In the paper, the fracture of functionally graded superconductor under pulsed magnetic field is numerically analyzed, and the effect of electromagnetic stress and thermal stress on crack problem under pulsed magnetic field is studied. A FEM model based on H formula and heat transfer equation is proposed for the electromagnetic thermal behavior of inhomogeneous superconductors with central cracks. The influence of the gradient parameter $\eta$ of critical current density on the stress intensity factor was investigated. The numerical results show that the gradient parameter $\eta$ has a great influence on the change of stress intensity factor caused by electromagnetic force and thermal strain with time, which makes the crack easy to expand. In addition, the results show that the electromagnetic stress decreases gradually with the increase of crack length, and the thermal stress has a significant effect on the stress intensity factor.

本文对脉冲磁场下功能梯度超导体的断裂进行了数值分析，研究了电磁应力和热应力对脉冲磁场下裂纹问题的影响。针对具有中心裂纹的非均匀超导体的电磁热行为，提出了一种基于H公式和传热方程的有限元模型。梯度参数的影响$\eta$研究了临界电流密度对应力强度因子的影响。数值结果表明梯度参数$\eta$对电磁力和热应变引起的应力强度因子随时间的变化有很大的影响，使裂纹容易扩展。此外，结果表明，随着裂纹长度的增加，电磁应力逐渐减小，而热应力对应力强度因子的影响显着。