脉冲励磁下高温超导线圈内部应力分布及裂纹扩展研究

Based on the strategic demand of the renewal of high temperature superconducting power device, considering the degradation and non-uniform distribution of critical current density under strong pulsed magnetic field, and focusing on the scientific problems associated with the safety and stability of HTS coils, by aiming at the key issues about how to accurately predict the distribution of magnetic field, current density and stress, and reduce the local strain in the HTS coils and suppress crack propagation. Therefore, in this proposal we should study intensively the stress distribution and its effect on the crack propagation in HTS coils under pulsed magnetic field excitation. We should determine the equivalent elastic modulus and equivalent thermal expansion coefficient according to the principle of energy equivalence and the theory of composite materials. Meanwhile, we should study the magnetic flux distribution of HTS coils in different excitation processes by a numerical method based on TDGL equations, which are verified by the analytical calculation results of the critical state model and viscous flux flow equations, and the actual current density of the HTS coils is estimated by the finite element analysis method in the case of re-distribution of the current, then the theoretical model could be modified to accurately predict the distribution of internal stress in HTS coils under different temperature and excitation speed according to the experimental results and considering the complex mechanical behavior and thermal phenomena of electromagnetic structures of HTS coils. Moreover, focusing on the problem of crack propagation in HTS coils, we should introduce the stress distribution by the construction of the spring element and the dummy node fault unit, and energy release rate and stress intensity factor are calculated by the finite element model which is based on the BSWI finite element virtual crack closure method, then the crack propagation law could be revealed by the wavelet multi-scale analysis method and the suppression method of crack propagation could be found, which could provide theoretical support for safe and stable operation of HTS coils.

面向超导电力装置升级换代的战略需求，针对如何精确预测超导线圈内部磁场、电流及应力分布并减小局部应变、抑制裂纹扩展，考虑脉冲强磁场作用下临界电流的退化及非均匀分布，本项目深入研究脉冲励磁过程中线圈内部应力分布及其对裂纹扩展的影响。根据能量等效原理和复合材料理论确定等效弹性模量和热膨胀系数；采用TDGL方程研究线圈在不同励磁过程中的磁通分布，通过临界态模型和黏性磁通流动方程的计算结果验证，利用有限元分析方法估算在电流重新分布情况下线圈中的实际电流密度，考虑复杂的热现象并结合实验结果修正理论模型使之能够精确预测不同温度和励磁速度下线圈内应力分布；针对裂纹扩展问题，通过构造弹簧单元和哑节点断裂单元引入应力，建立基于BSWI有限元虚拟裂纹闭合法的含多裂纹结构的有限元模型计算能量释放率和应力强度因子，通过小波多尺度分析揭示裂纹扩展规律并力图找到影响裂纹扩展的主要因素，为超导线圈安全稳定运行提供理论依据

高温超导线圈是变压器、限流器、电机、储能系统及磁约束热核聚变反应堆等超导电力装置的核心部件，其安全稳定运行十分重要。高温超导线圈运行电流达不到其设计要求的大部分原因来源于机械损伤与断裂破坏，即影响超导线圈性能的主要因素就是超导线圈所承受的应力应变，其临界电流密度退化主要也是由自场和应力作用引起的。面向超导电力装置升级换代的战略需求，针对如何精确预测超导线圈内部磁场、电流及应力分布并减小局部应变、抑制裂纹扩展，考虑脉冲强磁场作用下临界电流的退化及非均匀分布，本项目深入研究脉冲励磁过程中线圈内部应力分布及其对裂纹扩展的影响。针对洛伦兹力作用下的超导线圈中心含有穿透裂纹的断裂行为，假设裂纹对屏蔽电流与磁场的扰动可以忽略不计，将电磁力对裂纹的作用转换为施加在边界上的合力，并利用有限元方法求解在零场冷却与场冷却情况下，对超导线圈内的裂纹尖端的应力强度因子进行数值求解。考虑零场冷却、场冷却以及脉冲磁化过程，研究了具有非均匀临界电流分布的超导线圈中心裂纹的一般问题，引入了非均匀参数η用于表征非均匀超导线圈的临界电流密度分布。基于平面应变法和J积分理论，得到了非均匀参数η对磁场分布和应力强度因子变化的影响结果表明，超导线圈和金属管的杨氏模量和厚度比率都显着影响超导线圈中的应力分布。我们在脉冲励磁过程中通过指数临界状态模型系统地研究了上述超导线圈中磁通钉扎引起的应力。此外，金属管有效地降低了磁化过程中超导线圈的拉应力，适当选择金属管的材料参数和尺寸可以有效改善超导线圈的性能。本项目根据脉冲励磁过程中线圈磁通分布→实际电流密度→应力分布的分析过程，结合实验测量获得能够精确预测不同励磁过程中不同温度和励磁速度下线圈精确的磁场、电流和应力分布的理论模型，并基于BSWI 有限元虚拟裂纹闭合法建立复杂电磁结构裂纹扩展的小波多尺度分析模型，为线圈安全运行和维护提供理论依据。

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