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Research Papers: Design and Analysis

# The Combined Stress Intensity Factors of Multiple Longitudinally Coplanar Cracks in Autofrettaged Pressurized Tubes Influenced by the Bauschinger Effect

[+] Author and Article Information
C. Levy, S. Kotagiri

Department of Mechanical and Materials Engineering, Florida International University, Miami, FL 33199

M. Perl

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

It is only in the context of superposition of loads that a SIF can be considered negative.

J. Pressure Vessel Technol 130(3), 031208 (Jul 11, 2008) (6 pages) doi:10.1115/1.2937761 History: Received September 20, 2006; Revised March 26, 2007; Published July 11, 2008

## Abstract

The influence of the Bauschinger effect (BE) on the three dimensional, Mode I, combined stress intensity factor (SIF) distributions for arrays of longitudinal coplanar, surface cracks emanating from the bore of a fully or partially autofrettaged thick-walled cylinder is investigated. The combined SIFs, $KIN$, that depend on pressure effects and the “realistic”—Bauschinger effect dependent Autofrettage (BEDA), or, that depend on pressure effects and the “ideal”—Bauschinger effect independent autofrettage (BEIA), are obtained and compared for crack depth to wall thickness, $a∕t=0.01–0.25$; crack ellipticity, $a∕c=0.5–1.5$; crack spacing ratio, $2c∕d=0.25–0.75$; and autofrettage level, $e=30%$, 60%, and 100%. The 3D analysis is performed via the finite element method and the submodeling technique, employing singular elements along the crack front. Both autofrettage residual stress fields, BEDA and BEIA, are simulated using an equivalent temperature field. The combined SIF, $KIN$, is found to vary along the crack front with the maximum determined by the crack ellipticity, crack depth, and crack spacing ratio. For a partially autofrettaged cylinder, the influence of the BE on the combined SIF, $KIN$, is substantially reduced as the level of overstrain becomes smaller. For some cases, when comparing like crack distributions, the $KIN$ values obtained from the BEDA model are found to be as much as 100% higher than the $KIN$ values that are computed using the BEIA model. A pressurized thick-walled cylinder with BEDA can be most critical when small cracks are farther apart. As crack depth increases, or when the spacing between cracks is smaller, the SIFs increase. Though the differences in the BEDA SIF, $KIA$, between $e=100%$ and 60% are small (7–15%, in most cases), the increased level of autofrettage produces a 23–30% decrease in the combined SIF values, $KIN$. In certain cases, the BEIA model implies an infinite fatigue life, whereas the BEDA model for the same parameters implies a finite life. Therefore, it is important to perform a full 3D analysis to determine the real life cycle of the pressurized cylinder for materials that exhibit the BE.

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## Figures

Figure 2

The submodel covering the crack whose ellipticity is a∕c

Figure 3

(a) Normalized combined SIF, KIN∕KI0, for a shallow crack in a fully autofrettaged thick-walled cylinder, —◼—BEIA, —◻— BEDA and (b) normalized combined SIF, KIN∕KI0, for a deeper crack in a fully autofrettaged thick-walled cylinder, —◼— BEIA, —◻— BEDA

Figure 5

(a) Normalized combined SIF, KIN∕KI0, for a shallow slender semielliptical crack in a fully autofrettaged thick-walled cylinder, —◼— BEIA, —◻— BEDA and (b) normalized combined SIF, KIN∕KI0, for a deeper slender semielliptical crack in a fully autofrettaged thick-walled cylinder, —◼— BEIA, —◻— BEDA

Figure 9

(a) Maximum combined SIF normalized to K0=p√a as a function of relative crack depth for cracks spaced further apart and crack ellipticities a∕c=0.5–1.5 in a fully and partially autofrettaged tube under Bauschinger effect, —×— e=100%, —◻— e=30% and (b) maximum combined SIF normalized to K0=p√a as a function of relative crack depth for cracks spaced closer together and crack ellipticities a∕c=0.5–1.5 in a fully and partially autofrettaged tube under Bauschinger effect, —×— e=100%, —◻— e=60%

Figure 8

(a) Normalized combined SIF, KIN∕KI0, for a shallow transverse semielliptical crack in a fully or partially autofrettaged thick-walled cylinder, —◼— BEIA, —◻— BEDA and (b) normalized combined SIF, KIN∕KI0, for a deeper transverse semielliptical crack in a fully or partially autofrettaged thick-walled cylinder, —◼— BEIA, —◻— BEDA

Figure 7

(a) Normalized combined SIF, KIN∕KI0, for a shallow transverse semielliptical crack in a fully autofrettaged thick-walled cylinder, —◼— BEIA, —◻— BEDA and (b) normalized combined SIF, KIN∕KI0, for a deeper transverse semielliptical crack in a fully autofrettaged thick-walled cylinder, —◼— BEIA, —◻— BEDA

Figure 6

(a) Normalized combined SIF, KIN∕KI0, for a shallow slender semielliptical crack in a fully or partially autofrettaged thick-walled cylinder, —◼— BEIA, —◻— BEDA and (b) normalized combined SIF, KIN∕KI0, for a deeper slender semielliptical crack in a fully or partially autofrettaged thick-walled cylinder, —◼— BEIA, —◻— BEDA

Figure 4

(a) Normalized combined SIF, KIN∕KI0, for a shallow crack in a fully or partially autofrettaged thick-walled cylinder, —◼— BEIA, —◻— BEDA and (b) normalized combined SIF, KIN∕KI0, for a deeper crack in a fully or partially autofrettaged thick-walled cylinder, —◼— BEIA, —◻— BEDA

Figure 1

(a) Half the cylinder showing three longitudinal coplanar cracks and (b) the portion of the cylinder used in the FE analysis showing the planes of symmetry Z=0, Z=d∕2, and Y=0

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