Abstract
Autofrettage is an effective measure to even distribution of stresses and raise load-bearing capacity for (ultra-)high pressure apparatus. Currently, the research on autofrettage has focused mostly on specific engineering problems, while general theoretical study is rarely done. To discover the general law contained in autofrettage theory, by the aid of the authors’ previous work and according to the third strength theory, theoretical problems about autofrettage are studied including residual stresses and their equivalent stress, total stresses and their equivalent stress, etc. Because of the equation of optimum depth of plastic zone which is presented in the authors’ previous work, the equations for the residual stresses and their equivalent stress as well as the total stress and their equivalent stress are simplified greatly. Thus the law of distribution of the residual stresses and their equivalent stress as well as the total stress and their equivalent stress and the varying tendency of these stresses are discovered. The relation among various parameters are revealed. The safe and optimum load-bearing conditions for cylinders are obtained. According to the results obtained by theoretical analysis, it is shown that if the two parameters, namely ratio of outside to inside radius, k, and depth of plastic zone, k j, meet the equation of optimum depth of plastic zone, when the pressure contained in an autofrettaged cylinder is lower than two times the initial yield pressure of the unautofrettaged cylinder, the equivalent residual stress and the equivalent total stress at the inside surface as well as the elastic-plastic juncture of a cylinder are lower than yield strength. When an autofrettaged cylinder is subjected to just two times the initial yield pressure of the unautofrettaged cylinder, the equivalent total stress within the whole plastic zone is just identically equal to the yield strength, or it is a constant. The proposed research theoretically depicts the stress state of ultra-)high pressure autofrettaged cylinder more accurately and more reasonably and provides the reference for design of (ultra-)high pressure apparatus.
Similar content being viewed by others
References
ANTHONY P Parker. Bauschinger effect design procedures for compound tubes containing an autofrettaged layer[J]. Journal of Pressure Vessel Technology, 2001, 123 (2): 203–206.
ANTHONY P Parker. Autofrettage of open-end tubes-pressures, stresses, strains, and code comparisons[J]. Journal of Pressure Vessel Technology, 2001, 123 (3): 271–281.
ANTHONY P Parker, DAVID P Kendall. Residual stresses and lifetimes of tubes subjected to shrink fit prior to autofrettage[J]. Journal of Pressure Vessel Technology, 2003, 125(3): 282–286.
ANTHONY P Parker. A re-autofrettage procedure for mitigation of Bauschinger effect in thick cylinders[J]. Journal of Pressure Vessel Technology, 2004, 126(4): 451–454.
AMER Hameed, BROWN R D, JOHN Hetherington. A study of the residual stress distribution in an autofrettaged, thick-walled cylinder with cross-bore[J]. Journal of Pressure Vessel Technology, 2004, 126(4): 497–503.
LIU Yong, ZHANG Kangda, WANG Liangguo, et al. Elastoplastic stress analysis of autofrettaged internal cone-cylinder pressure vessel[J]. Journal of Mechanical Engineering, 1993, 29(3): 67–73. (in Chinese)
ZHENG Xiaotao, XUAN Fuzhen. Investigation on autofrettage and safety of the thick-walled cylinder under thermo-mechanical loadings[J]. Journal of Mechanical Engineering, 2010, 46(16): 156–161. (in Chinese)
LIN Yujuan, DONG Qiuxia, JiA Jingjing. Autofrettage damage residual stress of thick-walled cylinder[J]. Science Technology and Engineering, 2009, 9(24): 7 306–7 309. (in Chinese)
GAO Junwei, XIE Guangwei, ZHOU Houjun, et al. Research on autofrettage technology[J]. Mechanical Research & Application, 2008, 21(6): 21–23. (in Chinese)
ZHU Ruilin. Results resulting from autofrettage of cylinder[J]. Chinese Journal of Mechanical Engineering, 2008, 21(4): 105–110.
ZHU Ruilin. Ultimate load-bearing capacity of cylinder derived from autofrettage under ideal condition[J]. Chinese Journal of Mechanical Engineering, 2008, 21(5): 80–87.
ZHU Ruilin. Study on autofrettage of cylindrical pressure vessels[J]. Journal of Mechanical Engineering, 2010, 46(6): 126–133. (in Chinese)
ZHU Ruilin, ZHU Guolin. Analysis on autofrettage of cylinders[J]. Chinese Journal of Mechanical Engineering, 2012, 25(3): 615–623.
YU Guocong. Chemical pressure vessels and equipment[M]. Beijing: Chemical Industrial Press, 1990. (in Chinese)
TIMSHENKO S. Strength of materials[M]. New York: Van Nostrand Reinhold Company Ltd., 1978.
Author information
Authors and Affiliations
Corresponding author
Additional information
This project is supported by Scientific Research Fund of Hunan Provincial Education Department(Grant No. 12A087), and Innovation Fund for Technology Based Firms(Grant No. 09C26214305047)
ZHU Ruilin, born in 1962, is currently a professor at Hunan Normal University, China. He received his PhD degree from Zhejiang Universtiy, China, in 1998. His research interests include process machinery and equipment.
ZHU Guolin, born in 1974, is currently a lecturer at Jiangxi Police College, China. He received his master degree in Xiangtan University, China, in 2006.
Rights and permissions
About this article
Cite this article
Zhu, R., Zhu, G. Effect of optimum plastic depth on stresses and load-bearing capacity of autofrettaged cylinder. Chin. J. Mech. Eng. 26, 365–370 (2013). https://doi.org/10.3901/CJME.2013.02.365
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3901/CJME.2013.02.365