On June 24, 1993 at about 0920 eastern daylight time, a Cessna 172, N7817X was substantially damaged following a collision with terrain during a precautionary landing near Statesville, North Carolina. Neither the private pilot, nor his passenger were injured in the accident. The aircraft was being operated under 14 CFR Part 91 by the pilot. Visual meteorological conditions existed at the time, and a visual flight rules flight plan was in effect for the personal flight. The flight departed Siler City, North Carolina at about 0830, and was destined for Morganton, North Carolina. The pilot stated that following a descent, the engine lost power gradually, which he attributed to carburetor icing. He applied carburetor heat for approximately 3 seconds on two separate occasions. However, he said, when the throttle was increased, the problem got worse. He elected to attempt a precautionary landing in a corn field. The aircraft struck a fence and flipped over. The Icing Probability Chart shows at a temperature of 71 degrees fahrenheit (F) and a dew point of 63 degrees (F), serious icing conditions exist at glide power.(See Attached Chart.) The pilot failed to complete and return NTSB Form 6120.1/2, which was delivered with cover letter on July 1, 1993.