13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- which only the five significant parameters were stochastically modeled. Afterwards, the residual lifetimes were statistically analyzed by use of the distribution fitting toolbox in MATLAB. The scattering of the residual lifetimes corresponds to a logarithmic normal distribution, Figure 6. By knowledge of the distribution function residual lifetimes can be calculated for arbitrary probabilities of failure. Furthermore it is able to determine the range of scattering ܶ ே ൌ1:ܰ ୀୀ ଵଽ %ܰ% ൌ1: 3,0 ∙ 10 0,83 ∙ 10ହ ൌ1:3,6 (13) which is equal for both stochastic simulations. So the results of the sensitivity analysis are confirmed and the coefficients q and KC are insignificant. Figure 6: Residual lifetimes of stochastic crack propagation simulation with 7 stochastic parameters 5. Conclusion In the current investigations crack propagation data of 42CrMo4 are analyzed. This includes the determination of fitting coefficients of the Forman/Mettu-equation which describes the crack propagation curve analytically. For the automated adaption of the crack propagation curve a MATLAB program was developed. Herewith, first the experimental threshold values are calculated and analytically described by use of a one criteria concept. Next the whole crack propagation curve is adapted by the Forman/Mettu-equation. Therefore, the limits of cyclic crack propagation (threshold value and fracture toughness) are required. For the determination of the optimum fitting coefficients a search algorithm with nested intervals is used. Problematically in this context is the calculation of an error value by reason that the co-domain reaches about eight decades. Furthermore, the crack propagation data is statistically analyzed. By dividing the co-domain in several intervals regression functions and confidence intervals are calculated for each domain. Therewith, discrete quantile curves for pretended probabilities of survival are calculated using interpolation functions. From the adaption of quantile curves with constant probability of survival by the Forman/Mettu-equation the corresponding fitting coefficients are determined. The statistical analysis of these fitting coefficients leads to its distribution functions. To obtain statistically secured residual lifetimes stochastic crack propagation simulations are 0,83·106 3,0·106
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