镍钛铌形状记忆合金宏细观力学行为研究
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摘要
Ni_(47)Ti_(44)Nb_9形状记忆合金在一定条件下(Ms+30℃)变形(16%预变形)后可获得宽的相变滞后和良好的形状记忆效应，这对实际工程应用具有十分重要的意义。用这种合金制成的记忆合金连接件和紧固件可在常温下运输和存储而无需保存在液氮中,应用极为方便。
为研究该材料在预变形后马氏体逆相变温度As提高的热力学机理，以建立相应的数值方法并模拟Ni_(47)Ti_(44)Nb_9形状记忆合金管接头的装配过程，本文在分析国内外有关形状记忆合金本构行为研究现状的基础上，结合近年来有关Ni_(47)Ti_(44)Nb_9形状记忆合金试验研究得到的新现象，从试验、宏观本构模型、细观本构模型、数值模拟等方面对Ni_(47)Ti_(44)Nb_9形状记忆合金进行了较为系统的研究。主要研究工作和结论如下：
1、系统地研究了Ni_(47)Ti_(44)Nb_9形状记忆合金的典型热力学特性：研究了不同温度时合金在拉伸、扭转载荷作用下的响应特性以及升温回复特性。研究了在-60℃(即Ms+30℃)下合金在不同拉扭比例、非比例载荷作用下的应力应变响应特性以及对应的升温回复特性。结果表明，在简单拉伸和纯扭转变形下材料表现出不同的力学响应特性及升温回复特性。与拉伸变形相比，扭转变形中材料相变时未见应力跌落。升温过程中，拉伸与扭转方向产生的相变应变在同一温度有较大回复，与加载历史无关。文中还研究了在不同预变形下的约束升温特性，发现随预变形的增加，材料中的回复力增大。同时研究了不同回复应变下材料的约束升温特性以及常温下材料的循环特性。
2、建立了考虑塑性与相变相互影响的形状记忆合金宏观本构模型：根据塑性变形可以提高马氏体逆相变的温度和降低马氏体逆相变开始应力等试验现象，提出了考虑塑性变形的形状记忆合金材料的自由能表达式。在此基础上根据连续介质力学理论推导出应力、与相变和塑性有关的背应力、曳应力的表达式；构造了形状记忆合金的耗散势能函数，分别得出了与相变、塑性相关的内变量的演化方程，并提出相应的本构积分算法及切线刚度。根据所发展的理论及算法编制了ABAQUS用户子程序UMAT，分析了形状记忆合金的典型特性，包括伪弹性、形状记忆效应、约束升温特性、特别是塑性变形对马氏体逆相变的影响。建立了管接头的有限元模型，模拟了包含管接头低温扩孔、升温回复和降温等的安装过程，对管接头与被连接件间的接触压力进行了分析。
3、发展了Ni_(47)Ti_(44)Nb_9形状记忆合金的细观本构模型：将Ni_(47)Ti_(44)Nb_9形状记忆合金视为NiTi基体中嵌入软相的β-Nb夹杂的混合物，采用Mori-Tanaka方法发展了Ni_(47)Ti_(44)Nb_9合金的细观本构模型。比较了各向同性化基体切线刚度与各向异性基体切线刚度计算的Eshelby张量对材料响应特性的影响。结果表明，按各向同性化基体刚度计算出的Eshelby张量得出的应力应变曲线与有限元计算结果较为吻合。基于上述结果计算了SMA基体中嵌入弹性、弹塑性夹杂对材料整体响应特性的影响。得出了不同体积分数的弹性、弹塑性夹杂对拉伸应力应变曲线的影响以及对马氏体逆相变开始温度As的影响。结果表明，当体积分数小于10%时，弹塑性夹杂的塑性变形对As的提高贡献较小；考虑到基体中塑性变形对As的影响，采用所建立的本构模型对材料在不同温度、不同载荷路径下的响应特性进行了数值分析，结果表明，所发展的本构模型能较好地描述试验现象，包括不同温度下扭转响应特性及升温回复特性，与试验结果趋势较为一致。
4、对Ni_(47)Ti_(44)Nb_9形状记忆合金管接头的装配过程进行了数值模拟：将基于所发展宏观本构模型编写的用户自定义材料子程序嵌入有限元软件ABAQUS，计算了不同壁厚管接头在装配过程中接触压力等力学变量随着厚度的变化，发现装配完成后管接头中的应力沿径向分布不均匀，与管接头厚度有关；被连接管中应力不均匀，内壁应力较大，轴线方向上管中部应力较大；管接头与被连接管间的接触压力沿着轴线方向分布不均匀，与厚度密切相关。对计算结果分析表明可采用减少管接头内径、增加壁厚、减少装配间隙等手段提高管接头的径向压应力。
When elongated to about16%at Ms+30℃, a Ni_(47)Ti_(44)Nb_9alloy can achieve a largetransformation hysteresis and better shape memory effect, which is of significantimportance for the application of this alloy in the practical application. For instance, thepreformed pipe joint components made of the alloy can easily be stored at roomtemperature before assembly without being transformed back to the parent phase,instead of being stored at a low temperature condition.
