No glue is going to wok well with the stress that will be put on the joint. It may hold enough to get over your head, but most likely will break on the first use.
What type of plastic? If it is a polyethylene composition, no glue holds on it. If it is styrene, you have a shot welding them either by solvent or heat.
If looks are irrelevant, a splint or two of springy metal, like from a wide fish tape, or maybe from one of those hanging file folders, and then wrap the whole thing as tight as you can with nylon-filament strapping tape. No strong repair is gonna look pretty, so you may as well go with cheap and painless. And then look for a dead pair on ebay or craigslist, to strip for the correct parts. I'm surprised that a 'name' brand like Bose didn't put a spring steel core in the part to begin with. Plastic sucks for applications that flex constantly like that.
I don't believe any gluing option will repair it for long. Glue would work on something that doesn't get much stress, but in your case I would use a short length of stiff wire, like that found in a paperclip and then lay it over the joint one end, sliding a piece of adhesive filled heat shrink tubing (AFHST) over the left broken part and then insert the right side piece into the shrink tubing and wire and heat. Even plain shrink tubing will likely hold the wire in place, but adhesive filled heat shrink tubing will add significant strength to the new joint, especially if you can manage to double it up and "rebar" it. The adhesive keeps the rebar from working its way through the tubing after a certain number of flexions.
Glue, I fear, just won't work, without reinforcing that break substantially to make it serviceable again. I would run shrink from ear to ear, if I could, to make it look more like a rubberized headband and less like a break repair. It will probably even stay on your head better than the old one because it's a less slippery surface.
Without the "rebar" wire, not glue will hold. I say all this having grown up in a house of 'repaired by glue' things. (-: My dad was the head of the materials science division, (miss you Dad!) for the USN research lab in Annapolis and brought home loads of opened but salvageable test samples (these were the old days, before that all became illegal - ahem). We had epoxy-repaired everything all over the house as far back as I can remember. And if there was no reinforcement, there was no permanency.
Bose wants a fortune to buy them in the first place. I've owned them and have come to like both my cheaper Sennheiser and Sony headsets better.
That section of a headphone headband gets incredible stress placed upon it. If the original broke, so will an unreinforced repair no matter how you glue it, it will always be the weakest point. Unless you're willing to build up a enough glue on the band to make you look like you've had an eagle crap on your head, it just won't work.
The adhesive shrink tube and "rebar" method would make my father proud. I've repaired a lot of poorly designed plastic items using it. Sometimes I use two layers of tubing to really reinforce the joint. I learned about AFHST here on Usenet. Clearly on the top ten of useful things I've learned on the net, almost as good as discovering there were dual circuit breakers that allowed you to put two 20A lines in what was before a "one only" 20A panel slot and using a hose to cool down an attic job in midsummer. But that's another thread entirely.
Find out what plastic it is, and use the appropriate adhesive. ABS and PVC can be repaired very well with solvent (lacquer thinner, clear PVC glue, carburetor/throttle body cleaner), and polycarbonate can often be (you get one chance, but if it fails the surfaces turn to some white material). If solvent has no effect, then the plastic is probably high density polyethylene, polypropylene, or nylon, which can't be fixed with any glue but instead has to be welded back together (wood burning iron with Teflon tip is best, but soldering iron works, too), using a scrap of the same kind of plastic. Nylon and polypropylene weld together very well. If your first solvent weld with polycarbonate doesn't work, then heat welding will.
Super glue/crazy glue will give only a weak repair. Worse, it will stick just enough to the surfaces to prevent solvent from working. Epoxy won't work at all, and JB Weld is epoxy.
Smitty's suggestion of fiberglass cloth and epoxy is the only sure- fire repair that will work on any plastic.
You should tell Bose that the lack of repair parts is ridiculous for a high-end brand like theirs and makes them inferior to Harbor Freight in this respect (switch worked loose on an $8 HF heat gun, HF said they'd send me a new switch, and a week later I received a whole new heat gun).
I've used the rebar method on plastic parts too. I take a circuit board drill bit and drill one or two cavities on either side of the broken plastic and coat the rebar, small stiff wire roughened with sandpaper, with glue and put the thing back together. Heat shrink gives added strength. Before making such a repair, I do a quick cost analysis in my head. Am I doing this out of necessity or out of stubbornness? The other consideration is, am I doing it for fun? 8-)
Same here. In this case I'd probably not try to fix the band, but buy a cheap head phone set and use that band. Cheaper than glue. The fun would be in finding the band that would work.
I had the same failure on an AO set of hearing protection muffs. Contacted American Optical and they don't service the wire reinforced head band, only the ear cups. I opted to dump them. Some of the suggestions proposed here show great imagination.
Home Depot sells a really nice one by Ryobi. Designed for workmen in loud surroundings.
No electronics for quieting the sound, just excellent sound insulation.
And, you can plug in an audio source, eg mp3 player, radio, ...
And, facing forward are two wee microphones. With an off-on-volume knob that acrivates it. What purpose? So when the foreman comes up and wants to tell you something, you just turn them on. Pretty cool!
Price: $69. CHEAP! Super deal!
When flying, it shuts out engine noise BETTER THAN THE BOSE!
How do I know. I asked a guy if I could try his (and he could try mine).
In Manhattan, I can wear the things on the subway just fine.
Likewise on a busy street -- no problem.
EVEN at the lexington ave 14th st station (union square), when the train pulls in, coming around a tight turn, those steel wheels SCREECHING against the steel rails -- unbelievably loud -- I can still hear nicely, IF I use my hands to press them in against my head a bit.
(I wear glasses -- the ear-things let in a slight bit of noise.)
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