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Research Papers: Design and Analysis

Descriptions of Reversed Yielding in Internally Pressurized Tubes

[+] Author and Article Information
Sergei Alexandrov

Ishlinskii Institute for Problems in Mechanics,
101-1 Prospect Vernadskogo,
Moscow 119526, Russia
e-mail: sergei_alexandrov@yahoo.com

Woncheol Jeong

Department of Materials Science
and Engineering,
Seoul National University,
30-413, 1 Gwanak-ro, Gwanak-gu,
Seoul 151-742, Republic of Korea
e-mail: rippler@snu.ac.kr

Kwansoo Chung

Department of Materials Science
and Engineering,
Seoul National University,
33-212, 1 Gwanak-ro, Gwanak-gu,
Seoul 151-742, Republic of Korea
e-mail: kchung@snu.ac.kr

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received July 22, 2014; final manuscript received July 4, 2015; published online August 26, 2015. Assoc. Editor: Albert E. Segall.

J. Pressure Vessel Technol 138(1), 011204 (Aug 26, 2015) (10 pages) Paper No: PVT-14-1108; doi: 10.1115/1.4031029 History: Received July 22, 2014

Using Tresca's yield criterion and its associated flow rule, solutions are obtained for the stresses and strains when a thick-walled tube is subject to internal pressure and subsequent unloading. A bilinear hardening material model in which allowances are made for a Bauschinger effect is adopted. A variable elastic range and different rates under forward and reversed deformation are assumed. Prager's translation law is obtained as a particular case. The solutions are practically analytic. However, a numerical technique is necessary to solve transcendental equations. Conditions are expressed for which the release is purely elastic and elastic–plastic. The importance of verifying conditions under which the Tresca theory is valid is emphasized. Possible numerical difficulties with solving equations that express these conditions are highlighted. The effect of kinematic hardening law on the validity of the solutions found is demonstrated.

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Figures

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Fig. 1

Expansion of cylinder—notation

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Fig. 2

Geometric representation of the yield criterion

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Fig. 4

Variation of ρs with ρc at a=0.3 and several values of hr

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Fig. 5

Residual stress distributions in an a=0.3 cylinder at different values of ρc and hr : (a) radial stress and (b) circumferential stress

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Fig. 6

Residual strain distributions in an a=0.3 cylinder at different values of ρc and hr : (a) radial strain and (b) circumferential strain

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Fig. 7

Illustration of the validity of the solution found: (a) function Λ3(ρ,ρc) and (b) function Λ5(ρ,ρc)

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Fig. 8

Illustration of solution behavior of Eq. (44)

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Fig. 3

Variation of ρe with a at several values of hr

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