Tennis bracelets often come in for repair. The rod part of the tube hinge is usually the part that breaks. The wire has to drilled out and replaced. The tube counter part usually shows wear too, so it is best to build that up while it is apart.
Here is shown the drilled out wire and rebuilt tube before soldering in a new rod.
The wire is soldered in place, sanded and polished to complete the repair. Here is a picture before the final polish. 4 hinges were rebuilt on this occasion.
The owner must have been grateful to you. Amazing you are not cross eyed with all this exacting close up work. Great job!!!!