PSI - Issue 75

Marco Bonato et al. / Procedia Structural Integrity 75 (2025) 677–690

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/ Structural Integrity Procedia (2025)

Figure 6: Location of the crack initiation (left) and initiation (right) on prototypes undergoing vibration test.

3. Experimental Results and Correlation The post-processing of both the simulation and experimental results is based on the statistical analysis of the time to-failure. The datasets were analyzed using the software Weibull++ (2022 version) from HBK-Reliasoft. Three main criteria were considered to evaluate the level of correlation between the simulated and experimental points: - The plotting of the Weibull probability plot (with confidence bounds of 90%) - The plotting of the Weibull Reliability function (with confidence bounds of 90%) - The plotting of the Probability Density functions. - The contour plots of the Weibull parameters. 3.1 Reliability Parameters Estimations Reliability parameter estimation is concerned with fitting a probability of failure distribution through the simulated (or measured) life data. In this paper, the vibration fatigue life estimation are expressed by the Weibull distribution [Weibull (1939)]: ( ) = ( − ) −1 ∗ −( − ) Where p(x) is the Weibull Probability Density Function (PDF) of life x in the range (x≥γ≥0). η is the characteristic of life. β is the shape parameter (or slope). γ is the location parameter (or failure- free life if γ>0). The location parameter is used to shift a distribution in one direction or another. The location parameter defines the location of the origin of a distribution and can be either positive or negative. In terms of lifetime distributions, the location parameter represents a time shift. (This is commonly referred to as a 3-parameter Weibull curve. In the case of a 2-parameter Weibull curve, there is no location parameter, i.e. γ=0). In the following section, each iteration is compared to the experimental results. The first plot (top left) shows the life data plotted on Weibull probability paper. The solid line describes the regression line and the dotted lines the 2-sided 90% confidence bounds. This implies, with a confidence of 90%, that the true regression line will lie somewhere between these two extremities. The second plot (top right) shows an alternative view of the Weibull parameters. The contour plot describes the possible range of parameters β and η within the 90% confidence bounds. Knowledge of the confidence bounds are