13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- potential energy of an atom i is expressed by ∑ ∑ ∑ ≠ < = − + = j i ij i i i i j j i i f r F u ( ) ( ), |) (| ({ }) ρ ρ φ r r r (3) Where| ri –rj |is the distance between atoms i and j, Φ is a pair-wise potential function, f(r) is the contribution to the electron charge density ρi from atom of j at the location of atom i, and F(ρi) is an embedding function that represents the energy required to place atom i into the electron cloud. Since the electron cloud density is a summation over many atoms, usually limited by a cutoff radius, the EAM potential is a multibody potential. The EAM of alpha iron used in present study comes from ‘Interatomic Potentials Repository Project’ which is included in potentials base of LAMMPS. 3.2. Simulation models and methods The initial α–Fe planes were assumed to be perfect single crystal lattice having bcc structures. The simulations were performed on major slip plane of bcc iron. Edge crack model was chosen to analyze the crack growth characteristics in an infinite domain under plane strain condition acquired by perform periodic boundary condition in z dimension. The x-direction was defined forward in the crack plane, and the z-direction in the thickness direction. The schematic of the molecular dynamics simulation is shown in Figure 1. Three-dimensional model with a small thickness in order to reduce the calculation and to avoid the difficulty of the data analysis is constructed. The sizes of the simulation box were 858×297×5.7 (Å). It consisted of over 120000 atoms. There were two layers of transitional regions around the simulation domain. These layers were used to alleviate the effect of the boundaries and were not included in final results processing. The maximum positive and minimum negative strain loads were applied on the top and bottom boundaries at a certain strain rate to keep the crack faces apart (Figure 3). In all simulations, the initial crack was placed at the midpoint of the left side of the simulation lattice. And all related data including time step, coordinates, velocities, displacements, stresses, strains, temperatures etc. were saved. The initial α–Fe planes are perfect single crystal lattice having bcc structures was assumed in present paper. The simulations were performed on slip plane of bcc iron. The edge crack specimen geometry model adopted for the present simulation is illustrated in Figure 1. The initial crack was introduced by shutting off pairwise interactions between two slabs of atoms in perfect crystal to effectively create a sharp crack. The ratio of the initial crack length to the width of the specimen was a0/w = 0.067. The crystal orientation of the initial cracks in crack propagation system (0 0 1)[010] was concerned and illustrated in Figure 2. Crack growth simulation was implemented by moving the atoms with the linearly varied velocity along y dimension in accordance with a given constant deformation rate, which is shown in Figure 3. The strain rate used in simulation was 0.005. A typical simulation cell with a pre-crack is drawn in Figure 4. Surfaces on two transitional layers located at bottom and top constructed to alleviate the boundary effects were set free. The deformation loading was applied along y-direction perpendicular to the crack plane and varies linearly with y coordinate. The constant strain rate loading was applied in such a way that the velocity is linearly distributed along the y-direction in core region. The velocity in transitional layer at the bottom and the top were set to the maximum positive and minimum negative value, respectively. The used loading method can effectively eliminate the stress oscillation and impact effect produced by acting sudden load. In the z-direction the periodic boundary condition was assigned to keep an expected plane strain state. Another loading type used in simulation was to act forces directly on atoms in loading layers. External forces were applied in the way distributed in top and bottom surface boundary layers. The sizes of the simulation box are 578×458×2.86 (Å) which contains about 65000 atoms. Time step 0.002 ps was utilized in simulations. The cyclic loading and unloading timesteps was 20000. The initial crack length corresponds to 17.2,57.2 Å.
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