DA20 CAPTAIN REPORTS BRAKE MALFUNCTION THAT CAUSES ACFT TO VEER OFF THE RWY DURING ROLL OUT.

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NORMAL TOUCHDOWN ON CTRLINE AT 1000 FT MARKER. I LOWERED THE NOSEWHEEL AND CALLED FOR SPD BRAKES. COPLT EXTENDED SPD BRAKES. I STARTED TO APPLY BRAKING AND ACFT STARTED TO SLOW. THERE ARE NO THRUST REVERSERS ON THIS ACFT. SEVERAL SECONDS LATER; AS ACFT WAS SLOWING; ACFT VEERED TO THE L. I APPLIED FULL R RUDDER AND FULL R BRAKE AND RELEASED ALL PRESSURE TO THE L BRAKE AND RUDDER. I GRABBED THE STEERING TILLER AND TRIED TO TURN IT TO THE R. I COULDN'T MOVE IT. WE EXITED THE RWY AND WENT ONTO THE GRASS. THE SKID MARKS ON THE RWY SHOW THAT THE L OUTBOARD WHEEL LOCKED AND WHEN THE ACFT LEFT THE RWY; BOTH WHEELS WERE LOCKED AND DUG UP THE DIRT FOR ABOUT 20 FT BEFORE RELEASING AND ROLLING ON THE GRASS. PLEASE NOTE THAT DURING THIS WHOLE OCCURRENCE; I WAS PUSHING AS HARD AS I COULD ON THE R BRAKE BUT IT WOULD NOT RESPOND. SKID MARKS SHOW THAT THE L SIDE WAS REALLY DRAGGING AND LOCKED UP. I COULD NOT GET ANYTHING FROM THE R BRAKE OR VERY LITTLE; IF ANY. THERE WAS NO DAMAGE TO THE ACFT OTHER THAN THE R NOSE TIRE; WHICH BROKE THE BEAD AND WENT FLAT. IT DID NOT COME OFF THE RIM. THERE WERE NO INJURIES TO ANY PERSON; AND THERE WAS NO OTHER DAMAGE TO THE ACFT. ALSO; THERE WAS NO DAMAGE TO THE RWY OR RWY LIGHTS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE ACFT WAS EQUIPPED WITH ANTI-SKID BUT SHOWED NO FAULTS DURING THIS EVENT. POST FLIGHT REVEALED THAT THE LEFT BRAKE LOCKED WHILE THE ACFT WAS ON CENTERLINE; THE RIGHT BRAKE NEVER SHOWED ANY SIGN OF BRAKING OR SKIDDING. THE NOSEWHEEL SHOWED SIGNS OF STEERING SKID MARKS AS THE ACFT DEPARTED THE RWY. SHORTLY BEFORE THE ACFT CAME TO A STOP ON THE GRASS THE LEFT BRAKE RELEASED. NO DAMAGE WAS DONE TO THE ACFT HOWEVER NO MAINTENANCE HAS BEEN PERFORMED TO INVESTIGATE THE PROBLEM.