Probabilistic Method to Estimate the Scatter of the Fatigue Strength of Shafts in the HCF Region

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The fatigue strength of shafts is always subjected to scatter. Knowledge of this scatter is essential—especially in the high-cycle-fatigue (HCF) region—for producing safe shaft designs. Experimental determination is extremely time consuming and cost intensive. Therefore, this paper investigates the possibility of quantifying the scatter of (nominal) fatigue strength in the HCF region by means of a probabilistic model. The basis for establishing such a model is the identification of the parameters influencing the damage mechanism. In this context, the scatter-influencing parameters of external shape, surface and material condition were statistically modelled in a suitable manner. These influencing parameters act as input parameters in a local strength approach in addition to non-scattering parameters. Using a probabilistic model developed on the basis of Monte Carlo simulations, models of shafts and their surfaces can be randomly generated. The shafts so generated are submitted to local strength verifications by means of finite-element analyses of the entire failure-critical shaft surface. The stochastically generated shafts and the application of nominal stresses simulate the experimental testing at different nominal stress levels. By statistical evaluation of these fictitious nominal stress levels with respect to calculated failures and run-outs of the shafts, the probability distribution of the fatigue strength of the shaft population—and thus its scatter—can be determined. The probabilistic model is validated using a shaft population under non-scattering rotating bending load and compared with the experimentally determined scatter of the fatigue strength.


Original languageEnglish
Title of host publicationProcedia Structural Integrity
Number of pages9
Publication statusPublished - 22 Feb 2022

External IDs

Scopus 85129563418
Mendeley 3d234d07-1b51-33b7-9cd8-a6bb851d6def
ORCID /0009-0001-6766-2792/work/137557154


Subject groups, research areas, subject areas according to Destatis


  • Fatigue strength, Probabilistic method, Scatter