T-Stress solutions for a semi-elliptical axial surface crack in a cylinder subjected to mode-I non-uniform stress distributions

Abstract

Abstract This paper presents the T -stress solutions ( T 11 and T 33 ) for semi-elliptical axial surface cracks in a cylinder subjected to mode-I non-uniform stress on the crack surface. Two cylindrical geometries with inner radius ( R i ) to wall thickness ( t ) ratios R i / t = 5 and 10 were considered. The T -stresses were applied along the crack front for normalized crack depth values a / t of 0.2, 0.4 and 0.5 and aspect ratios a / c of 0.2, 0.4, 0.6 and 1.0. Three stress distribution; uniform, linear and parabolic were applied to the crack face. In addition to these solutions, concrete formulation of the superposition principle is given for the T 33 -stress, which is known as an elastic parameter that describes the out-of-plane crack tip constraint effect. Then, the validity of the formulation was shown through application of our T -stress solutions to the problem of an axial semi-elliptical surface crack in a cylinder subjected to internal pressure, and checking that the principle of superposition holds for the problem.