13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- Crack growth simulations were carried out in virtual microstructures (Fig. 8). The simulation is started with an initial crack on a slip band in an αp-grain. Then the crack grows autonomously through the microstructure. On the left hand side the crack propagates on a slip band, whereas intercrystalline crack growth on grain boundaries occurs on the right hand side. On the basis of these calculations a fatigue life assessment is possible. For this purpose 100 calculations were carried out for each stress amplitude considered. A starter crack of 0.2µm in length is assumed to lie in the middle of an αp grain, which is randomly selected from all αp grains exhibiting a Schmid factor of higher than 0.4. In Fig. 9 the growth of the projected crack length with the number of cycles is shown for stress amplitudes of 500MPa and 600MPa. At the lower stress amplitude most of the cracks stop at microstructural obstacles. Figure 9. Crack growth simulation results for stress amplitudes of (a) 500MPa and (b) 600MPa (ma condition). In these calculations, failure is defined to occur, when a critical value of the stress intensity factor at the crack tip is reached. This value is assumed to be 8 MPa m½. In order to take into account that a real fatigue sample forms numerous fatigue cracks and that the fastest growing crack determines fatigue life, 20 cracks were randomly selected from the 100 cracks simulated and the one that fulfils the failure criterion first defines cyclic life. Hence 5 data points result for stress amplitude. This data is depicted in Fig. 10 together with the experimentally observed number of cycles until failure for both heat treatment conditions. The agreement appears very promising. Figure 10. Comparison of observed and predicted fatigue lives for (a) ma condition and (b) sht condition. a b
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