Bubbles, that suggestion was beadman's, and I agree with it, and you, that sinew and/or rawhide could prove better. But flax is what I have and what I'm curious about, so that's what I'm going to continue to use.
I don't mind if the bow breaks again any more than a materials engineer minds that a test sample breaks. At this point I have nothing to lose by gluing this bow blank back together and testing more flax. Why throw these two limbs away without testing more?
So enough of the reasons why, I think I'm beating that horse to death here, and it's getting boring I bet. Let's talk about flax itself. What I'm seeing is what I think you'd expect of failure in flax.
Flax is reported to have high tensile strength for its weight, and have only 1% stretch. That's vs. 3% elongation for sinew. What that means to me is that flax will be great up until a point, but then it will break without stretching or warning. While sinew and rawhide will stretch more, and return for an equivalent amount of tensile strength at that loading. Stretch not by much, but some.
So if you are designing for flax, you want to overbuild the reinforcement so it doesn't come close to its break point. Presumably, it's still lighter when overbuilt than sinew or rawhide.
Okay, that's a theory. Not proof -- you'd have to do controlled tests to find that out, and specify all kinds of things like the quality of flax, glue/resin used, wood, test method etc. etc. and the same for the animal materials.
I'm not doing that. I'm doing it the sloppy, fun way, for me. My theory is that I went too thin on the backing, and I should have put it and the rings down in layers. I'm going to try that out on the same bow again. Maybe it will work, maybe it won't. Let's find out........
edit: wrote this before I saw Pearl Drums post...