No worries; there was always that to consider anyway, being an apartment dweller. If they let you use a gas grill on that balcony, that might do the job. If otherwise, well, yeah -- you'd have to totally get determined, playing tricks with your oven.
Contemplating riveted mail and its four times the time spent weaving it suggests you have something pretty serious in mind with that mail. Do you play with the Society for Creative Anachronism, or do rebated steel stuff à la HEMA? The former think real riveted mail is darn cool; the latter require it because they are slicing at each other with blunt steel weapons.
That soft black tie wire may need a normalization after the flattening stages to get rid of any workhardening that might have developed. We want to keep it from cracking there. It's gotten pretty thoroughly pounded and is now headed toward being fatigued. Heating it red hot fixes that, reshaping mashed microcrystalline structures. Eliminating the fatiguing of the metal lets it get softer and stretchier again, for opening up the rivet hole or slot -- a round hole for a round rivet, a slot, 14th-c-and-later style for triangular rivets.
Fatigue is how you bust a paper clip bending it back and forth several times. First it gets rather harder, and then it fractures -- that's what we're trying to escape here as we pierce the overlap zone with a "drift," which differs from a "punch" in not knocking out a slug of the metal where you're making the hole, but instead stretching the metal open, pushing it aside, to make the hole. This conserves metal -- and strength -- right at this vital spot -- there isn't an awful lot of metal to work with! Fortunately, after piercing for rivets, you're done with the rougher steps!
I doubt you'd notice if your riveted armor mail were stronger or weaker -- at this level of things, steel is just steel. Simply riveting steel links gives them twelve to fifteen times the strength of butted links of the same diameter and heavier wire anyway. The usual comment is fifteen times the strength of 14ga butted, for 5/8 the weight -- because the wire diameter is a mere .048", contrasted with 14ga's .080". You might be able to get it to half the 14ga stuff's weight, area for area, by keeping the spacer rings thin and economizing on metal that way.
There are really marvelous alloys out there in this aerospace age, but they are not commonly made into wire. I do have some titanium wire (exotic welding wire, junked for contamination) and about the only thing I could do with it mailshirt-wise is to make it of butted links; titanium's bizarre working properties show me I can't hammer flatten the stuff -- it fatigues really fast and really weird.
Mild, nongalvanized steel will serve you well in all you could realistically ask mail to do. Mail that would yield higher performance from a heat treat needs to start with music wire, get annealed, be worked and woven into mail, *then* get hardened and tempered to a spring temper -- oh, and without getting scaled completely away in oxides, so it's a good idea to do this in an oxygen-free environment. There are modern industrial furnaces that do that, and there are ways a smithy can do it too, burning the O2 into CO2 in the forge before it reaches your metal. Can be done, needs facilities.
Round rivets or triangular rivets call for different shapes of drift for their holes; you want the rivet to fit the hole and vice versa to make it strong. For a round-rivet mail link, the drift is like an awl. A flat triangular rivet gets a drift shaped like the blade of a precision screwdriver or a spear point. Thing's only a sixteenth of an inch across at this business end. One of the best things to make a drift out of is a masonry nail, with its pyramidal point ground to shape on a stone. These nails are extra hard and very cheap, you get a bunch of them in a boxful. It's a good idea to make up half a dozen or more at a time so if you bust that tiny point off of one, you don't have to stop but can just grab another. And do a little regrinding later.
In butted mail projects, you could try stainless wire, though it costs more money. It tends to be stiffer, which is favorable for butted mail. Holds together well. Those who get really interested in such things (we've seen 'em here) note that SS is just slightly heavier, link size for link size and area for area -- detectable on a scale, but not likely to be felt wearing it.
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.