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Ah, a chance to put my material science classes to use!

When you bend something (and a metal ruler is a great example) and it can spring back, we call that "elastic deformation".

On an atomic level, metal is made of atoms in a crystal lattice. Each atom is spaced a certain distance away from its neighbors. The atoms stay at that particular distance because electromagnetic forces from their electrons and their protons add up in such a way that that distance is a low-energy configuration, like a ball sitting at the bottom of a dip in the ground. You can push and pull the atoms closer or farther apart, but to do that you have to put energy in, and they'll "want" to go back to that optimal distance.

Next, consider the shape of the ruler. Obviously, when it's straight, both sides are the same length. But, you can bend the ruler into a curve. When you do this, the two sides aren't the same length any more. The outer side of the ruler is now longer than the shorter side. It's the same principle as taking a corner in a car; the wheels on the outside have to go farther.

If you've stayed within the limits of elastic deformation, what's happened at the atomic level is that on the outside, you've pulled the atoms farther apart. The same crystal lattice structure is still there, but the atoms are now spaced farther apart than the lowest energy positions. On the inside, the opposite has happened: the metal is compressed, and the atoms are closer together than the lowest energy distances.

When you release the ruler, the atoms go back to their optimal distances. The long side shrinks and the short side expands.

So, the information of the original shape is stored in the crystal lattice structure. As long as you don't disrupt the lattice structure, the atoms "want" to go back to their original places. The forces that do the unbending are electromagnetism. (realistically, the only two forces you'll ever experience directly in your life are gravity and electromagnetism. If you are directly experiencing the effects of the nuclear forces, you're having a very bad day.)

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Thanks so much!

When I thought of the lattice structure it honestly made sense from there but I really appreciate the in depth answer.

What would it be like experiencing the effects of nuclear forces?

To borrow a phrase from XKCD: "You wouldn't die of anything; you'd just stop being biology and start being physics."

Obviously we experience the results of nuclear events any time we're out in the sunlight. However, we receive those results via electromagnetism--and gravity, because the sun affects the tides. Nuclear forces govern the fission reactions at the heart of nuclear power, but the heat is transferred via EM forces. Even in the event of a nuclear weapon explosion, the gamma ray pulse is EM, the thermal pulse is EM, the visible light is EM, and when the blast wave hits, it's doing damage by EM forces, too.

Maybe it's just my lack of imagination, but I don't see how a person could directly experience the strong or weak nuclear forces without being part of a significant fission, fusion, or decay event.

However: it turns out that only about 1% of the mass of a proton is composed of the rest mass of the quarks that make it up. The other 99% is the binding energy holding everything together, which is an effect of the strong nuclear force.

So, get a liter bottle of water and wave it around. Feel the heft. You're pushing on that bottle via electromagnetic forces, but 990 grams of that mass you're playing with is nuclear force.

You're welcome! I really enjoy it when I can share my knowledge and other people find it helpful or interesting! :)

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What's the difference then with something like a metal bar, where if you bend it far enough it does actually stay bent, but if you bend it less it goes back?

Yes and as the energy of the deformation causes the ruler to return to its original shape, the momentum created in the ruler's motion causes it to overshoot to the other side, and then it's bent too far the other way, and oscillation occurs.

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If you bend it too far, you have passed the elastic limit. It is no longer undergoing elastic deformation, but instead, plastic deformation.

In that mode, you are applying enough force to overcome the atoms' tendency to stay put. Some of the atoms get moved out of place, and rearrange into new places in the crystal structure. They settle into places that are lower energy in the object's bent shape.

Once the crystal structure is deformed, and new atomic bonds form, those new bonds replace the old ones. The object's new shape is the lowest energy configuration, and that is now the shape it wants to stay in.

You good?

