JM-

Patrick has a good point, the location of the break will determine the
method & whether a fix is even possible.

At my Ace Hardware they have a two part "epoxy" that is specifically
menat for automotive plastics (mirror housings in particular)

Fixturing (holding the glasses in the correct position) until the
adhesive sets will be key to a successful repair.

I fixed a pair of my wife's designer sunglass (spring loaded hinge stud
pulled out of earpiece)

Fixturing was a pain but I got it to work........again using that
automotive "epoxy"

Lost the spring loaded behavior but they served for another six months
unitl they broke again eslewhere.................I told her "too bad,
they were "unfixable" this time.

cheers
Bob