A319 FLT CREW OVERSPD THE FLAPS DURING APCH TO ORD.

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DURING BASE TO FINAL TURN; FO INDICATED THAT HE WANTED FLAPS 2 DEGS EXTENDED BY HOLDING OUT 2 FINGERS. NORMALLY; BEFORE EXTENDING FLAPS; I ALWAYS XCHK THE AIRSPD INDICATOR TO ENSURE WE ARE BELOW THE APPROPRIATE EXTENSION SPDS; BUT FOR SOME REASON THIS TIME I DIDN'T. I EXTENDED THE FLAPS TO POS #2 AND IMMEDIATELY REALIZED THAT WE WERE TOO FAST FOR POS #2; SO I RETURNED THE HANDLE IMMEDIATELY TO POS #1. I'M NOT SURE HOW MUCH THE FLAPS EXTENDED BEYOND POS #1; BUT WE DID GET A FLAP OVERSPD WARNING THAT LASTED 2 SECONDS. WE WERE AT 205 KIAS AT THE TIME WHICH WAS A 5 KT OVERSPD. REMAINDER OF APCH WAS UNEVENTFUL. ON GND; WE ENTERED A MAINT WRITE-UP AND BRIEFED THE MECHS THAT WE HAD A 5 KT FLAPS 2 DEG OVERSPD FOR 2 SECONDS. THEY PERFORMED THE REQUIRED INSPECTION. I BELIEVE THAT FATIGUE WAS CONTRIBUTING FACTOR TO THIS MINOR INCIDENT. WE HAD A VERY LATE NIGHT BEFORE THIS FLT AS WE ARRIVED IN OAK AT XA30 (HOME TIME) AND I WAS UNABLE TO GET TO SLEEP UNTIL XC00. AT XG30 I COULD NOT SLEEP ANY LONGER SINCE MY BODY CLOCK IS NOT USED TO SLEEPING SO LATE THROUGH THE DAY. THIS RESULTED IN ONLY 5.5 HRS OF SLEEP FOR ME AFTER A 12 HR DUTY DAY. LOOKING BACK NOW; THE SIGNS OF FATIGUE WERE VERY SUBTLE; YET PRESENT. DURING THE FLT I HAD DIFFICULTY REMEMBERING OUR FLT NUMBER WHILE PERFORMING THE RADIO WORK AND MY FAILURE TO NOT XCHK THE AIRSPD WHILE EXTENDING FLAPS WAS ALSO OUT OF THE NORM FOR ME.