Question

According to Tresca theory, yielding begins when

• A. Maximum principal stress equals yield stress
• B. Maximum shear stress equals half the yield stress
• C. Distortion energy equals strain energy at yield
• D. Volumetric strain becomes zero

Hint:

Tresca (Maximum Shear Stress) criterion: \[ \boxed{ \tau_{\max} = \frac{\sigma_y}{2}. } \] It is commonly used for predicting yielding in ductile materials.

Answer 1

The Correct Option is B

Step 1: Recall Tresca's yield criterion. Tresca theory is also known as the \[ \boxed{\text{Maximum Shear Stress Theory}.} \] It states that yielding begins when the maximum shear stress reaches the shear stress at yielding obtained from a uniaxial tensile test.

Step 2: Write the yielding condition. For a uniaxial tensile test, \[ \boxed{ \tau_{\max} = \frac{\sigma_y}{2}, } \] where \[ \sigma_y \] is the yield stress. Hence, \[ \boxed{ \text{Maximum shear stress equals half the yield stress.} } \] Therefore, \[ \boxed{(B)} \] is the correct answer.