13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- Table 1: Fitting coefficients of the Forman/Mettu-equation and their distribution functions Parameter ΔK1 [N/mm3/2] ܥ ௧ ା C [mm/LW] n p q KC [N/mm3/2] P = 5 % 71,0 3,1 8,6·10-12 2,5 0,65 1,1 4350 P = 50 % 55,75 3,4 1,2·10-11 2,4 0,8 0,9 4200 P = 95 % 42,0 3,83 1,8·10-11 2,3 1,0 0,7 4050 Distribution normal normal log-normal normal normal normal normal μ 56,3 3,44 -10,91 2,4 0,82 0,9 4200 s 8,81 0,22 0,0975 0,06 0,11 0,12 91,2 Figure 4: Crack propagation data of R = 0,1 and the adaption by quantile curves 4. Stochastic crack propagation simulation To perform a sensitivity analysis of the fitting coefficients and to deduce statistical secured residual lifetimes stochastic crack propagation simulations were carried out by use of the analytical crack propagation software NASGRO 6.0 [9]. In a MATLAB script random input vectors of the fitting coefficients were generated using the determined distribution functions and a random number generator. To assure a probability of failure PA = 1 % the input vectors contain of 10.000 elements, according to equation (12). For every element the MATLAB script generates an input file, starts the crack propagation simulation and reads in the residual lifetime. The crack problem is a semi-elliptical surface crack in a hollow cylinder. The cylinder is loaded by a positive constant mean stress and a reverse bending stress. The amplitude of the bending stress is defined by a load frequency distribution. The initial crack size and the load were adapted, that the
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