WITNESSES OBSERVED THE ACFT MANEUVERING AT A LOW ALTITUDE, TRAILING WHITE SMOKE, WITH ROUGH ERRATIC ENGINE SOUNDS. A PVT PILOT REPORTED THE ACFT WAS FILLED WITH WHITE SMOKE. THE ACFT MADE A STEEP TURN, PITCHED NOSE UP, ROLLED INVERTED, AND DESCENDED NOSE DOWN TO IMPACT. EXAMINATION OF THE WRECKAGE REVEALED A FRACTURED COUPLING FLANGE ON THE LEFT INTERMEDIATE EXHAUST PIPE. METALLURGICAL EXAMINATION OF THE FRACTURED FLANGE REVEALED MULTIPLE ORIGIN FATIGUE FAILURE.