2.2 Atomic model
In order to study the characteristics of the interface between bcc-Fe
and cementite, and to reveal the origin of cumulative damage, molecular
dynamics (MD) simulations were performed using the Large-scale
Atomic/Molecular Massively Parallel Simulator (LAMMPS)
package.28 The MD model shown in Fig. 4 includes
cementite phase in the middle and bcc-Fe matrix on both sides. The
simulation model has a rectangular shape with dimensions\(L_{x}\) × \(L_{y}\) × \(L_{z}\)= 20 × 20 × 8.5 \(\text{nm}^{3}\)(~0.3 million atoms). The upper and lower boundary
layers will be applied loads along the x -axis or they -axis to generate shear deformation of the atomic model. The
length of the simulation model without boundary layers along thez -axis is specified \(L_{zz}\) = 7.4 nm . The
cementite inclusion has a length along the y -axis of\(L_{y}^{c}\) = 4.7 nm . The bcc-Fe matrix has a calculated
lattice parameter of \(a_{0}\) = 2.855 Å, and the lattice parameters of
orthorhombic cementite are a = 5.088 Å, b = 6.670 Å,c = 4.470 Å.29 The lattice orientation of the
atomic model can be expressed as\(x:{[111]}_{\alpha}\ ||{\ \left[100\right]}_{c}\),\(y:{[11\overset{\overline{}}{2}]}_{\alpha}\ ||{\ [010]}_{c}\)and\(z:{[\overset{\overline{}}{1}10]}_{\alpha}\ ||{\ [001]}_{c}\).
Here the subscripts α and c denote bcc-Fe and cementite,
respectively. The widely accepted Bagaryatskii orientation relation
between ferrite and cementite was referred and adopted
here.24,30 The interatomic potential of Fe–C proposed
by Liyanage et al.31, which is based on a modified
embedded atom method (MEAM), was adopted to describe the interatomic
force. The potential was proved to have high precision in MD annealing
and simulation.23 Periodic boundary conditions were
applied in all three directions to reduce the size limitations of the MD
simulation. Molecular statics energy minimization was carried out at
zero pressure and 0 K by using the conjugate gradient algorithm. Then MD
annealing was performed. The Nosé-Hoover isothermal-isobaric (NPT)
ensemble32-34 was used to the simulation system to
assign a temperature of 800 K and further equilibrate thermally at 800 K
for 100 ps. After that, the system was cooled down to 5 K within 50 ps.
The temperature of 5K was chosen to better observe the interface
reactions caused by shear motion rather than being dominated by
temperature.