I think you might be confusing fatigue failure and strain hardening which are different concepts. Strain hardening occurs when plastically deforming a metal and generating dislocations which are a type of defect in the crystal structure. Dislocations require the atomic bonds joining the atoms around the defect to stretch in different ways, creating areas of compression and tensile strain. The strain fields between different dislocations tend to repel each other, so as more dislocations are introduced to the material as it is deformed, they have a harder and harder time moving around due to the repulsions which in effect strengthens the material.

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There are a lot of different things that can happen, based on material and lattice structures temperature, etc.

If it's elastically deformed and released, the stored energy snaps it back into place.

If you deform and hold it, the stored energy can cause the lattice structure to shift over time in a process called ratcheting in order to permanently deform. Increased temperature speeds up the process.

If you go past elasticity, then you can think of the material acting like ice flows moving around past one another, though on a macro scale, it tends to act like a really stiff taffy, depending on the ductile nature.

It can even change the lattice structure from one kind to another, giving it properties of the same material in those alternative lattice structures.

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Why aren't crystal structures always perfect? Wouldn't defects be naturally worked out specifically because of the stress they put on the lattice?

Question: In a metal lattice of say iron, what holds the iron atoms together? They're all electrically neutral overall so I would think the attraction between the protons and electrons and the repulsion between the electrons would cancel out.

The charge cancels out, but that doesn't mean they can't stay put. Imagine a positive charge in the middle of a triangle and three smaller identical negative charges in the corners, for instance.

In reality it's a bit more complex than that. Electrons are fermions, and that means that they experience so-called Pauli repulsion. This is what prevents two atoms from falling on top of one another, and what prevents you from inserting your hand into the table. On top of that there are dynamical electromagnetic effects, known as dispersion, that lead to electromagnetic attraction even between uncharged objects. For instance two atoms of argon, both neutral, will attract one another unless they are very close to one another.

In an iron lattice the cohesion is due to the electrons stabilizing the nuclei.

At low temperatures the thermal energy is too low to overcome the activation energy barrier required for the defect to migrate.

This is super interesting. Hopefully you don't mind if I continue one more! When you bend the bar and it undergoes plastic deformation, why is it that if you bend the bar enough it will eventually begin to degrade and eventually "fail"? Failure in this context is weaken at the bend or break completely in half.

Based on what I've learned from your posts, it would appear that something happens at the atomic level to the bonds if you overwork the metal.

Thanks for that. There is so little I know and so much I can learn from others.

Think of a paperclip as a metal bar.

As kids we would keep flipping the inner part of a paperclip. And kept folding it till it breaks.

So, when you bend the paperclip into plastic deformation. It is difficult/impossible to bend it back. You would have to melt it completly. without melting it. It bends at the point of lease resistance. So after 1 bend, there is a new structure and new point of least resistance is somewhere else near the original bend. So even if you try to bend it back, it won't be the same structure. In this case some of the bonds might have completly broken, but there is still enough to hold it together.

When you keep bend a paper clip, some areas will have elastic defirmation, some will have plastic, and some will break. So if you keep bending it back and forth around a certain area, eventually enough break around the point that you are bending it, that it just splits into 2 pieces.

So basically when you bend metal, you're losing some information in the form of broken bonds? Bending enough times in the same location results in enough lost information to result in a fracture?

Acute radiation sickness. Specifically from neutron radiation. Even that is in a sense indirect - the neutrons knock nuclei about or get captured by the nuclear forces, but it's secondary emission of ionising radiation that does the real damage and that's electromagnetically.

Yes! Metal is ductile and malleable, so it can last a little longer than things that are more brittle, like a pen clip.

Suppose there are 5 bonds. when bend a metal clip, maybe 1 breaks, 2 reconnect to different pairs, and 2 stay the same.

In the example the "_" means a bond is broken

So if the connection is aa,bb,cc,dd,ee

it becomes a_,bc,cb,dd,ee. Notice how atom b and c switched their bonds. And the second time A_ , b_, c_, dc,ee

But with plastic it would be Aa,bb,cc,dd,ee then just break without switching A_,b_c_,dd,ee Then the second time, it breaks

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So, in a way, on an atomic level I am always choosing the path of least resistance?