In this dissertation, the thermodynamic mechanism of the increase in Asaftercertain deformation is investigated. Then the constitutive model and the correspondingnumerical algorithm are developed for the analysis of the assembly of Ni_(47)Ti_(44)Nb_9pipejoints. The main researches made and the main progresses achieved are as follows:
(1) The typical thermal-mechanical properties of Ni_(47)Ti_(44)Nb_9alloy are investigatedsystematically, involving the responses and the heating-induced strain recovery underproportional tensile-torsional straining at various temperatures. The results show thatthe response of the alloy under pure tension is quite different from that under puretorsion. Under tensile deformation, there are distinct stress drop and the following stressplateau, which do not appear in the case of pure torsion. In the case of constrainedheating-induced recovery stress, it is found that the recovery resistance increases withthe increase of pre-deformation. Recovery stress at various recovery strains and thethermal-mechanical properties of the alloy subjected to cyclic straining are alsoinvestigated.
(2) A constitutive model is developed, taking into account the effects of theinteraction between plasticity and transformation. Based on the experimental fact thatplastic deformation could substantially raise the temperature or reduce the stress forinverse transformation to start, a free energy is formulated for SMAs, taking intoaccount the effects of plastic deformation, with which, the expressions of stress, backstress and drag stress are obtained. The corresponding dissipation potentials are alsoformulated, with which, the evolutions of the internal state variables related respectivelyto transformation and plasticity are derived. The corresponding integral algorithm andthe tangent stiffness are proposed, and the UMAT is developed and embedded in thecommercially available FE code ABAQUS. The typical properties of shape memoryalloys, such as pseudoelasticity, shape memory effect, coupled transformation and plastic deformation, and especially, the effects of plastic deformation on inversetransformation, etc.
(3) A micromechanics model for Ni_(47)Ti_(44)Nb_9alloy is also developed. A Ni_(47)Ti_(44)Nb_9alloy is considered as a mixture of the NiTi matrix and β-Nb inclusions, and theMori-Tanaka scheme is used for the evaluation of the effect thermal-mechanicalproperties of the mixture. The evaluations with the Eshelby tensor using the tangentstiffness tensor of the elastoplastic matrix with or without being isotropicalized arecompared with each other. It shows that the result with the isotropicalized tangentstiffness tensor agrees better with the FE result. The properties of the mixture withelastic and elastoplastic inclusions are also evaluated respectively, in which variousvolume fractions of inclusions on the overall response and the increase in the Afof themixture is investigated. If the particle volume fraction is less than10%, the contributionof the softer particle inclusions to the increase of Asis insignificant. Taking into theeffect of plastic deformation on As, the responses of the Ni_(47)Ti_(44)Nb_9alloy subjected tovarious thermal-mechanical loading at different temperature are computed. Comparisonbetween the computed and the experimental results shows satisfactory agreement.
(4) The assembling process of Ni_(47)Ti_(44)Nb_9alloy pipe joints is numericallysimulated with the developed constitutive model, based on which, the UMAT isdeveloped and embedded in ABAQUS. The effects of wall-thickness and the initial gapbetween the pipe and the joint on the contact pressure, stress distributions in both thepipes and the joint, and the pullout force are investigated. The results can provideavailable information for the design and the optimization of the designing parameters ofthe high-performance SMA pipe joints.
