超导柱体、圆盘断裂力学理论模型、数值分析及实验研究

Because it can work in liquid nitrogen environment, the type II high temperature superconductors have great prospect. Cracks inevitably appear in this kind of material because of the special production and manufacturing process. Although some researches on fracture mechanics of superconducting materials have been made, all of the theory study, numerical analysis and experimental characterization are not enough. This project intends to both superconducting cylinder and disc as the study object. From three kinds of approaches, i.e., theoretical analysis, numerical simulation and experiment, the fracture characteristics of the type II high temperature superconductors are investigated under the electromagnetic force caused by either initial magnetic field or decline process of the applied magnetic field. The research contents include several aspects. Firstly, by using integral transform method and singular integral equation technique, the analytic solutions to both penny-shaped and annular crack problems of superconducting cylinder should be given to reveal effects of either initial magnetic field or decline process of the applied magnetic field on crack tip behaviors. Then, the application of some novel numerical methods, in particular, (multiple) isoparametric element and the coupling method of (multiple) isoparametric element with infinite element, in superconductor fracture mechanics will be studied, and the crack tip behaviors of several crack models of superconducting cylinder and disc will be further numerically analyzed. Finally, model experimental study should be carried out for some crack problems of superconducting cylinder and disc. The ultimate purpose of this project is to obtain reasonable degree of the crack models of superconducting materials based on these theoretical, numerical and experimental results, and further to lay the theoretical foundation for both design and manufacturing of superconducting components.

第II类高温超导体，由于可在液氮环境下工作，具有巨大的应用前景。该类材料制造和使用过程中常含裂纹，目前，尽管人们对超导材料断裂力学问题做了一些探讨，但无论理论研究、数值分析还是实验表征都还远远不够。本项目拟以超导柱体、圆盘为研究对象，从解析、数值模拟和实验三种途径分析第II类高温超导体在初始磁场和磁场下降过程中由电磁力致使的断裂特性。研究内容包括：首先采用积分变换和奇异积分方程技术给出超导柱体硬币形及环形裂纹问题的解析解，研究场冷和零场冷情形下，外加初始磁场和磁场下降对裂纹断裂行为的影响；探究数值方法特别是（多）等参元及（多）等参元和无限元耦合方法在均匀（非均匀）超导体断裂力学中的应用问题，数值分析超导柱体及圆盘中多种裂纹模型裂尖性态；进行超导柱体和圆盘的模型实验研究。研究的最终目的是根据这些解析、数值分析和实验结果，得到超导材料裂纹模型的合理度，为超导元器件的设计与制造奠定理论基础。

第II 类高温超导体，由于可在液氮环境下工作，具有巨大的应用前景。该类材料制造和使用过程中常含裂纹，因而关于这类材料裂纹问题研究具有重要价值。项目组通过四年的努力，在超导柱体、圆盘断裂力学理论等方面取得了一系列研究成果，主要包括不同形式裂纹超导柱在电磁力、热冲击荷载作用下的力学特性及断裂问题；含不同形式孔洞薄超导盘在垂直作用磁场中的磁致伸缩及应力分布问题；功能梯度超导薄膜的中心裂纹问题。在扩展有限元法应用方面取得新的突破，针对电磁弹性材料界面裂纹断裂行为数值分析,提出了一种分析二维无限大电磁材料界面裂纹问题的XFEM，建立了XFEM求解电磁材料界面裂纹问题的数值方案，给出了该问题新的裂尖增强函数。截止到2017年2月，已发表SCI收录论文20篇，另投稿论文2篇。尽管本项目取得大量成果，但限于时间和精力，课题组在Spectromag PT 系统和Q400 的联合开发、应用方面还没有取得实质性突破，项目组成员将在这个方面继续努力。

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