Question

A material was tested under the proportionally increasing state of stress: $2sigma_1 = -3sigma_2 = sigma_3$. Yielding was observed at $sigma_3 = 400 MPa$. a) What would be the yield stress of this material under simple tensile loading? b) If the same material is used under the conditions such that $sigma_1 = -sigma_2 = 2sigma_3$, at what value of $sigma_1$ will yielding occur? Solve the problem completely using: i. Von Mises yield criterion ii. Tresca yield criterion.

          A material was tested under the proportionally increasing state of stress:
$2sigma_1 = -3sigma_2 = sigma_3$.
Yielding was observed at $sigma_3 = 400 MPa$.
a) What would be the yield stress of this material under simple tensile
loading?
b) If the same material is used under the conditions such that $sigma_1 = -sigma_2 = 2sigma_3$, at
what value of $sigma_1$ will yielding occur?
Solve the problem completely using:
i. Von Mises yield criterion
ii. Tresca yield criterion.

A material was tested under the proportionally increasing state of stress:
2sigma1 = -3sigma2 = sigma3.
Yielding was observed at sigma3 = 400 MPa.
a) What would be the yield stress of this material under simple tensile
loading?
b) If the same material is used under the conditions such that sigma1 = -sigma2 = 2sigma3, at
what value of sigma1 will yielding occur?
Solve the problem completely using:
i. Von Mises yield criterion
ii. Tresca yield criterion.

Added by Ana B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

09/17/2023

Step 1

Von Mises yield criterion: According to the Von Mises yield criterion, yielding occurs when the equivalent stress reaches a critical value. The equivalent stress is given by the formula: σ_eq = √(σ₁² + σ₂² + σ₃² - σ₁σ₂ - σ₂σ₃ - σ₃σ₁) In this case, we have a Show more…

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A material was tested under the proportionally increasing state of stress: 2̃́1 = -3̃́2 = ̃́3. Yielding was observed at ̃́3 = 400 MPa. a) What would be the yield stress of this material under simple tensile loading? b) If the same material is used under the conditions such that ̃́1 = -̃́2 = 2̃́3, at what value of ̃́1 will yielding occur? Solve the problem completely using: i. Von Mises yield criterion ii. Tresca yield criterion.