Stress intensity factors and weight functions for semi-elliptical cracks using finite element alternating method

Abstract

Finite element alternating methods are used to evaluate the stress intensity factors and weight functions for semi-elliptical surface crack problems. The analytical solutions for an infinite solid with an embedded crack are determined using an elliptical coordinate system and gravity potential functions. The analytical solutions are derived for the cases of shear tractions and normal tractions, separately. Superposition gives the general solutions. The analytical solutions and the finite element method, in conjunction with alternating technique, are used to evaluate the stress intensity factors for a solid with a semi-elliptical surface crack, subjected to arbitrary loads. A general approach to evaluate the weight functions for a plate with a semi-elliptical surface crack is also formulated. The numerical results show good agreement with those from classical solutions. Finally, the method is applied to a welded plate T-joints with semi-elliptical surface cracks to obtain stress intensity factors.