GA Pilot reported the propeller struck an object while taxiing in a poorly marked area which resulted in damage to the aircraft.

Narrative

I completed a visual approach and landing on Runway 15 at SAF. After landing on 15 I rolled past Taxiway F and as I approached Runway 02/20 the Tower Controller issued taxi instructions to turn left on 20 and taxi to parking via Taxiways G and A. I did not hear the latter part of the transmission clearly and asked for a repeat. He repeated the instruction as I was turning left onto 02/20. During the turn I struck something; at this time I do not know what I hit but it was large enough to reach the prop and cause significant damage. I immediately informed the Tower Controller that I had hit an unknown object. He had not observed the event. During the approach to landing an airport maintenance truck requested permission to inspect the runway; he did not state why. I assume so but do not know if the sweep was completed or if the object I hit was found. My turn was across the transition paved surface between [Runway] 15 and 02/20. I do not recall any marking on this surface and I do not believe the edges of [Runway] 15 are marked. When I got the instruction to turn I believe I was too close to the surface over which I taxied to physically be able to see what was on the ground immediately in front of the aircraft. If I hit something like a runway light the runway environment at this location is very poorly marked. If maintenance knew there was a foreign object in the area they should have so stated and cleared the area before any further operations took place.