Abstract
An experimental investigation was undertaken to evaluate incremental-strain theories which have been proposed in the literature to predict the loads on thin-walled cylinders subjected to nonproportionate loading which follow prescribed strain histories. Test data were obtained for two materials, annealed SAE 1035 steel and normalized 4340 steel. Material-property tests for the SAE 1035 steel indicated that the stress-strain diagram was flat topped and the material followed the Tresca flow condition. Similar tests for the SAE 4340 steel indicated that this steel was a linear strain-hardening material that followed the von Mises flow condition.
Two incremental-strain theories were developed for thin-walled cylinders made of SAE 1035 steel. Both were based on the Tresca flow condition. One theory called the Tresca-Tresca theory used the stress-strain relations for the Tresca theory. The other theory called the Tresca-Mises theory used the Prandtl-Reuss stress-strain relations. In general, the test data fell between the two theories.
The incremental theory developed for thin-walled cylinders made of the SAE 4340 steel, called the Mises-Mises theory, was based on the von Mises flow condition and the Prandtl-Reuss stress-strain relations. The agreement between theory and experiment was poor.
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Abbreviations
- r, θ,z :
-
cylindrical coordinates and principal directions
- \(\sigma _t ,\sigma \theta ,\sigma _z \) :
-
stress components for cylinders
- \( \in _r , \in \theta \in _z \) :
-
strain components for cylinders
- \( \in _r ', \in \theta ' \in _z \) :
-
elastic components of strain
- \( \in _r , \in \theta \in _z \) :
-
plastic components of strain
- S r,S θ,S z :
-
deviatoric stress components
- e r,e θ,e z :
-
deviatoric strain components
- S, e :
-
mean normal stress and strain
- \(\bar \sigma ,\bar \in \) :
-
effective stress and strain
- E :
-
Young's modulus
- G :
-
shearing modulus
- ν:
-
Poisson's ratio
- \(\sigma _e \) :
-
yield stress in tension and compression
- \(\tau _e \) :
-
yield point in pure shear
- a :
-
strain-hardening factor
References
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).
Mendelson, A., Plasticity—Theory and Application, Macmillan, New York (1968).
Schlafer, J. L., “An Experimental Study of the Incremental and Total Strain Theories for Nonproportionately Loaded Thin-Walled Cylinders,” PhD thesis, Department of Theoretical and Applied Mechanics, University of Illinois (1968).
Hu, L. W. andMarin, J., “Anisotropic Loading Functions for Combined Stresses in the Plastic Range,”Jnl. Appl. Mech.,22 (1),444 (1955).
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Schlafer, J.L., Sidebottom, O.M. Experimental evaluation of incremental theories for nonproportionate loading of thin-walled cylinders. Experimental Mechanics 9, 500–506 (1969). https://doi.org/10.1007/BF02319693
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DOI: https://doi.org/10.1007/BF02319693