Abstract
Two analytical solutions are used to predict load-strain relations for unloading of thick-walled cylinders. The solutions assume that the material is an isotropic-hardening material that obeys the von Mises yield condition. The loading function for the material for the unloading of the cylinders was obtained from tension-compression specimens that were unloaded and reverse loaded from several points along the tension stress-strain diagram. Good agreement is indicated between the unloading load-strain curves obtained from two thick-walled cylinders made of SAE 1045 steel and the curves predicted by the analytical solutions. The analytical solutions predict that the beneficial circumferential compressive residual stresses at the inside of the cylinders decrease by about 50 percent during the unloading.
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Abbreviations
- r, θ,z :
-
cylindrical coordinates
- σ r :
-
true-stress components
- σ rR ,σθR :
-
residual-stress components
- ∈ r ,∈θ,∈ z :
-
true-strain components
- \( \in _r^p , \in _\theta ^p , \in _z^p \) :
-
true-plastic-strain components
- σ e ,:
-
true effective stress and true effective strain
- σ e ,∈ e :
-
true effective elastic and plastic strains
- r 1,r 2 :
-
inner and outer radii of the cylinder
- r i :
-
variable radius
- Δr :
-
r i+1−r i is thickness of volume element
- σ r(i) ,σθ(i) :
-
true-stress components atr i
- ∈ r(i) ,∈σ(i) :
-
true-strain components atr i
- σ r(i+1) :
-
true radial stress atr i+1
- ∈θ(i1) :
-
true circumferential strain atr i+1
- X, Y :
-
unknown functions ofr i and Δr
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Sidebottom, O.M., Chu, S.C. & Lamba, H.S. Unloading of thick-walled cylinders that have been plastically deformed. Experimental Mechanics 16, 454–460 (1976). https://doi.org/10.1007/BF02324102
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DOI: https://doi.org/10.1007/BF02324102