The student pilot reported that during the instructional flight the first landing was normal. The second approach and landing were also normal, but the airplane began to veer to the right during the landing rollout. The flight instructor took control of the airplane and performed an aborted landing. After communicating with another pilot who was on the ground at the airport, they determined that the right main landing gear wheel had separated from the airplane. On the subsequent landing, the airplane landed in the grass short of the paved runway, the remnants of the right main landing gear dug into the ground, and the airplane yawed sharply to the right. The airplane sustained substantial damage to the left wing and fuselage. Examination of the airplane after the accident revealed that the welded structure that held the wheel and wheel axle to the round landing gear leg had fractured. The lower portion of the weldment, along with the wheel and brake assembly, were found on the runway. Examination of the weldment showed a buckled portion of tube below the attachment to the round gear leg. The buckling was consistent with a hard landing occurring at some point in the life of the part. There was a complete fracture of the tube just above the buckled section and the interior of the tube was corroded. The fracture surfaces had features consistent with overstress failure. Based on the student pilot’s account and the physical evidence it is likely that the landing gear weldment had previous damage that went undetected until failure during the accident flight.