On May 19, 2015, about 1650 eastern daylight time, a Piper PA-28-181, N597JG, was substantially damaged during a forced landing near Corryton, Tennessee. The student pilot and certificated flight instructor (CFI) were not injured. The airplane was registered to and operated by Knoxville Flyers Incorporated under the provisions of 14 Code of Federal Regulations Part 91. Visual meteorological conditions prevailed and no flight plan had been filed for the instructional flight, which departed Knoxville Downtown Island Airport (DKX), Knoxville, Tennessee, at 1430.According to the CFI, his student was performing flight maneuvers when he heard a loud "bang" from the area of the engine. This was accompanied by engine roughness and a reduced rpm. The CFI took control of the airplane and the student pilot completed the engine restart checklist in an attempt to resolve the engine roughness. The engine continued to lose power and the airplane began losing altitude. The CFI declared an emergency and informed air traffic control that he would be conducting an off-airport landing. He then performed a forced landing in a field, and during the landing sequence the firewall was damaged. A detailed postaccidetn examination of the airplane revealed the nose gear mount attachment and firewall was buckled. No further damage was noted on the airframe. An examination of the engine revealed the No. 4 cylinder head was fractured circumferentially on the head at the outboard barrel thread. The cylinder was removed and sent to the NTSB Materials Laboratory for further examination. Detailed examination of the cylinder's fracture surfaces revealed that portion of the fracture surface had relatively smooth fracture features with curving crack arrest lines, features consistent with fatigue. Examination of the cylinder revealed that there were markings cast on the cylinder near the exhaust port opening that read ECI and AEL85099 IR. A stamp near the intake port opening read 51932-14. A review of the maintenance logbooks revealed that the engine was overhauled on February 7, 2008. On May 1, 2014, the engine had a time of 1,012.5 hours since overhaul. No anomalies were reported following a compression check performed during the annual inspection. The last engine service (oil change) prior to the accident was entered May 13, 2015, with a recorded time of 1509.7 hours since overhaul. A review of Airworthiness Directive (AD) 2009-26-12, effective February 4, 2010 required repetitive inspections or inspection and early replacement of cylinders with certain ECI part number AEL85099 heads installed on Lycoming 320, 360, and 540 series engines including the Lycoming O-360-A4M engine installed on the accident airplane. The serial number for the cylinder head in this accident was outside the range of serial numbers listed in AD 2009-26-12, and therefore was not subject to the inspection and replacement requirements.