Question

Which one of the following metal has maximum value of yield strength?

• A. Copper alloy
• B. High-carbon steel
• C. Mild steel
• D. Medium-carbon steel

Hint:

In carbon steels: Higher Carbon Content (%) $\rightarrow$ Higher Volume of Cementite $\rightarrow$ Higher Yield Strength and Hardness (but lower ductility and toughness). Therefore, the strength order is: High-Carbon > Medium-Carbon > Mild Steel.

Answer 1

The Correct Option is B

Concept: Yield strength ($\sigma_y$) is the threshold stress value at which a material transitions from elastic behavior to permanent plastic deformation. In carbon steels, mechanical properties are determined primarily by the weight percentage of carbon dissolved in the iron matrix. Carbon acts as an interstitial alloying element that fits into the spaces between iron atoms. These carbon atoms create localized stress fields that pin and restrict the movement of dislocations through the crystal lattice under load—a mechanism known as interstitial solid solution strengthening. Additionally, during cooling, carbon forms a hard iron carbide intermetallic compound called cementite ($\text{Fe}_3\text{C}$). As carbon content increases, the volume fraction of cementite grows, raising both the hardness and yield strength of the steel.

Step 1: Compare carbon steel classifications by composition and strength.
Let us classify the three carbon steels based on typical carbon composition and yield strength trends:

• Mild Steel (Low-Carbon Steel): Contains less than 0.25% Carbon by weight. It features high ductility and toughness but has the lowest yield strength among carbon steels (typically $\approx 250 \text{ MPa}$).

• Medium-Carbon Steel: Contains between 0.25% and 0.60% Carbon by weight. It offers a balanced compromise between ductility and strength, with typical yield strengths ranging from $300 \text{ MPa}$ to $600 \text{ MPa}$.

• High-Carbon Steel: Contains between 0.60% and 1.40% Carbon by weight. It has a high concentration of hard cementite, resulting in high hardness and the highest yield strength among standard carbon steels (often exceeding $600 - 1000 \text{ MPa}$ depending on heat treatment), though it has lower ductility.

Step 2: Compare with non-ferrous copper alloys.

• Copper Alloys (e.g., Brass, Bronze): While brass and bronze can be engineered to achieve reasonable strength through work hardening or solution strengthening, their typical yield strength limits remain lower than those of high-carbon structural steels.

Step 3: Identify the material with the maximum value.
Comparing all options, high-carbon steel has the highest carbon content and cementite fraction, giving it the highest yield strength. This matches Option (B).