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RESEARCH PAPERS

# The Effect of Autofrettage on Uniform Arrays of Three-Dimensional Unequal-Depth Cracks in a Thick-Walled Cylindrical Vessel

[+] Author and Article Information
M. Perl1

Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering,  Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

B. Ostraich

Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering,  Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

1

Aaron Fish Professor of Mechanical Engineering-Fracture Mechanics and Dean, Faculty of Engineering Sciences

J. Pressure Vessel Technol 127(4), 423-429 (May 04, 2004) (7 pages) doi:10.1115/1.2043210 History: Received December 19, 2002; Revised May 04, 2004

## Abstract

The distribution of the mode I stress intensity factor (SIF), resulting from autofrettage, along the fronts of radial, semi-elliptical surface cracks pertaining to large uniform arrays of unequal-depth cracks emanating at the bore of an overstrained thick-walled cylinder is studied. The three-dimensional analysis is based on the “two-crack depth level model” previously proposed and is performed via the finite element method employing singular elements along the crack front. The autofrettage residual stress field is simulated using an equivalent thermal load. The distribution of $KIA$, the stress intensity factor due to autofrettage, for numerous uneven array configurations bearing $n=n1+n2=8–128$ cracks, a wide range of crack depth-to-wall thickness ratios, $a1∕t=0.01–0.4$, and various crack ellipticities, $a1∕c1=0.3–1.5$, are evaluated for a cylinder of radii ratio $Ro∕Ri=2$. The results clearly indicate that unevenness, as reflected in $KIA$ distribution, depends on all three parameters (i.e., the number of cracks in the array, cracks’ depth, and cracks’ ellipticity). The “interaction range” for the different combinations of crack arrays and crack depths is then evaluated. The range of influence between adjacent cracks on the maximal SIF, $KAmax$, is found to be dependent on the density of the array, as reflected in the intercrack aspect ratio, as well as on the cracks’ ellipticity.

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## Figures

Figure 1

Schematic of the multicracked cylinder

Figure 2

The multicracked cylinder: (a) segment containing two unequal cracks: a1 and a2 are the crack depths of the fixed and varying crack subarrays, respectively; (b) definition of ϕ; and (c) typical element breakdown

Figure 3

Normalized maximal SIF as a function of the varying crack depth for an array of n1+n2=32 cracks, for fixed crack depth of a1∕t=0.2 and ellipticity a1∕c1=a2∕c2=0.5

Figure 4

(a)–(c) Variation of the normalized maximal SIF along the crack front for arrays of n1+n2=16,64,128 cracks, for fixed crack depth of a1∕t=0.15 and ellipticity a1∕c1=a2∕c2=0.7

Figure 5

(a)–(c) Variation of the normalized maximal SIF along the crack front for arrays of n1+n2=32 cracks, with fixed crack depths of a1∕t=0.1, 0.17, and 0.23 and ellipticity a1∕c1=a2∕c2=0.5

Figure 6

(a)–(c) Variation of the normalized maximal SIF along the crack front for arrays of n1+n2=64 cracks, with ellipticities of a1∕c1=0.3, 1, and 1.5, and fixed crack depth a1∕t=0.2

Figure 7

Relative size of the interaction range as a function of the number of cracks in the array, the fixed crack length, and ellipticity

Figure 8

Relative size of the interaction range as a function of the intercrack aspect ratio

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