Now I’ll prove just how wrong my therapist’s “oppositional defiance” diagnosis was!

Yes, that's literaly the cause of metal fatigue, if you bent a spoon back and forth enough times, it'll look ok but the slighest heating of shift and it breaks because you're breaking what's left of the oringinal form. This is the trick behind Yuri Geller rubbing spoons til they fall apart.

It's also why the british plane Comet crashed, the big windows let the metal flex enough just past the elastic limit to "fatigue" the metal and make little cracks in the structure. Over time they built up and you get planes falling from the sky.

It's more fundamental than that. A crystal with a defect has higher entropy than a crystal without any defects. For defects up to a particular number N (variable based on the crystal material and temperature and crystal size and so on), the Gibbs free energy released by defect formation (usually for simplicity's sake taken to be a vacancy) is larger than the energy consumed to generate the vacancy and the defects form spontaneously.

Only at absolute zero can a crystal be perfect.

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The Comet failures were driven far more by the fact that the windows had sharp corners, which concentrate stress, than by the absolute size of the windows.

You have likely experienced them directly when a cosmic rays hits you, otherwise you experience them indirectly from sunlight.

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Thanks for the correction.

Things like metal fatigue are due to creating cracks between metal crystals as they dislocate until they connect and form fractures.

There is a difference though, between bending a paperclip back and forth a few times so it plastically deforms and breaks - and fatigue.

The former is exceeding it's ultimate strength and breaking the paperclip. Fatigue is a different phenomenon caused by cyclic loading and not related to the ultimate yield strength - slip bands form and eventually cause a crack.

Seems like a technicality but they are two different phenomenon, and material health is asses completely differently when looking at overstress vs. fatigue!

When a metal is molten and cooling, it's atoms start forming bonds and binding together to form the lattice structure. But this cooling process happens simultaneously all over the structure. So all over, new lattices are forming in all different directions! The places where these differently-oriented lattices meet are called "grains boundaries" and they are the weakest points in the metals, where failure eventually happens.

But there are a few examples of perfect crystal lattices through a metal structure - the most well known (the only one I know of) is in Jet Engines. Jet turbines undergo so much stress yet need to be so reliable that they have developed manufacturing processes to make a whole turbine blade be a single crystal lattice. How they do it is a pretty closely held trade secret. But the advantages are huge:

• NO plastic deformation - since there are no dislocations/imperfections
• ~10x the material strength compared to the same metal cast normally

There are probably more but this isn't really my field of expertise, maybe someone else can add more..

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Electric forces.

The same thing happens when you push two magnetic north poles together, they spring apart again when you let them go, or when you lift a weight above the ground, it "springs" back downwards under gravity when you let go. The "information" of the molecules, as you call it, is simply the place where they have a state of equilibrium, where the net forces acting on them are equal in all directions, as they were before you changed their position by deforming the material.

In this case, though, the forces at work are electric.

So essentially for fatigue, the repetitive localized micro-plastic deformations, will keep shifting/form the slip bands until the straw breaks the camels back?

Could repetitive elastic deformation cause fatigue? My gut thought is that by defenition it can't? Basically if it does, it is actually micro plastic deformation and not elastic deformation.

Fatigue is sort of a mix of plastic and elastic deformation. It can happen when a material is only being elastically stressed - but the mechanism of operation is still dislocation motion (like plastic deformation).

The dislocations that move in this case require much lower stress to move - ie. not all dislocations move at exactly the yield stress of the material (that's sort of an average). But in this case, dislocations move back and forth along the same path (the path of low resistance), and eventually form a slip band which can eventually lead to failure of the material.

This is referred to generally as high-cycle fatigue, ie. it takes a lt of cycles to cause failure, because the stresses are low, and SN (stress vs #cycles) curves are used to assess damage and predict time to failure (compared with a stress/strain curve used to predict failure from overstress).