Accurate stress intensity factor solutions for corner cracks at a hole

Laboratory test and in-service experience shows fatigue cracks at holes exhibit unsymmetric growth; thus, the need for the new solutions is paramount. Stress intensity factor, K, solutions for symmetric and unsymmetric corner cracks at a hole subject to general loading were determined using a hp-version of the finite element method (FEM) in conjunction with a mathematical splitting scheme to enable efficient, accurate calculations. In traditional applications of the FEM, mesh generation is labor intensive; however, using the splitting scheme, stress intensity functions are obtained without explicitly including the crack in the FE mesh of the global structure. By using the hp-version of FEM, a set of K-solutions converging exponentially fast to the exact solution is obtained. The crack is analyzed in the local domain with easily generated FE meshes. All structurally significant crack shapes were considered; specifically, crack depth to crack length ratios (a/c) of 0.1–10.0, crack depth to sheet thickness ratios (a/t) of 0.10–0.99, and hole radius to sheet thickness ratios (r/t)=1.0. The loading conditions were remote tension, remote bending, and pin loading (bearing). In addition, all combinations of a/c and a/t are analyzed at each side of the hole; thus 226,875 solutions were developed with control of the error in the computed K solutions. Calculated relative error is generally much smaller than 1% along the entire crack front including the vertex regions. Comparisons are made to solutions in the open literature. The new K solutions show the literature solutions are, in general, accurate for all three load conditions; however, for the extreme cases of a/c, a/t, and r/t; the literature solutions differ by as much as 26%.