Thank you for taking the time to give me such a thorough response!
I actually had to read it over a couple times to fully understand it, you clearly have a lot of experience in this area! That said, I think the unfortunate truth is that based on your responses, I don't really have the capabilities to anneal the rings. My apartment is not as large as I would like and while I do have a balcony, the building is very sensitive about what is allowed to happen on it. Using a torch is likely tempting fate a bit much. I simply need to wait until I have a better living situation to revisit creating riveted maille.
That said, you did mention that black annealed tie wire comes soft already. Do you think I could fashion it into riveted rings without annealing? Would these rings be much weaker as armor than using annealed rings of a different material? If I misunderstood and annealing has to be done, do you know of any suppliers of riveted rings? Or would the cost of such rings be too much to even be worth it?
I feel the need to apologize for not being able to fully use all the advise you provided here. You clearly put a lot of effort into answering my questions and for that I am very grateful. If my living situation changes to one where I am able to perform the annealing process, I will return to this post to re-read your advice and learn from it.
Thanks so much for all the help here!
I might put another brick in the wall of text up there, adding that I do that two-step flattening process so that the overlapping ends, being flattened already, don't slip off each other trying to flatten the overlapped bits onto each other. Frustrating. But taking the flattening in two steps allows me to use very simple, generalist tools. Namely, a hammer, and a hard place. I have an anvil. A slab of 1" steel plate would do as well, except for a propensity to wear. Don't use concrete; it crumbles under this. For handmade links, this extra step isn't much trouble, and time-wise pretty much a wash: with pre-flattening you don't have to be time-consumingly precise getting anything lined up. They're good enough already.
Don't hit this overlapped place really hard or fast; let your hammer strike it a bit slow and pretty heavy, with a hammer of about 4 lb weight -- look in the hardware store for a "drilling hammer" this size. Those were John Henry's business end, drilling hard rock for blasting, and these hammers come in 1-pound (SWIDT) increments so you can tailor them to your strength quite well. They are somewhat soft in the head, these hammers, so they don't chip being whacked into drilling irons.
The cross section of the overlaps should be flat, like an = sign. Both parts flat. If the parts are triangular in section, like two doorstops stacked on each other, you're trying to hit too hard and fast, and you can't rivet through those pieces of metal. A slowish heavy stroke gives the metal a few hundredths of a second to spread out flat. The flattened overlapped ends bulge out a little bit, putting a lump in an otherwise perfect circle.
Welcome and well come, Arczuk. You've come to one of the two right places, I'd say -- the other being M.A.I.L.
To do riveted, you're going to want some way to heat your links to red to do a crude anneal, also known as normalizing. Heat to red, cool in air. For full, maximum annealting, cool in a steel bucket full of Vermiculite from red heat. This will take over an hour to get done. If it takes four hours, you've probably done simply everything to soften ordinary steel that you could. Got a balcony or outside patio? E-Z P-Z. How about a stove with gas burners, or buying a MAPP torch, perhaps along with some firebrick to build a little corner along three axes -- like a cell in one of those reflectors that work at about any angle of light shining on them. Probably the handiest apartment place to use such a setup is inside the maw of your kitchen oven, on its racks.
That is one of two basic recipes for making armor mail, the other being simply to rivet it all, which got a lot more common, for obscure reasons, around the third quarter of the fourteenth century. The Plague, from 1348? Economic reasons relating to production of metal, particularly metal wire (so it got cheap)? We don't know. Before the middle fourteenth, half-riveted-half-solid/punched was much more common. Neither one wiped out the other. You may find I've used the old term demi-clouée for half-and-half stuff onsite. Building mail this way cuts your weaving time in about half, since of course you don't need to rivet all the links. Find a manufacturer to sell you some tens of thousands of spacer rings, if you don't care to go in search of an old Roper Whitney No. 7 1/2 metal punch that you bolt onto a workbench. It gives about a 5-ton push to punch out sheet metal discs of sufficient size. (Roper-Whitney's No.5 Jr and XX models deliver 1.2 tons and that's not enough for punch-outs that are big enough; these punches max out at 11/32".) If you order spacer rings, I suggest getting them not as thick as the wire you're riveting the others out of, to kind of make the crisp corners of the punched rings tuck back into the mail fabric a little. Slightly lightens your mail, too.
