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Grain refinement in a polycrystalline material resulting from severe compressive deformation was simulated using molecular dynamics. A simplified model with four square grains surrounded by periodic boundaries was prepared, and compressive deformation was imposed by shortening the length in the y direction. The model first deformed elastically, and the compressive stress increased monotonically. Inelastic deformation was then initiated, and the stress decreased drastically. At that moment, dislocation or slip was initiated at the grain boundaries or triple junction and then spread within the grains. New grain boundaries were then generated in some of the grains, and sub-grains appeared. Finally, a microstructure with refined grains was obtained. This process was simulated using two types of grain arrangements and three different combinations of crystal orientations. Grain refinement generally proceeded in a similar fashion in each scenario, whereas the detailed inelastic deformation and grain refinement behavior depended on the initial microstructure.

The microstructures of metallic materials determine the mechanical properties. Thus, controlling the microstructure is important in materials processing. Heat treatments such as annealing, quenching, and tempering have long been used for this purpose, and various advanced techniques have been developed. These processes result in phase transformation along with grain refinement or coarsening, allowing both the phase and grain size to be controlled. However, since heat treatment requires large equipment and significant energy inputs, alternative methods are desired. One such alternative is mechanical processing, and various mechanical processing methods have been developed [

To clarify the mechanism of grain refinement and develop more effective refinement processes, many types of investigations have been conducted. For example, electron backscatter diffraction (EBSD) method can be used to study the polycrystalline microstructure [

Classical MD method is applied in this study. Newton’s equation of motion for all atoms in the system is solved numerically using the following fundamental equation:

r ¨ i = 1 m i F i = 1 m i ∑ j f i j , f i j = − d ϕ i j d r r i j | r i j | , (1)

where, m_{i} and r_{i} are the mass and position vector of the i-th atom, respectively, F_{i} is the force acting on the i-th atom, f_{ij} is the force acting on the i-th atom from the j-th atom, ϕ i j is the interatomic potential between the i-th and the j-th atoms, and r_{ij} is the position vector drawn from the i-th to the j-th atoms. The following Lennard-Jones function, which is often used for general investigation of fcc materials, is applied in this study:

ϕ = 4 D ( ( R / r ) 12 − ( R / r ) 6 ) , (2)

where, D and R are energy and length parameters, respectively. This function is standardized in the non-dimensional form of

ϕ * = r * − 12 − r * − 6 , (3)

where ϕ * = ϕ /(4D) and r^{*} = r/R. All other related physical quantities such as stress and temperature are also non-dimensionalized using these standards. The values presented in this study are in the non-dimensional ones, while the asterisk notion is omitted hereafter.

The simulation model is illustrated in

boundaries parallel to the x-y plane are considered; i.e. all grains correspond to infinitely long columnar grains because of the periodic boundary in the z direction.

Compression is imposed by shortening the length in the y direction (L_{y}) at a constant rate. At the same time, the stress components σ_{xx} and σ_{zz} are kept equal to zero by adjusting the lengths in the x and z directions (L_{x} and L_{z}, respectively). Shear deformation is not considered, and the model retains its rectangular parallelepiped form.

The model size is set as 50 × 50 × 5 fcc unit cells in the x, y, and z directions, respectively. Some atoms were added or removed around the grain boundary area when constructing the initial polycrystalline arrangement. The rotation angles of Grain k (k = I, II, III or IV), θ_{k}, are set as shown in ^{−1(}1/2) is shown in the insert image in

The initially provided atomic positions are not stable sites, especially around the grain boundaries. Therefore, the configuration is relaxed for 15,000 timesteps under a stress-free condition while keeping temperature constant at T = 0.05 in non-dimensional value. Compressive load is then imposed in the y direction by decreasing the edge length L_{y} at a constant rate of ΔL_{y}/τ_{s}, meaning that the total decrease in length (ΔL_{y}) is imposed in the compression period (τ_{s}, in timesteps). In this study, the values are set as ΔL_{y} = 25.0 and τ_{s} = 50,000. The length before compression, L y 0 , is approximately 73.0, although differs slightly for each model. Hence the total compressive strain is approximately 0.34. In the practical SPD processes, the stress state is more complicated including shear, and the order of applied strain reaches 1 by repeating the unit process for several times. In this

Model ID | Grain No. | ||||
---|---|---|---|---|---|

I | II | III | IV | ||

A1, B1 | +1/2 | −1/2 | +1/3 | −1/3 | |

A2, B2 | +1/2 | −1/3 | +1/3 | −1/2 | |

A3, B3 | +1/2 | +1/3 | −1/2 | −1/3 |

*values represent x of θ = tan^{−1}x.

paper, a single process with uniaxial compression is assumed for modeling the fundamental process. Temperature is kept constant at T = 0.05 using velocity-scaling method. Following the compression period, the model is unloaded by releasing the length restriction in the y-direction, and the calculation is continued for 5000 more timesteps.

