AFTER THE MAIN GEAR TOUCHED DOWN, THRUST LEVERS WERE PLACED IN THE IDLE REVERSE POSITION. ONCE THE AIRCRAFT'S NOSE GEAR CONTACTED THE RUNWAY, BRAKING AND FULL REVERSE THRUST WAS APPLIED. THE AIRCRAFT STARTED TO DRIFT TO THE LEFT OF THE RUNWAY CENTERLINE. THE PILOT APPLIED ASYMMETRICAL BRAKING WITH NO CHANGE IN DIRECTIONAL CONTROL. THE PILOT THEN COMBINED THE USE OF ASYMMETRICAL BRAKING WITH ASYMMETRICAL REVERSE THRUST. AS A FINAL EFFORT TO PREVENT THE AIRCRAFT FROM DEPARTING THE RUNWAY, THE CAPTAIN USED THE TILLER. THE AIRCRAFT CAME TO REST ON A GRASSY AREA BETWEEN THE PARALLEL RUNWAYS. THE AIRCRAFT IS EQUIPPED WITH 'LIGHTWEIGHT' CLAMSHELL THRUST REVERSERS. THE RIGHT HAND THRUST REVERSER ON THE NUMBER 2 ENGINE WAS FOUND FAILED IN THE OPEN (FORWARD THRUST) POSITION. THRUST REVERSER LIGHTS DID NOT INDICATE ANY ABNORMALITIES. AN OVERSTRESS FRACTURE OF THE LOWER INNER HINGE WITH A FATIGUE FRACTURE THROUGH THE FLANGE OF THE UPPER OUTER HINGE WAS FOUND BY METALLURGICAL EXAMINATION.