As for magnesium (Mg) alloys, it has been noted that they are inferior to plastic deformation, but improvement in the mechanical properties by further refinement of grain size has been recently suggested. It means the importance of atomistic view of polycrystalline interface of Mg crystal. In this study, to discuss the deformation mechanism of polycrystalline Mg, atomistic grain boundary (GB) models by using coincidence site lattice (CSL) theory are constructed and are simulated for their relaxed and deformatted structures. First, GB structures in which the axis of rotation is in
In recent years, improvement of fuel efficiency of the transportation equipment is demanded to reduce burden on the environment. Therefore, there is an issue concerning weight saving of the transportation equipment. For those purposes, one of the materials that attract much attention of researchers now is magnesium (Mg) alloy. Mg alloy is the lightest metal in practical use and its performance in recycling is noteworthy [
Regarding deformation mechanism of Mg crystal, there have been much efforts by many researchers in the world. By using sophisticated experimental apparatus and methods such as electron back-scattering diffraction (EBSD) analyzing technique or transmission electron microscopy observation with atomistic resolution, change of crystal orientation in single crystal and nucleation of defects including twin boundary and dislocation during deformation have been researched extensively [
In this study, to analyze the deformation mechanism of polycrystalline Mg, we first produce periodic GB models made up of Mg crystal in which the axis of rotation is
In this study, we use molecular dynamics (MD) method. This method is based on atomic dynamics and is to solve Newton’s equations of motion atom-by-atom simultaneously, by numerical integration over time. The basic equation is given by
All the GB models of Mg crystal studied in the present study are constructed by using coincidence site lattice (CSL) theory [
GB model analyzed by CNA.
We choose several rotation angles
Geometrical conditions of GB models (As GB model, the most energetically stable one is chosen.)
Tilt (rotation) axis | |
Lattice constants [nm] | 0.3202, 0.5228 |
Model | Misorientation angle | | Cell size in | The number of atoms |
---|---|---|---|---|
A | 11.7 | 97 | 10.30, 3.33, 25.19 | 36816 |
B | 23.1 | 25 | 10.46, 3.33, 22.35 | 33240 |
C | 30.5 | 58 | 9.95, 3.33, 19.42 | 27360 |
D | 44.4 | 14 | 11.07, 3.33, 20.21 | 31680 |
E | 63.0 | 11 | 12.01, 3.33, 20.79 | 35424 |
F | 78.5 | 10 | 10.75, 3.33, 20.05 | 30888 |
G | 88.8 | 49 | 11.21, 3.33, 21.88 | 35040 |
H | 91.2 | 49 | 10.98, 3.33, 22.37 | 34848 |
I | 101.5 | 10 | 10.12, 3.33, 21.41 | 30840 |
J | 117.0 | 11 | 11.04, 3.33, 23.75 | 37584 |
K | 122.9 | 35 | 10.71, 3.33, 21.84 | 33168 |
L | 135.6 | 14 | 11.86, 3.33, 22.03 | 37128 |
M | 146.0 | 35 | 10.94, 3.33, 21.28 | 33120 |
These geometrically obtained initial atomic configurations of periodic GB models are provided adequate structural relaxation by MD simulation, so that energy and stress components of the total system are just thermally equilibrated. After that, a GB excess energy
After structural relaxation, GB models are subjected to tensile loading in the
Details of an adaptive tensile loading method were described in [
Structural analysis of atoms is mainly conducted by common neighbor analysis (CNA) [
Calculation conditions for MD simulation.
Temperature | 10.0 |
Relaxation time | 50.00 |
Time step | 1.0 |
Strain rate | 50.0 |
As mentioned, Mg crystal preferentially slips on basal plane as schematically shown in Figure
Schematic of deformation mechanism possible in magnesium (Mg) crystal.
Slip deformation
Deformation twinning
In Figure
Relationship between
Example of the structural unit of GB for (a) model F and (b) model J.
In Figure
GB structures analyzed by CNA and potential energy attributed to each atom for models C, D, E, F, I ((a) and (b)) and for models J, K, L, M ((c) and (d)), respectively.
In contrast, as shown in Figure
GB structure consisting of edge dislocations (analyzed by CNA, for model A).
In Table
Relationship between GB models and identified deformation mechanisms.
Model | Nucleation point of dislocation emission | Identified deformation mechanism |
---|---|---|
A | Edge dislocation | Pyramidal slip |
B | Grain boundary | Twin |
C | Grain boundary | Twin |
D | Grain boundary | Twin |
E | Grain boundary | Twin |
F | Grain boundary | Twin & Basal slip |
G | Grain boundary | Basal slip |
H | Grain boundary | Basal slip |
I | Grain boundary | Basal slip |
J | In grains | Prismatic slip |
K | Grain boundary | Prismatic slip |
L | Grain boundary | Prismatic slip |
M | Grain boundary | Prismatic slip |
Deformation process during tensile test analyzed by CNA (model A;
In models “D”, “F”, and “I”, as category of high-angle GB, atoms inside GB region are rearranged and result in new dislocation emission. An example of this mechanism can be seen in Figure
Deformation process during tensile test for (a) analyzed by CNA. (b) Potential energy distribution (model F;
In other models (“B”, “C”, “E”, “G”, “H”, “K”, “L”, and “M”), dislocations are also released from the GB region. However, in these models, it is likely that any process of dislocation emission does not affect the equilibrium structure of the GB in itself. A visible example of this process is shown in Figure
Deformation process during tensile test (model K;
Only model “J”, as shown in Figure
Deformation process during tensile test (model J;
In the present work, we created grain boundary (GB) models of hexagonal Mg crystal for molecular dynamics (MD) simulation, in which the coincidence site lattice (CSL) theory with axis of rotation
From GB structures after relaxation calculation, we obtained correlation between the energy and the structure of each GB. Typical difference in local arrangement of atoms composing GB structures is found between low- and high-angle GBs, like other metals. In particular, some GBs possess a special atomic arrangement (structural unit) around the GB plane with some periodicity.
For tensile simulations, we also found a difference in dislocation emission mechanisms between low- and high-angle GBs. High-angle GBs work as a nucleation point of dislocation emission, but there is a special GB in which slip occurs rather inside grains, not in GB region.
Those results are for relatively simple GB structures, so there should be many other asymmetrical or three-dimensionally connected curved GBs in real system. Polycrystalline GB models will serve somewhat other insights [
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This work was supported by JSPS KAKENHI Grant no. 16K05994 (2016–2018, Grant-in-Aid for Scientific Research (C)) and by the Kansai University Grant-in-Aid for Progress of Research in graduate course, 2017 (Apr)-2018 (Mar). The authors also acknowledge the financial support from Nippon Steel & Sumitomo Metal Corporation.