On February 15, 1999, at 1515 central standard time, a Cessna 172RG, N9506D, operated by Vincennes University, was substantially damaged during landing. The Certified Flight Instructor (CFI) reported the right main landing gear failed to extend during landing. The CFI and dual student were not injured. The 14 CFR Part 91 flight had departed Lawrenceville, Illinois, at 1500 CST on a local instructional flight. Visual meteorological conditions prevailed and no flight plan had been filed. The CFI reported that during the climb-out both pilots heard a pop from the right side of the aircraft under the right seat. The CFI performed a landing gear extension. The CFI reported the left landing gear would extend and lock, but the right main gear would extend partially and then retract simultaneously as the left main landing gear would lower and lock. The CFI reported that the manual landing gear extension procedures were tried, but the right main landing gear failed to extend. The landing gear unsafe indicator illuminated. The CFI reported he circled overhead the airport for 1.5 hours before executing an emergency landing. The landing was made with the nose wheel and the left landing gear in the down position. The right gear remained in the retracted position. The CFI reported the airplane veered off the right side of the runway during the landing rollout. The right wing and right horizontal stabilizer were damaged when they impacted the ground. The right main landing gear actuator assembly, p/n 9882015-2, was sent to the National Transportation Safety Board's Materials Laboratory for examination. The examination revealed the actuator body was cracked in two locations near the cups for the bearings. The inspection of the cracks revealed that one of the cracks had fatigue striations that originated at the corner formed by the intersection of the 2.25 inch inner-diameter surface of the gear housing and the 1.0 inch inner-diameter surface of the linear actuator portion of the actuator housing. The examination of the corner revealed the presence of circumferential scouring marks consistent with grinding or filing marks. (See Materials Laboratory Factual Report) A review of the maintenance logbooks indicated that the landing gear actuator was originally equipped on the airplane and had a total of approximately 7,000 flight hours and 21,000 cycles. There is no life or component time limit listed for the component by the airplane manufacturer.