DURING TAKEOFF, AN UNCONTAINED FAILURE OF THE LEFT ENGINE OCCURRED. AN EXAMINATION REVEALED A FATIGUE FRACTURE THROUGH A REAR FLANGE BOLT HOLE OF THE COMBUSTION CHAMBER OUTER CASE, AT THE THREE O'CLOCK POSITION OF THE ENGINE. THE ENGINE HAD BEEN INSPECTED IN ACCORDANCE WITH AN APPLICABLE AIRWORTHINESS DIRECTIVE; HOWEVER, THE FRACTURE OCCURRED 2,060 CYCLES PRIOR TO THE NEXT SCHEDULED INSPECTION. ADDITIONAL INSPECTION REQUIREMENTS RESULTED FROM THE EXAMINATIONS OF THE ENGINE AND THE FRACTURE.