Question

Consider a hypothetical material that has a grain diameter of 2.1 × 10-2 mm. After a heat treatment at 600°C for 3 h, the grain diameter has increased to 7.2 × 10-2 mm. Compute the grain diameter when a specimen of this same original material (i.e., d0 = 2.1 × 10-2 mm) is heated for 1.7 h at 600°C. Assume the grain diameter exponent has a value of 2.

Answer 1

To compute the grain diameter when the specimen is heated for 1.7 h at 600°C, use the formula d = d0 * (t / t0)^(1/n), where d is the final grain diameter, d0 is the initial grain diameter, t is the heating time, t0 is the initial heating time, and n is the grain diameter exponent. The grain diameter when the specimen is heated for 1.7 h at 600°C is approximately 0.061174 mm.

Step-by-step explanation:

To compute the grain diameter when the specimen is heated for 1.7 h at 600°C, we can use the formula for grain growth, which is given by d = d0 * (t / t0)^(1/n), where d is the final grain diameter, d0 is the initial grain diameter, t is the heating time, t0 is the initial heating time, and n is the grain diameter exponent.

From the given information, we have d0 = 2.1 × 10^-2 mm, d = 7.2 × 10^-2 mm, t = 1.7 h, and t0 = 3 h. The grain diameter exponent, n, is given as 2.

Plugging in these values into the formula, we have:

d = (7.2 × 10^-2 mm) * (1.7 h / 3 h)^(1/2) = 0.061174 mm

Therefore, the grain diameter when the specimen is heated for 1.7 h at 600°C is approximately 0.061174 mm.