What was found
NR 2 ENGINE FAILED ON TAKEOFF AT GEAR RETRACTION. HEARD LOUD BANGS AND THE ITT SPIKED AT THE TOP OF RED. ENGINE WAS NOT PRODUCING POWER AT THIS POINT. FOLLOWED SOPS, RAN CHECKLISTS, SHUT ENGINE DOWN & BACK FOR LANDING. FELT VIBRATIONS COMING FROM THE ENGINE AFTER SHUT DOWN IN FLIGHT. NO INDICATIONS OF FIRE FOUND. NO VISIBLE DAMAGE FROM OUTSIDE, BUT THE ENGINE NOT WINDMILLING IN THE WIND. REMOVED THE ENGINE INSTALLED AN INSPECTED A SERVICEABLE ENGINE. PERFORMED FOLLOW ON CHECKS AS REQUIRED WITH SATISFACTORY RESULTS, NO LEAKS NOTED. MAINTENANCE ACCOMPLISHED IAW AMM 71-00-03.