13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- critical resolved shear stress and the critical accumulated slip [10]. However, the dynamic void nucleation process under the applied loads was unable to be observed using the above methods. Monte Carlo method, based on repeated random sampling algorithm [11], can be used to predict the grain size and structure [5], the crack growth and propagation [12, 13], the fatigue life and S-N curves [14, 15]. Monte Carlo method can also be used to simulate the diffusion and nucleation of the atoms under the applied loads (e.g. current, temperature, stress, etc.) [16-18]. To study the dynamic void nucleation and crack initiation process under fatigue, a novel way was introduced in this paper by incorporating the Monte Carlo method into the finite element models. Using this method, the dynamic motion of the atoms and vacancies before, during and after certain load cycle under the effects of temperature, stress, microstructure and surface condition forces and can be examined. The crack is assumed to initiate at the location of the void nucleation. Pure Al samples are used in this work. 2. Simulation Setup The simulation is first performed on a dog-bone Al sample with the dimension shown in Figure 1. The chemical composition and the material properties measured from the sample are shown in Table 1 and 2 respectively. Figure 1. The dimension of the Al sample Table 1. Chemical composition of the Al sample ppm (parts per million) Al Si Fe Cu Mn Mg Cr Ni Zn Ti Ga Pb B V Zr 99.996% 6.20 2.20 0.10 3.90 1.00 1.20 0.30 2.70 1.10 5.50 0.10 0.80 2.40 0.80 Table 2. Physical properties of the Al sample Young's Modulus (GPa) Poisson's Ratio Density (kg/m3) Thermal Expansion (1/oC) Yield Strength (GPa) Thermal Conductivity (W/m·oC) Specific Heat (J/kg·oC) 70 0.35 2700 2.24×10-5 280 221.75 899.56 The initial temperature of the sample is assumed to be 27 oC and it is placed inside an oven with a constant temperature of 100 oC and heated up for 10 minutes. The convection heat transfer coefficient of the sample is 25 W/m2·oC [19]. A force of 5 kN is applied at one side of the sample and the other side is fixed and is not free to move. Finite element SOLID 69 and SOLID 45 is used in the thermal and structural-thermal simulation in ANSYS respectively. To include the microstructure and the surface effects, a 70 µmx60 µmx30 µm sub-model is cut out from the central surface of the dog-bone sample (i.e. the full model), and the grain structures are added to the sub-model according to the EBSD map of this surface. The meshed full model and sub-model are shown in Figure 2. The nodal temperature and stress values extracted from the full model simulation are used as the boundary conditions for performing the sub-model simulation.
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