Three-dimensional finite element analysis of a semi-elliptical circumferential surface crack in a carbon steel pipe subjected to a bending moment

The study of crack growth is important to evaluate the structural integrity of nuclear power plant piping from the viewpoint of the leak-before-break concept. A thick-walled pipe with a semi-elliptical circumferential surface crack of different initial crack sizes subjected to a bending load is considered for the analysis. A three-dimensional finite element code using ANSYS (Version 8) has been developed with the capability to handle singularity and to evaluate the mode I stress intensity factor based (SIF) on the displacement extrapolation method. The crack growth rate has been calculated by applying the Paris law. The fatigue life predicted for crack penetration through the wall thickness has been compared with that of experimental results in published literature. The deviation is found to be within 17 per cent. Using the finite element model, data in respect of the stress intensity factor for different stresses, thicknesses, crack depths, and half-crack-length conditions have been predicted. Based on the data, a new correlation has been evolved to evaluate the stress intensity factor range in the depth and surface directions. The stress intensity factor has also been calculated by the empirical relations given in the ASM Handbook. The predicted fatigue life using the plate equation deviates from experimental results by a maximum of 77 per cent while the deviation of the prediction using the pipe equation is more than 100 per cent in many cases. The predictions with the proposed correlation give better results that fall within 21 per cent deviation from the experimental results.