For many metals the average grain diameter (d) as a function of time (t) during grain...

 

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For many metals the average grain diameter (d) as a function of time (t) during grain growth at elevated temperatures is described by the following empirical Grain Growth law: d^2-d0^2 = Kt Also for many metals at room temperature the Hall-Petch equation relates yield strength (y) to the average grain diameter (d), and is given as follows: y = 00 + ky (1/ Vd) Consider a metal alloy having an average grain diameter (d) of 0.012 mm and a yield strength (ay) of 250 MPa in its original state at room temperature. When the metal is heated to 520°C for 100 min d increases to 0.042 mm, and when cooled to room temperature, preserving the larger average grain diameter, the yield strength is found to be reduced to 150 MPa. i. Use the Grain Growth law to calculate the average grain diameter if a specimen of the original material is heated to 520°C for 200 min. ii. If this specimen is now cooled to room temperature, preserving the average grain diameter, use the Hall-Petch equation to calculate the yield strength, and the change in yield strength relative to the value for the original material at room temperature percentage For many metals the average grain diameter (d) as a function of time (t) during grain growth at elevated temperatures is described by the following empirical Grain Growth law: d^2-d0^2 = Kt Also for many metals at room temperature the Hall-Petch equation relates yield strength (y) to the average grain diameter (d), and is given as follows: y = 00 + ky (1/ Vd) Consider a metal alloy having an average grain diameter (d) of 0.012 mm and a yield strength (ay) of 250 MPa in its original state at room temperature. When the metal is heated to 520°C for 100 min d increases to 0.042 mm, and when cooled to room temperature, preserving the larger average grain diameter, the yield strength is found to be reduced to 150 MPa. i. Use the Grain Growth law to calculate the average grain diameter if a specimen of the original material is heated to 520°C for 200 min. ii. If this specimen is now cooled to room temperature, preserving the average grain diameter, use the Hall-Petch equation to calculate the yield strength, and the change in yield strength relative to the value for the original material at room temperature percentage

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