Three dimensional stress intensity factor for large arrays of radial internal surface cracks in a cylindrical pressure vessel

The objective of this study is to present the mode I stress intensity factor distribution (SIF) along the crack-front for a wide array of semicircular and semi-elliptical surface cracks inside of a pressurized thick-walled cylinder. A three-dimensional finite element package ANSYS is used to evaluate the SIF for multicracked cylinder with number of cracks from n=1 to 128, the ratio of crack-depth to the wall thickness a/t=0.05 to 0.6, the ellipticity of the crack (the crack-depth to the semi-crack length) a/c=0.2 to 1.5, the ratio of the outer to the inner radius ro/ ri=2. A substructuring technique is introduced which solved a coarse model meshed with ten-node isoparametric elements and applied the resulting displacements in the boundary surface of a submodel which is built employing singular elements along the crack-front to produce the 1/√r singularity . The SIF is evaluated using nodal-displacement method. To validate the modeling and analysis procedure of the present results various configurations were solved using this method and compared to other finite element solutions. The present results were in very good agreement: less than 5 % comparing with Raju and Newman\u27s results and within 8 % of Kirkhope\u27s results. An empirical equation to calculate the maximum SIF, was developed in this study. The equation was obtained by nonlinear fitting of the finite element results and the error was within ± 5.7 %