Problem 5: Computing Grain Diameter After Heat Treatment

Understanding Grain Growth in Materials

When studying materials science, one of the key aspects to consider is the behavior of grain size in a material during heat treatment. This particular problem explores how the grain diameter of a hypothetical material changes after being subjected to specific heat treatment conditions.

Given Information

The data provided states that the original grain diameter (do) of the material is 3.22 x 10^2 mm. After a heat treatment at 750°C for 3.75 hours, the grain diameter increases to 8.25 x 10^2 mm. We are also given that the grain growth exponent (n) is 2.

Computing the New Grain Diameter

Now, we need to determine the grain diameter of the material when a specimen is heated for 1.25 hours at 750°C. To do this, we can use the equation for grain growth:

df/do = (t/t0)^1/n

By substituting the given values into the equation and simplifying, we find that the new grain diameter (d) when the material is heated for 1.25 hours at 750°C is equal to 1 mm.

Conclusion

Understanding how grain size changes in materials during heat treatment is crucial for optimizing their properties and performance. By applying the concept of grain growth, we can predict and control the evolution of grain size in different materials under specific thermal conditions.