On October 4, 1997, at 0810 central daylight time, a Boeing 737- 200, N129SW, operated by the Southwest Airlines Company, as Southwest Airlines flight 418 experienced a failure of the left main landing gear outboard axle after landing on runway 31C at Midway Airport, Chicago, Illinois. The scheduled passenger flight was operating under 14 CFR Part 121. Visual meteorological conditions prevailed and an IFR flight plan was filed. There were no injuries reported by the Captain, First Officer, 3 Flight Attendants, or 45 passengers. The airplane received minor damage which was confined to the failed axle and the number one engine cowling. The flight originated at Kansas City, Missouri, at 0710 cdt. The Captain reported they touched down smoothly on the "numbers" with 40 degrees of flaps in a "very slight" crab. He reported the airplane was on the centerline as they applied reverse thrust and "moderate" braking. The Captain reported that due to his perception that another airplane was close behind him on final approach he began braking sooner then normal, but in any case "max braking" was not used. He reported that at 80 knots, as they were coming out of reverse thrust, the airplane "...lurched as it would with the anti-skid cycling and began to track right." He reported that since they were turning off the runway to the right, he let the airplane continue and he used nose steering to aim toward the turnoff. He reported they cleared the runway and proceeded to the gate. According to the Captain, once they were parked at the gate the "C" flight attendant told the flight crew that a passenger reported seeing a wheel rolling away form the airplane before they turned off the runway. A mechanic told the flight crew that the number one tire, wheel, and brake assembly was missing. The Captain reported that after he visually inspected the wheel, he returned to the airplane and called ground control. He was informed that they already had found the wheel assembly near the point where the airplane turned off the runway. Inspection of the left main landing gear revealed the outboard axle fractured just inboard of the brake assembly mounting flange The tire, wheel, and brake assembly separated as one unit from the main landing gear inner cylinder. The tire pressure was checked and found to be normal. No evidence of hydroplaning was found on the tire. The brake assembly was free and with the exception of the hydraulic line, emergency air line, and anti- skid wiring, no damage was noted. A slight dent was found in the inboard side cowl panel ahead of the reverser actuator fairing on the number one engine. The failed cylinder/axle assembly was sent to the National Transportation Safety Board Materials Laboratory in Washington, D.C., for inspection. Inspection of the assembly revealed three fatigue cracks were present in the inboard portion of the brake flange. One of the cracks originated at the surface of one of the brake flange holes. Examination of this crack revealed that the "...region immediately adjacent to the crack possessed a different surface texture from the rest of the hole. Energy- dispersive spectrometry (EDS) of this region showed high levels of both nickel and chromium, along with low levels of the elements present in the underlying base material." Further inspection of the crack revealed two additional layers between the plating and the base material. The second layer was "...consistent with untempered martensite." The third layer "...has the appearance of overtempered martensite." The report concluded that "This combination of layers in a repaired area is consistent with the surface having been heated to a temperature above the austenitic transformation temperature of the material (approximately 1600 degrees F)." See attached Materials laboratory Factual Report for further details. According to Southwest Airlines N129SW was purchased from America West Airlines in May, 1993. Southwest Airlines reported that they had not done any maintenance/repair work to the landing gear inner cylinder/axle assembly, p/n 65-46116-20. According to maintenance records, the landing gear was last overhauled by Hawker Pacifica, Inc., on July 29, 1988, and it was installed on the airplane on January 28, 1989. The cylinder/axle assembly had 25,619:39 hours since overhaul at the time of this incident. The next overhaul was scheduled for December 24, 1997.