What Does the Unit m-3/2 Mean in the Hall Petch Equation?

[richard9678]

Hi. Stress is measured on Pascals. It's force divided by area. Area of course is m x m. So when stress is given it's in units of MN / m₂ or MN m^-2.

Okay. I'm looking at something called the Hall Petch equation. There a constant in it labelled k.

In an example, k is given as 0.45 MN m^-3/2

Does this make any sense or is there an error with the description of k?

I mean, what is m^-3/2? Thanks.

P.S. Possible that there is an error in the text. And that k is MN m^1/2. However, if it is, I still don't know what m is as a unit. In other words I know m² is - square meters.

 

[pasmith]

The Hall-Petch equation asserts a relation of the form $$(\mathrm{stress}) = \frac{(\mathrm{coefficient})}{(\mathrm{length})^x}$$ or $$(\mathrm{coefficient}) = (\mathrm{stress})(\mathrm{length})^x.$$ It follows that in SI units the coefficient is measured in units of $\mathrm{Pa}\,\mathrm{m}^x$ or $\mathrm{N}\,\mathrm{m}^{x-2}$. $x$ need not be an integer.

 

[SteamKing]

Hi. Stress is measured on Pascals. It's force divided by area. Area of course is m x m. So when stress is given it's in units of MN / m₂ or MN m^-2.

Okay. I'm looking at something called the Hall Petch equation. There a constant in it labelled k.

In an example, k is given as 0.45 MN m^-3/2

Does this make any sense or is there an error with the description of k?

I mean, what is m^-3/2? Thanks.

P.S. Possible that there is an error in the text. And that k is MN m^1/2. However, if it is, I still don't know what m is as a unit. In other words I know m² is - square meters.

In fracture mechanics, the stress intensity factor for different types of flaws is expressed in units of MPa-m^1/2.

https://en.wikipedia.org/wiki/Fracture_mechanics