T. LI et al.: EFFECTS OF DIFFERENT LOADING DIRECTIONS ON THE ORGANIZATION AND PROPERTIES OF MAGNESIUM ... 699–706 EFFECTS OF DIFFERENT LOADING DIRECTIONS ON THE ORGANIZATION AND PROPERTIES OF MAGNESIUM SINGLE CRYSTALS BASED ON MOLECULAR DYNAMICS ANALIZA VPLIVOV RAZLI^NIH SMERI OBREMENJEV ANJA NA ORGANIZACIJO IN LASTNOSTI MAGNEZIJEVIH MONOKRISTALOV S POMO^JO MOLEKULARNE DINAMIKE Tuo Li, Chuanchuan Ma, Chun Xue, Ri Jin, Yuquan Li, Leifeng Tuo, Hailian Gui, Zhibing Chu * School of Materials Science and Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China Prejem rokopisa – received: 2024-06-08; sprejem za objavo – accepted for publication: 2024-09-30 doi:10.17222/mit.2024.1215 Magnesium and its alloys are widely used as high-quality metal materials in various fields. In this study, the tensile properties of magnesium single crystals under different loading directions were investigated based on the molecular dynamics theory. By ana- lyzing the changes in stress, potential energy, crystal structure, and dislocation lines, the following conclusions can be drawn: There are differences in strain values, dislocation line arrangement laws, and crystal structures of magnesium single crystals when dislocation lines are generated under different loading directions. However, the types of dislocation lines are generally the same, with 1/3 dislocations and dislocations with an unknown structure being dominant. Furthermore, the results indicate that the number of 1/3 dislocations is larger than that of dislocations with an unknown structure. These findings are of great signifi- cance for a deeper understanding of the deformation mechanism of magnesium single crystals. Keywords: molecular dynamics, magnesium single crystal, loading direction, crystal structure, dislocation line density Magnezij (Mg) in njegove zlitine se {iroko uporabljajo kot visoko kvalitetni kovinski materiali na razli~nih podro~jih. V ~lanku avtorji opisujejo raziskavo nateznih lastnosti Mg mono kristalov pri njihovem obremenjevanju v razli~nih smereh s pomo~jo teorije molekularne dinamike. Na osnovi analize napetostnih sprememb, potencialne energije, kristalne strukture in dislokacijskih linij so pri{li do naslednjih ugotovitve: obstajajo razli~ne vrednosti deformacije, zakonov ureditve dislokacijskih linij in kristalnih struktur, ko pride do generiranja dislokacijskih linij zaradi razli~nih smeri obremenjevanja. Vendar so prevladujo~i tipi dislokacijskih linij v splo{nem enaki, z 1/3 dislokacijami in dislokacijami neznane strukture. Nadalje rezultati analiz ka`ejo, da je {tevilo dislokacij 1/3 ve~je kot je {tevilo dislokacij z neznano strukturo. Avtorji tudi ugotavljajo, da so njihove ugotovitve zelo pomembne za globje razumevanje deformacijskih mehanizmov Mg mono kristalov. Klju~ne besede: molekularna dinamika; mono kristali magnezija; smeri obremenjevanja; kristalna struktura; linijska gostota dislokacij 1 INTRODUCTION Magnesium and its alloys are widely used as light- weight metallic materials in lightweight structural com- ponents in aerospace and other fields. They are consid- ered to be green materials that are resource-efficient and environmentally sustainable. 1–5 Magnesium has advan- tages such as high specific strength, specific stiffness, and good thermal and electrical conductivity. However, the densely arranged hexagonal crystal (HCP) structure of magnesium single crystals results in high anisotropy of their mechanical properties, which significantly limits the plastic deformation of metals. 6–10 Therefore, it is of great significance to improve the mechanical properties of metals by investigating the changes in the crystal structure of magnesium single crystals during the load- ing process at a microscopic level. Selvarajou, Balaji 11 et al. used nanoindentation exper- iments and crystal plastic finite element (CPFE) simula- tion to study the orientation-dependent properties of magnesium single crystals under local contact. Monnet Ghiath 12 et al. used molecular dynamics and hydrostatic simulations to investigate the core structure and motion of dislocations in the -Fe mechanism. Zhang Peng 13 et al. used a molecular dynamics approach to simulate the deformation process of nickel-based single-crystal high-temperature alloys and investigated the effect of the evolution mode of interfacial dislocations and the yield mechanism on the mechanical properties of nickel-based