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IssuesArchive of Issues2013-5pp.537-545

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S.E. Aleksandrov and R.V. Goldstein, "Stress-Strain State in an Elastoplastic Cylindrical Tube with Free Ends. I. General Solution," Mech. Solids. 48 (5), 537-545 (2013)
Year 2013 Volume 48 Number 5 Pages 537-545
DOI 10.3103/S0025654413050099
Title Stress-Strain State in an Elastoplastic Cylindrical Tube with Free Ends. I. General Solution
Author(s) S.E. Aleksandrov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, sergei_alexandrov@yahoo.com)
R.V. Goldstein (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, goldst@ipmnet.ru)
Abstract We obtain a general solution for the stress-strain state in an elastoplastic tube whose ends are stress-free. The tube is subjected to internal and external pressures which can vary in time rather arbitrarily. But it is assumed that the radius of the elastoplastic boundary does not decrease during the entire deformation process. The tube material obeys a yield condition depending on the mean stress. The corresponding yield surface has the shape of a cone in the space of principal stresses. The theory of plastic flow is used. The plastic potential is taken in the form of the von Mises condition. Thus, the associated plastic flow law is not satisfied, and the material is plastically incompressible. Numerical methods are only needed for successively solving several transcendental equations and calculating ordinary integrals.
Keywords cylindrical tube, elastoplastic deformation, yield condition, mean stress
References
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Received 06 April 2013
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