Standard bend tests: Beyond the Proportional Limit

[David Long]

Pretty sexy topic eh  Have a look at this stress/strain curve I lifted from a site about the mechanical properties of wood. We are used to thinking about wood bending in two general "zones". The first is when the amount of deflection (strain) is linearly proportional to stress (amount of force). This is the zone where stress and strain are below the "proportional limit" and you get,for example, a couple pounds for every inch you draw and the wood remains elastic. At higher stresses, beyond the proportional limit (see the diagram), you get more deflection for every couple pounds of force. In this zone we usually think of wood as being plastic, that is it deforms and takes set and eventually if forces are high enough it fails. But, and here is my main point, there is a zone where the linear relationship breaks down but the wood remains elastic and deflection is reversible. This is the zone the wood is stressed above the proportional limit but below the elastic limit. What this means to bowyers, I think, is that a bow stressed into this zone is expected to stack less and hit hard. The draw/force curve for such a bow would be expected to curve the opposite direction a hard stacking bow does. Baker et al in TBB and elsewhere do not mention this as near as I can tell. Does anyone know more about this property of wood? Have you seen evidence of this in your draw/force curves? I have a short bow I am working on now that doesn't seem to stack at all and I would expect it to. Doesn't take set either, although I think the wood is pushed up towards its limit.
Dave

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[woodenwonder]

David, find a Excel program called "selfbow 10 arc" written by "Woodbear" over at Paleoplanet. It has a tab in the spreed sheet which goes into great detail of what you'll looking for. Gary

[Badger]

       Dave, when you load wood up as in drawing a bow it is not getting harder to pull just because the wood is compressing, it is getting harder to pull mainly because of the string angles increasing. It gets a little harder due to compressing but not enough to affect stacking. Stacking is simply when your string angles are increasing too fast causing a rapid gain in draw weight.
       It is critical for a bowyer to understand when he is entering that zone of plasticity and leaving the zone of elasticity. This actually starts a little before the bow starts to take set. Measuring the set a bow takes is not really a true guage of how much deformation the wood has taken either. The back tension can pull a bow back into shape to one degree or another. The only true measure is to know what a specific draw weight was at a specific draw length before any wood cells started to crush. By setting reference points up as you tiller you can stay on top of the crushing wood cell problem. Steve

[David Long]

Thanks for that reference Gary. I had seen that, and if I am not mistaken that approach assumes that above the proportional limit wood is plastic and not elastic.
Steve, I can see how stacking is an unavoidable consequence of string angle. Further into the draw you go, for every inch you are bending the wood more. But what I am talking about is an effect that would tend to counteract the consequences of increasing string angle. If the wood turns to a noodle near the end of the draw- but remains elastic- then the bow would show less stack.
Dave

[Badger]

David, if the wood turns to a noodle it will shoot like a noodle I guarantee you. Steve

[David Long]

Yes I agree Steve I was being goofy with the noodle thing. But if you look at that Stress strain curve, I cannot understand why the curved part at the top below the elastic limit wouldn't come into play with bows. It's exactly the conditions we are working in, especially with the types of bows you are interested in. So you are saying that all bows of a given length equally drawn stack exactly the same? If the only thing that mattered was string angle I don't think compound bows would work like they do. In other words mechanical properties of the bow do matter. Sinew becomes progressively harder to pull the longer it is stretched, in other words it "stacks" for reasons unrelated to string angle. I think it has to be stretched much further than the percent or so it does as a backing to get beyond its linear behavior, so this doesn't come into play. But what about wood that does, at least in principle, show the opposite effect. I am trying to think of ways to see this or prove it has no effect for some such reason. Draw force curves are the logical way I guess.
Dave

[Badger]

David , Mechanical properties do play some part I agree. The tiller shape and braced profile as well as full draw profile also play a large part in how much energy the bow will store. I admit I wasn't able to fully understand the drawing. I can't figure out what that sudden drop means unless it is reffering to a breakover point once the wood starts bending. If thats the case That may also have somethign to do with the angles of force being applied to the wood. There is a simple little test you can do that demonstrates string angles using a string and a weight but no bow, just place a weight in the middle of a string about 4 feet long, stretch out your arms and try to straighten the string, not slowly move your arms together letting the weight go down, the closer your hands get together the lighter the weight feels, same with a bow and arrow. The angle is the most dramatic influence on draw weight but not the only influence. Steve

[David Long]

That's a cool demonstration with the weight Steve  I guess my questions have to do with the fact that the point labeled on the curve as "limit of proportionality" doesn't exactly correspond to the point labeled "elastic limit". That little curved part between the two is very interesting.

[Hickoryswitch]

I may be way off base here but isn't that little line between proportional limit and elastic limit the point where wood becomes weaker before breaking. Like I said I may be way off base.

[hawkbow]

you are making my head hurt  too much info for my limited brain to compute.... I was ok with just knowing the bow bent and shot well.. just kidding, I was bored so thought I would chime in.. stay cool... Hawk 

[JackCrafty]

These kinds of topics are fascinating....but I agree, they make my head hurt too.

I've actually created graphs like that one in college using machines that put bending stress on wood samples.  If I remember correctlty...every time you put stress on the sample, you put a little more than the last time.  You apply a load, you back off, record the result, then you add a little more load, back off, record the results, etc....

There are two things the chart does not show: wood will permanently deform if exposed to the same load over a period time (like a bow that is braced for long periods), and the elastic limit changes over multiple exposures to stress (like when you exercise the bow and shoot it in).  That little area is not something that remains constant as we build the bow.  Therefore, it is difficult to use it to any advantage.

As bowyers, we should always be working in the area under the proportional limit.  If you notice that the bow feels a bit "plastic" during tillering, you should be worried that you are over stressing the bow...not excited about feeling less stack.  JMHO.

[jkekoni]

I have made a bend test with hazel and en the end the pounds actually went down, while I increased draw.

Needles to say that the set was heavy...

One does not wish to to use that part of the elasticity in bow...

[David Long]

I guess I am wondering about the possibility that certain woods might remain useful (truly elastic) when pushed into that region and remain truly elastic. I do not doubt what you are saying jackcrafty  , but I would like to point out if we already do use some woods in that region of the curve, we might not know it. The geometrical effects of drawing the bow (stack) would mask it to a large degree. Pure linear elasticity is pretty rare in natural materials if I am not mistaken. Over on another thread Badger is remarking that a few woods come in at 10% less mass than expected. I don't think that anyone knows exactly why this is so (yet). Could it be something like this I wonder? The way I see it, a lot of you guys and gals have in a very impressive effort pinned down the first order effects in bow building. What remains is to tease out the second order ones, even harder to identify but still important. You made me laugh hawkbow! Dave

[PatM]

 I think you are talking about the region when a bow is usually described as "broken in". I know Steve has talked about never stressing bows into this region if you want maximum performance but most long lived bows are probably stressed into this zone at some point. That slight drop in performance you typically see followed by a stabilization is what most typical bows live in.
 A bow that shows what I would call a "solid" bit of low set rather than a mushy 3-4 inches would fall in this zone.

[Badger]

I see it the way you do Pat, I would rather have 2" hard set than 1" of mushy set. Last year I built an osage elb, 76" long about 140 # maybe a bit more, The bow took no set at all but was mushy at brace and not much harder to brace than a 70# bow might be. On the other side I have seen 70# elbs I could almost not get braced by myself. I think the tension wood on the back can pull them back into shape somewhat disguising real set. Steve