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Lead is solid at room temperature.

But it is quite soft, so under strong enough gravity, it should be possible to pour it out of a container like sand. What gravity is that?

Let's do a Fermi estimate. I know little of material science, but this looks like a job for the shear modulus. A dimensional analysis tells me the shear modulus is equivalent to a pressure. Assuming a cube of lead 10 cm on one side, the pressure at the bottom is

$$ pressure = \frac{density \times length^3 \times gravity}{length^2} $$

If deformation happens when $\text{pressure} > \text{shear modulus}$, we get

$$ gravity > \frac{shear\ modulus}{density \times length} = \frac{5.6 \times 10^9\ Pa}{11000\ kg.m^{-3}\times 0.1\ m} \simeq 5 \times 10^6 m.s^{-2} $$

Which is about a million times the gravity on earth. That seems high. Did I get something wrong? If not, does anybody have a more precise estimate (or knows how to get one)?

hft
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The answer seems highish, but not too crazy: max mountain heights scale as $1/g$, So under 5 million G a mountain would be a few cm.

But lead probably starts changing earlier: the yield limit and compressive strength is 4-12 MPa rather than in the GPa range. Plugging in that gives 3,600 to 11,000 m/s$^2$. Now we are in the few hundred to a thousand G range.

(Also, why shear modulus? Isn't Young's modulus the more obvious choice? Still, the yield limit is what really matters here.)

Anders Sandberg
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The compressive strength of lead is about 12 MPa (air pressure is about $10^5$ Pascal). If you know this you can calculate the strength of gravity needed to compress lead. It won't liquefy though.

That is if you put a piece of lead on top of another, in a strong enough gravity field, the piece of lead below will deform, thus so will both.

Deschele Schilder
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This picture is complicated by the fact that at room temperature, lead will creep (stretch out like taffy) at very low applied stress levels. This means if you had a really big cube of lead on hand, it would creep under its own weight without liquifying and slowly sag into a squatty cylindrical shape. Note that creep is not accounted for in citations of lead's tensile or shear modulus or tensile or shear strength.

That said, I'll bet that if you rearrange your own equation you can solve for how high a pile of lead needs to be to fail in shear under one g in the absence of creep.

niels nielsen
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When gravity becomes high enough, every material will liquify. When the force of gravity on the particles constituting the material will become higher than the binding forces keeping the particles together the particles will be set free from their bond. The material will disintegrate (or liquify, though the liquid will be quite flat).

The problem, though, is that you have to find something to put your material on. Probably the thing where you put it on will liquify too. So you have to find something to put this something on...

Deschele Schilder
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