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TECHNICAL PAPERS

Closed-Form Collapse Moment Equations of Throughwall Circumferentially Cracked Elbows Subjected to In-Plane Bending Moment

[+] Author and Article Information
J. Chattopadhyay, A. K. S. Tomar, B. K. Dutta, H. S. Kushwaha

Reactor Safety Division, Hall-7, Bhabha Atomic Research Center, Trombay, Mumbai—400085, India

J. Pressure Vessel Technol 126(3), 307-317 (Aug 18, 2004) (11 pages) doi:10.1115/1.1767177 History: Received May 29, 2003; Revised April 01, 2004; Online August 18, 2004
Copyright © 2004 by ASME
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References

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Goodall, I. W., 1978, “Large Deformations in Plastically Deforming Curved Tubes Subjected to In-plane Bending,” Research Division Report RD/B/N4312, Central Electricity Generating Board, UK.
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Shalaby, M. A., and Younan, M. Y. A., 1998, “Limit Loads for Pipe Elbows Subjected to In-Plane Opening Moment and Internal Pressure,” paper presented at the 1998 ASME/JSME Joint Pressure Vessels and Piping Conference held at San Diego, California, July 26–30, 1998, PVP-Vol. 368, pp. 163–170.
Chattopadhyay,  J., Nathani,  D. K., Dutta,  B. K., and Kushwaha,  H. S., 2000, “Closed-Form Collapse Moment Equations of Elbows Under Combined Internal Pressure and In-Plane Bending Moment,” ASME J. Pressure Vessel Technol., 122, pp. 431–436.
Chattopadhyay,  J., Dutta,  B. K., and Kushwaha,  H. S., 2001, “Derivation of γ Parameter From Limit Load Expression of Cracked Component to Evaluate J-R Curve,” Int. J. Pressure Vessels Piping, 78, pp. 401–427.
Chattopadhyay,  J., Dutta,  B. K., Kushwaha,  H. S., Mahajan,  S. C., and Kakodkar,  A., 1995, “Limit Load Analysis and Safety Assessment of an Elbow With Circumferential Crack Under Bending Moment,” Int. J. Pressure Vessels Piping, 62, pp. 109–116.
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Chattopadhyay,  J., Pavankumar,  T. V., Dutta,  B. K., and Kushwaha,  H. S., 2003, “J-R Curves From Throughwall Cracked Elbow Subjected to In-Plane Bending Moment,” ASME J. Pressure Vessel Technol., 125, pp. 36–45.
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Tan, Y., Matzen, V. C., and Yu, L., 2000. “Correlation of Test and FEA Results for the Non-Linear Behavior of Elbows,” Proceedings of Conference on Pressure Vessel and Piping Codes and Standards-2000, PVP-Vol. 407, pp. 307–314.
Yahiaoui,  K., Moffat,  D. G., and Moreton,  D. N., 2000, “Piping Elbows With Cracks, Part 1: A Parametric Study of the Influence of Crack Size on Limit Loads Due to Pressure and Opening Bending,” J. Strain Anal., 35, pp. 35–46.

Figures

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Load deflection curves from experiments on elbows by Chattopadhyay et al. 14
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(a) Geometry of a throughwall circumferentially cracked elbow under closing moment; and (b) geometry of a throughwall circumferentially cracked elbow under opening moment
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Typical finite element mesh of an elbow
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Moment rotation curves for cracked elbows (Rb/R=3,R/t=15) under closing bending
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Moment rotation curves for cracked elbows (Rb/R=3,R/t=15) under opening bending
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Variation of normalized collapse moment of deflect-free elbow under closing bending with elbow factor
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Variation of normalized collapse moment of deflect-free elbow under opening bending with elbow factor
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Variation of normalized collapse moment with crack angle for closing moment (symbols show the present FE results and solid lines show predictions of closed-form equations)
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Variation of axial stress at mid-plane of elbow (R/t=20 and Rb/R=3, no crack) under closing bending moment at the TES collapse moment
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Variation of axial stress at mid-plane of elbow (R/t=5 and Rb/R=3, no crack) under closing bending moment at the TES collapse moment
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Surface plot of weakening factor (ML/M0), crack angle and R/t for TCC elbows subjected to closing bending moment (symbols show the FE data points and wire mesh shows the smoothened surface)
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Variation of normalized collapse moment with crack angle for opening bending (symbols show the present FE results and solid lines show predictions of closed-form equations)
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Variation of axial stress at mid-plane of elbow (R/t=10 and Rb/R=3, no crack) under opening bending at load beyond the TES collapse moment
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Effect of bend radius on collapse moment—a comparison for R/t=5 and closing bending moment
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Effect of bend radius on collapse moment—a comparison for R/t=20 and closing bending moment
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Effect of bend radius on collapse moment—a comparison for R/t=5 and opening bending moment
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Comparison of experimental and finite element results for test no. ELTWIN8-2 18
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Intrados crack in elbow under opening bending—a comparison of weakening effect

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