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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

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Abstract

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.

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Abbreviations

r, θ, z :

cylindrical coordinates

σr, σθ, σ z , τ θz :

true-stress components

ɛ r , ɛ θ , γ θz :

true-strain components

ɛ r ,eng, ɛ θ ,eng :

engineering definition of radial and circumferential strains

σ e , ɛ e :

effective true stress and effective true strain

σ z ,ave :

average axial stress

r 01,r 02 :

inner and outer radii of undeformed cylinder

r 1,r 2 :

inner and outer radii of the deformed cylinder

r o :

variable radius of undeformed cylinder

r :

variable radius of deformed cylinder

u :

r-ro is the radial displacement

P :

axial load in addition to pressures acting on ends of cylinder

T :

torque

p 1,p 2 :

internal and external pressures

E :

Young's modulus

v :

Poisson's ratio

σo :

σo1 is yield stress

σoi :

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

ɛo :

ɛ o is yield strain

β:

ratio of ɛ z to ɛ e )r=r1)

η :

ratio of γθ z (r=r1) to ɛ e (r=r1)

K :

ratio of ɛ e (r=r1) to ɛ o

A o :

undeformed cross-sectional area of cylinder

References

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Authors and Affiliations

  1. Department of Theoretical and Applied Mechanics, University of Illinois, 61801, Urbana, IL

    O. M. Sidebottom (Professor)

  2. Research Directorate, GEN Thomas J. Rodman Laboratory, Rock Island Arsenal, 61201, Rock Island, IL

    S. C. Chu (Mechanical Engineer)

Authors
  1. O. M. Sidebottom
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  2. S. C. Chu
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Additional information

This investigation was funded by Rock Island Arsenal and was conducted at Research Directorate, GEN Thomas J. Rodman Laboratory, under the Laboratory Research Cooperative Program of ARO-D.

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Sidebottom, O.M., Chu, S.C. Bursting pressure of thick-walled cylinders subjected to internal and external pressures, axial load and torsion. Experimental Mechanics 15, 209–218 (1975). https://doi.org/10.1007/BF02319425

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  • DOI: https://doi.org/10.1007/BF02319425

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