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Here I will just outline the method of annealing copper alloys. This is usually only done by detectorists to straighten objects, and though it has much in common with annealing other metals, other metals have their own properties, temperatures and methods which are slightly different, and so the advice here is not directly applicable to them (the last link briefly covers many)
By copper and its alloys we are talking of raw copper , brass and bronze. These are where copper makes up the major portion of the metal. All of these might have impurities or smaller amounts of still other metals mixed in with them. It isn't just modern technical alloys that have these smaller additions, ancient alloys would often include purposeful lesser quantities of lead, arsenic and so on to improve qualities, and they often included unintentional traces of yet more metals or elements. I am approaching this from a broad perspective obviously, more hands on (or hands off maybe), because the addition of minute (fig 8.25 page 61 first link) amounts of other elements can change the characcter of the metal by a large degree.
Unless you have read about and analysed whatever metal you have in hand, annealing is going to be used for later straightening when cold. There are some copper alloys which work form better when at a specific hotter temperature. They are few, the temperature has to be correct, and normally hot working is only used for forming, not straightening. I don't imagine detectorists hammering glowing pieces of antique in the kitchen, sure it has been tried though.
Some copper alloys become hot short (or red short). That is to say when worked hot they are weak. This can be for a number of reasons, sometimes just impurities, a particular alloy, and so on. If you try to work these hot they crack or crumble.
Working copper metals hot is not a good idea, and is unnecessary.
When annealing the temperature is raised to allow the crystals to reform in a certain way. This alleviates stresses that have formed and allows movement of the metal until a new limit of stress is reached. Some copper alloys do not anneal, I know high tin bronze and aluminium bronzes can be very difficult or impossible in this respect. Aluminium is a recent addition so I won't cover it here, there are procedures and limits for it that can be found online. High tin bronze is basically not possible to straighten without very controlled conditions, but then you will likely not find bent high tin bronze, only cracked or broken objects.
Apart from those any other copper alloy might have inclusions, or have changed composition with age, making straightening it also a very difficult task. When a metal is bent enough the outside radius elongates, that will not always return to shape on being bent back, but will instead act as leverage stretching the inside of the bend as the object is straightened, and you end up with two halves of an object instead of one whole one.
Once softened by annealing the metal is actually weaker, comparable to say plasticine vs wood. To shape something, you need it soft, but soften means it might rip instead of break - hardened metal is stronger but more brittle. To straighten a piece you have to be aware of the various limits the metal has at any point in the process. I think it is great when people straighten finds that need straightening, by themselves, and when the result is successful. There are some margins for error, but to actually know how to handle a metal with certainty takes experience that few of us have. It is just my way of saying that if an object is valuable at all, then it is a good idea to have someone who knows how to handle it do the work. The results otherwise are damaged objects that cannot be easily repaired. Anything which has a design on it that is valuable (e.g. a coin) , will be altered if later welded and cannot return to original except by reworking , which obviously somewhere detracts from that originality . Even heating for annealing changes the structure of the object, not only will patina be lost, but the actual matrix of the metal will be changed. I actually feel heating somehow erases something of the history of the piece, that is a personal view. What is certain though is that those who study the metal composition to figure out how objects were made will no longer have the original state of the metal to analyse - this is not usually a question as far as average finds go, but it does underline how an item being annealed is also being altered.
As you raise the temperature of a metal the crystals of metal rearrange. The hotter and longer, the more they do so, and there is nothing completely predictable as to how. Some copper alloys actually harden if kept at a set temperature for a long time, some metal inclusions even rearrange at room temperature. The rate of cooling also affects how the metal restructures, but because here we are going to be talking of annealing to a low temperature, that effect is limited. In copper alloys, broadly speaking, rapid cooling has no great effect one way or the other, unlike say steel.
Rapid cooling might stop unwanted crystal types of formation, or it more likely will cause stresses by the differential of outside to inside temperatures. So the short of it is that the best method is to allow an item to cool normally in air, as far as we are concerned.
