Hall Petch Equation: Is My Math Right?

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In summary, the Hall-Petch equation is an empirical relation used in materials science to describe the relationship between grain size and yield strength. It is used to understand material properties and design stronger materials. The equation takes the form σy = σ0 + kdg-1/2, where σy is the yield strength, σ0 is a constant, k is the Hall-Petch coefficient, d is the average grain size, and g is a constant. However, it is only applicable to materials with a fine-grained microstructure and may not accurately predict the behavior of materials with coarse or non-uniform grain sizes. To ensure accuracy, it is important to compare results with experimental data and double-check input values and units.
  • #1
richard9678
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What is the Hall Petch equation. When I Google (images) I get::

σy = σo + ky / √d

or

σy = σo + ky d1/2

In the first ky is divided by √d and in the second multiplied by √d.

The second equation is in a study book I have.

Am I making a math error? Thanks.
 
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  • #2
I saw from different references that is ##\sigma_{y}= \sigma_{0}+k_{y}d^{-\frac{1}{2}}##
 
  • #3
Ssnow said:
I saw from different references that is ##\sigma_{y}= \sigma_{0}+k_{y}d^{-\frac{1}{2}}##

Yes, the minus sign should be there. :-)
 

Related to Hall Petch Equation: Is My Math Right?

1. What is the Hall-Petch equation?

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

2. How is the Hall-Petch equation used in materials science?

The Hall-Petch equation is used to understand the mechanical properties of materials and to design stronger and more durable materials. It is also used to predict the effect of grain size on material properties in different manufacturing processes.

3. What is the mathematical form of the Hall-Petch equation?

The mathematical form of the Hall-Petch equation is σy = σ0 + kdg-1/2, where σy is the yield strength, σ0 is a constant, k is the Hall-Petch coefficient, d is the average grain size, and g is a constant (usually between 0.3-0.5).

4. Can the Hall-Petch equation be applied to all materials?

No, the Hall-Petch equation is only applicable to materials with a fine-grained microstructure, such as metals and alloys. It does not accurately describe the behavior of materials with coarse or non-uniform grain sizes.

5. How can I determine if my calculations using the Hall-Petch equation are correct?

To ensure the accuracy of your calculations, you can compare your results with experimental data or use different methods to calculate the yield strength of the material. It is also important to double-check your input values and units to avoid any errors.

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