The pilot reported that as full power was applied on the take-off run, he heard a loud bang and the aircraft yawed to the right. He shut down the right engine and brought the aircraft to a stop. Initial inspection revealed that the right propeller assembly had failed at the hub. One blade had separated from the hub and struck the nose section of the aircraft. It was determined that the hub had failed from fatigue which had originated at the root of the blade retention thread. It was estimated that the fatigue crack had propagated over about 900 engine start cycles, and had occurred at some time after a regular inspection to check for this type of cracking.