A hypothetical metal alloy has a grain diameter of 2.4 10-2 mm. After a heat treatment at 575C for 500 min, the grain diameter has increased to 7.3 10-2 mm. Compute the time required for a specimen of this same material (i. e., d0

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The time required is 476 mins.

Explanation:

Given:

Initial grain diameter () = mm

Time taken for the treatment () = mins

Grain diameter exponent () =

Case I :

Final diameter () = mm

For many poly-crystalline materials grain diameter () varies with time and follows the below rule.

⇒

Plugging the values we will find the (the time independent constant).

⇒

So,

⇒

⇒ (approx)

Case II :

Now we will use this K value.

Here the final diameter () = mm

Arranging the equation and finding the value of t.

Where,

⇒

⇒

⇒ (approx)

So the time required for a specimen of the same material to achieve a grain diameter of 5.5 × 10−2 mm while being heated at 575°C is 476 mins (approx).