single-crystal high-temperature alloys. V . Kaushik 14 et al. investigated the fracture behavior of magnesium single crystals by experimenting with notched three-point- bending specimens with three crystal orientations. Zhou Nian 15 et al. simulated the nanoindentation of three face-centered cubic (FCC) metals (Al, Cu, and Ni) and two body-centered cubic (BCC) metals (Fe and Ta) using molecular kinetic dynamics and investigated the main types of single-crystal dislocation structures during Materiali in tehnologije / Materials and technology 58 (2024) 6, 699–706 699 UDK 631.824:537.312.9 ISSN 1580-2949 Original scientific article/Izvirni znanstveni ~lanek Mater. Tehnol. *Corresponding author's e-mail: chuzhibing@tyust.edu.cn (Zhibing Chu) nanoindentation. Chen Bin 16 et al. used molecular dy- namics simulations to investigate the fracture behavior of Ni-based alloys under different impact velocities and the change in the crystal structure. Vasilev Evgenii 17 et al. experimentally investigated the mechanism of the hexag- onal close-packed (HCP) to body-centered cubic (BCC) phase transition of magnesium single crystals during plastic deformation. Chao Lou 18 et al. experimentally in- vestigated the local stress induced by the interaction of twinned phases of magnesium single crystals on the microstructural evolution. Mao Lou 19 et al. also experi- mentally investigated the local stress induced by the in- teraction of twinned phases of magnesium single crystals on the microstructural evolution. 2 MODEL CONSTRUCTION AND MODELING METHODS In this paper, the properties of magnesium single crystals under different loading directions are investi- gated based on molecular dynamics. A magnesium sin- gle-crystal model was established using Atomsk soft- ware. 20–23 Crystal orientation indices in a densely packed hexagonal structure are expressed in four-axis coordi- nates, while the model orientation is expressed in three axes, where the x, y, and z coordinates correspond to the [-12-10], [-1010], and [0001] crystal orientations, re- spectively (as shown in Figure 1a. The size of the model created is (12.8 × 22.24 × 20.85) nm, consisting of a to- tal of 256,000 atoms (as shown in Figure 1b. Simula- tions were carried out using the LAMMPS program combined with the tessellated embedded atom method (EAM) potential function. The simulations were con- ducted under the following conditions: a loading temper- ature of 300 K, a loading rate of 0.01 s –1 , loading direc- tions of X, Y, and Z, and a time step of 0.001 ps until the total strain reached 20 %. By analyzing the stress-strain, potential strain, crystal structure, and dislocation line data from the simulation results, the changes in the per- formance and deformation mechanisms of single-crystal magnesium under a tensile action in different loading di- rections were investigated. 3 SIMULATION RESULT ANALYSIS 3.1 Effect of loading direction on the tensile stress- strain relation in magnesium single crystals Figure 2 shows the stress-strain curves of sin- gle-crystal magnesium in tension under different loading directions. From the figure, it can be seen that the stress-strain curves under different loading directions show obvious changes, where the curve changes in the X loading direction are obviously different from those in the Y and Z directions, and the curve movements in the Y and Z loading directions have the same tendency. The peaks of the curves in the X, Y and Z loading directions increase in turn, and the strain values corresponding to their peaks also increase in turn. The peak point in the Z direction is the highest, and can reach 2.18 GPa, corre- sponding to 10.5 % of the strain, followed by the peak point in the Y direction, which is 1.20 GPa, correspond- ing to 9.2 % of the strain, and the peak point of the stress in the X loading direction, which is 0.43 GPa, corre- sponding to 3.9 % of the strain. It can be seen that the stress and strain values are minimum in the X direction and maximum in the Z direction. The main reason for this phenomenon is the fact that magnesium single crys- tals have a dense hexagonal crystal structure. Under a tensile load, the first change in the slip sys- tem is different for different loading directions. The crys- tal change in the X loading direction occurs along the densest row of surfaces in the hexagonal crystal struc- ture, which corresponds to the easiest slip system. There- fore, the required stress in the X loading direction is small. The crystal change in the Y loading direction oc- curs along a dense row of surfaces in the hexagonal crys- tal structure, but it does not correspond to the easiest slip system. Therefore, the required stress in the Y loading di- rection is higher than that in the X loading direction. The crystal change in the Z loading direction occurs along the prismatic face of the magnesium single crystal, T. LI et al.: EFFECTS OF DIFFERENT LOADING DIRECTIONS ON THE ORGANIZATION AND PROPERTIES OF MAGNESIUM ... 