Statistical error in crack growth parameters deduced from dynamic fatigue tests

In dynamic fatigue, specimens are fractured at several stress application rates. The fracture mechanics parameters affecting the rate of crack growth are then deduced from a regression analysis in which the logarithm of fracture stress is the dependent variable and the logarithm of the stress application rate is the independent variable. A simulation approach to determine the sampling variability of crack growth parameters deduced from dynamic fatigue experiments is proposed. The simulation is readily conducted using spreadsheet type software and exploits the known sampling behavior of the slope and intercept in linear regression theory in which the response variable is gaussian distributed. This enables the results of a dynamic fatigue test to be simulated without simulating the individual fracture strengths at each stress application rate. The simulation time is therefore independent of the number of specimens tested at each stress rate. The method is illustrated with a case previously considered in the literature and plots are given showing how the precision of estimation varies with the number of test specimens fractured at each stress application rate. The additional variability due to uncertainty in the mean of the logarithm of the so-called fast fracture strength is considered. It is shown how confidence limits for one crack growth parameter may be computed when the other is assumed to be known. The use visualized for the proposed methodology is in exploratory assessments of the required sample size for dynamic fatigue experiments in which the experimentalist uses as input, pairs of parameter values believed to cover the likely region of uncertainty.