Answer:
The answer is explained below:
Explanation:
STEP 1
Given data:
Uncold-worked brass specimen average grain size = 0.008 mm
Yield strength + 160 MPa (23,500 psi)
ky = 12.0 MPa mm1/2 (1740 psi mm1/2)
STEP 2
In this problem it is asked to calculate the yield strength of an alloy after it has been heated to 600°C for 1000 seconds
We will use Hall-Petch equation: σy= σo+ ky d^-1/2
In order to calculate the yield strength of alloy after it has been to, first we have to find
i- average diameter of alloy at 600°C for 1000 seconds
ii- constant σo value
STEP 3
Finding the value of constant σo
σo= σy- ky d^-1/2
σo = [160MPa] - [( 12.0 MPa mm1/2) ( 0.008 mm)^1/2]
σo= 25.836MPa
STEP 4
Average grain size calculation
Consider plot which describes logarithm of grain diameter versus logarithm of time grain growth in brass at several temperatures.
From this we find that at 600°C for 1000 seconds the average size of the grain is about 0.070 mm
STEP 5
The final step is to find yield strength after heating:
σy= (25.836 MPa) + [( 12.0 MPa mm1/2) ( 0.070 mm)^1/2]
σy= 71.192 MPa will be the yield strength of alloy after it has been heated to 600°C for 1000 seconds.
