兰州大学机构库 >土木工程与力学学院
Nb3Sn超导股线临界特性的应变依赖性及标度关系研究
Alternative TitleStudy On The Scaling Relation And The Strain Dependence of The Critical Properties of Nb3Sn Superconducting Wires
王哲
Thesis Advisor高原文
2016-05-29
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
KeywordNb3Sn 应变依赖性 标度律 McMillan方程 第一性原理 二次模型 全量模型 有限元方法 横向载荷
AbstractA15相Nb3Sn超导股线因其具有良好的超导性能,被广泛应用于多种大尺度的高场超导磁体(大于13T)中。然而,由于Nb3Sn的超导临界特性(临界温度Tc、上临界场Bc2、临界电流Ic)强烈依赖于应变,因此在发生应变时,磁体系统会发生性能退化。这些应变通常来源于系统冷却过程中的机械载荷(由于复合材质中热收缩的差异)以及操作(由于产生洛伦兹力)。因此,了解超导临界参数的应变依赖性至关重要,尤其是临界电流。 标度关系(标度律)是描述临界电流密度随磁场、温度、应变关系的基本理论。计算Nb3Sn 超导股线中的临界电流密度的关键是标度理论中描述应变依赖性的“应变依赖函数”。在过去的几十年,许多从理论或实验角度提出的标度依赖函数模型被广泛提出。然而,目前还没有一种公认的模型能从理论和实验两方面都能很好的诠释上临界场的应变依赖性。 本文根据Migdal-Eliashberg理论并结合第一性原理计算结果首先给出了最常见的单轴应变状态下应变依赖标度模型的简单表征形式。从McMillan方程出发,通过平均声子频率和电声耦合参数,得到了将单轴应变εa联系到临界温度Tc的方法。由于平均声子频率ωln和电声耦合参数λ随单轴应变εa的“钟形”变化关系可用抛物关系近似,根据McMillan方程将临界温度Tc和单轴应变εa联系起来。再根据上临界场和临界温度的关系,进而得到上临界场Bc2随单轴应变的变化关系(本文应变值均以百分比表示)。通过这种方法,得到了新的Nb3Sn的应变依赖函数以及标度律。 按照应变张量不变量观点,根据临界温度、平均声子频率、电声耦合参数分别随应变变化关系的一致性,得到了应变依赖函数的新全量不变量模型。全量不变量模型和二次模型都能很好拟合不同规格Nb3Sn股线的实验测量结果,并且与其他已有标度模型相比,具有更简单的表达形式。此外,全量不变量模型对上临界场Bc2随应变的测量结果具有更好的外推能力。 此外,本文还应用有限元方法研究了Nb3Sn超导股线在受到横向载荷作用下的力学性能。考虑了压元接触面形状对股线力学性能的影响,并对超导股线内部的Nb3Sn 超导丝域精细化程度进行了研究,找到了对股线建模的优化方法,并最终验证了提出的两种应变依赖标度模型。
Other AbstractThe A15 phase Nb3Sn superconducting wire is widely used in a variety of large-scale high-field superconducting magnets (above 13T) because of its good superconducting properties. However, since the critical superconducting properties (critical temperature Tc, critical upper field Bc2 and critical current Ic) of Nb3Sn are strongly dependent on the applied strain on account of its strain sensitivity, an overall performance degradation can take place when the magnets are strained. This applied strain usually comes from the mechanical loads during cooling (due to different thermal contractions between the composite) and operation (due to Lorentz forces). Hence, it is of importance to have knowledge of the strain dependence of the superconducting critical parameters, especially for the critical current. Scaling law is the basic theory to describe the critical current density with field, temperature and strain. The key of the calculation of the critical current density in Nb3Sn strands is the so called ‘strain function’ which describes the strain-dependent upper critical field in the series of equations of scaling law. Several strain function models have been proposed based on theoretical analysis or experiments over the last decades of years. However, there is still not a perfect model which can describe the strain dependence of the upper critical field both theoretically and experimentally. In this paper, we first propose a simple form of the strain function based on Migdal-Eliashberg theory with the results of first principles calculations in the case of the most common uniaxial strain situation. From the McMillan Equation, we derive a method to bond the axial strain εa to the critical temperature Tc, with the electron-phonon coupling λ and the averaged phonon frequency ωln. As the ‘bell shape’ of the curves of these two parameters with the applied uniaxial strain can be approximated as parabolic, we then connect Tc with εa following the McMillan formula. With the relationship between Tc and Bc2, we give the upper critical field with the axial strain (expresses by percentage and all in this paper). In this way, we derive the scaling law for the strain dependence of Nb3Sn. From the view of invariants of the strain tensor, we derive a new invariant strain function model according to the consistency of the relationship between the critical temperature, the averaged phonon frequency and the electron-phonon with general strain state respectively. Both...
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/226749
Collection土木工程与力学学院
Recommended Citation
GB/T 7714
王哲. Nb3Sn超导股线临界特性的应变依赖性及标度关系研究[D]. 兰州. 兰州大学,2016.
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