Alexander Klawonn

• The subject of this thesis is the probabilistic reliability assessment of notched metallic components under periodic constant-amplitude loads with respect to the failure mode of high-cycle fatigue. The latter refers to the crack initiation within the considered component caused by a high number, typically millions, of load cycles characterized by their small magnitude in terms of the material's static strength. In order to estimate the probability of failure due to high-cycle fatigue for a specified component under given loads, a new empirical model based on weakest-link theory is developed which describes a probabilistic and component specific constant-life diagram with respect to the anticipated design life. A conventional, non-probabilistic constant-life diagram reflects a discrete design boundary in terms of mean stress and stress amplitude, typically based on test results with respect to unnotched coupons made from the material of interest. Its application to the design of a notched component is established by identifying the stress conditions at the component's hot spot with those acting in the smooth coupons during the tests, and comparing those hot-spot conditions with the design boundary described in the constant-life diagram. Disregarded influences, such as notch and statistical size effect have to be incorporated by respective correction factors. The proposed probabilistic model on the other hand describes a continuous field of failure probabilities in the design stress plane, taking into account not only the hot-spot stresses, but the entire cyclic stress field acting throughout the component. In this way, the methodology directly accounts for notch and statistical size effects. Responsible for providing this greater scope is the weakest-link concept, which represents a non-local stochastic approach for quantifying the failure probability of loaded solids. The four model parameters can be calibrated with fatigue test data sets containing entirely unrelated test results on arbitrary specimen geometries, obliterating the constraining need for test data following staircase or probit schemes. This work contains the formulation, analysis, validation and application of the proposed model. After its introduction and a comparison with existing methods, it is analyzed in terms of its numerical properties when applied to finite element models, its efficient calibration and the corresponding model uncertainty. The validation is split into two parts. In a first analysis, the model is fitted to test data, containing results on several types of notched specimens, reflecting predominantly elastic material behavior. In a second step, this restriction is lifted and the model is used in order to predict the failure behavior of notched test specimens experiencing notch root plasticity due to high mean stresses. In both validation studies, the derived model predictions are, for the most part, well in line with the experimentally observed failure behavior of the test specimens. Finally, the applicability of the proposed probabilistic methodology in a design context is demonstrated on the example of a gas turbine compressor blade and the corresponding compressor stage.