5. A non-cold-worked brass specimen of average grain size 0.01 mm has a yield strength of 150 MPa. Estimate the yield strength of this alloy after it has been heated to 500°C for 1000 s, if it is known that the value of σ0 is 25 MPa.

97.17 MPa

Explanation:

Given:-

- The nominal strength of the grain, σ0 = 25 MPa

- The average grain size of the brass specimen, d * = 0.01 m

- The yield strength of the non-cold worked specimen, σy = 150 MPa

- Conditions of cold-working: T = 500°C, t = 1000 s

Find:-

Estimate the yield strength of this alloy after cold - working process

Solution:-

- The nominal strength of the grain is a function of yield strength of the material, grain yield factor (Ky) and the grain size.

- the following relation is used to determine the grain strength:

σ0 = σy - (Ky / √ (d))

- We will use the above relation to determine the grain yield factor (Ky) for the alloy as follows. Note: here we will use the average value of grain size:

Ky = (σy - σy) * √ (d*)

Ky = (150 - 25) * √0.01

Ky = 12.5 MPa - √mm

- Now we will use the cold working conditions of T = 500 C and time of the process is t = 1000 s. We will look up the elongated size of the grain after the cold-working process in lieu with its yield factor (Ky). Use figure 7.25.

- The cold-worked grain size with the given conditions can be read off from the figure 7.25. The new size comes out to be d = 0.03 mm.

- We will again use the nominal grain strength relation expressed initially. And compute for the new yield strength of the cold-worked alloy.

σ0 = σy - (Ky / √ (d))

σy = σ0 + (Ky / √ (d))

σy = 25MPa + (12.5 / √ (0.03 mm))

σy = 97.17 MPa

- We see that the yield strength of the alloy decreases after cold-working process. This happens because the cold working process leaves with inter-granular strain (dislocation of planes) in the material structure which results from the increase in grain size.