The fourteenth century also saw the use of the triangular rivet vice some other shape (some were strange little things). Looks like a 1/48-scale slice of pizza for shape and size; pointy end gets pushed through and the wide end clinches things down on that end of the rivet while the pointy end gets upset into a little teensy rivet head with such a tool as either setting pliers (which tool you will have to make from long-handled farriers' nippers/nail pullers -- they look like tongs) or a nail set with a cup-type point. And something to back up that rivet on, to be your anvil while you hammer, if you go the nail-set route. Pliers/tongs would be more convenient.
Size: mail links run from about 1/8" ID to maybe as much as 1/2" ID, which latter may have primarily been used to armor warhorses of Renaissance times where mail would have been convenient. The top of the bell curve of diameters was in the range of about 1/4" to 5/16" ID. Within reasonable limits you can go with heavier wire as your links become larger.
Mail I've been working on is first coiled around a 3/8" diameter mandrel. They are cut into cheerios and flattened with a big hammer. The flattend links are then squeezed down around a 5/16" mandrel, using needlenose pliers for handy seeing of what I'm doing. Takes about three crimp-squeezes per link to get 'em to this fianalized diameter and hence the ends overlapped. More flattening happens next, of the overlapped ends; now they are ready for piercing for riveting, and there's about 3/16" of the link's circumference to work in. Sometimes I have to twiddle a hand-cut link to get that 3/16", and at this point, incorrectly sized links are culled out and set aside for other use.
Softens it temporarily until you do something else dramatic to it again, like case hardening -- an option, but you kind of want a backyard workshed or a smithy to do it in. Bottom line: can be done, needs facilities. Also needs you to get yourself a canister of Cherry Red(tm) compound that makes iron carbides and nitrides to put a hard "skin" on steel. Ultra performance!
The specifics of heat treat do depend on the alloy of the steel -- but won't be a concern for you because steel wire is the simpler kind of steel, and only becomes somewhat more complex if you were using stainless wire, which does not anneal as well as plain simple carbon-steel baling wire. Armourers tell us stainless is fiercer, trickier stuff to work. Fortunately, you won't be, as I'll lay out below.
If you've decided to use Black Annealed Tie Wire -- baling wire/rebar wire such as you find in hardware stores in 3.5-lb rolls, just as black colored as it says -- it comes very soft already, though you might still need to anneal it after coiling, cutting, pre-flattening and then overlapping and final flattening, before you get round to piercing it to rivet it. Hard is one way for steel to resist damage, but what mail really needs is like the wire it is made of: it needs to be tough more than it needs to be stiff, so it doesn't break and get torn open, at which point it has failed. You don't have to do much of anything demanding to the metal's interior structure; you need to do your part in clinching your rivets. They're reeeeally really eentsy. It doesn't hurt to start by practicing riveting these little links just by themselves for a dozen or two links to master your method.
Black annealed tie wire is about half again as thick as such wire would ideally be for building a hauberk out of. The ideal wire is about 1mm/18 gauge SWG, and this baling wire seems only available in 1.6mm/16 gauge. This stout stuff suits the larger diameters of mail links, or links which are very very flattened to spread 'em out good in the flattening phase. It produces a hefty mail, a/k/a "double mail," and is plenty sturdy at a price in weight. To get wire around .050"/1mm/18ga, the easiest way is to get it from a welder supply shop in diameters close to those (they don't do gauges, so ask for your diameter). (Gauge is sometimes not worth the pain) Get welder wire for welding mild steel; you don't need the stainless, unless you really want to go there one day. Welding wire always comes workhardened and springy so it will feed through the welding gun without kinking; you will have to anneal this stuff down to get it cooperative. Some people use a hibachi -- and sufficient ventilation -- for this job.