A non–cold-worked brass specimen of average grain size 0.008 mm has a yield strength of 160 MPa (23,500 psi). Estimate the yield strength of this alloy after it has been heated to 600C for 1000 s, if it is known that the value of ky is 12.0 MPa mm1/2 (1740 psi mm1/2).

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.

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