Project ForgeThe homogeneous state of stress for a metal part undergoing plastic deformation is T = [[10, 5, 0], [5, 20, 0], [0, 0, −10]] MPa. Using von Mises yield criterion, the value of estimated shear yield stress, in MPa is
- A9.50
- 16.07
- C28.52
- D49.41
Explanation
The stress tensor decouples: the in-plane 2×2 block [[10,5],[5,20]] has eigenvalues 15±√((10−20)²/4+5²)=15±√50=22.071 and 7.929, and the third principal stress is simply −10 (already diagonal). Von Mises equivalent stress σe=√(½[(σ1−σ2)²+(σ2−σ3)²+(σ3−σ1)²])=√(½[14.142²+17.929²+(−32.071)²])=√(775)≈27.84 MPa. By von Mises theory σy=√3·τy, so the estimated shear yield stress τy=σe/√3=27.84/1.732≈16.07 MPa.
Source: GATE ME 2012 (Booklet Code A) (2012)
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