13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- Figure 2. The micro-scale sub-model (left) cut out from the real-sized full model (right) The nucleation of the voids is due to the movement of the atoms and the vacancies in the material, which is in turn determined by their energy states. With the presence of the external and internal factors, the atoms move and fill in the position of their neighboring vacancies in order to lower the total energy state of the system. The continuous movement causes the nucleation of the voids and the formation of the micro-cracks. There are three types of energies that determine the total energy state of an atom, namely the thermal energy, the strain energy, and the pairing energy. The thermal and strain energy are external excitations due to the applied temperature and force respectively. The pairing energy is the energy required to excite the atom from its lowest energy state and free it out from its surrounding atoms. The pairing energy is the sum of the total bonding energy of the atom with its nearest neighbors, and is affected by the lattice orientation, the presence of the vacancies and impurities, as well as the surface condition. The external excitations rise the energy state of the atom and when they are high enough to overcome the energy barrier (i.e. the pairing energy), the atom will become unstable and move to its neighboring vacant lattice site, as shown in Figure 3. Figure 3. The movement of an atom from its original position into a vacant lattice site Atom Vacancy Distance Energy Barrier (100) (110) (111) Grain boundary Grain boundary Grain boundary (110) (111)
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