PSI - Issue 37

Sebastian Vetter et al. / Procedia Structural Integrity 37 (2022) 746–754 Sebastian Vetter / Structural Integrity Procedia 00 (2019) 000 – 000

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In addition to the scattering parameters described, the probabilistic model is also based on parameters that are assumed to be non-scattering (see Table 2). These parameters assumed to be non-scattering also include the measurement area for hardness . The other required areas ℎ , and are calculated in the probabilistic model based on the parameters already mentioned and the FEA parameters. Table 1. Scatter-influencing parameters of shaft population used in the present paper. Scatter-influencing parameter Mean value for the population ̅ ̅ Scatter of mean values for the population ̅ Shaft inherent variation coefficient ℎ External shape Diameter 36.0065 mm 0.0175 - Radius 187.368 mm 0.25 - Surface condition Depth 6.05 µm 1.29 µm 0.089 Radius 217.0 µm 41.9 µm 0.084 Material condition Local hardness 317.6 HV 9.1 HV 0.039 Table 2. Non-scatter-influencing parameters of shaft population used in the present paper. Non-scatter-influencing parameter Value Young's modulus (MPa) 212,000 Poisson’s ratio 0.3 Fatigue threshold for macrocracks (Nmm – 3/2 ) ∆ , ℎ 220 Geometry factor 1.12 Mean stress effect 0.135 Plastic strain fatigue limit , , 0.00026 Strain-hardening exponent ′ 0.1633 Statistical support factor 1 Surface notch width (µm) 105.3 Measurement area for local hardness (mm 2 ) 0.028 5.2. Results The probabilistic model can be executed with the help of the determined influencing parameters of the shaft population described in Table 1 and Table 2. In this case, 1000 components are simulated with a stress multiplier of 0.99. The histogram of the fatigue strengths of the simulated components is shown in Fig. 4 (a). Regressing the survival probabilities per nominal stress level assuming a normal distribution, a mean value and a standard deviation of the fatigue strength are obtained according to Table 3. In the experimental investigations using the horizon method with a limit of 10 million cycles, the mean value and standard deviation of the fatigue strength could be determined assuming a normal distribution according to Table 3. A number of 29 specimens were tested at two stress levels.

Table 3. Results of probabilistic model and experimental test for the investigated shaft population. Distribution parameter Probabilistic method Experimental test Mean value of fatigue strength ̅ (MPa) 356.1 353.8 Standard deviation of fatigue strength (MPa) 15.2 19.3

The regressed normal distributions of the fatigue strength using the probabilistic method and those determined experimentally are shown in the probability plot in Fig. 4 (b). Comparing the distribution parameters, it can be seen that the deviation of the mean values is only ∆ ̅ = 0.7 % and the deviation of the variation coefficients is ∆ ≈ 21 %