为研究该材料在预变形后马氏体逆相变温度As提高的热力学机理，以建立相应的数值方法并模拟Ni_(47)Ti_(44)Nb_9形状记忆合金管接头的装配过程，本文在分析国内外有关形状记忆合金本构行为研究现状的基础上，结合近年来有关Ni_(47)Ti_(44)Nb_9形状记忆合金试验研究得到的新现象，从试验、宏观本构模型、细观本构模型、数值模拟等方面对Ni_(47)Ti_(44)Nb_9形状记忆合金进行了较为系统的研究。主要研究工作和结论如下：
1、系统地研究了Ni_(47)Ti_(44)Nb_9形状记忆合金的典型热力学特性：研究了不同温度时合金在拉伸、扭转载荷作用下的响应特性以及升温回复特性。研究了在-60℃(即Ms+30℃)下合金在不同拉扭比例、非比例载荷作用下的应力应变响应特性以及对应的升温回复特性。结果表明，在简单拉伸和纯扭转变形下材料表现出不同的力学响应特性及升温回复特性。与拉伸变形相比，扭转变形中材料相变时未见应力跌落。升温过程中，拉伸与扭转方向产生的相变应变在同一温度有较大回复，与加载历史无关。文中还研究了在不同预变形下的约束升温特性，发现随预变形的增加，材料中的回复力增大。同时研究了不同回复应变下材料的约束升温特性以及常温下材料的循环特性。
2、建立了考虑塑性与相变相互影响的形状记忆合金宏观本构模型：根据塑性变形可以提高马氏体逆相变的温度和降低马氏体逆相变开始应力等试验现象，提出了考虑塑性变形的形状记忆合金材料的自由能表达式。在此基础上根据连续介质力学理论推导出应力、与相变和塑性有关的背应力、曳应力的表达式；构造了形状记忆合金的耗散势能函数，分别得出了与相变、塑性相关的内变量的演化方程，并提出相应的本构积分算法及切线刚度。根据所发展的理论及算法编制了ABAQUS用户子程序UMAT，分析了形状记忆合金的典型特性，包括伪弹性、形状记忆效应、约束升温特性、特别是塑性变形对马氏体逆相变的影响。建立了管接头的有限元模型，模拟了包含管接头低温扩孔、升温回复和降温等的安装过程，对管接头与被连接件间的接触压力进行了分析。
3、发展了Ni_(47)Ti_(44)Nb_9形状记忆合金的细观本构模型：将Ni_(47)Ti_(44)Nb_9形状记忆合金视为NiTi基体中嵌入软相的β-Nb夹杂的混合物，采用Mori-Tanaka方法发展了Ni_(47)Ti_(44)Nb_9合金的细观本构模型。比较了各向同性化基体切线刚度与各向异性基体切线刚度计算的Eshelby张量对材料响应特性的影响。结果表明，按各向同性化基体刚度计算出的Eshelby张量得出的应力应变曲线与有限元计算结果较为吻合。基于上述结果计算了SMA基体中嵌入弹性、弹塑性夹杂对材料整体响应特性的影响。得出了不同体积分数的弹性、弹塑性夹杂对拉伸应力应变曲线的影响以及对马氏体逆相变开始温度As的影响。结果表明，当体积分数小于10%时，弹塑性夹杂的塑性变形对As的提高贡献较小；考虑到基体中塑性变形对As的影响，采用所建立的本构模型对材料在不同温度、不同载荷路径下的响应特性进行了数值分析，结果表明，所发展的本构模型能较好地描述试验现象，包括不同温度下扭转响应特性及升温回复特性，与试验结果趋势较为一致。
4、对Ni_(47)Ti_(44)Nb_9形状记忆合金管接头的装配过程进行了数值模拟：将基于所发展宏观本构模型编写的用户自定义材料子程序嵌入有限元软件ABAQUS，计算了不同壁厚管接头在装配过程中接触压力等力学变量随着厚度的变化，发现装配完成后管接头中的应力沿径向分布不均匀，与管接头厚度有关；被连接管中应力不均匀，内壁应力较大，轴线方向上管中部应力较大；管接头与被连接管间的接触压力沿着轴线方向分布不均匀，与厚度密切相关。对计算结果分析表明可采用减少管接头内径、增加壁厚、减少装配间隙等手段提高管接头的径向压应力。
When elongated to about16%at Ms+30℃, a Ni_(47)Ti_(44)Nb_9alloy can achieve a largetransformation hysteresis and better shape memory effect, which is of significantimportance for the application of this alloy in the practical application. For instance, thepreformed pipe joint components made of the alloy can easily be stored at roomtemperature before assembly without being transformed back to the parent phase,instead of being stored at a low temperature condition.
