Nb_3Sn材料及其股线的若干力—电性能研究
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摘要
Nb3Sn超导材料具有良好的超导临界性能,其复合股线在ITER磁体系统和其它强磁场工程中有着非常重要的应用。Nb3Sn材料及其股线的临界电流密度、有效弹性模量、统计强度、接触行为等力电性能直接关系到超导磁体的安全稳定运行,对其的预测和评估是超导磁体科学和技术的关键问题。因而,本文针对Nb3Sn材料及其股线的力-电性能开展了理论研究工作。
基于电子散射钉扎机制,由Boltzmann输运方程得到了超导多晶材料中受晶粒尺寸和电子晶界散射性质影响的电子有效平均自由程,并利用合作钉扎理论建立了描述Nb3Sn超导材料临界电流密度晶粒尺寸效应的模型。研究表明,有效临界电流密度不仅与晶粒尺寸有关,而且还强烈地依赖于透射率的大小；当透射率小于一定值时,存在临界电流密度的最佳晶粒尺寸,从而澄清了已有研究工作中Nb3Sn超导材料临界电流密度是否存在最佳晶粒尺寸的问题。本文建立的BT模型-小磁通线束钉扎机制的预测结果与实验结果吻合良好,并得到了能反映临界电流密度晶粒尺寸效应的Nb3Sn超导复合股线临界电流密度的标度关系。
建立了一个描述纤维断裂和初始损伤导致的青铜法制备的Nb3Sn超导复合股线轴向刚度退化的解析模型。此模型由三个子模型构成：含损伤的纤维有效模量模型；超导内层有效模量模型；Nb3Sn超导复合股线有效模量模型。本文的研究证实初始损伤影响超导复合股线的有效轴向模量并导致股线刚度的退化,而且复合股线的刚度退化表现出明显的非线性特征而且依赖于初始损伤参数和总损伤的演化。由此预测得到的结果与实验由第一次加载应力-应变曲线得到的弹性模量值基本吻合。
从剪滞模型出发,利用基于Weibull/Poisson统计理论和GLS机制的Curtin-Zhou模型描述复合股线中纤维碎片化过程,得到了Nb3Sn超导复合股线拉伸统计平均强度和失效概率分布函数；提出了分析CICC中复合股线周期性弯曲载荷因子的模型,并利用其联系拉伸统计强度得到了股线的周期性弯曲强度。研究结果表明,初始损伤对拉伸统计强度和周期性弯曲统计强度的影响都非常显著,两者都随着初始损伤参数的增加而迅速减小。通过与已有研究结果的对比可以发现,本文模型预测的周期性载荷因子的大小和随Weibull模量的变化规律都是正确的,并填补了已有研究的空白。
提出了一套离散元框架和方法来分析CICC横截面内横向电磁载荷下股线的二维接触力学行为,并且能有效地描述股线间的接触力学特征。本文模拟发现,相对接触力、相对法向接触力以及相对切向接触力大小分布的概率密度函数都呈负指数函数形式的衰减；接触力、法向接触力、切向接触力方向分布的概率密度函数都表现出各项异性,存在6个概率密度较大的方向。本文经在三级子股线圆盘单元间预加弹簧方法模拟得到的CICC横向压缩的载荷-位移曲线与已有横向压缩实验测得的载荷-位移曲线吻合良好。
总之,本文的研究,有利于更好地预测和评估Nb3Sn超导材料和结构的多场有效性能,并对评估和保证ITER超导磁体的安全稳定运行提供了有价值的理论依据。
Nb3Sn materials have excellent critical superconducting properties, so the Nb3Sn composite strands have important applications in ITER magnetic system and other high magnetic field engineering. Because the mechanical and electrical properties of Nb3Sn materials and structures, such as the critical current density, the effective elastic modulus, the statistical strength, the contact mechanical behavior, of Nb3Sn superconducting materials and structures, are strongly related to the safe and stable running of superconducting magnets, the prediction and evaluation of them are key problems in the high magnetic field science and technology. Hence, this dissertation presents theoretical investigations on the mechanical-electrical properties of Nb3Sn superconducting materials and strands.
