Experimental Mechanics

, Volume 15, Issue 6, pp 209–218 | Cite as

Bursting pressure of thick-walled cylinders subjected to internal and external pressures, axial load and torsion

An incompressible, finite-total-strain analytical solution is presented for thick-walled cylinders subjected to internal pressure, external pressure, axial load and torsion
  • O. M. Sidebottom
  • S. C. Chu


A finite-total-strain, incompressible, analytical solution is presented to predict load-deformation relations for loads from zero to failure for thick-walled cylinders subjected to internal pressure, external pressure, axial load and torsion. The solution assumes that the material is an isotropic hardening material that obeys the von Mises yield condition. The flow law incorporates the prandtl-Reuss stressstrain relations and a loading function represented by the tension true-stress vs. true-strain diagram. Poisson's ratio is assumed to be equal to one-half for both elastic and plastic strains. The difference between the strains given by the incompressible solution and the correct strains are calculated for one set of elastic loads; the strains given by the incompressible solution are then corrected based on the assumption that each correction is proportional to the increase in the given component of load. Good agreement is indicated between the corrected incompressible solution and data obtained from cylinders made of either SAE 1045 steel, OFHC copper, or aluminum alloy 1100.


Aluminum Alloy Plastic Strain Internal Pressure Axial Load Isotropic Hardening 
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List of Symbols

r, θ, z

cylindrical coordinates

σr, σθ, σz, τθz

true-stress components

ɛr, ɛθ, γθz

true-strain components

ɛr,eng, ɛθ,eng

engineering definition of radial and circumferential strains

σe, ɛe

effective true stress and effective true strain


average axial stress


inner and outer radii of undeformed cylinder


inner and outer radii of the deformed cylinder


variable radius of undeformed cylinder


variable radius of deformed cylinder


r-ro is the radial displacement


axial load in addition to pressures acting on ends of cylinder




internal and external pressures


Young's modulus


Poisson's ratio


σo1 is yield stress


stress at intersection of eqs (1) and (2)


ɛ o is yield strain


ratio of ɛ z to ɛ e )r=r1)


ratio of γθ z (r=r1) to ɛ e (r=r1)


ratio of ɛ e (r=r1) to ɛ o


undeformed cross-sectional area of cylinder


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Copyright information

© Society for Experimental Mechanics, Inc. 1975

Authors and Affiliations

  • O. M. Sidebottom
    • 1
  • S. C. Chu
    • 2
  1. 1.Department of Theoretical and Applied MechanicsUniversity of IllinoisUrbana
  2. 2.Research DirectorateGEN Thomas J. Rodman Laboratory, Rock Island ArsenalRock Island

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