Stress and Stress Intensity Factor Near Notches in Thick Cylinders

Abstract

This work investigates the impact of semi-elliptical notches (erosion grooves) at the bore of pressurized and autofrettaged thick cylinders. It provides a robust yet rapid method to determine the rapidly varying stress in the near-notch region prior to crack development and crack tip stress intensity factor after a crack develops at the notch root. The procedure involves a sequence of asymptotic solutions and adjustments. A superposition is presented for the stress concentration factor (SCF) of a small edge notch in a pressurized cylinder with bore pressure infiltrating and acting upon the notch surface. A procedure for adjusting this SCF to account for a varying pre-existing stress field is described. This provides accurate predictions for notch depths of up to 15% of wall thickness. Stress variation beyond the notch root is determined by scaling analytic solutions. Solution accuracy appears to be approximately 5%. Stress profiles were used to calculate stress intensity factor (SIF) for cracks emanating from the notch root and deep into the wall. There are notable differences between SIF behavior in the pressurized tube and in the autofrettaged tube. The main reason for this difference is that compressive reyielding near the notch disrupts the residual compressive stress profile over an extended distance. This leads to the conclusion that a crack originating from a notch in an autofrettaged tube exhibits a much higher cyclic SIF range during pressurization than the same length crack originating from the bore. This will cause higher fatigue crack growth rates and shorter fatigue lifetimes.