Date: 201904
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: VMC
Weather elements / visibility: 10
Light: Daylight
Aircraft: DA40 Diamond Star
Operator: FBO
Operating under: Part 91
Flight plan: VFR
Mission: Training
Flight phase: Initial Climb
Airspace: Class C ZZZ
ATC / advisory: Tower ZZZ
Aircraft component: Exterior Pax/Crew Door
Component problem: Failed
Reporter organization: FBO
Reporter function: Trainee
Reporter qualification: Flight Crew Student
Human factors: Distraction; Situational Awareness; Time Pressure; Workload
Second reporter function: Instructor
Anomaly: Aircraft Equipment Problem Critical; Inflight Event / Encounter Other / Unknown
Detector: Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Provided Assistance; Flight Crew Returned To Departure Airport; Flight Crew Landed in Emergency Condition; Flight Crew Requested ATC Assistance / Clarification
Contributing factors: Aircraft
Primary problem: Aircraft

Narrative: During the aircraft pre-flight; it was noted that the door closure annunciation system was tagged as inoperative. The aircraft was still airworthy per maintenance. The inop had been labeled in a conspicuous spot and was noticed. The issue was also documented in the flight binder with the maintenance records. The pre-flight was unremarkable; doors were secured in position I; down and locked. No abnormalities noted while taxiing to runway XXL. No incidents in which the door may have opened. Prior to departure; the rear door was again checked and found to be in the closed position. The latch handle was flush against the door panel in the closed position. A soft-field takeoff was performed at the request of the instructor. At approximately 900' AGL; the instructor heard an abnormal sound coming from the rear canopy. He turned around to diagnosis the issue and discovered the door appeared to be still in the latched position; however; the door was cracked open. I continued to fly the aircraft while he determined what to do. At approximately 1;000' AGL the door separated from the aircraft. The controls were not affected; however; it became difficult to hear radio communications due to the wind noise in the cockpit. I reported the issue to the tower. The instructor took control of the aircraft. On review; the rear door was missing; the tail appeared to be intact and the airplane was flying well. ATC approved us for an emergency landing on XYL. The aircraft was turned; flaps to landing and a successful landing was made on XYL. ARFF (Airport Rescue and Firefighting) arrived and advised the aircraft looked okay to taxi and were actively searching for the missing door. The door was found near XXL and in one piece. It had sheared from the door pins at the carbon fiber hinges. The door latch was covered in mud from contact with the ground and in the open position. Aircraft was taxied to the ramp successfully and the issue was reported to school staff.


Second narrative: During the initial climb from XXL; I as the instructor noticed a noise of rushing air. I looked back to the rear door and noticed it was slightly open. I reached for the door and before I could close it the door departed the aircraft. The student and I then [notified ATC] and landed XYR.


Synopsis: DA-40 student and Instructor reported rear door separated from aircraft during climb out.