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| Plastic Deformation | |||||||||||||||
| von
Mises Model
· von
Mises proposed an alternate critical shear stress criterion that used
the strain energy per unit volume of the material at the uniaxial stress
yield point as the value that must be reached in the multi-axial situation.
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| ·
For
a linear elastic material loaded uniaxially to the yield point: σ1
= σy
and: σ2
= σ3
= 0.
The energy per unit volume is then: U1 ={(1 + ν )/6E}[2σy2] . · von Mises' criterion equates the uniaxial and triaxial elastic energies at yield to give: [(σ1- σ2)2 + (σ2- σ3)2 + (σ1- σ3)2] =[2σ2y] = C. · This is a cylinder in principal axis space centered on the hydrostatic line. |
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