-
glue to hold together some plastic
I wouldn't hold out too much hope whatever kind of plastic, but if you actually know what it is your best results will come from using the appropriate activator on the bond surfaces before applying the adhesive, e.g. https://www.loctiteproducts.com/en/products/fix/super-glue/loctite_plasticsbondingsystem.html is a two part product for bonding polythene and polypropylene which are common plastics used for flexible consumer products.
-
JB Weld - remove the old glue, re-glue and allow to set, add more to form a 'collar' around the join, possibly incorporating structural splints.
Possibly alternative - a carbon fibre repair kit?
Much will depend on aesthetics and the replacement cost of your headphones as any repair will be weaker than the original...
Any recommendations for a glue to hold together some plastic that is under slight tension and torque? My daughter stepped on my headphones and broke part of the headband. I tried some loctite superglue powerflex last night and left it over night but it broke instantly again this morning.