On July 18, 2020, about 0745 central daylight time, a Cessna 140 airplane, N140AB, was substantially damaged when it was involved in an accident near Arlington, Texas. The flight instructor and student pilot were uninjured. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 instructional flight. The flight instructor reported the purpose of the flight was to fly the airplane cross-country for tire repairs, and at the same time, train the student pilot in the airplane. The student pilot started the engine about 0715. The recorded weather indicated the temperature was 79° F and the dew point was 73° F. The flight instructor mentioned that since the outside air temperature was close to the dew point, they would have to be careful and cautious about carburetor icing, even if there was no visible moisture in the air. The flight instructor related a previous occurrence when he flew this airplane for the first time with another instructor. Then, the condition was almost 100% relative humidity and the carburetor heat was kept on about "10%" during the flight when at cruise power setting, and full carburetor heat at lower than cruise power. However, a rough engine or any sign of carburetor ice was not encountered during that flight. During the accident flight, the airplane's engine performed as expected during the run up. The student pilot set the carburetor heat on cold for takeoff and departed without issues. The flaps were retracted and the airplane was accelerated to best climb airspeed. The rate of climb was about 250 ft per minute and the engine was running at full power. About two minutes into the flight, the engine started to run a "little bit rough and shaky." The instructor pulled the carburetor heat on about 10% hot and left it in this position in accordance with his training for this airplane. The engine roughness disappeared, and the airplane kept climbing at the same rate. About one minute later, the roughness came back, more severe this time. The instructor pulled the carburetor heat all the way on to full hot and waited. The roughness continued and the power available was not allowing the airplane to continue the climb at the same rate. The airplane's pitch attitude was progressively lowered to maintain the airspeed, and full power was not sufficient to keep the airplane in a level flight attitude at 1,200 ft. There was no suitable area ahead for about the next 8 to 10 miles to perform an off-field emergency landing, so the instructor elected to turn back to the departure airport. He was not confident that the airplane could maintain altitude in the traffic pattern, so he elected to land on a closer runway with a quartering tailwind. During the landing roll, as the airplane slowed down, he retracted the flaps to remove any residual lift and applied the yoke "slightly diving" away from the wind. While the airplane was still moving forward at a low ground speed, the nose "suddenly" yawed very "quickly and strongly" to the right. The instructor pilot applied ailerons, elevators, and full left rudder and brake, but these did not stop the yaw. The airplane subsequently ground looped and came to rest in the grass resulting in substantial damage to the aft fuselage and tailwheel. Using the pilot's reported departure weather, the plotted relative humidity at this temperature and dew point spread was about 80%. A review of the icing probability chart contained in Federal Aviation Administration Special Airworthiness Information Bulletin CE-09-35 revealed that the weather conditions at the time of the accident were "conducive to serious icing at glide power." The operator of the airplane was asked to run the engine after the accident. The engine started and operated "normally."