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RESEARCH PAPERS

# The Influence of the Bauschinger Effect on 3D Stress Intensity Factors for Internal Radial Cracks in a Fully or Partially Autofrettaged Gun Barrel

[+] Author and Article Information
M. Perl1

Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576

C. Levy, V. Rallabhandy

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

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

1

Aaron Fish Professor of Mechanical Engineering and Former Dean of the Faculty of Engineering Sciences. On sabbatical leave from the Department of Mechanical Engineering, Pearlstone Center for Aeronautical Engineering Studies, Ben Gurion University of the Negev, Beer Sheva, 84105, Israel.

J. Pressure Vessel Technol 128(2), 233-239 (Nov 30, 2005) (7 pages) doi:10.1115/1.2172622 History: Received November 10, 2005; Revised November 30, 2005

## Abstract

The influence of the Bauschinger effect (BE) on the three-dimensional, mode I, stress intensity factor (SIF) distributions for arrays of radial, internal, surface cracks emanating from the bore of a fully or partially autofrettaged thick-walled cylinder is investigated. A thorough comparison between the prevailing SIFs for a “realistic” (Bauschinger effect dependent autofrettage (BEDA)) and those for an “ideal” (Bauschinger effect independent autofrettage (BEIA)) is done. The three-dimensional (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. More than 300 different crack configurations are analyzed. SIFs for numerous crack arrays ($n=1–64$ cracks), a wide range of crack depth to wall thickness ratios $(a∕t=0.01–0.2)$, various ellipticities $(a∕c=0.5–1.5)$, and different levels of autofrettage $(ε=30–100%)$ are evaluated. The Bauschinger Effect is found to considerably lower the beneficial stress intensity factor due to autofrettage, $KIA$, by up to 56%, as compared to the case of ideal autofrettage. The reduction in $KIA$ varies along the crack front with a maximum at the point of intersection between the crack plane and the inner surface of the cylinder, decreasing monotonically toward the deepest point of the crack. The detrimental influence of the BE increases as the number of cracks in the array increases and as crack depth decreases. For a partially autofrettaged cylinder, as the level of overstrain becomes smaller the influence of the BE is considerably reduced. As a result, the SIFs due to 100% BEDA differ by $<10%$ as compared to 60% BEDA, and on the average the difference is only about 2–4%.

###### FIGURES IN THIS ARTICLE
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Copyright © 2006 by American Society of Mechanical Engineers
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## Figures

Figure 8

KIA∕K0 variation along the crack front of slender semi-elliptical radial surface cracks in a fully autofrettaged cylinder

Figure 11

KIA∕K0 variation along the crack front of transverse semi-elliptical radial surface cracks in a fully autofrettaged cylinder

Figure 12

KIA∕K0 variation along the crack front of a semi-circular radial surface crack in a fully and partially autofrettaged cylinder

Figure 7

KIA∕K0 variation along the crack front of semi-circular radial surface cracks in a fully autofrettaged cylinder

Figure 6

KIA∕K0 variation along the crack front of semi-circular radial surface cracks in a fully autofrettaged cylinder

Figure 5

Meshed submodel

Figure 4

(a) Cylinder segment employed in the FE model and (b) the definition of the angle ϕ for SIF calculations

Figure 3

(a) σθθ∕σyp distribution through the wall of a 30% autofrettaged cylinder for BEIA due to Hill (2) and for BEDA due to Parker (10), and (b) σθθ (Parker)/σθθ (Hill), the ratio between the two residual hoop stress distributions for the inner portion of the cylinder thickness

Figure 2

(a) σθθ∕σyp distribution through the wall of a 60% autofrettaged cylinder for BEIA due to Hill (2) and for BEDA due to Parker (10), and (b) σθθ (Parker)/σθθ (Hill), the ratio between the two residual hoop stress distributions for the inner portion of the cylinder thickness.

Figure 1

(a) σθθ∕σyp distribution through the wall of a fully autofrettaged cylinder for Bauschinger effect independent autofrettage (BEIA) due to Hill (2) and for Bauschinger effect dependent autofrettage (BEDA) due to Parker (10), and (b) σθθ (Parker)/σθθ (Hill), the ratio between the two residual hoop stress distributions for the inner portion of the cylinder thickness

Figure 9

KIA∕K0 variation along the crack front of slender semi-elliptical radial surface cracks in a fully autofrettaged cylinder

Figure 10

KIA∕K0 variation along the crack front of transverse semi-elliptical radial surface cracks in a fully autofrettaged cylinder

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