- Are you using the wire lengthwise, as a decorative element?
- Or are you trying to solder the end of the wire perpendicularly to the sheet?
Either way, keep in mind that greater surface area contact means a better solder joint.
If it's lengthwise:
Form the wire to shape, then anneal it just like Loopy suggested and hammer it flat on a bench block with a plastic or rawhide mallet.
Put a piece of fine sandpaper on your bench. Lightly rub the bottom of the wire design on the sandpaper just enough to flatten it slightly. You don't need to sand until you've got half-round wire. You just need to create a bit more surface area than round wire would provide.
Then you can flip the wire over and, using flux, sweat solder a small amount along the length of the wire. Clean both pieces up in pickle.
Flux both pieces, and put the wire on your sheet. Focus the majority of the heat of your torch on the sheet, and the solder should run along the length of the wire. Pickle, and check your join. If need be, heat again to flow the solder in any areas that might've been missed.
If it's the end of the wire you want to join like for an earring post:
Surface area is again your friend. I like to use a tiny ball bur (just a smidge larger than the diameter of my wire) in my flex shaft to cut a small depression in the sheet where I'd like the wire to go.
Then, holding the piece of wire in my insulated tweezers, and using flux, I'll join a tiny blob of solder to the end. Pickle the pieces to clean them up.
Apply flux to both pieces, and heat the sheet up until the flux turns clear and glassy. Then lower the wire into the depression until the solder flows. The solder will fill up the depression, and the larger connection surface area created makes a stronger bond than just soldering a flat wire to a flat sheet.
Good luck and have fun experimenting!
~Addie~