13th International Conference on Fracture June 16–21, 2013, Beijing, China 3. Determination of fatigue design limit curves The determination of the fatigue design limit curves consists of six steps. First step: determination of measuring values. Values of threshold stress intensity factor range ( ΔKth) and two parameters of Paris-Erdogan law (C and n) were calculated according to ASTM prescriptions [14]. Fatigue crack propagation rate was determined by secant method or seven point incremental polynomial method. Values of fatigue fracture toughness ( ΔKfc) were calculated from crack size determined on the fracture surface of the specimens by the means of stereo-microscope. Second step: sorting measured values into statistical samples. On the basis of calculated test results, mathematical-statistical samples were examined for each testing groups. As its method, Wilcoxon-probe was applied [15], furthermore statistical parameters (average, standard deviation and standard deviation coefficient) of the samples were calculated. Standard deviation coefficients (standard deviation/average) of the samples were generally less than 0,2, which means reliable and reproducible testing and data processing methods. Table 3 summarizes the mathematical-statistical samples and their characteristics of experimental results on S690QL steel, as an example. Table 3. Mathematical-statistical samples and their characteristics of experimental results on S690QL steel Orientation Element number Parameter Unit Average Standard Standard deviation of the sample deviation coefficient T-S 5 n – 3,959 0,946 0,2390 L-S 5 3,735 0,273 0,0731 T-S and L-S 10 3,847 0,667 0,1734 T-L 5 2,441 0,615 0,2519 T-S 5 ΔKfc MPam1/2 100,22 6,685 0,0667 L-S 5 102,68 4,574 0,0446 T-S and L-S 10 101,45 5,553 0,0547 L-T 5 125,11 8,385 0,0670 Third step: selection of the distribution function. Afterwards it was examined, what kind of distribution functions can be used for describing the samples. For this aim Shapiro-Wilk, Kolmogorov, Kolmogorov-Smirnov and χ2 statistical probes were used at a level of significance ε = 0,05 [15-17]. It was concluded, that three parameter Weibull-distribution is the only function suitable for describing all the samples. Fourth step: calculation of the parameters of the distribution functions. Parameters of three parameter Weibull-distribution function were calculated for all the samples: ( ) ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ β − = − − α 1/ 0 x N F x 1 exp (2) where N0 is the threshold parameter, α is the shape parameter and β is the scale parameter of the three parameter Weibull distribution function. Fifth step: selection of the characteristic values of the distribution functions. Based on the calculated distribution functions, considering their influencing effect on life-time, characteristic values of ΔKth, n and ΔKfc, were selected. With the help of these values a reliable method can be proposed for determination of fatigue crack propagation limit curves: − the threshold stress intensity factor range, ΔKth, is that value which belongs to the 95 % -5-
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