ACR WDB ACFT CAPT INADVERTENTLY ALLOWED ACFT TO ROLL OVER THE ACFT TOW BAR AFTER PUSH BACK FROM GATE.

Narrative

FOLLOWING PUSH BACK AND ENG START THE CAPT TOLD THE TUG DRIVER TO DISCONNECT. THE FLT ATTENDANTS INDICATED THEY HAD A PROBLEM SO THE CAPT TOLD THE GND CREW TO STANDBY. WHILE DISCUSSING THE SITUATION THE CAPT THOUGHT IT PRUDENT TO MOVE THE ACFT AS IT WAS BLOCKING THE TAXIWAY AND ASKED THE FO TO CALL FOR TAXI CLRNC. AFTER RELEASING THE PARKING BRAKES THE ACFT BEGAN TO MOVE FORWARD AT IDLE PWR AS WE WERE LIGHT-LOADED. WE FELT A SLIGHT SCUFFING; STOPPED; AND UPON INVESTIGATION REALIZED THE NOSE TIRE HAD CONTACTED THE TOW BAR. SUBSEQUENT INVESTIGATION WITH THE TUG DRIVER DETERMINED THE NOSE TIRE HAD BEEN CUT AND REQUIRED CHANGING. WE SHUT DOWN THE ENGS AND WERE TOWED BACK TO THE GATE TO CHANGE THE NOSE TIRE. THIS INCIDENT OCCURRED BECAUSE OF A BREAKDOWN IN THE NORMAL SEQUENCE OF EVENTS. SPECIFICALLY; THE FO DID NOT CHALLENGE THE CAPT WITH 'DO YOU HAVE A SALUTE?' AS IS SOP; AND THE CAPT MAY HAVE RELEASED THE BRAKES BEFORE TAXI CLRNC WAS RECEIVED. A CONTRIBUTING FACTOR MAY HAVE BEEN THE LONG DUTY DAY AT THE TIME OF THE INCIDENT. WE SIGNED-IN AT XX45 Z IN SFO; ARRIVED HNL AT XY09 Z (6 HRS 24 MIN LATER ) THEN HAD 3 HRS 6 MIN OF SIT TIME IN HNL BEFORE DEPARTING THE GATE AT OZ15 Z FOR A SHORT TRIP TO AND FROM OGG. THIS INCIDENT OCCURRED AT APPROX ZZ25 Z; OR 9 HRS AND 16 MIN AFTER INITIAL SIGN-IN. AN AMOUNT OF FATIGUE AND EAGERNESS TO COMPLETE OUR WORK DAY MAY HAVE PLAYED A ROLE IN THIS INCIDENT.