A fatigued B757-200 flight crew oversped the flaps when performing a go around from an unstabilized approach.

Narrative

We initially went through the localizer and turned back left to intercept. The aircraft was a bit high once back on final approach. The aircraft was configured to gear down flaps 20 and we began the descent. At 500'; flaps 30 and 160 knots the aircraft was not slowing and a go around was accomplished. As go around thrust was applied the First Officer noted a momentary airspeed of 170 knots while flaps and gear were being selected. The maximum airspeed for flaps 30 is 162 knots. We were radar vectored with right traffic back for another approach which was accomplished to a normal landing. The event occurred due to the fact that we initiated a go around at 160 knots with less margin for error combined with the fact we were all very tired after a long day of 12:55 of flight and 17:30 of duty.I made an entry in the AML of the flap overspeed; noting airspeed and flap configuration. A phase 1 flap inspection was accomplished by our mechanic. No damage was found. As a preventive measure I suggest no more 12 plus hours of flight and long duty days.