Hello,
Wow, your tapes are so thin they are really foils. (1.97 mils to 3.94 mils thick and 0.394 to 1.968 inches wide or rounded say 2 to 4 mils thick and 0.4 to 2 inches wide.)
The thinnest tapes that we ever used in coaxial cable longitudinal copper, outer sheath welding were 8 mils and that included transverse welding to splice the copper tape. (I have a great deal of experience with this process.) After successful transverse welding, the tape was placed in a press and the weld flattened to have the weld thicknesses precisely the same as the tape. The tape was also welded at an angle to distribute the the weld position during longitudinal forming and welding.
The transverse welder was automatic, large (About 1/2 the size of a desk.) and TIG (tungsten inert gas). The gas was argon. The arc was struck at the point where the head started across the tape and stopped when the head left the tape. This left two little notches in the tape but this did not matter because the tape was sheared with a rotary knife to a precise width just prior to longitudinal forming and welding. The notches were on discarded width. (Please note that the ends of the two tapes tapes were butted together, after shearing each end for accuracy, and spliced. There was no overlap.)
I am aware that the company that made this equipment so long ago boasted that they could manufacture stainless steel hypodermic needles with much smaller versions of our machine and to the thicknesses that you are talking about but the welding for copper would be in my opinion so "iffy" that I don't think it is the right application for you.
Instead, I think you should consider ultrasonic spot welding or more preferably continuous ultrasonic welding across the foil tape just as I outlined above, but of course overlapped at the weld.
If you go to the WAI Virtual Trade Show, (
www.wirenet.org/vts/vts_search.cfm ), select welders-ultrasonic and then press the "Submit Query" button, you will find three manufacturers. If you click on the "View Details" for each of the companies, you will get more information including a link to their website. I recommend that you discuss your application in detail with each of them.
I am not clear as to the as to the work hardening created by the ultrasonic welding but I am sure a quick electric anneal and a light sanding would easily resolve that issue if indeed it is required.
Regards
Peter J. Stewart-Hay
Principal
Stewart-Hay Associates
www.Stewart-Hay.com
519 641-3212