Weight function method and stress intensity factor for two unsymmetric through-thickness and quarter-elliptical corner cracks at circular hole

Two unsymmetric through and quarter-elliptical corner cracks at a circular hole are frequently encountered in aircraft structures. Stress intensity factors for these crack geometries are the prerequisite for aircraft damage tolerance analysis. However, compared to single and symmetric double crack(s) case, the present two unsymmetric through and corner cracks at a hole is much more complicated because more geometric variables are involved. In the present article, the twodimensional displacement-based weight function method is extended to derive the weight functions of two unsymmetric hole-edge cracks. Accurate and wide-range weight functions and stress intensity factors are obtained. The two-dimensional weight function for the hole-edge cracks is further used in the slice synthesis weight function method to compute stress intensity factors for two unsymmetric quarter-elliptical corner cracks at a circular hole. The solution accuracy is extensively verified through comparisons to stress intensity factors obtained using finite element analysis. Compared to 3D finite element method, the present slice synthesis weight function method is 500 times faster, and therefore can provide accurate and very efficient tool for fatigue and fracture analysis of structures containing through and quarter-elliptical corner hole-edge cracks.

Automated summary

This article discusses the stress intensity factor calculation problem of two commonly encountered unsymmetric through and corner cracks in aircraft structures. By extending the two-dimensional displacement-based weight function method, accurate weight functions and stress intensity factors are obtained. The weight function is further used in the slice synthesis weight function method to compute stress intensity factors for two unsymmetric quarter-elliptical corner cracks at a circular hole. The solution accuracy is verified by comparing with results obtained using finite element analysis. The slice synthesis weight function method is 500 times faster than the 3D finite element method and provides an accurate and efficient tool for fatigue and fracture analysis.