PA-28 instructor pilot reported engine power loss on climbout. The instructor pilot requested priority handling and performed an air turn back to make a precautionary landing at departure airport.

Narrative

Prior to this event a student and I had been practicing normal takeoffs and landings with no indication of performance reduction from the engine. We completed 4 takeoffs and landings to full stops followed by us taxiing back to the hold short line of the active runway. On the 5th departure we were climbing at Vy (85 MPH) up to around 950 feet MSL; read on the altimeter. Prior to turning crosswind we had a 50% RPM loss. From this point forward I; the flight instructor; took the flight controls and started performing a left turn at best glide (83 MPH) back for the opposing runway; Runway XX. In the bank we descended about 300 feet while maintaining 83 MPH. There was violent vibrations inside the cabin with occasional clouds of smoke rising over the windshield. When the 180 degree turn was completed we were established on final roughly around 600 feet MSL in a clean configuration. I descended for the runway and once in ground effect I brought 30 degrees of flaps down to increase drag. We touchdown about 3;000 feet down the 6;000 foot runway and exited on Taxiway XX. At this point I shut all the electronics off and pulled the mixture; mags off; and turned the master off and exited the aircraft with my student. During the entire event we were able to hold roughly around 1;200 RPMs. After investigating and speaking with the mechanics they came to the conclusion that the cylinder had split in half causing the dramatic loss of power. Everyone onboard exited the aircraft with no injuries.