In this dissertation, the thermodynamic mechanism of the increase in Asaftercertain deformation is investigated. Then the constitutive model and the correspondingnumerical algorithm are developed for the analysis of the assembly of Ni_(47)Ti_(44)Nb_9pipejoints. The main researches made and the main progresses achieved are as follows:
(1) The typical thermal-mechanical properties of Ni_(47)Ti_(44)Nb_9alloy are investigatedsystematically, involving the responses and the heating-induced strain recovery underproportional tensile-torsional straining at various temperatures. The results show thatthe response of the alloy under pure tension is quite different from that under puretorsion. Under tensile deformation, there are distinct stress drop and the following stressplateau, which do not appear in the case of pure torsion. In the case of constrainedheating-induced recovery stress, it is found that the recovery resistance increases withthe increase of pre-deformation. Recovery stress at various recovery strains and thethermal-mechanical properties of the alloy subjected to cyclic straining are alsoinvestigated.
(2) A constitutive model is developed, taking into account the effects of theinteraction between plasticity and transformation. Based on the experimental fact thatplastic deformation could substantially raise the temperature or reduce the stress forinverse transformation to start, a free energy is formulated for SMAs, taking intoaccount the effects of plastic deformation, with which, the expressions of stress, backstress and drag stress are obtained. The corresponding dissipation potentials are alsoformulated, with which, the evolutions of the internal state variables related respectivelyto transformation and plasticity are derived. The corresponding integral algorithm andthe tangent stiffness are proposed, and the UMAT is developed and embedded in thecommercially available FE code ABAQUS. The typical properties of shape memoryalloys, such as pseudoelasticity, shape memory effect, coupled transformation and plastic deformation, and especially, the effects of plastic deformation on inversetransformation, etc.
(3) A micromechanics model for Ni_(47)Ti_(44)Nb_9alloy is also developed. A Ni_(47)Ti_(44)Nb_9alloy is considered as a mixture of the NiTi matrix and β-Nb inclusions, and theMori-Tanaka scheme is used for the evaluation of the effect thermal-mechanicalproperties of the mixture. The evaluations with the Eshelby tensor using the tangentstiffness tensor of the elastoplastic matrix with or without being isotropicalized arecompared with each other. It shows that the result with the isotropicalized tangentstiffness tensor agrees better with the FE result. The properties of the mixture withelastic and elastoplastic inclusions are also evaluated respectively, in which variousvolume fractions of inclusions on the overall response and the increase in the Afof themixture is investigated. If the particle volume fraction is less than10%, the contributionof the softer particle inclusions to the increase of Asis insignificant. Taking into theeffect of plastic deformation on As, the responses of the Ni_(47)Ti_(44)Nb_9alloy subjected tovarious thermal-mechanical loading at different temperature are computed. Comparisonbetween the computed and the experimental results shows satisfactory agreement.
(4) The assembling process of Ni_(47)Ti_(44)Nb_9alloy pipe joints is numericallysimulated with the developed constitutive model, based on which, the UMAT isdeveloped and embedded in ABAQUS. The effects of wall-thickness and the initial gapbetween the pipe and the joint on the contact pressure, stress distributions in both thepipes and the joint, and the pullout force are investigated. The results can provideavailable information for the design and the optimization of the designing parameters ofthe high-performance SMA pipe joints.
引文
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