The aircraft was being operated from a clay pan strip on a dry lake bed. There had been no rain for approximately 48 hours and the pilot had flown his aircraft from the strip twice in that period. On each occasion he had taxied along the strip to the west and taken off into the east. However, on this occasion, he was departing to the west and the take-off run was along the section of strip used during the previous taxying. The pilot stated that during the take-off roll, the aircraft appeared to break through the clay surface crust and drag to one side. He said that he reduced power and attempted to bring the aircraft to a full stop before it ran off the side of the strip. However, the nosewheel broke through the surface and bogged in the soft clay causing the aircraft to overturn.