On Numerical Analyses of Rail Steel Fatigue Crack Growth Data

For a given material and set of test conditions, fatigue crack propagation behavior can be described by the relationship between cyclic crack-growth rate, da/dN and the fluctuation of stress intensity factor, △K. Such test data are usually displayed in a log-log plot. At intermediate values of △K, fatigue crack-growth data fall along a straight line such that a power-law equation may be used as a curve-fit to the data. Various numerical techniques are applied in order to (1) derive the crack-growth rate and (2) determine the parameters for the power-law equation. Using data from laboratory tests conducted on rail steels, this paper explores the various numerical methods used to characterize fatigue crack-growth behavior. Tests were conducted using two different fracture-mechanics specimens (a standard compact tension specimen and a non-standard single edge notch specimen). Three different numerical techniques were applied to determine the fatigue crack-growth rate, da/dN from test data measuring crack length, a versus number of fatigue cycles, N: (1) secant method, (2) modified secant method, and (3) incremental polynomial method. Four different least squares regression analyses were then applied to determine the parameters for the power law. Moreover, the outcome of these analyses is to determine the combination of numerical techniques which yields the least amount of error when the crack-growth rate equation is integrated and compared to the original a versus N data. Fatigue life calculations performed by integrating the crack-growth rate equation demonstrate the sensitivity of predicted growth rates to the power-law parameters derived from the different regression analyses. This paper explores the various numerical methods and techniques employed to analyze fatigue crack growth data using test data on rail steels.