If we overheat an object, there are few benefits and various drawbacks. For ongoing practical discussions on this anyone might read up on brass cartridge annealing for ammunition, where a specific range of softness is sought. The temperature range of where an alloy moves from hardened to annealed is very narrow (see second link) and depends also on the composition of the alloy. Once we heat past this there are few benefits to be had. For brass this temperature is a just visible glow in a darkened room, another method is to watch for the flame turning yellow on the metal as carbon particles become incandescent. I will add that the same temperature and method is used for most silver alloys (some say quench in water , others not but the difference in annealing softness is said small between each - so better not to quench in my opinion ) , but gold alloys, aluminium and platinum have distinct requirements. It is not possible here to provide a list for all copper alloy annealing temperatures , or even those that can be successfully annealed. The typical alloy only has to reach the required temperature, it does not have to be held there. It is more sensible to heat a broader area or the whole object than to try to heat up a particular point, because the effect is more visible and you avoid local stresses.
Once temperature increases much beyond that, various things occur:
Metals in the alloy can start to segregate, some might sweat out or evaporate.
Absorption of oxygen might increase, causing oxidation under the surface, particularly with silver copper alloys.
In impure copper, called pitch copper, gases absorbed turn to steam and split the copper or alloy.
The piece melts.
One trouble with high temperatures is crystal grains start to become very large. This might make the metal softer still, but also very weak in certain directions - you don't have a mishmash of smaller grains all doing their small part in various directions, instead you have strong large grains which are weak in certain directions. They are open to being reduced and stressed by working, but might shear also.
When annealing, the very hottest part of a flame (the brightest) also carries oxygen, and that will oxidise the surface removing metal, further out there is a zone that reduces (takes oxygen) that will help protect the metal some. A firecoat of flux, in fact plain borax disolved in water is the simplest, can also be used to seal the metal. So generally the softer part of a flame is used to broadly heat the item. Small items can and will melt with even small butane gas torches, a stove is less likely to.
So there you have some advice on how to anneal copper alloys. This is just annealing, not how to straighten, which you would probably have to ask a jeweler or similar to get proper advice. The rule tends to be frequent annealing.
For something valuable best is to find someone experienced, they are much less likely to make errors.
On annealing and re-crystallisation, quite long and technical
http://www.ndhu.edu.tw/ezfiles/29/1029/ ... 041223.pdf
Cartridge brass annealing vs temperature
https://www.nzhuntingandshooting.co.nz/ ... e%402x.png
Here is one discussion that covers other metals also
https://orchid.ganoksin.com/t/quenching ... s/36543/23
And finally a watchable video on the practical basics of annealing, with demonstration
The question of best temperature to heat to will keep appearing. Above outlined is best practice from various sources. Jewellers work metals under slightly different conditions to say a single bend in a coin, the metals we find might be already altered somehow, the gun owning community look for a certain minimum strength to be retained in their cartridges under specific conditions and hold heated debate with those with the most practical experience usually winning, forgers and metal workers deal with a variety of parameters at once. None of these are nescessarily completely identical to straightening an item, what they all note is the complexity of circumstance, that includes due to overheating an object. Here is a long practical explanation on grain size and workability
https://www.thefabricator.com/thefabric ... -operation
and to put it in short, higher temperature both makes the metal more ductile but also weaker and more likely to fail. You have to balance these out, that is to say will the stiffness overide the remaining strength, or will more softness not be enough to cover for the added weakness. That is anybody's call, I'm just noting what is broadly recommended. It would be nice if someone who has experience straightening items would chip in their approach, but I doubt anyone with that experience would be willing to recommend one way or another because they probably adjust their technique for so many parameters, include what they observe as they move along with the work.
Next time, I just got it bright red hot and flattened it, no annealing....worked well .
Probably just pure luck though
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Or it was right for that metal (meaning not just metal type but its state). That is what all the above underlines, there is nothing given or obvious about any metal, just "best practice" and its reasoning, and experience of how the metal is behaving being a bonus.