高温超导块材在电磁力作用下的断裂特性理论研究
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摘要
高温超导体中的裂纹问题是超导体力学特性研究的一个重要方面。基于裂纹对超导体应用的限制,本博士论文研究了超导体受电磁力和温度变化引起的热应力对含有裂纹超导体的影响,对无限长超导体和有限长超导体在电磁力和热应力作用下的裂纹问题做了详细的研究。
首先,研究了无限长超导体在电磁力作用下,超导体内包含Ⅰ型、Ⅱ型以及混合型裂纹的应力强度因子随磁场的变化关系。分别讨论了零场冷和场冷情形时这三种裂纹的断裂参数随磁场的变化关系,在磁场减小的过程中,超导体内部的裂纹在电磁力的作用下将会有开裂的趋势,开裂趋势反映在应力强度因子与J积分的变化过程中。
其次,研究了有限长超导体在电磁力作用下的断裂行为。将无限长超导裂纹问题扩展到有限尺度的超导体上,在零场冷和场冷激励下,讨论了磁化系数和长径比对超导体断裂参数的影响。在磁化系数不变的情形下,超导体尺度越短,应力强度因子越大;磁化系数对较短超导体的应力强度因子有明显的影响,当超导体尺度较长时,磁化系数的影响很小。此外,Ⅰ型应力强度因子的数值大于Ⅱ型应力强度因子的值,这表示裂纹的开裂主要是基于拉伸的Ⅰ型开裂。
最后,研究了脉冲场激励和热致对超导体断裂参数的影响。考虑了脉冲场激励下三种类型裂纹在磁化过程中的断裂趋势,随着磁场的减小,应力强度因子增大;由于在脉冲磁场的最大点处超导体整体受最大压力,所以在这一时刻应力强度因子最小且为负值,由这一时刻开始,应力强度因子逐渐增大;最大磁场较大的脉冲场,所对应的应力强度因子变化越快。继而讨论了热致因素对超导断裂问题的影响。从超导态到正常态转变过程中,巨大的温差所引起的热应力对热应力强度因子影响较为明显。随着温度的上升,热应力强度因子增大,这表示在超导体由临界温度向室温的变化过程中,裂纹变得容易开裂。此外,不同的裂纹长度对热应力强度因子也有较大的影响,裂纹长度越长,热应力强度因子越大。
It has been known that some fracture or crack is induced, which plays an important role in the safety design when a bulk superconductor is used in practice. In practical applications, the superconductor is often subjected to several forces like electromagnetic force, thermal stress, which maybe lead to fracture of superconductors. This dissertation presents some analysis of fracture behavior of the superconductors subjected to the environment of electromagnetic fields and low temperature, where the bulk superconductors have either infinite or finite size.
Firstly, the crack problem of the infinite superconductor is considered in the process of zero-field cooling (ZFC) and field cooling (FC). The superconductor contains three type of cracks, namely, Mode-Ⅰ, Mode-Ⅱand mixed Mode. The fracture behaviors change with the magnetic field when the applied field is decreased. Both the stress intensity factors and J integral can be used to describe the trend of crack growth.
Next, the fracture behaviors of finite superconductors are simulated under electromagnetic force by using the numerical method. A model for the calculation of the fracture behavior of finite type-Ⅱsuperconductors is presented. The demagnetization effect is considered by using a simple approximation of a constant demagnetization factor. The stress intensity factors of finite superconductors are calculated in the process of zero-field cooling (ZFC) and field cooling (FC). Numerical results obtained show that the stress intensity factors increase with the increase of applied field. The effects of the susceptibility and ratio of length to diameter are presented. From the results, the stress intensity factors increase with the decrease of applied field, comparing to the Mode-Ⅱ, a larger change is found in the stress intensity factors of the Mode-Ⅰ, these results display that the crack growth is the Mode-Ⅰfracture mainly.
Finally, the fracture behaviors of infinite superconductors are displayed in the process of pulse magnetic field and temperature change. The fracture trend is predicted in pulse field magnetization. The lower the magnetic field is, the larger the stress intensity factors. When pulse magnetic field is maximum, the superconductor subject to maximal pressure so that the stress intensity factors have minimum value. The change of stress intensity factors is faster for the larger pulse field. Additional, the effects of temperature are considered. A theoretical analysis is used to investigate the fracture behavior of a large single domain YBCO superconductor under thermal stress based on the two-dimensional theory of anisotropic thermoelasticity. The thermal stress intensity factors are obtained due to a uniform heat flux by a line crack in a generally half plane superconductor. It is found that the thermal stress intensity factors decrease with the decrease of temperature, and while the longer the crack length is, the larger the stress intensity factors. Furthermore, the J integral at the crack tip is also investigated, a similar behavior to the thermal stress intensity factors is found. These results are benefit for us to understand the fracture mechanism of superconductor both in theory and application.
