The pilot of the tailwheel-equipped airplane reported that, he performed a precautionary landing in a bean field due to a rough running engine. The pilot then had an Airframe & Powerplant mechanic look at the airplane and perform multiple engine runups. The rough running engine was determined to be caused by carburetor ice. The pilot then loaded his two passengers into the airplane and attempted to takeoff from the bean field. He added that, as the airplane began to gain altitude, the airplane approached the end of the open bean field. Subsequently, the landing gear encountered corn stalks in an adjacent field, descended into the corn field and came to rest inverted. The airplane sustained substantial damage to both wings, the fuselage and empennage. The pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.