Composite Materials MCQ with answer and solution

Concept

Yield strength increases as grain size decreases. Smaller grains mean more grain boundaries, which block dislocation motion.

Formula

σ_y = σ₀ + k_y / d^1/2

Step-by-step solution

1. Hall-Petch equation: σ_y = σ₀ + k_y × d^-1/2. 2. Here d is the average grain diameter. 3. If d decreases, σ_y increases. 4. So the relationship links yield strength to grain size. 5. Answer is A.

Explanation

The Hall-Petch relationship links yield strength to grain size. Fine grains have more grain boundaries. These boundaries stop dislocations from moving, so the metal becomes stronger.

Why the other options are wrong

B: Temperature effects are described by other laws, not Hall-Petch. C: Dislocation density is related by the Taylor equation. D: Applied stress is the load, not what the relation describes.

Shortcut

Hall-Petch = grain size. Finer grain = stronger metal.

Common mistake

Thinking that larger grains give higher strength. It is the opposite.