Abstract
A method is presented for solving the three-dimensional axisymmetric field equations for a perfectly plastic material which obeys the von-Mises yield criterion and the Levy-Mises flow law. The method is used for the particular case in which a small axisymmetric perturbed flow is superposed on a uniform flow without flow reversal taking place. The method then leads to solving a fourth order differential equation for the velocity potential. The special case of a thick cylindrical shell under compressive flow is examined. The solution so obtained, being derived, from the three dimensional theory, includes a correct treatment of transverse shear distortion. A preferred mode of instability is identified having a wave-length in reasonable agreement with that obtained experimentally by other workers.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Florence A, Goodier JN. Dynamic plastic buckling of cylindrical shells in sustained axial compressive flow.J Appl Mech, Trans ASME, Series E, 1968, 35: 80–86
Vaughan H. The response of a plastic cylindrical shell to axial impact.ZAMP, 1969, 20:321–328
Jones N, de Oliviera JG. Impulsive loading of a cylindrical shell with transverse shear and rotary inertia.Int J Solids Structures, 1983, 19: 263–279
Jones N. Structural Impact. Cambridge University Press, 1989
Hill R. On the problems of uniqueness in the theory of a rigid-plastic, solid-III.J Mech Phys Solids, 1957, 5: 153–161
Hill R. A general theory of uniqueness and stability in elastic-plastic solids.J Mech Phys Solids, 1958, 6: 236–249
Hill R. Constitutive dual potentials in classical plasticity.J Mech Phys Solids, 1987, 35: 23–33
Ariaratnam ST, Dubey RN. Instability in an elastic-plastic cylindrical shell under axial compression.J Appl Mech, 1969, 36: 47–50
Hutchinson JW, Miles JP. Birfurcation analysis of the onset of necking in an elastic-plastic cylinder under uniaxial tension.J Mech Phys Solids, 1974, 22: 61–71
Storakers B. On buckling of axisymmetric thin elastic-plastic sheels.Int J Solids and Structures, 1975, 11: 1329–1346
Bruhns O. On the stability of thin-walled pressure vessels.Nuclear Engnr Design, 1980, 58: 359
Kumar A, Niyogi BB. Bifurcations in axially compressed thick elastic-plastic tubes.Int J Engng Sci, 1983, 21: 677–680
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vaughan, H., Zhuping, H. Three-dimensional axisymmetric flow in perfectly plastic metals. Acta Mech Sinica 9, 337–344 (1993). https://doi.org/10.1007/BF02486862
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02486862