In May 2011, a derailment of a passenger train occurred in a tunnel in the northeast region of the United States. Fortunately, no serious injuries or fatalities resulted from this derailment. The probable cause of the derailment was determined to be a broken rail from a defect originating in the base of the rail. This internal rail base defect is characterized as having a crescent, thumbnail, or semi-elliptical shape. In addition, the formation and growth of this defect may have been exacerbated by corrosion.

This paper describes engineering calculations to estimate the growth rate of this type of rail base defect. These engineering calculations are based on applying the principles of fracture mechanics and beam theory. Fracture mechanics principles are applied to determine stress intensity factors for the semi-elliptical shaped defect with different aspect ratios. Stress intensity factors are then used to estimate the growth of the defect under the accumulation of tonnage from repeated wheel passages. For this purpose, the rail is assumed to behave as a beam in bending.

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