Experimental Mechanics

, Volume 13, Issue 6, pp 238–245 | Cite as

Evaluation of finite-plasticity theories for torsion-tension members made of tresca materials

Incremental theories are developed for solid circular torsion-tension members subjected to any presented loading path and subjected to loads that produce finite strains
  • O. M. Sidebottom
  • Rabi K. Bhattacharyya
Article

Abstract

Finite-incremental Tresca and von Mises theories are developed for solid circular-section torsion-tension members subjected to proportionate and nonproportionate loading. The materials are assumed to be isotropic and even. Two Tresca theories and a von Mises theory are compared with test data obtained from torsion-tension members. Three different kinds of steels were tested; they are hot-rolled mild steel, annealed mild steel, and hot-rolled SAE 1017 steel. The fully plastic values of axial load and torque predicted by the Tresca theories agree with the experimental results; however, the deformations, in the strain-hardening region, predicted by both of the Tresca theories were greater than observed. The von Mises theory is nonconservative in predicting the fully plastic loads of torsion members and torsion-tension members and in predicting the deformations of torsion members in the strain-hardening region, but gives good correlation between predicted and experimental deformations for the torsion-tension members in the strain-hardening region.

Keywords

Torque Mechanical Engineer Fluid Dynamics Test Data Mild Steel 

List of Symbols

r, θz

cylindrical coordinates

\(\sigma _1 ,\sigma _2 ,\sigma _3 \)

principal true-stress components

\(d \in ^p ,d \in _2 ^p ,d \in _3 ^p \)

principal components of plastic-strain increments

\(\sigma _z ,\tau _{\theta z} \)

axial and shearing true-stress components in torsion-tension member

\(d \in _z ^p ,d\gamma \theta z^p \)

axial and shearing components of plastic-strain increments

\(\sigma _e , \in _p \)

effective true-stress and effective true-plastic strain

\(d_{ \in p} \)

increment in effective plastic strain

\( \in _z '\)

defined by eq (7)

\( \in _r '\)

defined by eq (8)

γθz′

defined by eq (9)

\( \in _r '\)

defined by either eq (10) or eq (22)

B

2 or defined by eq (25)

\( \in _{et} \)

yield stress

m

strain-hardening factor

a

radius of undeformed torsion-tension member

R

radius of deformed torsion-tension member

Rσ,Rε

radii of Mohr's circles of stress and plastic-strain increments

P

axial load

T

torque

A

cross-sectional area

J

polar moment of inertia

E

Young's modulus

G

shearing modulus

ν

Poisson's ratio

\(\left( { \in _z } \right)_e \)

P/AE

(γθz)e,max

TR/GJ

γθz,max

maximum shearing strain in torsiontension member

\( \in _z \)

true axial strain in torsion-tension member

\( \in _z ,eng\)

engineering value of axial strain in torsion-tension member

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Wahl, A. M., “Analysis of Creep in Rotating Disks Based on the Tresca Criterion and Associated ‘Flow Rule’,”J. Appl. Mech., Trans. ASME,23 (78),231–238 (1956).MATHGoogle Scholar
  2. 2.
    Taira, S., Ohtane, R. and Kakihara, Y., “Creep of Thick-Walled Cylinders With Radial Temperature Gradient Under Internal Pressures,” Proc. Ninth Japan Cong. on Testing Materials, The Soc. of Mat. Sci., Japan, 33–38 (1966).Google Scholar
  3. 3.
    Mendelson, A., Plasticity: Theory and Application, Macmillan, New York, 108, 159 (1968).Google Scholar
  4. 4.
    Hill, R., Plasticity, Oxford at the Clarendon Press (1950).Google Scholar
  5. 5.
    Pickel, T. W., Jr., Sidebottom, O. M. andBoresi, A. P., “Evaluation of Creep Laws and Flow Criteria for Two Metals Subjected to Stepped Load and Temperature Changes,”Experimental mechanics,11 (5),202–209 (1971).CrossRefGoogle Scholar
  6. 6.
    Sidebottom, O. M., “Note of the Effective Plastic Strain for a Tresca Material,”J. Appl. Mech., Trans. ASME, Series E,38, (4),1049–1050 (1972).Google Scholar
  7. 7.
    Sidebottom, O. M., “Evaluation of Finite-plasticity Theories for Nonproportionate Loading of Torsion-Tension Members,”Experimental mechanics,12 (1),18–24 (1972).Google Scholar
  8. 8.
    Mendelson, Op Cit, Ch. 7, 9.Google Scholar
  9. 9.
    Dharmarajan, S. and Sidebottom, O. M., “Inelastic Design of Load Carrying Members, Part I-Theoretical and Experimental Analysis of Circular Cross-Section Torsion-Tension Members Made of Materials that Creep,” WADD Tech. Rept. 60-580 (1961).Google Scholar
  10. 10.
    Morkovin, D. and Sidebottom, O. M., “The Effect of Nonuniform Distribution of Stress on the Yield Strength of Steel,” Eng. Experiment Station Bull. No. 372, Univ. of Illinois (1947).Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 1973

Authors and Affiliations

  • O. M. Sidebottom
    • 1
  • Rabi K. Bhattacharyya
    • 1
  1. 1.Department of Theoretical and Applied MechanicsUniversity of IllinoisUrbana

Personalised recommendations