Date: 18/04/2019 15:13:16
From: mollwollfumble
ID: 1376669
Subject: Material hardness

I’ve been thinking about this. As recently as 1970, fluid viscosity was given in seconds (s) on a standard meter. After that it was properly given in units of centistokes and the SI equivalent.

What about hardness. Currently, hardness is still quoted as distance on a standard meter, such as Rockwell, Brinell, Vickers, Mohs or rebound. What would hardness be if properly measured in SI units?

Would it be the same units as strain energy under a stress-strain curve with plastic flow, for example?

It’s been a rocky road of thought, determining what is actually measured in a Rockwell test. Let’s say that what is actually measured is the force required to create a crater of given volume. Then we could sat that hardness can be measured is force / volume which has units pressure / length = GPa / m. The original Mohs scratch test would be different – brittle failure in shear – but a more recent (but still very old) update to the Mohs test measures the width of groove rather than just the existence of a scratch, and that can be related back to a Rockwell-like value.

But having GPa / m assumes that force is proportional to volume. Thinking some more about the failure mechanism of a material in a hardness testing machine, takes me to the testing of an ideal bulk material with a flat surface under the effect of a point load. And looking at the failure volume there leads me to think that the force is proportional to the crater volume to the power 2/3. That gives force / area = failure stress in MPa.

So I strongly suspect that the scientific units for hardness would be the same as those for stress.

I’d like to confirm that using finite elements, if possible. Are there any easily available finite element programs around?

Ideally a FE program that handles elastic 3-D behaviour with a Tresca and/or von Mises failure criterion. But I’m not fussy, I’ll take 2-D elastic-only if that’s what is available.

PS, in a ductile material, is the flow path of plastic flow of metal under a point load the same as a source-sink dipole geometry, like walking on wet sand. Or would it be a Vee shape flow pattern like that of a bullet-hole through glass?

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Date: 18/04/2019 17:25:12
From: The Rev Dodgson
ID: 1376737
Subject: re: Material hardness

Some suggestions here:
https://www.researchgate.net/post/What_is_the_best_open_source_finite_element_software_for_mechanical_problems

Of those listed on the first couple of pages, the only one I have tried is Opensees. It is intended for seismic analysis, but will do general purpose stuff as well.

If you’d like a look at a free 2D program that will run in Excel without additions, and will handle Mohr-Coulomb failure, you could try:
https://newtonexcelbach.com/2016/08/13/plane-strain-fea-non-linear-staged-analysis/

For serious purposes I use Strand7 which will do just about everything, but is a bit pricey for hobby purposes. If you can specify a problem I’d be happy to give it a go in Strand7, time permitting. An axial-symmetric analysis seems like the simplest option.

Alternatively, wouldn’t Roarke’s Formulas for Stress and Strain, or similar, give you what you want?

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