PSI - Issue 75

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

689 13

/ Structural Integrity Procedia (2025)

Table 1. Reference values (Weibull parameters and reliability) for correlation.

Dataset

Beta

Eta (minutes)

R50% (minutes)

B10 (minutes)

Experimental

7.3

45.5

43.2

33.4

FEA #1

1.7

144.5

116.0

37.5

FEA #2

4.0

53.2

48.5

30.2

FEA #3

4.0

47.1

42.9

33.9

FEA #4

6.9

45.6

43.2

32.9

The analysis of time-to-failure in case of wear-out mechanisms such as vibration fatigue are better expressed by the Weibull 3-parameter distribution [Bonato (2024); Strzelecki(2021)]. Fatigue is a cumulative effect, and one might reasonably expect a “time of latency” before such degradation occurs, which is the so - called “free failure period” defined by the location parameter ( ) of the Weibull distribution (see Equation 1) In this study, it was decided to rely on the Weibull 2- parameters distribution, to avoid “compatibility issues” between the experimental and simulation results. It is inappropriate to correlate the shape parameters of a Weibull 2 parameter vs 3-parameter distribution [Halfpenny (2019)]. Moreover, in the automotive industry, it is the Weibull 2 parameters which is used for reliability assessment. Table 1 shows that the more one is able to tune the FEA model with the appropriate material parameters, the more the simulated life results converge towards the experimental measurements. A similar conclusion can be reached by comparing the statistical plots. In general, if the simulation results lie mostly within the 90% confidence bounds of the test results, the simulation is correlated. Again, the more realistic the material parameters (from iteration #1 to #4), the closer the FEA results are to the experimental data. In particular, the plots (from Figure 7 to Figure 10) shows that: 1st FEA iteration: when the FEA model is based on average material data for aluminum alloys currently used in the automotive industry (case when the material card is unknown, the simulation results are badly correlated to the experimental measurement; In particular, the scatter is significantly higher (Weibull beta = 1,7 compared to beta = 7.3 from the physical prototypes). Nevertheless, it is noticed that the population shows a good correlation in the zone of low fatigue life, at a high level of reliability (around 10% probability of failure). For even higher reliability, the FEA results are more conservative than the experimental data. This results shows that within the boundary conditions of automotive reliability (1% to 10% probability of failure), the stochastic simulations based on generic material parameters are still useful, because they permit the validated phase of design validation with an acceptable level of conservatism. 2nd FEA iteration : This run of simulation is performed by introducing a new parameter for the surface finishing (on nCode DesignLife software, the Roughness value is based on machining and sandpaper that was for the surface finish on the specimen). In this case the results show an acceptable level of correlation only for reliability level > 50%. The contour plot shows that there is no overlap between the Weibull parameters of the experimental vs simulated time-to-failure, therefore overall the correlation is not good. 3rd FEA iteration: a much better level of correlation is achieved by keeping one FEA parameter related to the material SN curve: the fatigue exponent Basquin's b = 8. Here for the first time it is possible to notice a "generic" level of statistical correlation, since there is an overlap between the contour plots of the two populations (Figure 9). 4th FEA iteration; in this final iteration, the Basquin b fatigue exponent is kept unchanged (as in #3, b = 8) but moreover the value of the damping is tuned to the experimental values measured during the preliminary measurements (research of natural frequency, see Section 2.4.