Advertisement

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
Article

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.

Keywords

Aluminum Alloy Plastic Strain Internal Pressure Axial Load Isotropic Hardening 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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

σz,ave

average axial stress

r01,r02

inner and outer radii of undeformed cylinder

r1,r2

inner and outer radii of the deformed cylinder

ro

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

p1,p2

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

Ao

undeformed cross-sectional area of cylinder

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Manning, W. R. D. andChem, A. M. I., “The Overstrain of Tubes by Internal Pressure,”Engineering,159,101–102 and 183–184 (1945).Google Scholar
  2. 2.
    Crossland, B. andBones, J. A., “Behavior of Thick-Walled cylinders Subjected to Internal Pressure,”Proc. Inst. Mech. Eng.,172,777 (1958).Google Scholar
  3. 3.
    Hannon, B. M., and Sidebottom, O. M., “Plastic Behavior of Open-End and Closed-End Thick-Walled Cylinders,” ASME Paper 67-WA/PVP-8 (1967).Google Scholar
  4. 4.
    Davis, E. A., “Creep Rupture Tests for Design of High-Pressure Steam Equipment,”Trans. ASME, J. Basic Eng., Series D,82,453–461 (1960).Google Scholar
  5. 5.
    Ohnami, M. and Motoie, K., “Creep and Creep Rupture of Cylindrical Tube Specimens Subjected to Combined Axial Load and Internal Pressure at Elevated Temperatures,” Proc. 9th Japan Cong. Test. Mat., 39–43 (1966).Google Scholar
  6. 6.
    Ohnami, M., Motie, K., and Yoshida, N., “Experimental Examinations for Creep Analysis of High Pressure Cylindrical Tube at Elevated Temperatures,” Proc. 10th Japan Cong. Test Mat., 54–59 (1967).Google Scholar
  7. 7.
    Ohnami, M. and Yoshida, N., “Creep of High Pressure Cylindrical Tube at Elevated Temperatures (Experimental Examinations under Combined. Cyclic Axial Load and the Internal Pressure),” Proc. 12th Japan Cong. Mat. Res., 87–90 (1969).Google Scholar
  8. 8.
    Ohtani, R., “Creep and Creep Fracture of Metallic Materials under Multiaxial Stress at Elevated Temperatures,” PhD Thesis, College of Engineering, Kyoto University, Kyoto, Japan.Google Scholar
  9. 9.
    Panarelli, J. E. andHodge, P. G., Jr.Interaction of Pressure, End Load, and Twisting Moment for a Rigid-Plastic Circular Tube,”J. of Appl. Mech., Trans. ASME,85,396–400, (1963).Google Scholar
  10. 10.
    Chu, S. C., “A More Rational Approach to the Problem of Elastoplastic Thick-Walled Cylinder,”J. Franklin Ins.,294,57–65 (1972).Google Scholar
  11. 11.
    Sidebottom, O. M., “Evaluation of Finite-plasticity Theories for Nonproportionate Loading of Torsion-Tension Members,”Experimental Mechanics,12 (1),18–24 (1972).Google Scholar
  12. 12.
    Sidebottom, O. M., “Evaluation of Multiaxial Theories for Room-temperature Plasticity and Elevated-temperature Creep and Relaxation of Several Metals,”Experimental Mechanics,13 (1),14–23 (1973).CrossRefGoogle Scholar

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

Personalised recommendations