700 Materiali in tehnologije / Materials and technology 58 (2024) 6, 699–706 Figure 1: a) Atomic model diagram of magnesium and b)magnesium single-crystal model which does not correspond to the densest row of surfaces in the hexagonal crystal structure. Therefore, the re- quired stress in the Z loading direction is the highest among the three directions, and the change is the most significant. 3.2 Effect of loading direction on the tensile potential energy-strain relation of magnesium single crystals Figure 3 shows the corresponding potential en- ergy-strain curves for a single crystal of magnesium stretched under different loading directions. From the figure, it can be seen that after a systematic chirp, the po- tential energy returns to the same initial value when it is not stretched. When loading along the X direction, the potential energy reaches its maximum value at 9 %, which is –378.21 keV . When loading along the Y direc- tion, the potential energy reaches its maximum value at 9.5 %, which is –371.51 keV . When loading along the Z direction, the potential energy reaches its maximum value at 11 %, which is –365.46 keV . Considering Fig- ure 2 as well, it can be observed that the corresponding values of strain and potential energy are lower when loading along the X direction. These lower values are mainly achieved because the magnesium single crystal is more prone to change in this direction. The higher abso- lute values of the strain and potential energy in the Z loading direction are due to the fact that the Z loading di- rection is not the most likely crystallographic direction for dense hexagonal rows, and more energy is required to break the metal bonds. 3.3 Effect of loading direction on the change of crystal structure of magnesium single crystals In the crystal structure, the arrangement of atoms de- termines various properties of the material, including electronic structure and mechanical properties. In mag- nesium single crystals, there are strong metallic bonds between the atoms in their crystal structure, giving mag- nesium single crystals good electrical and thermal con- ductivity. Additionally, the crystal structure of magne- sium single crystals determines their mode of plastic deformation. Due to the uniqueness of their hexagonal closest packing (HCP) structure, magnesium single crys- tals undergo dislocation slip during plastic deformation. Under ambient conditions, magnesium single crystals adopt a HCP crystal structure; however, as the loading process continues, the HCP structure of magnesium sin- gle crystals is transformed into an FCC or BCC struc- ture. 24,25 For this reason, the study of the HCP crystal structure transformation is important to understand the mechanical properties of the material and its deformation behavior under strain loading. 26–31 Figure 4 shows the number of different crystal struc- tures versus strain at different loading directions. Fig- ure 4a represents the X loading direction, Figure 4b rep- resents the Y loading direction, and Figure 4c represents the Z loading direction. The five values of strain in Fig- ures 4d to 4f correspond to the beginning of strain, the strain corresponding to the yield point, the strain corre- sponding to the same number of HCP and OTHER struc- tures, the 15-% strain, and the 20-% strain, respectively. In Figure 4a, the HCP structure is first transformed into BCC and OTHER structures. The HCP structure de- creases sharply, and the BCC structure increases dramat- ically at a strain of 3.9 %. The HCP structure has the same number as the BCC structure at 7.2 %, which is the inflection point. The number of BCC structures is larger than the number of HCP structures. At 9.4 %, the HCP structure starts to reappear, the BCC structure starts to decrease, and the FCC structures begin to appear