首先,研究了无限长超导体在电磁力作用下,超导体内包含Ⅰ型、Ⅱ型以及混合型裂纹的应力强度因子随磁场的变化关系。分别讨论了零场冷和场冷情形时这三种裂纹的断裂参数随磁场的变化关系,在磁场减小的过程中,超导体内部的裂纹在电磁力的作用下将会有开裂的趋势,开裂趋势反映在应力强度因子与J积分的变化过程中。
其次,研究了有限长超导体在电磁力作用下的断裂行为。将无限长超导裂纹问题扩展到有限尺度的超导体上,在零场冷和场冷激励下,讨论了磁化系数和长径比对超导体断裂参数的影响。在磁化系数不变的情形下,超导体尺度越短,应力强度因子越大;磁化系数对较短超导体的应力强度因子有明显的影响,当超导体尺度较长时,磁化系数的影响很小。此外,Ⅰ型应力强度因子的数值大于Ⅱ型应力强度因子的值,这表示裂纹的开裂主要是基于拉伸的Ⅰ型开裂。
最后,研究了脉冲场激励和热致对超导体断裂参数的影响。考虑了脉冲场激励下三种类型裂纹在磁化过程中的断裂趋势,随着磁场的减小,应力强度因子增大;由于在脉冲磁场的最大点处超导体整体受最大压力,所以在这一时刻应力强度因子最小且为负值,由这一时刻开始,应力强度因子逐渐增大;最大磁场较大的脉冲场,所对应的应力强度因子变化越快。继而讨论了热致因素对超导断裂问题的影响。从超导态到正常态转变过程中,巨大的温差所引起的热应力对热应力强度因子影响较为明显。随着温度的上升,热应力强度因子增大,这表示在超导体由临界温度向室温的变化过程中,裂纹变得容易开裂。此外,不同的裂纹长度对热应力强度因子也有较大的影响,裂纹长度越长,热应力强度因子越大。
It has been known that some fracture or crack is induced, which plays an important role in the safety design when a bulk superconductor is used in practice. In practical applications, the superconductor is often subjected to several forces like electromagnetic force, thermal stress, which maybe lead to fracture of superconductors. This dissertation presents some analysis of fracture behavior of the superconductors subjected to the environment of electromagnetic fields and low temperature, where the bulk superconductors have either infinite or finite size.
Firstly, the crack problem of the infinite superconductor is considered in the process of zero-field cooling (ZFC) and field cooling (FC). The superconductor contains three type of cracks, namely, Mode-Ⅰ, Mode-Ⅱand mixed Mode. The fracture behaviors change with the magnetic field when the applied field is decreased. Both the stress intensity factors and J integral can be used to describe the trend of crack growth.
Next, the fracture behaviors of finite superconductors are simulated under electromagnetic force by using the numerical method. A model for the calculation of the fracture behavior of finite type-Ⅱsuperconductors is presented. The demagnetization effect is considered by using a simple approximation of a constant demagnetization factor. The stress intensity factors of finite superconductors are calculated in the process of zero-field cooling (ZFC) and field cooling (FC). Numerical results obtained show that the stress intensity factors increase with the increase of applied field. The effects of the susceptibility and ratio of length to diameter are presented. From the results, the stress intensity factors increase with the decrease of applied field, comparing to the Mode-Ⅱ, a larger change is found in the stress intensity factors of the Mode-Ⅰ, these results display that the crack growth is the Mode-Ⅰfracture mainly.
Finally, the fracture behaviors of infinite superconductors are displayed in the process of pulse magnetic field and temperature change. The fracture trend is predicted in pulse field magnetization. The lower the magnetic field is, the larger the stress intensity factors. When pulse magnetic field is maximum, the superconductor subject to maximal pressure so that the stress intensity factors have minimum value. The change of stress intensity factors is faster for the larger pulse field. Additional, the effects of temperature are considered. A theoretical analysis is used to investigate the fracture behavior of a large single domain YBCO superconductor under thermal stress based on the two-dimensional theory of anisotropic thermoelasticity. The thermal stress intensity factors are obtained due to a uniform heat flux by a line crack in a generally half plane superconductor. It is found that the thermal stress intensity factors decrease with the decrease of temperature, and while the longer the crack length is, the larger the stress intensity factors. Furthermore, the J integral at the crack tip is also investigated, a similar behavior to the thermal stress intensity factors is found. These results are benefit for us to understand the fracture mechanism of superconductor both in theory and application.
引文
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