13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- The crack propagation on a slip band is calculated from the range of the crack tip slide displacement ∆CTSD by a power law function, which is analog to the model of [9]. A physical explanation for the mechanism of crack propagation is given in [11]. During the loading and the unloading cycle dislocations of opposite sign are created in a dislocation source in front of the crack tip and move towards the crack. Thus, vacancies are generated, which lead to a crack advance. For crack propagation on a grain boundary the crack growth is related to the range of the crack tip opening displacement ∆CTOD. 5. Virtual microstructure The simulation model can be used for a virtual optimization of the microstructure for maximum high-cycle-fatigue strength. The aim is to carry out crack growth simulations in virtual microstructures with different properties to find out, how the stage I-crack growth resistance can be improved. Therefore, an algorithm for the generation of virtual microstructures has been developed, which is based on the Voronoi technique. Initially, such a Voronoi diagram has a normal distribution of the grain diameter and is single-phased. By assigning different phases to individual grains, a microstructure consisting of primary alpha grains and colonies of alpha lamellae is created. Furthermore, the average grain size and grain size distribution is modified by dividing selected grains. Figure 6. Virtual microstructure of forged Ti6Al4V in the sht condition. In a first step a virtual microstructure has been generated, which represents the real microstructure of the ma condition shown in Fig. 1a. The virtual microstructure is shown in Fig. 6 and has a primary alpha volume fraction of 70.5%, compared to 70.9% of the real one. A good agreement is found in the mean diameter of the αp-grains and lamellar grains, which are 10.0µm and 6.8µm for the virtual and 9.9µm and 6.8µm for the real microstructure. Also the grain size distribution shows a reasonably good agreement. The slip systems in the model are chosen based on the experimental observations during the fatigue
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