Help! How much mass increase with compression?

You are right that density is simply mass divided by volume. And you are also right that compressing an object will reduce its volume and thus increase its density. The amount that an object will compress, as related to how much force/pressure you apply to it, is measured by its "bulk modulus".

When you plastically deform a solid substance like a metal, it doesn't normally permanently change its density much (enough to usually worry about) when the pressure is released. As you roll metal, it elongates, preserving its volume. That's why tables list standard densities for metals without regard for any cold work that has been done to it.

Don Kansas City

Now I'm very confused. I read where the electrical conductivity of the material drops with residual stress. I think this means that if I squish the material, permanently denting it, in that area (based upon residual stress) I have less conductivity.

That seems backwards, squishing the material together should make it more conductive (more molecules and therefore more electrons in the volumne)

Any ideas?

- Robert -

depends on the material.

I think this means that if I

if your theory were valid, then one would assume that the higher one goes in the periodic table, since there is more mass per volume going up, the more conductive the elements will be.

That is not the case, and so your theory is incorrect.

And even if you use the same element, the conductivity varies widely with its matrix (see carbon).

Aluminum 2024-T351 and Aluminum 7050-T7451

I was thinking in terms of number of carriers in the volume, not in terms of some type of deformation of a crystal lattice.

I just read a paper describing how shot peening the surface of a 2024 caused a very measurable drop in conductivity - bulk resistance went up. I just can't figure the relationship.

For the measure of residual stress what is KSi ?

Is stress compression, or tension? Or somehow both? As in "absolute" value. Makes sense, since to be in equilibrium the two must be equal. Right?

- Robert -

The mass per unit volume does not necessarily go up as the atomic number increases. The mass per *mole* of element increases. How the element adheres to itself determines how many moles can fit into a given space. If the atomic weight determined mass density, then oxygen would be heavier than carbon and radon gas would be heavier than lead.

Don Kansas City

Dear Robert Macy:

Conduction isn't as closely related to interatomic distance, as it is to the number of grain boundaries it has to jump on a given path. Cold working increases the number of grain boundaries, decreasing conductance.

David A. Smith

T H A N K Y O U !

Now I see why metglas is so resistive. But I don't understand why metal being stretched then compressed at 0.5 Hz has conductivity that "follows" the tension/compression.

You're saying that *if* I have a beautiful crystal of aluminum, that will be the lowest possible resistance? If I have "amorphous" aluminum, I'll have higher resistance?

Let me take that further, imagine that I have a hole in an aluminum plate and I enlarge that hole using a mechanical device which suddenly becomes slightly bigger than the hole used to be. That pushes the edges of the hole outwards permanently leaving residual stresses and the hole is slightly larger.

Now, moving from the edge of the hole straight out into the aluminum, I will traverse regions of varying stress until I'm so far away from the hole that there is very little stress. The plot of this variation in stress shows a "polarity" associated with the stress. First, very negative at -600MPa to positive 100MPa that then declines back to zero. Will the conductivity follow the coefficient? For example, low conductivity at the inside surface of the hole to higher than original conductivity, to normal conductivity?

- Robert -

Dear Robert Macy:

Conductivity is affected by a number of things, and not just grain boundaries (which are only affected in plastic deformation).

Strain gages work in much this way. URL:

Pure aluminum, yes.

An unstressed structure is in its lowest energy state. As energy is added (by either compression or tension), the conduction path is adversely affected.

This link sucks, but it is informative: URL:

Yes. See: URL:

David A. Smith

ksi = "kilopounds" per square inch (1000 lbs per square inch)

Thank you for your reply. The definitions help crystalize the thought process.

I did a search, and a search, and more searching. That's why I came to this group.

After all that searching, I still could not tell you a simple thing like what is the expected change in conductivity as one moves around a hole that's been squished.

I've seen papers talking about 10% changes in conductivity from 22MS/m down to 20MS/m. And I've seen papers discussing less than 0.1% changes.

At this point, don't know. It is important to find out, though.

- Robert -

an excellent point.

However, fwiw, I thought that solid oxygen was heavier than solid carbon, and radon vapor was heavier than lead vapor?

That and Poisson's ratio. When you compress a metal, it's cross-section increases. Bulk modulus alone will only tell you how much compression has occured, and nothing about the expansion of the metal perpendicular to the load.

Dave

It's not that simple. It still depends on how the element combines with itself, what types of bonds it forms and what the crystalline structure is. That's why lead (82) is not heavier than gold (79) is not heavier than platinum (78). This is elementary (no pun intended) chemistry.

Don Kansas City

Well, actually if you're just smashing a solid end-to-end in free air, this is not a good application of the bulk modulus, since any reduction in volume is at least partially made up for by expanding elsewhere. The bulk modulus assumes that uniform pressure is applied all over the object (like at the bottom of the ocean, for example). And for a solid it is a very small amount.

Don Kansas City

Dear Robert Macy:

That should not be surprising, since attrbution of strain "around a hole that has been squished" is NOT simple. If you have the strain distribution, then you can get to conductivity. Contrariwise, if you can measure the conductivity (in some way, like eddy-currents), you can infer the strain.

I think you're going to have to:

Things aren't always simple.

David A. Smith

fwiw - did some research in my kid's library (Univ chem grad), learning something every day --

according to the handbook of chemistry P4-123, lead is heavier than gold (10.67 gm/cc for Pb and gold is 9.32 gm/cc) platinum is heavier than either - 18.91 gm/cc -- as liquids

-all three are categorized as face-centered cubic structures when solid, oddly enough.

-solid, the molar volume has platinum the heaviest, followed by gold, and then lead.

- the molecule volumes are largest for lead, followed by gold, with platinum having the smallest volume

- solid, platinum has a molecular wt of 195 and density of 21,5 g/cc gold----------------------------- 197 and density of 19.3 g/cc lead ----------------------------- 207 and density of 11.3 g/cc

-resistivity at 273K, 10^-8 ohms/m platinum - 9.6 gold - 2.1 lead - 19.2

- the elastic constants of the individual crystals tracks with density - (10^11 n/m^2) platinum 3.47 gold 1.92 lead .50

so I learn something new - instead of the usual ("check it again before you seal it")