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Research Papers

# Stress and Stress Intensity Factor Near Notches in Thick Cylinders

[+] Author and Article Information
Anthony P. Parker

Defence Academy of the United Kingdom,  University of Cranfield, Swindon, SN6 8LA, Englandparker.ETR@tiscali.co.uk

Edward Troiano

US Army WS & T Center, Benet Labs, Watervliet, NY 12189–4050edward.troiano@us.army.mil

John H. Underwood

Battelle Scientific Services, Watervliet, NY 12189–4050treaclemine@hughes.net

J. Pressure Vessel Technol 134(4), 041002 (Jul 09, 2012) (7 pages) doi:10.1115/1.4006348 History: Received November 07, 2011; Revised December 02, 2011; Published July 09, 2012; Online July 09, 2012

## 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.

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Topics: Stress , Cylinders , Pressure

## Figures

Figure 1

(a) Internal pressure in tube with notch, (b) external tension on tube with notch, and (c) external pressure on solid disk

Figure 2

Predicted stress concentration factors for pressurized thick cylinder, b/a = 2, with moderate-size notch

Figure 3

Complex plane with elliptical hole under remote uniaxial tension T

Figure 4

Stresses close to elliptical hole in sheet under uniaxial tension T

Figure 5

Hoop stresses in pressurized, semicircular notched tube, b/a = 2; current model, finite element solution [19], and analytic lame solution for tube without notch

Figure 6

Hoop stresses in an ideally autofrettaged, semicircular notched tube, b/a = 2; current model, finite element solution [19], and analytic Tresca plane-stress solution for tube without notch

Figure 7

Near-notch stress intensity factors in pressurized tube, inner radius 60 mm, semicircular notch depth 3 mm

Figure 8

Near-notch stress intensity factors in autofrettaged tube, inner radius 60 mm, semicircular notch depth 3 mm

Figure 9

Composite plot of stress intensity factors and positive stress intensity factor ranges

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