EFFECT OF NON-UNIFORMITY OF CRITICAL CURRENT DENSITY ON ELECTROMAGNETIC MECHANICAL PROPERTIES OF SUPERCONDUCTING THIN STRIP
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摘要: 高温超导材料因其高载流能力、低交流损耗等优点而备受科学界和工程技术领域的广泛关注，然而，在实际应用中出现的一系列电磁力学问题严重阻碍了其在工程技术领域的发展。基于此，该文开展了临界电流密度的非均匀性对矩形超导薄板内电学及力学特性影响的研究。考虑临界电流密度沿超导薄板宽度方向非均匀分布，给出了薄板内感应磁场及感应电流分布的解析表述，基于超导临界态Bean模型和弹性力学平面应力方法，得到了超导薄板内磁通钉扎力、应力、应变及磁致伸缩的解析表达式。计算结果表明，临界电流密度的非均匀性并不改变超导薄板内的磁通钉扎力、应力及应变沿板宽度方向的分布规律。然而，非均匀分布的临界电流密度促使薄板内的磁通线穿透深度增大，超导薄板内的最大压应力值增大，且最大压应力发生的位置随传输电流的增大向薄板中心靠近。当传输电流从最大值减小时，薄板内产生的最大拉应力值减小。临界电流密度非均匀分布时，薄板内发生的最大磁致伸缩量较均匀分布情形下显著减小，磁致伸缩曲线形态发生改变。因此，临界电流密度的非均匀性是超导材料力学和电学性能的研究中不可忽视的因素。Abstract: High temperature superconducting materials have attracted many attentions in the field of science and technology due to their outstanding advantages such as high current carrying capacity and low AC loss, etc. However, a series of electromagnetic mechanical problems in practical applications seriously hinder its development in the field of engineering technology. Thusly, a superconducting thin rectangular strip is considered to transport current. The influence of the inhomogeneous critical current density on the electrical and mechanical properties are analyzed. The critical current density is assumed to distribute nonuniformly along the width of the superconducting thin strip, then the analytical expressions for the induced current and magnetic field in the thin strip are developed. Based on a superconducting critical Bean model, the analytical expression of the flux pinning force is obtained. The plane stress method of the elastic theory is adopted to calculate the flux pinning stress and strain, then the magnetostriction in the superconducting thin strip are obtained. The simulating results show that: the nonuniformity of the critical current density has no influence on the distribution law of the flux pinning force induced in the superconducting thin strip, the same as the flux pinning stress and strain do. However, the nonuniformly distributed critical current density increases the penetration depth of the trapped magnetic flux. The value of the maximum compressive stress is also increased, and its position approaches to the center of the thin strip when the transport current increases. The maximum tensile stress appears in the thin strip when reducing the transport current from its maximum value, and its value decreases with the decrement of the transport current. The shape of the magnetostriction curve changes when the distribution of the critical current density is inhomogeneous, and its maximum value is less to that with homogeneous critical current density. All in all, the influence of the inhomogeneous critical current density cannot be neglected during the study of the superconducting materials.
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图 7 超导薄板内的应变随梯度参数β的分布
Figure 7. Distribution of strain with gradient parameter β in superconducting thin strip
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