C-172 pilot reported malfunction/failure of flaps in flight. Pilot returned to departure airport and completed a no flap landing.

Narrative

Flight started from ZZZ and returned to ZZZ.While doing the slow flight maneuver; entry was below flap speeds. Flaps were added at and below the flaps speed of 85. Flaps 10 were added below 80; and flaps 20-30 were added below 75.On exit from slow flight; the flaps were incrementally retracted. When it was time to retract flaps from 10-0; there was a large pop/bang noise from the right wing. Immediately I looked out to see the right flap was not retracted properly. The outboard portion of the flap was at 0 (stowed) but the inboard portion of the flap was stuck at 10. The flap was clearly curving due to this and within the next minute; the flap slowly slid into the stowed position.There was no obvious damage seen from the inside of the plane on the underside of the wing; so I elected to not use flaps anymore and work my way back to the airport. Upon executing a no flap landing at ZZZ with no issue I taxied to park the plane in the hanger. Upon stopping the plane I extended the flaps to inspect what may have happened to find that the flap was bent and damaged on the upper surface. The guide track bar on the flaps inboard rail was very bent; and the upper surface had been very dented and bent due to the flaps getting stuck in the retraction from 10-0.After discovering this I immediately got in contact with the chief instructor.