Question

The basis on which the Von Mises criterion is preferred compared to maximum shear stress criterion theoretically is:

• A. It has lower accuracy
• B. It considers all three principal stresses
• C. It considers maximum shear stress
• D. Its energy is associated with change of volume of material

Hint:

Von Mises theory is more accurate for ductile metals under complex loading.

Answer 1

The Correct Option is B

Concept: Von Mises yield criterion is based on the distortion energy theory. It predicts yielding when the distortion energy in a material reaches a critical value. The Von Mises stress depends on all three principal stresses: \[ \sigma_1, \sigma_2, \sigma_3 \]

Step 1: Von Mises criterion expression.
\[ \sigma_v = \sqrt{\frac{(\sigma_1-\sigma_2)^2+(\sigma_2-\sigma_3)^2+(\sigma_3-\sigma_1)^2}{2}} \] Clearly, all three principal stresses are involved.

Step 2: Comparison with Tresca theory.

• Tresca → depends only on maximum shear stress
• Von Mises → considers full stress state

Step 3: Reason for preference.
Von Mises is preferred because:
• It gives better experimental correlation for ductile materials
• It accounts for complete 3D stress state Final Answer: \[ \boxed{\text{It considers all three principal stresses}} \]