Answer:
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.
