In this paper, a square central crack problem is investigated for an infinitely long square cross section superconducting column under electromagnetic forces. The generalized Irie-Yamafuji critical current densities model and the magnetically impermeable crack surface condition are adopted for both the zero-field cooling (ZFC) and the field cooling (FC) activation processes. The distributions of magnetic field and current density are derived in the superconductor, where the crack affected region is introduced. Based on the finite element method (FEM), the stress intensity factors (SIFs) at the edge of square crack in the process of field descent are numerically calculated. Numerical results show that the SIFs at the corner points of square crack are generally larger than the values of other dots at the four edges of square crack in the process of magnetization. In the meantime, the FC process is usually easier to promote crack propagation than the ZFC activation. In addition, both the crack sizes and the introduced index $\gamma$ in the generalized Irie-Yamafuji critical current density model have important and different effects on the crack growth in the ZFC and FC activation processes. These results should be useful for the application of superconducting materials.

本文研究了无限长正方形截面超导柱在电磁力作用下的正方形中心裂纹问题。零场冷却（ZFC）和场冷却（FC）激活过程均采用通用的Irie-Yamafuji临界电流密度模型和不透磁裂纹表面条件。在超导体中导出了磁场和电流密度的分布，在超导体中引入了裂纹影响区域。基于有限元法（FEM），数值计算了场下降过程中方形裂纹边缘的应力强度因子（SIF）。数值结果表明，在磁化过程中，方形裂纹拐角处的SIF通常大于方形裂纹四个边缘处的其他点的值。同时，与ZFC活化相比，FC过程通常更容易促进裂纹扩展。此外，裂纹尺寸和引入的指数$\gamma$在广义的Irie-Yamafuji临界电流密度模型中，ZFC和FC活化过程中的裂纹扩展具有重要且不同的影响。这些结果对于超导材料的应用应该是有用的。