On August 10, 2013, about 0700 mountain standard time, a Piper PA-28-180, N9752J, was substantially damaged during a forced landing following a partial loss of engine power during takeoff from the Mogollon Airpark, Overgaard, Arizona. The airplane was registered to and operated by the pilot under the provisions of Title 14 Code of Federal Regulations Part 91. The airline transport rated pilot, sole occupant of the airplane, was not injured. Visual meteorological conditions prevailed and no flight plan was filed for the personal cross-country flight which was originating at the time of the accident with an intended destination of Scottsdale, Arizona. The pilot reported that during takeoff from runway 21, the airplane became airborne and did not accelerate as he expected and felt that the engine was not producing full power. The pilot adjusted the mixture to full rich and switched fuel tanks with no change in performance. Subsequently, the pilot initiated a forced landing to an open area beyond the departure end of the runway. During the landing roll, the airplane struck a ravine and came to rest upright. Examination of the airplane by the pilot revealed that the left wing was structurally damaged. The wreckage was recovered to a secure location for further examination. Examination of the Lycoming O-360-A4A, serial number RL-10614-36A, revealed that it remained attached to the airframe via all its mounts. All engine accessories remained attached to their respective mounts. The top spark plugs were removed. The cylinders were examined internally using a lighted borescope and were unremarkable. The crankshaft was rotated by hand and compression was noted on all four cylinders. The top spark plugs were reinstalled. Throttle, mixture, and carburetor heat control continuity was established from the cockpit controls to the engine. The airframe fuel filter bowl was removed and contained a few ounces of fuel, which was free of debris. An external fuel source was attached to the left inlet port on the fuel selector valve. The engine was primed utilizing the carburetor accelerator pump by moving the throttle. The engine was started, warmed up, and advanced to 1800 rpm. A magneto check was conducted on each mag with a drop of about 75 RPM was noted. A drop of about 50 to 75 RPM was observed when carburetor heat was applied. The throttle was advanced to the full forward stop and the engine accelerated to about 2000 RPM. The engine began to run rough with black smoke originating from the exhaust. As the mixture was leaned to about half way from the full rich position, the engine smoothed out; however, engine RPM would not increase. The carburetor fuel screen was removed and found free of debris. The carburetor, a Precision MA-4-5 was removed and shipped to the manufacturer for further examination. No evidence of any preexisting anomalies that would have precluded normal operation of the carburetor was found. The exhaust assembly was inspected and no exhaust leaks or damage was noted prior to its removal from the engine. The forward muffler was removed from the number 1 and 2 cylinder stacks. The interior surfaces of the stacks revealed white and grey deposits consistent with normal operation. The muffler baffling, as viewed from the number 2 stack attachment, was separated from its left side attachment. A loose section of the baffling covered the exhaust port outlet. The baffling, as viewed from the number 1 stack attachment, was corroded. Loose fragments were heard moving around freely from inside the muffler. The muffler was removed from the number 3 and 4 cylinder stacks. The interior surfaces of the stacks revealed white and grey deposits consistent with normal operation. The muffler baffling, as viewed from the exhaust port and the number 4 stack attachment was separated from its left side attachment. The baffling as viewed from the number 3 stack attachment was distorted and damaged. There were no loose fragments heard from inside the muffler. No additional mechanical anomalies that would have precluded normal operation were observed with the recovered engine. Review of the airframe and engine maintenance logbook records revealed that the most recent annual inspection was completed on April 1, 2013, at an airframe total time of 4,498 hours, engine time since overhaul (TSOH) of 1,257 hours. Within the annual inspection logbook entry for the engine, it was noted that the exhaust system was inspected. At the time of the accident, the airplane had accumulated about 8 hours of operation since the annual inspection. No entries depicting replacement of the exhaust system were located throughout the engine or airframe logbook records. The Piper Cherokee Service Manual states in part "…a very thorough inspection of the entire exhaust system including exhaust heater shroud assembly, muffler and muffler baffles, stacks, and all exhaust connections and welds must be accomplished at each 100-hour inspection. The possibility of exhaust system failure increases with use. It is recommended that the system be checked more carefully as the number of hours increase, therefore inspection at the 700 hour period, that the exhaust system has been in use would be more critical than ones in the 100 hour period. The system should also be checked carefully before winter operation when the cabin heat will be in use. NOTE: Piper recommends that all PA-28 airplanes be fitted with a new muffler at or near the 1000 hour period of which the muffler has been used."