Why Are Thin Materials Stronger?

Tuesday, December 04, 2018

Why Are Thin Materials Stronger?

Why Thin Glass Is Strong

In the last post, we established what strength was and that thicker pieces of glass were weaker than what their theoretical strength suggested. Now we will try to answer why this is the case. Thinking intuitively, it is quite a weird property of materials because you would probably think more material means more strength...

When most liquids freeze, they crystallize and are more orderly, better packed and therefore more dense than liquid. The problem with glass is that it is so viscous that molecules do not have time to sort into crystals. This means glass is more of a solidified liquid rather than a crystalline solid (glass is actually an amorphous solid).
As it can't sort itself, it has a disordered structure with many defects.

Defects are bad for materials as it increases the stress concentrations in the material. What this means is that the force that usually would've been transmitted, no longer can be transmitted because there is a gap between atoms due to a crack. This means the force has to be redirected around the crack into the atom on the edge of the crack. This means this interatomic bond has to resist a very big force. This weakens the material as any increase in the overall stress, will result in a much larger increase in the stress concentration. Eventually, the bond will not be able to resist the force and it will break. The next bond will then have an even worse stress concentration and also break. This will continue through the material until it shatters.

A Stress Concentration Diagram

If the surface of glass was kept smooth however, then it could be just as strong as thin glass.
The reason why thin glass is strong, is that there pretty much isn't enough space to accommodate for cracks and so it is crack free.

Usually, glass fractures in a brittle manner and we see it shatter into many pieces. If we could manage to prevent cracks however, such as by putting it into compression, then it would fail by flowing in shear like putty.
For glass, the shear stress is a lot larger than its normal fracture stress and so we do not see this often.

Shear stress and the viscosity of glass are very dependent on the temperature of the glass. If glass was made crack free, then it may be as likely to fail by shear as by cracking. In this case, cooling would be very useful as it raises it's viscosity and therefore strengthens it because it's shear stress increases.

Glass is relatively strong in compression however in general, non-metallic crystals tend to be weak.

Metals

Now let's consider metals. Are thin pieces of metals also stronger than the bulk material?

Metal whiskers are long thin needle crystals which can be grown from most substances. They are usually 0.5 micrometers thick and a couple of millimeters long.
In 1952, it was seen that tin whiskers could be bent to high strains and would still recover elastically. This was another case of thin materials being strong.

Something you may have already suspected is that the strength vs thickness curve looked similar Griffith's curve for glass. The first guess might be to suggest that metals have cracks just like glass.
In addition, it was impossible to distinguish two metals when plotting strain vs thickness.
Cracks would be a good way to explain the reason for these things however no one could find cracks.

The explanation for why metals are weak is in the way that they grow.
The way crystals grow means that there are step like structures on their surface. This causes bad stress concentrations in the metal (these can be regarded as half cracks).

Whiskers in large pure materials fit at the boundaries well and so the boundaries are not a source of weakness. The source of weakness are the half cracks on their surface.
Grain boundaries between crytallites also explain why some alloys can be weak. Adding impurities weakens metals because when liquids freeze, they try to expel impurities. Impurities therefore accumulate at grain boundaries of metals and the boundary becomes weak. This is why impurities can ruin alloys if they are not added properly.

For metals, strength boils down to the surface smoothness of the metal. Surprisingly, for brittle crystals, internal defects are unimportant for their strength. When we talk about ductile crystals however, internal defects will start to play a role.

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