拟.功能材料, 2007, 38(7):1114-1118 http://www.cnki.com.cn/Article/CJFDTOTAL-GNCL200707019.htmQian Hui, Li Hongnan, Song Gangbing, et al. Constitutive model of shape memory alloy based on plastic theory:experiment and simulation. Journal of Functional Materials, 2007, 38(7):1114-1118 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GNCL200707019.htm [34] 杨强军, 阚前华, 康国政等.超弹性NiTi合金循环相变诱发塑性本构模型.功能材料, 2015, 46(10):10018-10022 http://www.cnki.com.cn/Article/CJFDTOTAL-GNCL201510004.htmYang Qiangjun, Kan Qianhua, Kang Guozheng, et al. Constitutive model on cyclic transformation included plasticity of super-elastic NiTi alloy. Journal of Functional Materials, 2015, 46(10):10018-10022 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GNCL201510004.htm [35] Kan QH, Kang GZ. Constitutive model study on transformation ratcheting of superelastic NiTi alloy. International Journal of Plasticity, 2010, 26(3):441-464 doi: 10.1016/j.ijplas.2009.08.005 -
下载:
点击查看大图
图(8) / 表(1)
计量
- 文章访问数: 1158
- HTML全文浏览量: 244
- PDF下载量: 472
- 被引次数: 0
