Question

Dendrite arm spacing decreases with

• A. slower cooling rate
• B. higher cooling rate
• C. greater diffusion
• D. increased alloy solubility

Hint:

Remember:
- Fast Cooling \(\rightarrow\) Fine Dendrites \(\rightarrow\) Small DAS \(\rightarrow\) High Mechanical Strength.
- Slow Cooling \(\rightarrow\) Coarse Dendrites \(\rightarrow\) Large DAS \(\rightarrow\) Lower Mechanical Strength.
This structural relationship explains why metal molds (chills) are often placed in sand molds.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question asks how the cooling rate during solidification affects the resulting dendrite arm spacing (DAS) in cast alloys.
Dendrites are the characteristic tree-like crystal structures that grow during the solidification of metallic alloys.

Step 2: Key Formula or Approach:
Dendrite arm spacing (both primary and secondary) is directly controlled by the local solidification time and the average cooling rate.
The relationship is modeled by the power-law equation:
\[ \text{DAS} = a \cdot R^{-n} \]
where:
\( a \) is a material-dependent constant.
\( R \) is the average cooling rate during solidification (\( ^{\circ}\text{C/s} \)).
\( n \) is an exponent (typically \( n \approx 0.3 \text{ to } 0.5 \) for secondary dendrite arm spacing).

Step 3: Detailed Explanation:

• Cooling Rate and Spacing:
- From the relationship \( \text{DAS} \propto R^{-n} \), as the cooling rate \( R \) increases, the value of DAS must decrease.
-

Physical Mechanism: A higher cooling rate corresponds to a very short local solidification time.
- Because the time window is short, there is very little time available for solute diffusion and dendritic coarsening.
- New dendrite arms must initiate closer together to accommodate the rapid heat removal, leading to a much finer dendritic structure (smaller DAS).

• Mechanical Properties: A smaller DAS is highly desirable in cast parts.
- It minimizes micro-segregation, reduces casting porosity size, and significantly increases the tensile strength, ductility, and fatigue resistance of the cast component.


Step 4: Final Answer:
Dendrite arm spacing decreases with an increase in the cooling rate.
Therefore, the correct choice is option (B).