13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- From Figure 6, it can be seen that most of the vacancies nucleate at the grain boundary triple point region, as shown by the arrows and circles. This is because the stress inhomogeneity between different grains causes the concentration in strain energy along the grain boundary, especially at the triple point, as can be seen in Figure 7. Hence the vacancies tend to move to these regions in order to lower the total energy of the system. On the other hand, the presence of the impurities increases the stress around them slightly. This causes a slight instability in energy in the regions around the impurities. Therefore the impurities are able to attract some of the vacancies as well, and a few red spots are found around the blue spots in Figure 6. The presence of the residue stress may increase or decrease the stress state on the sub-surface depending on whether it is tensile or compressive. This can affect the void nucleation process as well. The simulation is performed again with 10% increase in sub-surface stress due to tensile residue stress and the final vacancy position is shown in Figure 8. It can be seen that the presence of the residue stress attracts some vacancies to the surface, as shown by the arrows and the rectangle in Figure 8. Additional cracks may form at this region. Figure 8. The vacancy position at the end of the simulation with the presence of the residue stress. 4. Conclusions A finite element model that simulated the void nucleation process under thermal fatigue using the combination of finite element modeling and Monte Carlo method was presented in this paper. The simulation was first performed on a real-sized full model that contained the real time temperature and stress profile of the sample. The simulation was then carried out on a micro-scale sub-model that contained the microstructure and the imperfections, as well as different bonding and surface energies caused by the change in lattice orientation. The movement of the vacancies due to the uneven energy distributions of the model was observed and the void nucleated at the region with higher strain energies (i.e. the “weak spot”). Experimental verification of our method is underway.
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