Building closed loops with springy wire

Question

Background: I am a mathematician who is attempting to build some simple visual aids to assist in the presentation of my research.

To build the desired models, I need two things:

1. Exceptionally springy wire. By springy, I mean that it should quite difficult to put a permanent bend in it. Guitar wire seems like it could be a possible candidate here, but I'm not sure.

2. A way to fuse this wire together. It could be soldering, crimping, etcetera—I simply need to be able connect two loose ends together in a permanent way. (Note: Any sort of connection that allows the wire to twist will not suit my purposes. I need to maintain torsional pressure on the wire.)

I've already managed to build models of what I want using the wire manufactured for high tensile cattle fence (you can get crimps that go with that wire), but the wire is so stiff that my models are too big to travel with. Does anyone know of any potential material and/or methods I could use in place of the fence wire and crimps? I'm at somewhat of a loss, so any advice here is much appreciated.

Not the most professional pictures, but this is what I have right now (banana for context):

Answer 1

You could also use bicycle brake-cable wire— it's very bendy, tough, and virtually impossible to permanently fold. If you know any bikers, they might have old brake cables you could get for free. You should join it with crimp sleeves.

Answer 2

What you are looking for is called spring steel or spring-tempered wire. Tempering is a process where the wire is hardened by heating which allows the resulting spring steel to return to its original shape, despite significant deflection or twisting. When you bend a spring wire, it will maintain a strong, circular loop without kinking anywhere along its circumference.

Product Search: Spring Tempered Wire

To close the the loop, you can use a wire crimp sleeve. They come in many many lengths and diameters, so it shouldn't be too difficult to find one that fits your needs.

Product Search Wire Crimp Sleeve

Answer 3

Hardened wire is difficult to "use in a perpendicular" way. It really isn't meant to bend, or twist. It is a flowing substance, like for bicycle cables!

Guitar strings, you can just buy a set of new ones for a few dollars.

To fuse the ends is relatively easy. If you have a Propane Torch, check to see if it is MAPP gas compatible. If you don't know, just got to the Hardware or Lumber Center & ask for a MAPP torch, and maybe an extra "yellow" can of MAPP gas. Also ask for pre-fluxed brazing rods. You are almost going to weld, more molecular transfer of one metal to another. That is what brazing is. You get the ends positioned so they don't move. A couple 7" or larger vice Grips should work. Put the vice grips both parallel to the surface you are using for brazing. An old lawnmower blade will work. NOT concrete, plastic, wood, or any thing that will catch on fire. Steel or Iron.

You should have "Brazing Safety Glasses" They are specially tinted, no don't use sun glasses. ... flat surface.

Position the grips ~2" from the end of the wire, they will still get dangerously HOT. On the parallel part of the blade. Now the fun. Start the MAPP torch, centered, on the center of the 2 wires. Back to the torch, it should make the 2 ends "RED HOT" relatively quick, depending on their diameter. Red, not sparking... sparking means you are trying to weld. That is another day. The flux covered rod, goes right on the red hot parts of the wire. There is that microscopic bond. You can take a regular bastard file (yes that is the name of a file) and smooth off any large protuberances!

My next question is do you want to bend them to a shape, that stays, or are you doing 2d-3d stuff that the "circle has to go back flat" ? If that is so, you will just have to make the shape, and get the number of hands needed to hold it. If you want it static in shape. Mark the bend points with a marker. Get that very nice MAPP torch, keep it back a couple inches (not welding, or brazing) as it starts to get red bend it, let it cool and it will stay that shape. You've taken the temper out of the steel, by relaxing the crystalline structure of the steel. It will not spring back! Do the same for other bend spots.