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7 November, 00:56

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.

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  1. 7 November, 04:32
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    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.
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