and gradually increase. The OTHER structures exist in a smooth form after their appearance. In Figure 4b, the HCP structures are first transformed into OTHER struc- tures, then the BCC structures appear, and finally the FCC structures appear. The OTHER structure becomes obvious at 5.4-% strain and gradually increases. The BCC structure increases significantly at 8.9 % and starts T. LI et al.: EFFECTS OF DIFFERENT LOADING DIRECTIONS ON THE ORGANIZATION AND PROPERTIES OF MAGNESIUM ... Materiali in tehnologije / Materials and technology 58 (2024) 6, 699–706 701 Figure 3: Potential energy strain curves under three loading directions Figure 2: Stress-strain curves under three loading directions to decrease at 10.8 %. At this time, the HCP structure fluctuates slightly, but the overall trend is considered to be decreasing, while the FCC structure arises and in- creases gradually. At 12.6 %, the HCP structure starts to recover slowly and finally tends to become flat. In Fig- ure 4c, before the stress peak, the HCP structure is first transformed into the OTHER structure. After the stress peak, the FCC and BCC structures begin to appear, while the OTHER structure starts to decrease, and then reaches a relative equilibrium state. The HCP structure recovers slightly and then tends to level off. It can be seen that when acting in the X loading direction, it is easier to be converted to the BCC structure to promote motion. When acting in the Z loading direction, it is converted to an unknown structure, which has no obvious effect on the promotion of motion. Figure 5 shows the corresponding crystal structure changes at different strains in different directions. The first picture corresponds to different loading directions and represents the beginning of the crystal structure changes in that loading direction. The second picture represents the beginning of the crystal structure changes in the next loading direction. The third and fourth pic- tures represent the crystal structure changes in different loading directions when the corresponding strains are 15 % and 20 %, respectively. The green color represents the FCC structure, the red color represents the HCP structure, the blue color represents the BCC structure, the yellow color represents the ICO structure, and the white color represents the OTHER structure. From the figure, it can be seen that as the strain progresses, the HCP structure is increasingly converted into other crystal T. LI et al.: EFFECTS OF DIFFERENT LOADING DIRECTIONS ON THE ORGANIZATION AND PROPERTIES OF MAGNESIUM ... 702 Materiali in tehnologije / Materials and technology 58 (2024) 6, 699–706 Figure 4: Crystal structure change curves and structure diagrams; a), b), c) show the crystal change curves under different loading directions; d), e), f) show the crystal structures under different strains structures. When loading in the X direction, a disordered unknown structure starts to appear and is then converted into a large area of the BCC structure. It gradually transi- tions into a regular distribution accompanied by the gen- eration of FCC structures. In the Y direction, there is ini- tial generation of relatively regular turbulence points. As the strain progresses, the HCP structure is converted into a regular distribution of BCC structure and an irregular distribution of OTHER structure. At higher strains, the number of BCC structures decreases, the number of OTHER structures increases, and FCC structures are generated. The crystal exhibits an overall irregular distri- bution with local regularity. In the Z loading direction, there are irregular disordered points at the beginning. Then, the HCP structures are mainly converted into OTHER structures, and a small number of BCC and FCC structures gradually appear. Finally, the crystal shows an overall irregular distribution with local regularity. It can be seen that in the X loading direction, the crystal struc- ture is mainly BCC structure, and it is regular. In the Y loading direction, the main structure is BCC, and as the strain progresses, there are more FCC structures and un- known structures, resulting in an overall irregular distri- bution with local regularity. In the Z loading direction, the dominant structure is an unknown structure, and as the strain proceeds, small amounts of BCC and FCC T. LI et al.: EFFECTS OF DIFFERENT LOADING DIRECTIONS ON THE ORGANIZATION AND PROPERTIES OF MAGNESIUM ... Materiali in tehnologije / Materials and technology 58 (2024) 6, 699–706 703 Figure 6: a), b), and c) represent strain-dislocation density curves at X, Y, and Z loading directions, respectively Figure 5: a), b) and c) show the crystal structure changes under different strains in X, Y and Z loading direction, respectively structures appear, resulting in an overall irregular distri- bution with local regularity. 