The atomic configuration is initially relaxed under a stress-free condition. As shown in

An external compressive load is imposed starting at the 15,000th timestep. The length in the y direction decreases, but the atomic configuration is not affected (

At the 24000th timestep, three regions indicated by different color densities, marked by circles in

These regions spread rapidly inside the grains, and other deformation regions are successively generated. Finally, the deformation regions occupy the entire model by the 26,000th timestep, as shown in

timestep, another initiation is observed at the left-bottom corner of Grain III (marked with a red circle), and the stress stops increasing at this moment. This deformation region spreads quickly, as shown in

In the above process, two types of deformation regions are observed: linear deformation regions like those marked with yellow circles in

At the completion of the extension of the deformation region at the 26,000th timestep, some defects or mismatches in crystal orientation have been introduced. For instance, in Grain II, a vertical grain boundary is generated, as shown in

The addition of compressive load stops at the 65,000th timestep, and the stress in the y direction is released to zero. The edge length in the y direction is then slightly extended. This recovery is slight, and a permanent strain of approximately 0.31 is retained (

Simulations for other models are conducted under the same conditions.

at the 18,000th timestep, whereas no specific change in atomic configuration is observed at this moment, as shown in the snapshot at the 20,000th timestep (

The variation in atomic configuration during this stress plateau is shown in

Subsequently, the stress decreases drastically at the 26,000th timestep. At this moment, a planar deformation region is generated (

The second peak in stress for Model A3 is not remarkable compared to those in Models A1 and A2. Instead, obvious peaks and decreases in stress are repeated. The horizontal grain boundary traversing the model is quite stable and immobile. The vertical grain boundaries also become clear and remain straight after the first drop in stress, as shown in

with the exception of the horizontal clear boundary. The crystallographic relationship among grains and grain boundaries relative to the loading direction might have caused the specific behavior observed in this model.

As shown in

defects are then generated at the 25,000th timestep (marked by circles), and the stress begins to decrease at this moment. Subsequently, the deformation regions spread to the entire domain by the 27,000th timestep, when the drop in stress is completed.

In Model B3, as shown in

the stress plateau followed by the spread of planar deformation regions with a drastic decrease in stress. Therefore, the difference in peak stress is attributed to the structures of the grain boundaries: when one of the grain boundaries is easy to become a source of the linear defect or dislocation, the model is easy to yield and the peak value in stress becomes lower.

Microstructural changes of a polycrystalline material as a result of severe compressive deformation were simulated using molecular dynamics method. A simplified model consisting of four grains fulfilling the periodic boundary condition was prepared. Two types of grain arrangements and three combinations of crystal orientations were applied. The results obtained are summarized as follows. Following elastic deformation, yielding occurs in some of the grains. The source of the yielding is linear defects initiated at grain boundaries and planar deformation regions which are often generated at triple junctions. When the linear defects or dislocations are generated, the stress stops increasing and tends to remain constant, even as the number of dislocations increases. When a planar deformation defect or slip occurs, the stress decreases drastically until the deformation region extends to the entire model. New boundaries dividing the original grains into two or more grains then appear, and a refined microstructure containing various grain sizes is obtained. The first peak stress depends on the grain arrangement and crystal orientation relative to the loading direction, for which grain boundary structure is considered to be dominative.

The following points remain unclarified: the detailed relationship between the initial microstructure and yield stress; the effect of grain boundary structure on defect generation; the relationships between the initial microstructure and the characteristics of refined grains (size, shape, and distribution); and the change in material properties resulting from the grain refinement. These points will be investigated in future works using the present model, which was validated in this study. The model and method will be applicable to more practical problems for various materials including alloys and composites by using appropriate potential function. Comparison with the experimental results will also become available by accomplishing fully three-dimensional modeling.

Uehara, T. (2017) Molecular Dynamics Simulation of Grain Refinement in a Polycrystalline Material under Severe Compressive Deformation. Materials Sciences and Applications, 8, 918-932. https://doi.org/10.4236/msa.2017.812067