Probabilistic Schmid factors and scatter of low cycle fatigue (LCF) life

We investigated the scatter in the cycles to crack initiation for conventionally cast specimens of the superalloy RENE 80 in total strain controlled low cycle fatigue (LCF) tests at 850 °C. The grains at the location of crack initiation are investigated using electron backscatter diffraction (EBSD) measurements with scanning electron microscopy (SEM). This results in determination of maximal Schmid factors for the slip system that lead to the initiation of the low cycle fatigue surface crack. It is shown using stress - life and strain - life models, that taking into account the Schmid factor considerably reduces the scatter in low cycle fatigue life estimation. This is used to propose a probabilistic model for low cycle fatigue life based on random grain orientations. Using Monte Carlo simulation, we determined the probability distribution for the maximal Schmid factor in an uniaxial stress state under isotropic random orientations of the grain. This is used to calculate failure probabilities under the above mentioned model and to compare them with experimental data. Based on extreme value statistics, it is discussed whether a high maximal Schmid factor can be considered as causally related to an early initiation of a low cycle fatigue crack and we present some rather surprising experimental evidence. In the last section conclusions are formulated and future directions of research are outlined.