Weight function and stress intensity factors for external circumferential surface cracks with high aspect ratio in cylinders

Surface cracks with crack aspect ratio greater than unity have been detected in pipes and cylindrical vessels vulnerable to fatigue and stress corrosion cracking. Accurate solutions of stress intensity factors are prerequisite for predicting the crack growth behaviour of cracked cylinders. In this study, a weight function for the calculation of stress intensity factors for external circumferential surface cracks with high aspect ratio in hollow cylinders is developed. First, three-dimensional finite element models for the surface cracks with aspect ratios 1.0 ≤ a/c ≤ 2.0, ratios of crack depth to thickness 0.1 ≤ a/T ≤ 0.8 and ratios of thickness to inner radius 0.02 ≤ T/R_i ≤ 0.2 are developed and validated. An efficient numerical integration scheme using isotropic elements and the Gauss-Legendre quadrature is suggested for evaluating the integral involving weight function. The unknown weight function coefficients can be then determined by the stress intensity factors obtained from finite element models. Comprehensive comparisons between the results predicted by the derived weight function and finite element analysis are performed for various one-dimensional and two-dimensional stress distributions, indicating a fairly good agreement. The maximum relative errors with respect to finite element solutions are within 8 % for both the surface and deepest points. The present results can complement the database of stress intensity factors and weight function previously developed for external circumferential surface cracks with low aspect ratios 0.2 ≤ a/c ≤ 1.0 in cylinders.