Exact solutions of burst pressure for thick-walled cylinders in power-law strain hardening steels

Zhu, Xian-Kui; Wiersma, Bruce; Johnson, William R.; Sindelar, Robert

doi:10.1016/j.ijpvp.2023.105053

Exact solutions of burst pressure for thick-walled cylinders in power-law strain hardening steels

Journal Article · Tue Sep 05 00:00:00 EDT 2023 · International Journal of Pressure Vessels and Piping

DOI:https://doi.org/10.1016/j.ijpvp.2023.105053· OSTI ID:2570434

^[1]; Wiersma, Bruce ^[1]; Johnson, William R. ^[1]; Sindelar, Robert ^[1]

Savannah River National Laboratory (SRNL), Aiken, SC (United States)

Exact solutions of burst pressure for defect-free, thick-walled cylindrical pressure vessels with capped ends are developed using the flow theory of plasticity in terms of the Tresca, von Mises, and Zhu-Leis yield criteria. The material is assumed to obey a power-law strain hardening rule, and the finite strain theory is adopted to describe large plastic deformation. On this basis, internal pressure is obtained as a complex polynomial function of effective strains on the inside and outside surfaces of the pressure vessel with the use of the Bernoulli numbers. At burst failure, the effective strains and stresses on the inside and outside surfaces are first determined, and then three flow solutions of burst pressure are obtained as a power series function of the diameter ratio (D_o/D_i), strain hardening exponent (n), and ultimate tensile strength (UTS). The power series solution is confirmed to agree well with the exact flow solution of burst pressure in a closed-form for each yield criterion, and the results show that the von Mises flow solution is an upper bound prediction, the Tresca flow solution is a lower bound prediction, and the Zhu-Leis flow solution is an intermediate prediction of burst pressure. In conclusion, two sets of full-scale burst test data are then utilized to evaluate and validate the proposed flow solutions of burst pressure for both thin-walled pipes and thick-walled cylindrical pressure vessels.

View Accepted Manuscript (DOE)

Research Organization:: Savannah River National Laboratory (SRNL), Aiken, SC (United States)

Sponsoring Organization:: USDOE Office of Environmental Management (EM); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89303321CEM000080

OSTI ID:: 2570434

Alternate ID(s):: OSTI ID: 2369977

Report Number(s):: SRNL--STI-2023-00475

Journal Information:: International Journal of Pressure Vessels and Piping, Journal Name: International Journal of Pressure Vessels and Piping Vol. 206; ISSN 0308-0161

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (28)

