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In a metal forming operation when the material has just started yielding, the principal stresses are σ1 = +180 MPa, σ2 = -100 MPa, σ3 = 0. Following Von Mises criterion, the yield stress is ________ MPa.
Correct answer is between '245,246'. Can you explain this answer?
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In a metal forming operation when the material has just started yieldi...
As per Von-Mises criteria
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Calculating Von Mises Yield Stress:
To calculate the Von Mises yield stress, we first need to determine the equivalent stress using the principal stresses given in the problem.
Equivalent Stress Formula:
The Von Mises equivalent stress is calculated using the following formula:
σ_v = √(σ1^2 + σ2^2 + σ3^2 - σ1*σ2 - σ2*σ3 - σ3*σ1)
Given Principal Stresses:
σ1 = +180 MPa
σ2 = -100 MPa
σ3 = 0 MPa
Plugging in the Values:
σ_v = √((180)^2 + (-100)^2 + (0)^2 - 180*(-100) - (-100)*0 - 0*180)
σ_v = √(32400 + 10000 - (-18000))
σ_v = √(42400 + 18000)
σ_v = √60400
σ_v ≈ 245.86 MPa
Therefore, the Von Mises equivalent stress when the material has just started yielding is approximately 245.86 MPa. This is the yield stress based on the Von Mises criterion in this metal forming operation.
To calculate the Von Mises yield stress, we first need to determine the equivalent stress using the principal stresses given in the problem.
Equivalent Stress Formula:
The Von Mises equivalent stress is calculated using the following formula:
σ_v = √(σ1^2 + σ2^2 + σ3^2 - σ1*σ2 - σ2*σ3 - σ3*σ1)
Given Principal Stresses:
σ1 = +180 MPa
σ2 = -100 MPa
σ3 = 0 MPa
Plugging in the Values:
σ_v = √((180)^2 + (-100)^2 + (0)^2 - 180*(-100) - (-100)*0 - 0*180)
σ_v = √(32400 + 10000 - (-18000))
σ_v = √(42400 + 18000)
σ_v = √60400
σ_v ≈ 245.86 MPa
Therefore, the Von Mises equivalent stress when the material has just started yielding is approximately 245.86 MPa. This is the yield stress based on the Von Mises criterion in this metal forming operation.
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In a metal forming operation when the material has just started yielding, the principal stresses are σ1= +180 MPa, σ2= -100 MPa, σ3= 0. Following Von Mises criterion, the yield stress is ________ MPa.Correct answer is between '245,246'. Can you explain this answer?
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