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Arc Hyperbolic sine creep theory applied to torsion-tension member of circular cross section

Investigation is undertaken to determine the feasibility of using isochronous stress-strain diagrams of a material obtained from constant-stress creep curves to predict the deformations of members having multiaxial states of stress

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Abstract

A multiaxial creep theory is presented in this paper which will predict the total deformations of a load-carrying member at any specified time after load. Load-deformation relations are derived based on the assumption that the isochronous stress-strain diagram of the material can be represented by an arc hyperbolic sine function [see, eq (2)]. A closed solution was obtained for the torsion-tension member considered in this investigation. Experimental data were obtainsed for nylon and high-density polyethylene members in a controlled-environment room and for 17-7PH stainless-steel members at 972° F. Good agreement was found between theory and experiment.

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Abbreviations

z,r, θ:

cylindrical coordinates

∈ z , ∈ r , ∈ θ , γ θz , γ θr , γ rz :

strain components

σ 2 , σ r , σ θ , τ θz , τ rθ , τ rz :

stress components

e z ,e r ,e θ , γ θz , γ θr , γ rz :

deviatoric strain components

S z , S r , S θ , τ θz , τ θr rz :

deviatoric stress components

ρ:

Poisson's ratio

n :

(1−2ν)/2(1+ρ)

B,n, σ0, ∈0 :

experimental constants

G :

σ 0 /2 ∈0 (1 +v) shearing modulus of elasticity

\(\bar \sigma , \bar \in\) :

effective stress and effective strain

t :

time

b :

outer radius of torison-tension member

a :

inner radius of torison-tension member

ϕ:

unit angle of γθZ/r

β:

proportionality constant which varies from 0 to 1

α:

\(\sqrt {\beta ^2 + r^2 (1 - \beta ^2 )/b^2 }\)

H :

\(\sqrt {\beta ^2 + a^2 (1 - \beta ^2 )/b^2 }\)

A :

cross-sectional area

K :

\(\bar \in / \in _0\)

P :

axial load

T :

torque

J :

πb 4/2

Bibliography

  1. Orowan, E., “The Creep of Metals,” West Coast of Scot, Iron and Steel Inst. (July 1947).

  2. Lubahn, J. D. and elgar, R. P., “Plasticity and Creep of Metals,” Wley (1961).

  3. Finnie, I. and Heller, W.R., “Creep of Engineering Materials,” McGraw-Hill (1959).

  4. Sidebottom, O.M., Costello, G.A. and Dharmarajan, S., “Theoretical and Experimental Analyses of Members Made of Materials That Creep,” Engineering Experiment Station, University of Illinois, Bulletin 460 (1961).

  5. Shanley, R. F., “Weight-Strength Analysis of Aircraft Structures,” McGraw-Hill, Chapter 19 (1952).

  6. Costello, G. A., Sidebosttom, O. M. and Pocs, E., “Inelastic Design of Load Carrying Members—Part II The Effect of End Conditions on the Collapse Load of Columns,” TAM Report No. 178, University of Illinois or WADD Technical Report 60–580 (1960).

  7. Dewhirst, D. L. and Sidebottom, O. M., “Inelastic Design of Load Carrying Member—Part V Theoretical and Experimental Analyses of Bean Columns,“ TAM Report No. 201, University of Illinois or WADD Technical Report 60–580 (1961).

  8. Sidebottom, O. M. and Dewhirst D. L., “Theoretical and Experimental Creep Analyses of Beam-Columns,” ASME, Paper 62-WA-229 (1962).

  9. Schweiker, J. W. and Sidebottom, O. M., “Creep of Thick-Walled Cylinders Under Internal Pressure and Axial Load,” TAM Report No. 196, University of Illinois (1961).

  10. Gubser, J. L., Sidebottom, O. M. and Shammamy, M. R., “Creep torison of Prismatic Bars,” Paper Accepted by The Joint International Conference on Creep (August 1963).

  11. Shammamy, M. R. and Sidebottom, O. M., “Creep Torison of SAE 1020 Steel Bars at Elevated Temperatures,” TAM Report No. 208, University of Illinois (1962).

  12. Hagglund, R. R. and Sidebottom, O. M., “A theoretical and Experimental Analysis of the Creep of Curred Beams Loaded in Purs Bending,” TAM Report No. 209, University of Illinois (1962).

  13. Sokolowsky, W. W., “Theory of Plasticity,” Chapter II (both in Russian and in German), Moscow (1946).

  14. Dharmarajan, S. and Sidebottom, O. M., “Inelastic Design of Load Carrying Members-Part I Theoretical and Experimental Analyses of Circular Cross-Section Torison-Tension Members Made of Materials that Creep,” TAM Report No. 174, University of Illinois or WADD Technical Report 56–330 (1960).

  15. Marin, J. and Pao, Y. H., “A Theory for Combined Creep Strain-Stress Relations for Materials with Different Properties in Tension and Compression,” Proceedings of the First U. S. National Congress of Applied Mechanics, 586 (1951).

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Authors and Affiliations

  1. Department of Engineering, Mechanics, San Diego State College, San Diego, Calif.

    S. Dharmarajan (Assistant Professor)

  2. Department of Theoretical and applied Mechanics, University of Illinois, Urbana, Ill.

    O. M. Sidebottom (Professor)

Authors
  1. S. Dharmarajan
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  2. O. M. Sidebottom
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Formerly with Department of Theoretical and Applied Mechaaics, University of Illinois, Urbana, Ill.

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Dharmarajan, S., Sidebottom, O.M. Arc Hyperbolic sine creep theory applied to torsion-tension member of circular cross section. Experimental Mechanics 3, 153–160 (1963). https://doi.org/10.1007/BF02327423

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  • DOI: https://doi.org/10.1007/BF02327423

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