Elastic modulus

[Ford Prefect]

I'm a law student, so while I could tell you what elastic modulus is in a general sense, I couldn't exactly claim to know much more beyond that. Anyway, I became curious about what happens to things when they get accelerated so fast that the force exerted on said thing exceeds its, for example, Young's modulus. I mean, I get the impression that it's going to deform or break apart or something, but I was interested in learning a little more about how this works. It's mostly just for my own curiousity.

[starslayer]

Most materials are going to break, because their Young's moduli are far, far greater than their maximum yield strength (a common example in this category is steel). All the Young's modulus of a material is is its elastic modulus under tensile stress, and basically tells you how much the material will stretch under a given stress (not necessarily force, because you can exert a tremendous force on something, but put it under very little stress (stress = force/area)).

A material's Young's modulus is defined as tensile stress/tensile strain. Strain is the fractional change in an object's length when put under stress, i.e., it is the change in the stressed object's length over its original length. Therefore, the object's new length is L = ΔL + L0 = L0*(1+ε), where ε is the strain. So, in order to find out how much an object will stretch under a given tensile stress, we can simply solve for ε in the original equation for Young's modulus and replace it with ΔL/L0. This gives a change in length ΔL = σ*L0/E, where E is the Young's modulus of the material, and σ is the tensile stress. From this is it easy to see that exerting a stress on an object equal to its Young's modulus will double its length. Most things don't take kindly to this, and thus break or tear apart when subjected to such stresses, although some materials can, most notably rubber.

[Wyrm]

Yes, and there's the fact that the Young's modulus only applies while you're in the elastic region of the material, typically only a small fraction of its ultimate strength. Past that, you need to consult the stress/strain curve of the material.

[Darth Wong]

Yes, and there's the fact that the Young's modulus only applies while you're in the elastic region of the material, typically only a small fraction of its ultimate strength. Past that, you need to consult the stress/strain curve of the material.

Small nitpick: the yield stress of a typical engineering material is usually a fairly large fraction of its UTS.

[Darth Wong]

I'm a law student, so while I could tell you what elastic modulus is in a general sense, I couldn't exactly claim to know much more beyond that. Anyway, I became curious about what happens to things when they get accelerated so fast that the force exerted on said thing exceeds its, for example, Young's modulus.

The Young's Modulus is the slope of the stress-strain curve in the elastic region, which is the region where the stress is below the yield stress and all deformation is temporary (ie- it snaps back to its original shape when the stress is released). It is not an actual stress figure, per se. What you mean is "what happens to things when they are accelerated so quickly that reaction forces cause the material to exceed its yield stress".

I mean, I get the impression that it's going to deform or break apart or something, but I was interested in learning a little more about how this works. It's mostly just for my own curiousity.

Once you exceed the yield stress, it will deform permanently, ie- it will not snap back to its original shape afterwards. Once that happens, it's outside its engineered limits and anything goes. Once you start to get necking, then failure is pretty much inevitable.

[Ford Prefect]

Yeah, well, it's clear I don't know what I'm talking about. Obviously this is because it's well outside of my area of expertise, but some of these yield stress numbers seem totally bonkers, like human bone needing over a hundred MPa to deform permantently. It makes me want to understand modes of mechnical failure more in depth, but good luck with that.