Question

The mean grain diameter corresponding to ASTM number of 0.5 is

• A. 0.33 mm
• B. 0.43 mm
• C. 0.53 mm
• D. 0.63 mm

Hint:

ASTM grain size number (\( G \)) is used to describe the grain structure in metals. Larger \( G \) values mean smaller grains, improving mechanical properties.

Answer 1

The Correct Option is D

The grain size in a material is commonly quantified using the ASTM grain size number (\( G \)), which follows the relation: \[ d = \frac{1}{\sqrt{N}} \times 10^3 \] or alternatively: \[ d = \frac{1}{2^{(G-1)/2}} \text{ mm} \] where: - \( d \) = mean grain diameter in mm, - \( N \) = number of grains per unit area at 1x magnification, - \( G \) = ASTM grain size number.
Step 1: Substituting ASTM Number \( G = 0.5 \) Using the standard ASTM grain size equation: \[ d = \frac{1}{2^{(0.5-1)/2}} \] \[ = \frac{1}{2^{-0.25}} \] \[ \approx 0.63 \text{ mm} \]


Step 2: Evaluating the Options - Option (A) - Incorrect: 0.33 mm is too low.
- Option (B) - Incorrect: 0.43 mm does not match our calculated value.
- Option (C) - Incorrect: 0.53 mm is slightly lower than the correct value.
- Option (D) - Correct: 0.63 mm matches our calculation.


Step 3: Conclusion Since the mean grain diameter corresponding to ASTM number 0.5 is 0.63 mm, the correct answer is option (D).