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TECHNICAL PAPERS

# Mode Mixity for Circular Hollow Section $X$ Joints With Weld Toe Cracks

[+] Author and Article Information
X. Qian

Department of Civil and Environmental Engineering,  University of Illinois, Urbana, IL 61801, U.S.A.

Robert H. Dodds1

Department of Civil and Environmental Engineering,  University of Illinois, Urbana, IL 61801, U.S.A.

Y. S. Choo

Center for Offshore Research and Engineering,  National University of Singapore, Singapore 117576

1

Corresponding author; email: rdodds@uiuc.edu

J. Offshore Mech. Arct. Eng 127(3), 269-279 (Jan 26, 2005) (11 pages) doi:10.1115/1.1951771 History: Received August 21, 2004; Revised January 26, 2005

## Abstract

This paper describes the mode mixity of stress-intensity factors for surface cracks at weld toes located at the saddle point in circular hollow section $X$ joints. The remote loading applies a uniform tensile stress at the end of the brace along its axis. The three-dimensional finite element models employ mesh tieing between a topologically continuous, global mesh and a separate, local crack-front mesh. Analyses of a simple plate model that approximates key features of toe cracks at the brace-chord intersection verify the negligible effects of the recommended mesh-tieing scheme on stress intensity factors. The linear-elastic analyses compute the mixed-mode stress intensity factors along the crack front using an interaction-integral approach. The mixed-mode stress intensity factors indicate that the crack front experiences predominantly mode I loading, with $KIII→0$ near the deepest point on the front $(ϕ=π∕2)$. The total crack driving force, described by the $J$ integral, reaches a maximum value at the deepest point of the crack for the crack aspect ratio $a∕c=0.25$ considered here. The mode-mixity angle, $ψ=tan−1(KII∕KI)$, at $ϕ=π∕2$ is compared for a range of practical X-joint configurations and crack-depth ratios. The present study demonstrates that the mode-mixity angle $ψ$ increases with increasing brace-to-chord diameter ratio $(β)$ and decreasing chord radius to wall thickness ratio $(γ)$. Values of the nondimensional stress intensity factors ($FI=KI∕σ¯brπa$ and $FII=KII∕σ¯brπa$), however, show an opposite trend, with higher crack driving forces for small $β$ and large $γ$ ratios. The variations in the brace-to-chord wall thickness ratio $(τ)$ and the crack depth ratio $(a∕t0)$ do not generate significant effects on the mode mixity.

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## Figures

Figure 1

Geometric configuration of a typical circular hollow section X joint with a weld toe crack at the saddle point: (a) Front view; (b) Side view; (c) Close-up view of the weld toe at the saddle point; (d) Planar view of the surface crack.

Figure 2

Typical finite element mesh for a CHS X joint with a weld toe surface crack (20-noded bricks, with 50,000-80,000 nodes): (a) Overall view; (b) Closeup view of the six-faced crack-front block tied to the global model.

Figure 3

Comparison of the stress intensity factors evaluated from the interaction-integral method via a half model and a quarter model of a CHS X joint

Figure 4

Geometric configuration of the plate model to approximate features of the brace-chord intersection at the saddle point for mesh-tieing verification, with different boundary conditions.

Figure 5

(a) Different mesh schemes employed in the mesh tieing for the plate model; (b) Comparison of the J integral computed from meshes in (a) with linear-elastic analysis; (c) Comparison of the linear-elastic J values for different crack depth ratios using Mesh A.

Figure 6

Variation of the nondimensional Fi along the crack front for different joints

Figure 7

Von Mises stress contours and schematic stress distributions across the chord wall thickness (x=0 symmetry plane) for (a) β=0.95 and (b) β=0.4.

Figure 8

Variation of the J values along the crack front for different joints

Figure 9

Effects of nondimensional joint geometric parameters and crack depth ratios on FI values

Figure 10

Effects of nondimensional joint geometric parameters and crack depth ratios on the FII values

Figure 11

Variation of the mode-mixity angle ψ with respect to nondimensional geometric parameters and crack depth ratios in X joints

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