Does Young's Modulus Vary with Changes in Size?

[gkiverm]

Does Young's Modulus change with drastic changes in size? For example, suppose you exert a force on the micro scale or maybe even the nano scale. Would the same Young's modulus uphold at such a small scale?

 

[Philip Wood]

Are you concerned with small forces or small specimens?

For small forces, I see no reason why the YM shouldn't stay constant as the applied force approaches zero.

For small specimens, I suspect that things are different. The YM, as usually measured for a metal, is pretty much axis-independent. This is because metals are usually polycrystalline, so the specimen contains many randomly orientated small crystals. A very small specimen wouldn't, so one might expect to get different values of the YM according to orientation of specimen.

On a smaller scale still – specimens containing less than 30 atoms, say, planes of atoms (if this idea even makes sense on this scale) won't be 'bathed' in an infinite sea of free electrons, so I'd expect further deviations from the macroscopic value.

 

[UltrafastPED]

Philip Wood is correct - there can be significant variations.

For example, see http://www.hindawi.com/journals/jnm/2011/670857/

There are many papers which cover specific materials under varying conditions. Due to the interest in nanomaterials there is much research going in in this area.

 

[AlephZero]

For small specimens, I suspect that things are different. The YM, as usually measured for a metal, is pretty much axis-independent. This is because metals are usually polycrystalline, so the specimen contains many randomly orientated small crystals. A very small specimen wouldn't, so one might expect to get different values of the YM according to orientation of specimen.

That doesn't only apply to "very small" specimens. There are engineering components (e.g. jet engine turbine blades) made from single metallic crystals with sizes of the order of 10 to 100mm.

These crystals are anisotropic, so the idea of a single "Young's modulus" value isn't useful to describe their elastic properties. The most general form of anisotropic material needs 21 parameters to describe its elastic behavior.

In fact the anisotropic material properties are useful, because you can make identically shaped blades with different orientations of the crystal structure to give different vibration frequencies. This can avoid resonance effects if a set of maybe 100 "identical" blades all vibrated at the same frequency.

 

[gkiverm]

What if the material is isotropic and bulk (on the macroscale). But I'm talking about a situation in which the force exerted, and the area it is exerted on, is on the micro-scale.

 

[Philip Wood]

Do you mean that the forces are exerted over small parts of a much larger cross-sectional area? [I say forces (plural) because you need at least two separated forces acting on the specimen in order to constitute a stress.]