13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- frequency distribution is at least repeated 30 times to prevent load sequence effects [16]. The non-interaction material model was used. 4.1. Sensitivity analysis of the fitting coefficients on the residual lifetime To identify the dependencies of the residual lifetime a sensitivity analysis was performed by use of the software Visual-XSel 12.0 [17]. The input factors are the seven fitting coefficients C, n, p, q, ΔK1, ܥ ௧ ା and KC. The output factor is the residual lifetime. To derive the sensitivities a regression analysis was performed by use of a quadratic model with interaction effects [17]. To increase the accuracy of the regression model the output factor was transformed by the natural logarithm, which followed from the Box-Cox-transformation. The reduced model, containing only the significant factors, explains 99,8 % of the data. The relative effects of the input factors are plotted in Figure 5. As can be seen the coefficients C, n and q are inversely proportional to the residual lifetime. Figure 5: Relative effects of the fitting coefficients on the residual lifetime Furthermore, it is obvious that the coefficients q and KC are less significant and thus are not required as stochastic parameters in the stochastic crack propagation simulation. The coefficients C, n, ΔK1, ܥ ௧ ା and p are significant. That means they have to be statistically analyzed and are required for the stochastic crack propagation simulation. Although, p has a small effect it cannot be neglected, due to the interaction effects between ΔK1 and ܥ ௧ ା. The results of the sensitivity analysis are inconsistent to the statistical analysis of crack propagation data in literature [2, 10 – 14]. On the one hand it is not necessary to statistically analyze KC in terms of a residual lifetime calculation. On the other hand a statistical analysis should include the coefficients n, p and ܥ ௧ ା. 4.2. Determination of statistical secured residual lifetime The stochastic crack propagation simulations with stochastic input vectors, created by a random number generator correspond to a basic Monte Carlo simulation. Additionally and based on the results of the sensitivity analysis a second stochastic crack propagation simulation was performed in
RkJQdWJsaXNoZXIy MjM0NDE=