Modeling transgranular crack growth in random 3D grain structures under cyclic loading

A probabilistic method to predict the crack formation in polycrystalline materials with a random microstructure under cyclic loading is developed. In particular, transgranular crack growth in 3D grain structures generated randomly by the Voronoï process is considered. The potential crack extension planes in the individual grains are dependent on the different grain orientations and the crystal structure of the considered material. Under cyclic loading fatigue cracks initiate and propagate along the slip planes of the crystal structure. For this reason, an energy-based criterion is used in order to describe the successive material damage under cyclic loading which is completely projected into the crack extension planes and finally causes the crack propagation. Subsequently, the computation of the crack path in a number of randomly generated grain structure models provides a raw data base in order to determine probability distributions of the number of cycles up to a pre-defined crack depth. As an input for many fracture mechanics evaluation concepts which are based on an assumed incipient crack depth, the number of cycles and the corresponding scatter band width up to a postulated incipient crack depth is of great interest.