Direct and Inverse Problems for PDEs with Random Coefficients - Abstract
Mechanical components fail under cyclic loading with stress amplitudes that are far below the ultimate tensile strength of the material. This effect is known as fatigue. The formation of fatigue cracks however is highly stochastic. In this talk, the modelling of failure probabilities for low cycle fatigue is reviewed. Using the 'first discretize then adjoin' approach, the shape gradients for a model gas turbine compressor and a turbine blade are calculated. We then use shape gradient information for failure probabilities to calculate the impact from geometric deviations in the production process to component reliability. As an example, we apply this method to white light scan data of cast turbine blades.