Abstract
Incremental and total-strain theories have been presented in the literature for hollow and solid circular torsion-tension members. The differential equations obtained for the incremental theory have been solved only for the conditions that the torsion-tension member is made of a nonstrain-hardening material and is subjected to restricted deformation histories. Computer programs were written to obtain numerical incremental solutions for hollow and solid circular torsion-tension members made of strain-hardening materials and subjected to any deformation or loading path. Test data were obtained for three different materials: (a) a nonstrain-hardening steel, annealed SAE 1035 steel, with identical properties in tension and compression; (b) a strain-hardening steel, annealed rail steel, with identical properties in tension and compression; (c) a strainhardening alumimum alloy, 2024-T4, with different properties in tension and compression. In all cases, the average of the tension and compression stress-strain diagram was approximated by two straight lines to obtain material properties.
Test data for proportionate loading were in excellent agreement with either the total-strain theory or the incremental-strain theory. Data for nonproportionate loading, in which one deformation was kept constant as the other was increased, fell between the two theories and were in closer agreement with the predictions of the incremental theory.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- r,θ,z :
-
cylindrical coordinates
- σ z ,σ r , σθ, τ θz ,σ zr , σ rθ :
-
stress components for torsion-tension member
- ∈ z ,∈ r , ∈ θ , γ θz ,γ zr , γ rθ :
-
strain components for torsion-tension member
- ∈ z ′,∈ r ′, ∈ θ ′, γ θz ′,γ zr ′, γ rθ ′:
-
elastic components of strain
- ∈ z ″,∈ r ″, ∈ θ ″, γ θz ″,γ zr ″, γ rθ ″:
-
inelastic components of strain
- S z,S r,S θ, τ θz ,τ zr τ rθ :
-
deviatoric stress components
- e z,e r,e θ, γ θz ,γ zr γ rθ :
-
deviatoric strain components
- τ G , γ G :
-
octahedral shearing stress and strain
- \(\bar \sigma ,\bar \in\) :
-
effective stress and strain
- E :
-
Young's modulus
- G :
-
shearing modulus
- ν:
-
Poisson's ratio
- σ e :
-
yield stress in tension and compression
- α:
-
strain-hardening factor
- a :
-
mean radius of hollow member and outer radius of solid member
- t :
-
thickness of hollow member
References
Smith, J. O., and Sidebottom, O. M., “Inelastic Behavior of Load Carrying Members,” John Wiley and Son, Inc. (1965).
Hill, R., “The Mathematical Theory of Plasticity,” Oxford at the Claredon Press (1950).
Sokolovsky, W. W., “Theory of Plasticity,” Moscow, USSR (1946).
Dharmarajan, S. andSidebottom, O. M., “Arc Hyperbolic Sine Creep Theory Applied to Torsion-Tension Member of Circular Cross Section,”Experimental Mechanics,3 (7),153–60 (1963).
Patnaik, N., and Sidebottom, O. M., “Creep of Circular Torsion-Tension Members Subjected to Nonproportionade Load Changes,” University of Illinois Engineering Experiment Station Technical Report No. 6 (1963).
Shammamy, M.R., “Comparison of Incremental and Total Theories with Test Data for Circular Torsion-Tension Members Subjected to Proportionate and Nonproportionate Loading,” PhD Thesis, Department Theoretical and Applied Mechanics, University of Illinois (1965).
Dharmarajan, S., and Sidebottom, O. M., “Inelastic Design of Load Carrying Members—Part I Theoretical and Experimental Analyses of Circular Cross-Section Torsion-Tension Members Made of Materials that Creep,” TAM Report No. 174, University of Illinois or WADD Technical Report 56-330 (1960).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shammamy, M.R., Sidebottom, O.M. Incremental versus total-strain theories for proportionate and nonproportionate loading of torsion-tension members. Experimental Mechanics 7, 497–505 (1967). https://doi.org/10.1007/BF02326324
Issue Date:
DOI: https://doi.org/10.1007/BF02326324