The pilot reported that he was conducting a night flight to comply with the 14 Code of Federal Regulations Part 61.57 (b) night takeoff and landing experience requirements. He added that, on his second approach, the airplane encountered wind shear during the landing flare. The airplane was blown about 40° nose left of the runway centerline. The pilot tried to correct to the right, but the airplane stalled and landed hard. The nose landing gear tire separated from the wheel, and the airplane bounced. The airplane settled on the runway, and a propeller strike occurred as the airplane slid off the left side of the runway. After the runway excursion, the nose landing gear wheel burrowed into the dirt surface, and the airplane nosed over. The airplane sustained substantial damage to both wings and the empennage. The METAR reported that the wind about the time of the accident was from 050° at 8 knots. Critical wind shear or low-level wind shear were not observed at any time during the day or night per the METAR on the date of the accident. The pilot reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation.