The stress intensity factors (SIFs) for two-dimensional cracks are extracted using the p-version finite element method (P-FEM) and the contour integral method. Several numerical experiments, e.g., crack initiating from the edge of a circular hole under an unidirectional uniform tension and two equal-length, unequal-length hole–edge cracks, respectively, at a rectangular plate, an inclined centered crack under uniaxial tension at a square plate and a pipeline crack model, are used to demonstrate the accuracy and effectiveness of the approaches. SIFs are presented for the effects of various crack lengths and length–width ratio. Numerical results are analyzed and compared with reference solutions and results obtained by the Voronoi cell finite element method, boundary element method, high-order extended finite element method (high-order XFEM) and commercial finite element software ABAQUS in the available literature. Numerical results are in good agreement with the benchmark problems and show faster convergence rate, higher accuracy and better numerical stability.

使用p版本有限元方法（P-FEM）和轮廓积分方法提取二维裂纹的应力强度因子（SIF）。几个数值实验，例如，在单向均匀拉力下从圆形孔的边缘产生裂纹，在矩形板上分别出现两个等长，不等长的孔-边缘裂纹，在单轴拉力下在一个单轴拉力下出现一个倾斜的中心裂纹。方板和管道裂纹模型用于证明该方法的准确性和有效性。提出了SIF，以说明各种裂纹长度和长宽比的影响。分析了数值结果，并将其与参考解进行了比较，并通过Voronoi单元有限元方法，边界元方法，高阶扩展有限元方法（high-order XFEM）和商业有限元软件ABAQUS在可用的文献中。数值结果与基准问题吻合良好，并且显示出更快的收敛速度，更高的精度和更好的数值稳定性。