13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- us to make several recommendations to improve the methodology used to derive cohesive laws from MD simulations. Furthermore the numerical analysis presented here helps to better understand the crack propagation behavior of X70 pipeline steel. 2. MD model and simulation procedure 2.1. EAM/FS potential function Molecular dynamics method, which considers the atomic movement is governed by Newton equations under the experience potential field which was determined by all other atoms in multi-body system, can be used to calculate system dynamic problems consisting of a large number of atoms. The interaction between the atoms can be reflected through potential function. Proper selection of the potential function types as well as the potential function parameters plays the key roles in the simulation results. As a representative of the multi-body potential, the basic idea of Embedded Atom Method (EAM) is to divide the total potential energy into pair potential among the interaction of atomic crystal and the embedded potential of nucleus, which are embedded in the electron cloud and representing the interaction of multi-body. In 1984, based on EAM potential, Finnis and Sinclair[12] developed a kind of multi-body potential with embedded energy function, hereinafter referred to as the FS-EAM potential. Like the majority of the potential functions based on EAM potential, the FS-EAM potential can be used to simulate the atomic-scale mechanisms of deformation and failure in metal materials, and the ith atom potential energy can be expressed by the equation: ( ) ( ) 1 2 i ij ij j i j i E F r r α αβ αβ ρ φ ≠ ≠ = + ∑ ∑ (1) The form of EAM potential and FS-EAM potential is consistent, but the ρ is the function of the type of atom i and j, which means the contribution of different elements on the same position of the atoms of the total electron density is not equal, and it can be given by the following expression: (2) In expression (2), ( ) ( ) ( ) 2 3 1 j ij k k ij k ij k r A R r H R r ρ = = − − ∑ (3) ( ) ( ) ( ) 6 3 1 ij ij k k ij k ij k r a r r H r r φ = = − − ∑ (4) Thereinto, ( ) ( ) ( ) 0 0 1 0 x H x x > = < (5) In which, Ak, Rk, ak, rk for constants, and R1>R2 , r1>r2>…>r6. The melting point of α-Fe was obtained by LAMMPS in order to verify the FS-EAM potential. The initial configuration of the simulated system was composed of 8×8×5 bcc-Fe cellular, a total of 640 atoms, the time step was 0.005ps, using three-dimensional periodic boundary conditions, let the system in the 2.5K relaxation 100000 steps, and then use the Nose-Hover method to keep the pressure around zero, and then elevated system temperature from T=2.5K to 2500K the rate of 4.1625×1011K/s. During the simulation, the thermodynamic results were output every 1000 steps, as shown in Fig.1 and Fig.2, respectively. The average atomic volume almost linear increase with
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