General aviation Flight Instructor reported a loose piece of concrete on the ramp at JVL struck and caused damage to the propeller during taxi.

Narrative

My student and I conducted a flight from ZZZ to JVL. A standard preflight inspection; preflight planning; and weather briefing were conducted. We had an uneventful flight up to JVL that went quite well. We taxied to the main ramp. As we were taxiing the airplane to park; the propeller sucked up a loose piece of concrete nestled in the cracked corner of where two slabs of concrete meet. This piece was invisible to us at the time and about half the size of a golf ball. Upon returning to the aircraft; during the preflight inspection for the next leg; we noticed a portion of the leading edge of the propeller had eroded. The damage did not result in the release of any portion of the propeller. The damage was isolated to one spot on one blade approximately 4 inches from the propeller tip along the leading edge.We did not contact the Ground or any obstacle or cause damage to any persons or property. The only damage occurred to the propeller itself. Rather; we taxied on a ramp with deteriorating concrete that was not visible to us at the time and encountered Foreign Object Debris (FOD). Upon further investigation; we noticed between our left main wheel and propeller a rogue piece of concrete half the size of a golf ball. Being that the engine rotates clockwise from the pilot's perspective; it makes sense the piece of broken concrete half the size of a golf ball would be kicked to the left from the pilot's perspective; where we found it between the left main wheel and propeller.I determined this propeller erosion to be a no-dispatch item. I informed the airport authority of this occurrence. The airplane was towed to a hangar and has not operated since the shutdown on the ramp at JVL when we initially arrived. The airplane will not be operated until an FAA licensed Mechanic and pilot determine it to once again be in airworthy condition after all applicable maintenance has been completed.In order to prevent an occurrence like this one from happening again; I will reach out to each respective airport or FBO we visit to inquire as to the state of their facility in terms of FOD. Additionally; my student and I will remain extra vigilant of FOD anytime we are operating in any airport environment. I will also encourage any other crew I may share a cockpit with to do the same. To correct the situation; I have informed the local airport authority to prompt airport personnel to take steps to ensure another aircraft will not encounter FOD. I have also informed Maintenance to start the process of returning the airplane to an airworthy condition by means that an FAA licensed Mechanic deems necessary. I believe my decision not to fly after discovering the erosion was the right one despite it stranding the airplane away from its home base. My personal risk management simply did not tolerate the added risk in this situation; which is what ultimately led to my decision to discontinue the lesson. I am very grateful to have learned from this occurrence that you can never be too vigilant in ensuring your aircraft's safety; especially in a ramp environment. Most importantly; I am very grateful no persons or property were hurt during our operation.