Based on the electron scattering pinning mechanism, this study proposes a model describing the grain size effects on the effective critical current density of Nb3Sn superconducting materials by using the collective pinning theory, where the electron effective mean free path which is affected by grain size and the grain boundary scattering properties is obtained through Boltzmann transport equation. The investigation indicates:the effective critical current density is not only dependent on the grain size but also on the electron transmistivity at grain boundaries; when the transmistivity is less than a specific value, there exists a best grain size for the effective critical current density. So, this clarifies the question about whether there exists a best grin size for the critical current density in the prior work. The results predicted by the proposed BT model- small vortex bundle pinning mechanism are in good agreement with the experimental results。Furthermore, we get a new critical current density scaling relation for Nb3Sn strands, which can describe the grain size effects.
An analytical model is developed to simulate this degradation of bronze route strands induced by initial damage and filament fracture. The model contains three sub-models:the model of the effective modulus of a filament with initial damage; the model of the weakened stiffness of the superconducting layer; the model of the effective axial modulus of the strand. The results indicate that the stiffness reduction of a strand presents obvious nonlinear behavior and depends on the initial damage parameter and the evolution of total damage. The predicted effective axial modulus from the present model is in basic agreement with that determined from the first loading stress-strain curve.
We use the shear lag model combined the Curtin-Zhou model which is based on the Weibull/Poisson statistics and GLS schema to describe the filament fragmentation in composite strands, and get the statistical average tensile strength and the failure probability distribution function of these superconducting composite strands. Furthermore, we propose a model to analyze the load factor of the periodic bending strand, and obtain the periodic bending strength which is related to the tensile strength by using the load factor. The study points out that the initial damage parameter affects evidently the tensile strength and the periodic bending strength which all decreases as the initial damage parameter value increases. Comparing to the results of previous research, the periodic bending load factor values and dependence on the Weibull modulus predicted by our model is correct. Our research fills the gap of previous work.
We propose a discrete element frame and method to analyze the 2D contact mechanical behavior and characteristics of strands in the CICC cross-section under the applied transverse electromagnetic loads. The discrete element simulation finds: among strands in the CICC cross-section, the probability density function distributions of the magnitudes of the relative contact force, the relative normal contact force and the relative tangential contact force all decay as a negative exponential law; the probability density function distributions of the directions of the contact force, the normal contact force and the tangential contact force all are anisotropic, and all have six directions with relatively large probability density values. The simulated transverse load-displacement curves, where the treatment of applying pre-spring between the triplet strand disc elements is taken, agree well with the experimental test curves.
After all, through the investigations in the dissertation, it is valuable and important to predict and assess the multi-field effective properties of Nb3Sn superconducting materials and structures, and can provide certain theoretical guidance to assess and promise the safety and stability of ITER superconducting magnets.
基于电子散射钉扎机制,由Boltzmann输运方程得到了超导多晶材料中受晶粒尺寸和电子晶界散射性质影响的电子有效平均自由程,并利用合作钉扎理论建立了描述Nb3Sn超导材料临界电流密度晶粒尺寸效应的模型。研究表明,有效临界电流密度不仅与晶粒尺寸有关,而且还强烈地依赖于透射率的大小；当透射率小于一定值时,存在临界电流密度的最佳晶粒尺寸,从而澄清了已有研究工作中Nb3Sn超导材料临界电流密度是否存在最佳晶粒尺寸的问题。本文建立的BT模型-小磁通线束钉扎机制的预测结果与实验结果吻合良好,并得到了能反映临界电流密度晶粒尺寸效应的Nb3Sn超导复合股线临界电流密度的标度关系。
建立了一个描述纤维断裂和初始损伤导致的青铜法制备的Nb3Sn超导复合股线轴向刚度退化的解析模型。此模型由三个子模型构成：含损伤的纤维有效模量模型；超导内层有效模量模型；Nb3Sn超导复合股线有效模量模型。本文的研究证实初始损伤影响超导复合股线的有效轴向模量并导致股线刚度的退化,而且复合股线的刚度退化表现出明显的非线性特征而且依赖于初始损伤参数和总损伤的演化。由此预测得到的结果与实验由第一次加载应力-应变曲线得到的弹性模量值基本吻合。
从剪滞模型出发,利用基于Weibull/Poisson统计理论和GLS机制的Curtin-Zhou模型描述复合股线中纤维碎片化过程,得到了Nb3Sn超导复合股线拉伸统计平均强度和失效概率分布函数；提出了分析CICC中复合股线周期性弯曲载荷因子的模型,并利用其联系拉伸统计强度得到了股线的周期性弯曲强度。研究结果表明,初始损伤对拉伸统计强度和周期性弯曲统计强度的影响都非常显著,两者都随着初始损伤参数的增加而迅速减小。通过与已有研究结果的对比可以发现,本文模型预测的周期性载荷因子的大小和随Weibull模量的变化规律都是正确的,并填补了已有研究的空白。
提出了一套离散元框架和方法来分析CICC横截面内横向电磁载荷下股线的二维接触力学行为,并且能有效地描述股线间的接触力学特征。本文模拟发现,相对接触力、相对法向接触力以及相对切向接触力大小分布的概率密度函数都呈负指数函数形式的衰减；接触力、法向接触力、切向接触力方向分布的概率密度函数都表现出各项异性,存在6个概率密度较大的方向。本文经在三级子股线圆盘单元间预加弹簧方法模拟得到的CICC横向压缩的载荷-位移曲线与已有横向压缩实验测得的载荷-位移曲线吻合良好。
