Hall-Petch Relation Calculation?

In summary, using the Hall-Petch relation, we can estimate the yield strength of a Cu-Zn alloy (brass) to be 97.17 MPa when the average grain diameter is 30 μm. This calculation is based on the internal friction stress of 25 MPa and the material constant of 12.5 MPa·mm1/2. However, it is recommended to show your working in order to verify the accuracy of the answer. Thank you.
  • #1
Dave_
7
0
Using the Hall-Petch relation, estimate the yield strength, σy, of a Cu-Zn alloy (brass) when the average grain diameter is 30 μm.

where:
σy = is the yield strength
σ0 = 25 MPa is the internal friction stress
ky = 12.5 MPa·mm1/2 is a material constant
d = is the average grain size

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I get an answer of 97.17 MPa, is this correct, if not i'll post all of my working. Thanks!
 
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  • #2
This would require me to completely work out the problem myself!

We would much rather see your work, and then follow it to see if there is an error. The usual errors in a simple calculation like this are in the units.
 

What is the Hall-Petch Relation?

The Hall-Petch Relation is an empirical relationship between the grain size and the yield strength of a material. It states that as the grain size of a material decreases, the yield strength increases.

What is the significance of the Hall-Petch Relation?

The Hall-Petch Relation helps scientists and engineers understand the relationship between the microstructure of a material and its mechanical properties. It also helps in predicting the strength of materials at different grain sizes.

How is the Hall-Petch Relation calculated?

The Hall-Petch Relation is calculated using the equation σy = σ0 + k√d, where σy is the yield strength, σ0 is a constant, k is a material-dependent constant, and d is the grain size.

What are the limitations of the Hall-Petch Relation?

The Hall-Petch Relation is only applicable to materials with a regular microstructure, such as metals and ceramics. It also assumes that all grains have the same orientation, which is not always the case.

What are some real-world applications of the Hall-Petch Relation?

The Hall-Petch Relation is used in the development of stronger and more durable materials, such as in the aerospace and automotive industries. It is also used in the study of material failure and in the design of structures that require high strength and reliability.

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