Probabilistic Failure Prediction of High Strength Steel Rocket Motor Cases Krishnaveni, A.; Christopher, T.; Jeyakumar, K. Journal of Failure Analysis and Prevention, Vol. 14, Issue 4 https://doi.org/10.1007/s11668-014-9829-z	journal	May 2014
An estimation of maximum pressure for a thick-walled tube subjected to internal pressure Hamada, M.; Yokoyama, R.; Kitagawa, H. International Journal of Pressure Vessels and Piping, Vol. 22, Issue 4 https://doi.org/10.1016/0308-0161(86)90009-8	journal	January 1986
An exact elasto-plastic solution for a closed-end thick-walled cylinder of elastic linear-hardening material with large strains Gao, Xin-Lin International Journal of Pressure Vessels and Piping, Vol. 56, Issue 3 https://doi.org/10.1016/0308-0161(93)90004-D	journal	January 1993
A comparative study on failure pressure estimations of unflawed cylindrical vessels Christopher, T.; Rama Sarma, B. S. V.; Govindan Potti, P. K. International Journal of Pressure Vessels and Piping, Vol. 79, Issue 1 https://doi.org/10.1016/S0308-0161(01)00126-0	journal	January 2002
Validation of the NG-18 equations for thick walled pipelines Lyons, C. J.; Race, J. M.; Chang, E. Engineering Failure Analysis, Vol. 112 https://doi.org/10.1016/j.engfailanal.2020.104494	journal	May 2020
Exact solution of burst pressure for thick-walled pipes using the flow theory of plasticity Zhu, Xian-Kui International Journal of Mechanical Sciences, Vol. 259 https://doi.org/10.1016/j.ijmecsci.2023.108582	journal	December 2023
Average shear stress yield criterion and its application to plastic collapse analysis of pipelines Zhu, Xian-Kui; Leis, Brian N. International Journal of Pressure Vessels and Piping, Vol. 83, Issue 9 https://doi.org/10.1016/j.ijpvp.2006.06.001	journal	September 2006
Prediction of failure strain and burst pressure in high yield-to-tensile strength ratio linepipe Law, M.; Bowie, G. International Journal of Pressure Vessels and Piping, Vol. 84, Issue 8 https://doi.org/10.1016/j.ijpvp.2007.04.002	journal	August 2007
Evaluation of burst pressure prediction models for line pipes Zhu, Xian-Kui; Leis, Brian N. International Journal of Pressure Vessels and Piping, Vol. 89 https://doi.org/10.1016/j.ijpvp.2011.09.007	journal	January 2012
A review on defect assessment of pipelines: Principles, numerical solutions, and applications Qin, Guojin; Cheng, Y. Frank International Journal of Pressure Vessels and Piping, Vol. 191 https://doi.org/10.1016/j.ijpvp.2021.104329	journal	June 2021
Burst pressures of thin-walled cylinders constructed of steel exhibiting a yield plateau Wang, Haifeng; Zheng, Tiancheng; Sang, Zhifu International Journal of Pressure Vessels and Piping, Vol. 193 https://doi.org/10.1016/j.ijpvp.2021.104483	journal	October 2021
Effect of autofrettage on the ultimate behavior of thick cylindrical pressure vessels Mohan, A.; Julyes Jaisingh, S.; Goldin Priscilla, C. P. International Journal of Pressure Vessels and Piping, Vol. 194 https://doi.org/10.1016/j.ijpvp.2021.104546	journal	December 2021
Analysis of the impact factor of burst capacity models for defect-free pipelines Sun, Mingming; Chen, Yanfei; Zhao, Haisheng International Journal of Pressure Vessels and Piping, Vol. 200 https://doi.org/10.1016/j.ijpvp.2022.104805	journal	December 2022
A parametric finite element study for determining burst strength of thin and thick-walled pressure vessels Johnson, William R.; Zhu, Xian-Kui; Sindelar, Robert International Journal of Pressure Vessels and Piping, Vol. 204 https://doi.org/10.1016/j.ijpvp.2023.104968	journal	August 2023
Investigation of Burst Pressures in PWR Primary Pressure Boundary Components Namgung, Ihn; Giang, Nguyen Hoang Nuclear Engineering and Technology, Vol. 48, Issue 1 https://doi.org/10.1016/j.net.2015.11.001	journal	February 2016
Finite Element Prediction of Static Burst Pressure in Closed Thick- walled Unflawed Cylinders of Different Diameter Ratios Kadam, Mahesh; Murugan, G. Bala; Bujurke, Aditya A. Procedia Engineering, Vol. 173 https://doi.org/10.1016/j.proeng.2016.12.102	journal	January 2017
The Plastic Flow of Thick-Walled Tubes with Large Strains MacGregor, C. W.; Coffin, L. F.; Fisher, J. C. Journal of Applied Physics, Vol. 19, Issue 3 https://doi.org/10.1063/1.1715060	journal	March 1948
Influence of Yield-to-Tensile Strength Ratio on Failure Assessment of Corroded Pipelines Zhu, Xian-Kui; Leis, Brian N. Journal of Pressure Vessel Technology, Vol. 127, Issue 4 https://doi.org/10.1115/1.2042481	journal	June 2005
Strength of Thick-Walled Cylindrical Pressure Vessels Marin, Joseph; Weng, Tu-Lung Journal of Engineering for Industry, Vol. 85, Issue 4 https://doi.org/10.1115/1.3669909	journal	November 1963
Failure Pressure in Corroded Pipelines Based on Equivalent Solutions for Undamaged Pipe Bony, M.; Alamilla, J. L.; Vai, R. Journal of Pressure Vessel Technology, Vol. 132, Issue 5 https://doi.org/10.1115/1.4001801	journal	August 2010
A Quantitative Comparison of Flow and Deformation Theories of Plasticity Hodge, P. G.; White, G. N. Journal of Applied Mechanics, Vol. 17, Issue 2 https://doi.org/10.1115/1.4010097	journal	June 1950
The Bursting Pressure of Cylindrical and Spherical Vessels Svensson, N. L. Journal of Applied Mechanics, Vol. 25, Issue 1 https://doi.org/10.1115/1.4011694	journal	March 1958
Strength Criteria Versus Plastic Flow Criteria Used in Pressure Vessel Design and Analysis1 Zhu, Xian-Kui Journal of Pressure Vessel Technology, Vol. 138, Issue 4 https://doi.org/10.1115/1.4031284	journal	April 2016
Burst Pressure Solutions of Thin and Thick-Walled Cylindrical Vessels Zhu, Xian-Kui; Wiersma, Bruce; Johnson, William R. Journal of Pressure Vessel Technology, Vol. 145, Issue 4 https://doi.org/10.1115/1.4062334	journal	May 2023
Model Error Assessment of Burst Capacity Models for Defect-Free Pipes Zhou, W.; Huang, G. (Terry) Volume 4: Pipelining in Northern and Offshore Environments; Strain-Based Design; Risk and Reliability; Standards and Regulations https://doi.org/10.1115/IPC2012-90334	conference	September 2012
Modified Svensson’s Formula for More Accurate Burst Pressure Predictions of Thin Cylindrical Shells With Small Shell Length to Diameter Ratios Kang, Sang-Guk; Young, Kuao-John Volume 3: Design and Analysis https://doi.org/10.1115/PVP2015-45316	conference	July 2015
Corrosion Assessment Models for Predicting Remaining Strength of Corroded Thick-Walled Pipelines Zhu, Xian-Kui; Wiersma, Bruce; Johnson, William R. Volume 5: Materials & Fabrication https://doi.org/10.1115/PVP2023-106911	conference	July 2023
Behaviour of Thick-Walled Steel Cylinders Subjected to Internal Pressure Crossland, B.; Bones, J. A. Proceedings of the Institution of Mechanical Engineers, Vol. 172, Issue 1 https://doi.org/10.1243/PIME_PROC_1958_172_061_02	journal	June 1958

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36 MATERIALS SCIENCE
Tresca criterion
Zhu-Leis criterion
burst pressure
flow theory of plasticity
power-law material
thick-walled cylinder
von Mises criterion

Exact solutions of burst pressure for thick-walled cylinders in power-law strain hardening steels

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