modeling a laminate longbow

[Anonymous]

hey guys/gals I am working on a longbow project and am wondering if i can simulate the layering and flexibility of the limbs. I'm looking at using carbon fiber, foam, and fiberglass to make the limbs. I have all the technical specs of the materials i want to use but is there a way to calculate the draw weight of the bow when drawn to 28" as per AMO standards. i am assuming that i will have to model each layer individually and then assemble them together.

[John_Holtz]

Hi @Anonymous

Just to make sure I understand, this is a bow, as in a bow and arrow. Correct?

You are correct that to make the model, each layer would be a different body or component, all positions correctly to make the bow. Out of curiosity, what are the minimum thicknesses that you would have? What is a typical cross section of the arms?

But I think we need more information about the material properties before saying whether the simulation would be valid or not. For example, foam is typically a nonlinear material due to the compression, woven fiberglass is typically a composite, orthotropic, or anisotropic material. So the question is, how do you want to treat the materials during the analysis?

• If the stress-strain curve for all of the materials can be considered linear during the analysis (modulus of elasticity = constant), then it should not be much of a problem.
• If anything has a nonlinear stress-strain relation over the range of stress it will experience in the analysis, then we need to understand those details better. (To use simulation terminology, we need to understand what type of "material model" needs to be used for each material. The material model is the mathematics that describe how the material deforms when loaded. As mentioned, a foam material behaves much differently than a metal which is different from rubber, which is different from the string (tension only, no compression), and so on.)
• If some materials are orthotropic, I need to find out if the material axis moves with the model during the large deformation. (I assume that the deformation of the bow is "large". Keep in mind that in engineering, displacements on a 6 foot structure larger than 0.1 inch would be considered large!)

The last issue that I need to confirm is whether contact between 9 layers in a thin (?) cross-section with major bending will behave correctly. I am working on that for another case.

[Anonymous]

So the max thickness i would have an individual layer of carbon fiber would be .045" thick from APC composts. the fiberglass would be available .030"-.050" unidirectional Bo-tough fiberglass from Gordon Fiberglass, and the foam core is product from BearPaw Archery unfortunately i haven't been able to get the information on its physical properties as of yet.

It would be a five layer limb consisting of [fiberglass] [Carbon-fiber] [Foam-core] [Carbon-fiber] [fiberglass] around a 1/4" cross section and a 1" width tapering to about 1/2 at the tip depending on the total amount of poundage the bow produces at 28" draw

As I understand the physics on it the front of the bow will be under tension stresses where the belly will be under compression, with the core mainly acting as a neutral binder keeping the two from splitting apart. So I assume the core would be under shear forces.

And yes a long bow can flex over 15-20 inches from its brace height of (8"-9") to its full draw. also the bow will already be bent and under stress just having been strung 

I will link all the necessary information I have on the materials.

Fiberglass: http://www.gordoncomposites.com/products/TDS/GC-70-UL.pdf

Carbon Fiber: https://store.acpsales.com/products/2366/carbon-fiber-unidirectional-sheets

Foam Core: https://shop.bearpaw-products.com/WebshopB2C/Bearpaw_Power_Stabil_Core_Stripes/P-3429/1?Origin=Navig...

AMO standards: http://www.a-rchery.com/amostandards2000.pdf

[John_Holtz]

Hi,

I am not confident that a Fusion simulation would give accurate results for this type of analysis. The problems are:

1. You have composite materials which are orthotropic materials -- different mechanical properties in different directions. At this time, Fusion simulation cannot analyze such materials. (Fusion can analyze isotropic material -- materials that have a the same material properties in all directions.) It is hard to know what effect the orthotropic properties have on the result, but they are probably important.
2. The thin layers may be a problem for the analysis. 

Good luck.