In a metal forming operation when the material has just started yielding, the principal stresses are: σ 1 = +180MPa,σ2 = -100 MPa, σ3 = 0 Following Von Mises criterion, the yield stress is ________ MPa
Question
In a metal forming operation when the material has just started yielding, the principal stresses are: σ 1 = +180MPa,σ2 = -100 MPa, σ3 = 0 Following Von Mises criterion, the yield stress is ________ MPa
Solution
The Von Mises criterion is a formula used to predict the yield of ductile materials. It is defined as:
σv = sqrt[(σ1 - σ2)² + (σ2 - σ3)² + (σ1 - σ3)²] / sqrt(2)
Where σ1, σ2, and σ3 are the principal stresses. In this case, σ1 = +180MPa, σ2 = -100MPa, and σ3 = 0.
Substituting these values into the formula, we get:
σv = sqrt[(180 - (-100))² + ((-100) - 0)² + (180 - 0)²] / sqrt(2) = sqrt[(280)² + (-100)² + 180²] / sqrt(2) = sqrt[(78400) + (10000) + (32400)] / sqrt(2) = sqrt[120800] / sqrt(2) = 347.64 MPa
So, according to the Von Mises criterion, the yield stress is 347.64 MPa.
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