After gear retraction during takeoff, at approximately 150' AGL, the aircrew heard a loud noise and noted the #2 engine had failed. They secured the engine, dumped fuel, and landed without further incident. An exam of the #2 engine revealed the combustion chamber outer case, PN 616315, had failed from high stress, low-cycle fatigue. The failure originated at a 4.6 inch crack at the rear drain boss to case weld. At the last shop inspection, a suspected crack was visually observed in this area. The case was prepared for non-destructive testing by grit blasting it with aluminum oxide beads to strip off nickel-cadmium plating. However, the testing did not reveal a crack. Therefore, the case was recoated with nickel-cadmium and returned to service. After the failure, an exam of the fracture area revealed the presence of nickel and cadmium (0.5 to 0.75 inch, centered on the fracture origin area). There was evidence that grit blasting (prior to non-destructive testing) had mechanically closed the previous crack, thus preventing detection. The operator revised the shop procedure to a shell blasting method.