Abstract
Based on the assumption that the material was isotropic and even, and satisfied the condition of isotropic hardening for a von Mises material, finite-incremental and total-strain theories were derived for solid circularsection torsion-tension members subjected to nonproportionate loading. Torsion-tension members made of SAE 1045 steel and aluminum alloy 7075-T6 were subjected to proportionate and nonproportionate loading. During the nonproportionate loading, either the axial loal P or torque T was held constant while the other was increased. Excellent agreement was found between the incremental theory and experimental data indicating that the assumption of isotropic hardening is valid for this type of loading. For some of the nonproportionate loading paths, incremental and total-strain theories gave nearly identical results.
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Abbreviations
- r, θ,z :
-
cylindrical coordinates
- \(\begin{gathered} \sigma _r ,\sigma _\theta ,\sigma _{z,} \hfill \\ \tau _{r\theta } ,\tau _{\theta z} ,\tau _{zr} \hfill \\ \end{gathered}\) :
-
true-stress components
- \(\begin{gathered} \varepsilon _r ,\varepsilon _\theta ,\varepsilon _{z,} \hfill \\ \gamma _{r\theta } ,\gamma _{\theta z} ,\gamma _{zr} \hfill \\ \end{gathered}\) :
-
true-strain components
- \(\sigma _e ,\varepsilon _p\) :
-
effective true-stress and effective true-plastic strain
- \(d\varepsilon _p\) :
-
increment in effective plastic strain
- \(\varepsilon _z ^\prime\) :
-
defined by eq (8)
- \(\varepsilon _r ^\prime\) :
-
defined by eq (9)
- \(\gamma '_{\theta z}\) :
-
defined by eq (10)
- \(\varepsilon _{et}\) :
-
defined by eq (11)
- \(\sigma _o\) :
-
yield stress
- a :
-
radius of torsion-tension member
- R :
-
radius of deformed torsion-tension member
- 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
- \((\varepsilon _z )_e\) :
-
P/AE
- \((\gamma _{\theta z} )_{_{e,max} }\) :
-
TR/GJ
- \(\gamma _{\theta z,max}\) :
-
maximum shearing strain in torsiontension member
- \(\varepsilon _o\) :
-
\(\sigma _o /E\)
- p :
-
superscript indicating inelastic component of strain
References
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Sidebottom, O.M. Evaluation of finite-plasticity theories for nonproportionate loading of torsion-tension members. Experimental Mechanics 12, 18–24 (1972). https://doi.org/10.1007/BF02320785
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DOI: https://doi.org/10.1007/BF02320785