Experimental Mechanics

, Volume 13, Issue 1, pp 14–23 | Cite as

Evaluation of multiaxial theories for room-temperature plasticity and elevated-temperature creep and relaxation of several metals

Investigation is undertaken to evaluate the isotropic-hardening model for several ductile metals at both room temperature, where the inelastic deformation could be considered to be time independent, and at elevated temperatures, where the inelastic deformation was primarily time dependent
  • Omar M. Sidebottom


Based on the assumption that the material satisfies the condition of isotropic hardening for either a von Mises or a Tresca material, finite-strain theories are derived for solid circular torsion members for the conditions that the inelastic deformations are either time independent or time dependent. In the latter case, both creep and relaxation theories are derived. At room temperature the theories are evaluated for each of eight metals using finite-strain data from tension, compression and torsion members. Of the six metals that are found to satisfy the condition required for the isotropic-hardening model, two are von Mises, one is Tresca, and the other three are between von Mises and Tresca. At elevated temperatures, the theories are evaluated for each of five of the latter six metals, using data from tension and torsion members. Material properties obtained from the tension specimens are used to predict creep and relaxation curves for the torsion members. Contrary to the results at room temperature, creep curves for the torsion members do not all fall within the region bounded by von Mises and Tresca theories. In the case of relaxation, either excellent agreement is obtained between the von Mises strain-hardening theory and experimental data or the theory is conservative.


Mechanical Engineer Material Property Elevated Temperature Fluid Dynamics Excellent Agreement 
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List of Symbols

r, θ,z

cylindrical coordinates

Δr, Δθ, Δz trθ, tθz, tzr εrc εθc, εzc

true-stress components

γrθc, γθzc, γzrc

true-creep-strain components (superscriptp denotes plastic components)

δ1, δ2, δ3

principal true-stress components

ε1c, ε2c, ε3c

principal true-creep-strain components (superscriptp denotes plastic components)


effective true stress

εc, εp

effective true creep strain and effective true plastic strain

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effective creep rate

ε, ε1

normal true strain in tension specimen


engineering strain in tension specimen


shearing stress in torsion member


shearing strain in torsion member

γc, γp

creep and plastic components of shearing strain in torsion member

% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4SdCMbai% aaaaa!379D!\[\dot \gamma \]

