
(a)
Interpretation:
The Hall-Petch equation's constants needs to be calculated.
Concept Introduction:
The relation between the grain size to the yield strength is shown as follows:
Here, the yield strength is

Answer to Problem 4.51P
The Hall-Petch equation constants are
Explanation of Solution
The properties of a Cu-Zn alloy are as follows:
Grain Diameter (mm) | Strength (MPa) |
| |
| |
| |
| |
S.N. | Grain Diameter (mm) | | Strength (MPa) | |
| | | | |
| | | | |
| | | | |
| | | |
In the above table, we have calculated
With the help of equation number
For strength
Therefore,
For strength of titanium is
Therefore,
Solving equation
And
Hence, the hall-Petch equation constants are
(b)
Interpretation:
For a strength of 200MPa, the required grain size needs to be calculated.
Concept Introduction:
The Hall-Petch equation relates the grain size to the yield strength as follows:
Here,
The yield strength is

Answer to Problem 4.51P
The grain size which is required is
Explanation of Solution
Now, we have the Hall-Petch equation after we calculated the constants, then the equation
Here, the strength required,
Hence, the grain size required is
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Chapter 4 Solutions
Essentials of Materials Science and Engineering, SI Edition
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