So I am having difficulty accounting for the shear elongation of different foam types. For example, a PVC foam like H80 has a shear strength 138psi and a shear modulus of 4.5ksi. Typically to find ultimate shear strain you would divide your strength by your modulus (think stress over strain gives you the slope E…therefore stress/E=strain). So for H80 you would expect an ultimate strain of 3.07%. Now PVC foams are typically more brittle than SAN foams, so next we look at CoreCell A600. Shear strength is 187psi and shear modulus is 6.1ksi, giving the exact same ultimate strain of 3.07%. Now here is the kicker, ultimate strain is listed as 18% for the PVC and 55% for the SAN. What am I misunderstanding? How can the claimed strength, modulus, and strain all be correct?
I know modulus is supposed to be linear but since this is foam I have to ask, are you within the plastic range of the foam? Maybe ask the manufacturer for stress strain graphs so you can see what’s going on and maybe find out what error is.
If you do please post them here, you’ve piqued my curiosity.
Your assumption that the ultimate strength occurs at the same point as the ultimate strain is incorrect.
So are you saying that the material stats listed for elongation assume plastic deformation of the foam? So both foams would begin to plasticly deform at the same curvature?
I don’t think they’re assuming anything. What Fleisch is saying is that you’re assuming the material has a linear stress strain relation until failure proportional to the modulus. In reality this elastic range is very short and for foam I’m assuming all sorts of non linear effects are taking place.
What do you mean by plastically deform at the same curvature?
It has been a long time since I took my material science engineering course but as I recall the onset of plastic deformation is not dependent on either the modulus or the shear strength. It is simply a material property all by itself.
Then the ultimate strength is another independent property all by itself. Meaning that one material (say foam A) may allow for only a little bit of plastic deformation before hitting the ultimate strength value. A different material (foam B) may allow for much more plastic deformation before reaching the ultimate strength.
I think when he said plastically deform at the same curve he must have meant is the behavior between the onset of plastic deformation and ultimate strength the same between materials. The answer is no, not necessarily and you can’t assume that it would ever be the case.
JPoland: you were close to what I meant. I was saying that if both foams seem to have a 3.07% allowable strain (before plastic deformation, and yes, assuming a linear elastic region), then both would begin to plastically deform at this same point. I can see now that my use of the word curvature was confusing. I was not referring a curve on a graph, but the curve of a flexed foam beam (I forgot that I hadnt explained what I was using this for im my mind). It would be disappointing if the foam manufacturer’s touted benefit of high strain only means that it can plastically deform a bunch before breaking…in any of my applications plastic deformation of the core qualifies as failure. That would seem to be a misleading product description…guess I will have to get a hold of a CoreCell engineer.
With plastics the plastic stress strain region maybe not be linear. for example you could have a parabolic stress strain relation and still have the part return to zero strain after unloading. Even some metals like Nitonol have funny effects, like two moduli. If you get the data though do you mind posting it here? I’m curious to see how the foams you picked react under load.
Ah I see! Yes I suppose you would just want to clarify their definition of failure as well. If it is fracture then obviously that doesn’t cut it for you.
Sorry, I forgot I commented on this post and haven’t been back for a while to see if you responded.
So are you saying that the material stats listed for elongation assume plastic deformation of the foam?
Well, for most polymers ultimate strain would absolutely involve plastic deformation. Not only is the stress/plastic strain relationship non linear, but the ultimate strength of a material does not necessarily occur at the failure strain.
So both foams would begin to plasticly deform at the same curvature?
Almost assuredly no, they would not behave the same when plastic deformation occurs.
This is all speculation unless we can actually see the data. If you do get the stress strain curves for the materials, post them up and we can analyze them further for you.
I was able to get stress-strain curves for both corecell and divinycell. The corecell tech was very interesting and said that yield points are rarely given since competitors often will perform a test at extreme strain rates to get impossibly ideal results. Any elongations published are strain at peak (ultimate), not necessarily at break, and definitely not at yield. Now the odd thing is that one curve determines yield point as the end of the linear region, the other uses back-extrapolation to find the point. This is a technique I had never seen before (only ever seen .2% offset used), so am doing a little research about which method is better for my purposes. Anyone know the benefit of using back-extrapolation (the intersection point of the elastic and ultimate plastic tangent lines)?
I imagine that the reason for this is that (contrary to what most of us have learned in our basic materials research), the modulus of elasticity is not always a linear stress/strain relationship. If I remember correctly, this is more common in polymers. Another common material that also behaves this way is grey cast iron (this might be a good thing to look into to get a good explanation of the phenomena).
I have always been told that ultimate strain is, by definition, the strain at break. As here… http://www.google.com/#hl=en&q=ultimate+strain&tbs=dfn:1&tbo=u&sa=X&ei=aaOATvmSMcuitgem1ojCCQ&ved=0CCAQkQ4&bav=on.2,or.r_gc.r_pw.&fp=c7e5b3799a5d75c2&biw=1280&bih=780
While some materials do break at their ultimate strain, others do not (or at least this has always been my impression). If you picture some strain curves you have seen, many plastic regions rise and then drop slightly before ending (breaking point). Intuitively it makes sense too that as some materials plastically deform they reach a point where it becomes increasingly easy to continue deforming. The peak stress, not the final stress, is the ultimate stress. Again this is what I have been taught but it clearly differs from the definition you cited.
Ah ha, I see the issue now. Strain is defined as the change in length of a sample compared to its original length. regardless of what the stress does (as you have written it can go up and go down over the course of the curve), as long as you are stretching a sample the strain will increase… until it breaks. Therefore, the ultimate strain always occurs at failure.
Ok, I should have read everything closer before responding. I think we just uncovered why textbooks never seem to use the phrase “ultimate strain” but instead use “elongation at break”. Yield strain and yield stress occur at the same point, so it is easy to assume that ultimate strain will be defined at the same point as ultimate stress (as I did). My appologies, I spoke (typed) before thinking it through.
It’s no problem, really. This is what the forum is for.