Question

According to Irwin, the local stresses near a crack depend on the product of

• A. Nominal stress and square root of crack length
• B. Nominal stress and crack length
• C. Nominal strain and crack length
• D. Yield stress and crack width

Hint:

Crack tip severity increases with both stress level and crack size.

Answer 1

The Correct Option is A

Concept: According to Irwin’s linear elastic fracture mechanics (LEFM), the stress field near a crack tip is characterized by the stress intensity factor $K$, which governs crack-tip stresses.

Step 1: Irwin’s stress intensity factor.
For a crack of length $a$ under nominal stress $\sigma$: \[ K \propto \sigma \sqrt{\pi a} \]

Step 2: Physical meaning.
Local stress near crack tip depends on:
• applied nominal stress $\sigma$
• crack size $\sqrt{a}$ Thus controlling parameter is: \[ \sigma \sqrt{a} \] Final Answer: \[ \boxed{\text{Nominal stress and square root of crack length}} \]