The most likely evidence of an energy transformation taking place when a wire is twisted and turned breaks is that the broken ends of the wire turn warm (even very hot if it was twisted and turned vigoroulsy).
The heat (thermal energy) evolves due to the internal friction developed by the relative motion of the internal particles of the wire, being kinetic energy transformed into heat energy.
It is the same phenomenon that is observed when a saw cuts a piece of metal and the reason why a cooling fluid is poured over the pieces of metal to avoid that the temperature raises too much.