13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- α-Ti. y[2110] z[0001] x[0110] o 1) Figure 1. The elemental crystal structure of α-Ti 2 EAM/alloy potential function Zhou[11]have developed a procedure to generalize the conventional EAM potentials and their cut-off distance. These potentials are well fitted to basic material properties such as lattice constants, elastic constants, modulus of bulk. In the generalized EAM (EAM/alloy) potential, the total energy E of the crystal can be expressed as: ( ) ( ) , , 1 2 ij ij i i i j i j i E r F φ ρ ≠ = + ∑ ∑ (1) Where φij represents the pair energy between atoms i and j separated by rij, and Fi stands for the embedding energy to embed an atom i into a local site with electron density ρi. ρi can be calculated using: ( ) , i j ij j j i f r ρ ≠ = ∑ (2) With fj(rij) the electron density at the site of atom i arising from atom j at a distance rij away. Alloy EAM potentials can be constructed from elemental EAM potentials if the potentials are normalized and unified cutoff functions are used. To fit such an EAM potential set, the generalized pair potentials were chosen to have the form: ( ) 20 exp 1 exp 1 1 1 e e e e r r A B r r r r r r r α β φ κ µ − − − − = − + − + − (3) Where re is the equilibrium spacing between nearest neighbors, A, B, α, β are four adjustable parameters, and κ , µ are two additional parameters for the cut off[12]. The electron density function is taken with the same form as the attractive term in the pair potential with the same values of β, and µ, i.e., ( ) 20 exp 1 1 e e e r f r f r r r β µ − − = + − (4)
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