shearing-strain creep rate in torsion member


increment of shearing creep strain in torsion member

t, Δt

time and increment in time


initial diameter of tension specimen


deformed diameter of tension specimen


outer radius of torsion member


variable radius of torsion member


unit angle of twist






maximum shearing strain


Young's modulus


shearing modulus


Poisson's ratio


polar moment of inertia


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  1. 1.
    Sidebottom, Omar M., “Evaluation of Finite-plasticity Theories for Nonproportionate Loading of Torsion-Tension Members”,EXPERIMENTAL MECHANICS,12, (1),18–24 (1972).Google Scholar
  2. 2.
    Hu, L. W. andMarin, J., “Anisotropic Loading Functions for Combined Stresses in the Plastic Range”,J. Appl. Mech.,22 (1),444 (1955).Google Scholar
  3. 3.
    Bertsch, P. K. andFindley, W. N., “An Experimental Study of Subsequent Yield Surfaces-Corners, Normality, Bauschinger and Allied Effects”,Proc. 4th U.S. Nat. Cong. Appl. Mech.,2,893–907 (1962).Google Scholar
  4. 4.
    Schlafer, J. L. andSidebottom, O. M., “Experimental Evaluation of Incremental Theories for Nonproportionate. Loading of Thin-walled Cylinders”,EXPERIMENTAL MECHANICS,9, (11),500–506 (1969).CrossRefGoogle Scholar
  5. 5.
    Shammamy, M. R. andSidebottom, O. M., “Incremental Versus Total Strain Theories for Proportionate and Nonproportionate Loading of Torsion-Tension Members”,EXPERIMENTAL MECHANICS,7 (12),497–505 (1967).CrossRefGoogle Scholar
  6. 6.
    Sidebottom, O. M. and Johnson, K. R., “Strain-history Effect on Isotropic and Anisotropic Plastic Behavior”, Paper presented at SESA Spring Meeting, Cleveland, OH (May 23–26, 1972).Google Scholar
  7. 7.
    Manning, W. R. D., “The Overstrain of Tubes by Internal Pressure”,Engineering,159,101–102 and 183–184 (1945).Google Scholar
  8. 8.
    Crossland, B. andBones, J. A., “Behavior of Thick-Walled Cylinders Subjected to Internal Pressure”,Proc. Inst. Mech. Eng.,172,777 (1958).Google Scholar
  9. 9.
    Hannon, B. M. and Sidebottom, O. M., “Plastic Behavior of Open-End and Closed-End Thick-Walled Cylinders”, ASME paper 67-WA/PVP-8 (1968).Google Scholar
  10. 10.
    Taira, S., Ohtani, R. and Ishisaka, A. “Creep and Creep Fracture of a Low Carbon Steel Under Combined Tension and Internal Pressure”, Proc. 11th Japan Cong. Material Research, 76–81 (1968).Google Scholar
  11. 11.
    Ohtani, R., “Creep and Creep Fracture of Metallic Materials Under Multiaxial Stress at Elevated Temperatures”, PhD Thesis, College of Engineering, Kyoto Univ., Kyoto, Japan.Google Scholar
  12. 12.
    Sidebottom, O. M., “Note on the Effective Plastic Strain for a Tresca Materials”,J. Appl. Mech., Series E,38, (4),1049–1050 (1971).Google Scholar
  13. 13.
    Morkovin, D. and Sidebottom, O. M., “The Effect of Non-Uniform Distribution of Stress on the Yield Strength of Steel”, Engineering Experiment Station Bulletin No. 327, Univ. of Illinois, (1947).Google Scholar
  14. 14.
    Mendelson, A., “Plasticity: Theory and Application”,Macmillan, New York, Ch. 7, 9 (1968).Google Scholar
  15. 15.
    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
  16. 16.
    Frederking, R. M. W. andSidebottom, O. M., “An Experimental Evaluation of Plasticity Theories for Anisotropic Metals”,J. Appl. Mech., Series E,38 (1)15–22 (1971).Google Scholar
  17. 17.
    Lietzke, M. H., “A Generalized Least Squares Program for the IBM 7090 Computer”,ORNL Report No. 3259, Oak Ridge Nat'l. Lab., Oak Ridge, TN (1962).Google Scholar
  18. 18.
    Gubser, J. L., Sidebottom, O. M. and Shammamy, M. R., “Creep Torsion of Prismatic Bars”, Joint Intl. Conf. on Creep, 2–99 to 2–108 (1963).Google Scholar
  19. 19.
    Chu, S. C. andSidebottom, O. M., “Creep of Metal Torsion-Tension Members Subjected to Nonproportionate Load Changes”,EXPERIMENTAL MECHANICS,10 (6),225–232 (1970).CrossRefGoogle Scholar
  20. 20.
    Pickel, T. W., Jr., Sidebottom, O. M. andBoresi, A. P., “Evaluations 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
  21. 21.
    Boresi, A. P. and Sidebottom, O. M., “Creep Under Multiaxial States of Stress”, First. Intl. Conf. on Structural Mechanics in Reactor Technology,5,Structural Analysis and Design, Part L. Thermal and Mechanical Analysis, 1971. Also TAM Report No. 347, Dept. of Theoretical and Applied Mechanics, Univ. of Illinois, Urbana, IL.Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 1973

Authors and Affiliations

  • Omar M. Sidebottom
    • 1
  1. 1.Department of Theoretical and Applied MechanicsUniversity of IllinoisUrbana

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