Stress Intensity Factor Solutions for Internal Longitudinal Semi-Elliptical Surface Flaws in a Cylinder Under Arbitrary Loadings

The behavior of semi-elliptical surface flaws in cylinders is of interest in the technology of pressure vessels. The object of this study is to determine the stress intensity factor distribution around the crack front under arbitrary loading conditions for a longitudinal semi-elliptical flaw with a/c = 1/3 and R_i/t = 10; where a is the semi-minor axis of the ellipse, c is the semi-major axis, R_i is the inside radius of the cylinder, and t is the cylinder thickness. Three crack depths are studied under various loading conditions: a/t = 0.25, 0.50, and 0.80.

The finite element method is used to determine the displacement solution. Parks' stiffness derivative method is used to find the stress intensity factor distribution around the semi-ellipse. The immediate crack tip geometry is modeled by use of a macroelement containing over 1600 degrees of freedom.

Four separate loadings are considered: (1) constant, (2) linear, (3) quadratic, and (4) cubic crack surface pressure. From these loadings nondimensional magnification factors are derived to represent the resulting stress intensity factors. By the method of superposition, comparisons are made with other investigators for pressure loading of a cylinder; the results agree within 8 percent of published results.