总之,本文的研究,有利于更好地预测和评估Nb3Sn超导材料和结构的多场有效性能,并对评估和保证ITER超导磁体的安全稳定运行提供了有价值的理论依据。
Nb3Sn materials have excellent critical superconducting properties, so the Nb3Sn composite strands have important applications in ITER magnetic system and other high magnetic field engineering. Because the mechanical and electrical properties of Nb3Sn materials and structures, such as the critical current density, the effective elastic modulus, the statistical strength, the contact mechanical behavior, of Nb3Sn superconducting materials and structures, are strongly related to the safe and stable running of superconducting magnets, the prediction and evaluation of them are key problems in the high magnetic field science and technology. Hence, this dissertation presents theoretical investigations on the mechanical-electrical properties of Nb3Sn superconducting materials and strands.
Based on the electron scattering pinning mechanism, this study proposes a model describing the grain size effects on the effective critical current density of Nb3Sn superconducting materials by using the collective pinning theory, where the electron effective mean free path which is affected by grain size and the grain boundary scattering properties is obtained through Boltzmann transport equation. The investigation indicates:the effective critical current density is not only dependent on the grain size but also on the electron transmistivity at grain boundaries; when the transmistivity is less than a specific value, there exists a best grain size for the effective critical current density. So, this clarifies the question about whether there exists a best grin size for the critical current density in the prior work. The results predicted by the proposed BT model- small vortex bundle pinning mechanism are in good agreement with the experimental results。Furthermore, we get a new critical current density scaling relation for Nb3Sn strands, which can describe the grain size effects.
An analytical model is developed to simulate this degradation of bronze route strands induced by initial damage and filament fracture. The model contains three sub-models:the model of the effective modulus of a filament with initial damage; the model of the weakened stiffness of the superconducting layer; the model of the effective axial modulus of the strand. The results indicate that the stiffness reduction of a strand presents obvious nonlinear behavior and depends on the initial damage parameter and the evolution of total damage. The predicted effective axial modulus from the present model is in basic agreement with that determined from the first loading stress-strain curve.
We use the shear lag model combined the Curtin-Zhou model which is based on the Weibull/Poisson statistics and GLS schema to describe the filament fragmentation in composite strands, and get the statistical average tensile strength and the failure probability distribution function of these superconducting composite strands. Furthermore, we propose a model to analyze the load factor of the periodic bending strand, and obtain the periodic bending strength which is related to the tensile strength by using the load factor. The study points out that the initial damage parameter affects evidently the tensile strength and the periodic bending strength which all decreases as the initial damage parameter value increases. Comparing to the results of previous research, the periodic bending load factor values and dependence on the Weibull modulus predicted by our model is correct. Our research fills the gap of previous work.
We propose a discrete element frame and method to analyze the 2D contact mechanical behavior and characteristics of strands in the CICC cross-section under the applied transverse electromagnetic loads. The discrete element simulation finds: among strands in the CICC cross-section, the probability density function distributions of the magnitudes of the relative contact force, the relative normal contact force and the relative tangential contact force all decay as a negative exponential law; the probability density function distributions of the directions of the contact force, the normal contact force and the tangential contact force all are anisotropic, and all have six directions with relatively large probability density values. The simulated transverse load-displacement curves, where the treatment of applying pre-spring between the triplet strand disc elements is taken, agree well with the experimental test curves.
After all, through the investigations in the dissertation, it is valuable and important to predict and assess the multi-field effective properties of Nb3Sn superconducting materials and structures, and can provide certain theoretical guidance to assess and promise the safety and stability of ITER superconducting magnets.
引文
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