Comment by hwillis | Hacker News Reader

Comment by hwillis | Hacker News Reader

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https://royalsocietypublishing.org/doi/10.1098/rsif.2014.132...

> The tensile strength of discrete volumes of limpet tooth material measured using in situ atomic force microscopy was found to range from 3.0 to 6.5 GPa

Also "compressive strength" is not really a thing, in that it's only a metric that is useful for practical applications. It's proportional to tensile strength, and unlike tensile strength it does not generalize well to things like modeling stress. Tensile strength is a much more fundamental quality than compressive strength.

Strength of a material is force per area. In ideal terms it is measured over an infinitely short length; if you measure over a long distance then the sample is stretched and becomes thinner, changing the measurement. If you test on a shorter and shorter sample you get closer and closer to the ideal value.

The same is not true for compressive strength tests. If you measure compressive strength by pressing on a very very thin disc of material it will just resist all force; it has effectively infinite strength. The actual failure mode of compression is always tensile strength in the radial direction, or buckling or something. You press the sample and it stretches sideways until it exceeds the sample's tensile strength in that direction. The shorter the sample is, the less it can expand radially and the stronger it appears to be. There is no "ideal" compressive strength, only useful test setups.

>Also "compressive strength" is not really a thing.

This is true, but neither is "tensile strength" really a thing for the same reason. A simple uni-axial tensile test is not really uni-axial, but a combination of orthogonal normal stresses that ultimately results in shear failure. I've heard it said that "all failure is shear failure", and I think that's true. When you look closely at the ductile fracture surface of a ruptured tensile specimen, the characteristic "cupping"[0] appearance consists of various surfaces at 45 degrees from the direction of the applied load. Principle shear stresses are always oriented 45 degrees from the principle normal stresses.

[0]https://upload.wikimedia.org/wikipedia/commons/1/1b/DuctileF...

You could take that further and say that shear does not exist. It's a construct we have created to deal with tension failures in other planes. Everything basically comes down to a truss model. The failure you idealize as a shear stress is really a failure of a tension element in a miniature truss. This is true in bolt shear, scissors, etc.

This is why the code forces you to use strut and tie model deep concrete beams. As much as you may want to idealize a shear stress, really what's happening is the beam is arching over the span.

Ha, yes! I've even heard some argue that stress isn't even real! Whatever "real" means. Nothing is real; it's models all the way down.

All models are wrong… Some are useful

For those who are interested in learning more:

"All failure is shear failure" - this is a simple explanation of Tresca's Yield Criterion. For materials with higher compressive than tensile strength, the equivalent is the Mohr-Coulomb failure criterion.

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

For a simple example try twisting a ductile aluminum bolt (or clay), twisting a brittle piece of chalk (or concrete), or twisting a composite (twig). They all fail differently (and the first two at 45deg to each other. Mohr's circle is interesting, and fatigue failure more interesting still.

https://youtu.be/1YTKedLQOa0?t=533

> This is true, but neither is "tensile strength" really a thing for the same reason.

Well, not the same reason. Shear strength is in many ways more important because failure usually propagates from an origin like a rip- by shearing.

But fundamentally, tensile strength and shear strength are both much more empirical than compressive strength. Tensile strength can be used with ~99% accuracy on a wire that is microns long or miles long. If you double the relative width of a testing sample it will dramatically change the measured compressive strength even without buckling.

The "infinite" compressive strength for a sample that cannot expand laterally is only an approximation valid for small pressures.

At high enough pressures, all materials change their molecular and crystalline structures into structures with higher densities of atoms per volume and the volume of the tested samples diminishes, so the samples collapse at certain pressure thresholds.

The well known transformation of graphite into diamond is just an example of what happens with any substance at high pressures. Diamond is a more unusual example just because it remains stable even after the pressure that has created it is removed.

Moreover, for non-homogeneous materials, like concrete or many natural rocks used in construction, which are composed of harder particles cemented in a weaker matrix, it is normal to have a tensile strength that is many times smaller than the compressive strength, because when subjected to tension the weaker matrix allows pieces to detach, but in compression the strength may be determined mostly by the threshold where the harder particles break.

The snail teeth are also made of composite materials, mineral crystals in a protein matrix, so they are also likely to have different strengths depending on what kind of stresses are applied and in what directions.

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