3.4 Effect of loading direction on the variation of mag- nesium single-crystal dislocation curves The plots of dislocation density versus strain for dif- ferent loading directions are given in Figure 6, where Figure 6a shows the X loading direction, Figure 6b shows the Y loading direction, and Figure 6c shows the Z loading direction. We can see that the types of disloca- tions appearing under tensile loading in different loading directions are: 1/3, 1/3, 1/3, , and dislocations, and that there are also some unidentifiable dislocations, defined as other dislocations. From the figure we can see that the overall trend of each dislocation is converging with strain, where the density of dislocation lines is the small- est in the X direction and the density of dislocation lines is the largest in the Z direction. In Figure 6a, disloca- tions start to appear at a strain of 10.2 %, with the domi- nant role played by 1/3 dislocations and other disloca- tions. The overall trend of these two kinds of dislocations is increasing, but the fluctuation is larger as the strain progresses. The number of 1/3 dislocations is larger than that of other dislocations. In Figure 6b, dislocations start to be generated at 10.7 % strain and gradually increase with the strain. The dominant types are 1/3 and other dis- locations, with their numbers being basically the same. Additionally, a small number of 1/3 dislocations are gen- erated and their number tends to stabilize during the straining process. In Figure 6c, at a strain of 11.3 %, there are dislocations, mainly consisting of 1/3 disloca- tions and other dislocations. Both types of dislocations are gradually increasing, with the number of 1/3 disloca- tions always being larger than that of the other disloca- tions. The 1/3 dislocations are generated at 12.3 %, and their number tends to stabilize as the strain progresses. It can be seen that the 1/3 dislocations and other disloca- tions play a dominant role in different loading directions with the strain, in which the number of 1/3 dislocations is larger than that of other dislocations, and the 1/3 dislo- cations play a secondary role, not determining the direc- tion of strain occurrence. Figure 7 shows variation curves of dislocation den- sity with strain under different loading directions. The first graph represents dislocation line graphs under the corresponding strain when dislocations are generated, while the second graph represents dislocation line graphs corresponding to the strain when dislocations are gener- ated in the next loading direction. The third and fourth graphs correspond to dislocation line graphs under the strains of 15 % and 20 %, respectively. From the graphs, we can observe that the dislocation line density increases to varying degrees as the strain progresses under differ- ent loading directions. In the X loading direction, the dis- location lines start to be generated at 10.2 % strain, and their distribution is disordered. As the strain progresses, dislocation lines grow and their number gradually in- T. LI et al.: EFFECTS OF DIFFERENT LOADING DIRECTIONS ON THE ORGANIZATION AND PROPERTIES OF MAGNESIUM ... 704 Materiali in tehnologije / Materials and technology 58 (2024) 6, 699–706 Figure 7: a), b), and c) represent the change in the dislocation line under the X, Y and Z loading direction, respectively creases, eventually showing a regular distribution. This is mainly because in the X loading direction, dislocations are generated along the direction where the crystal is prone to change, requiring less energy and producing less stress. This results in fewer atomic structure disrup- tions and corresponds to a lower number of dislocations. In the Y loading direction, dislocation lines start to be generated at 10.7 % strain, and their distribution is disor- dered. As the strain increases, the dislocation lines grow, merge, and split, eventually exhibiting an overall irregu- lar and locally regular distribution at larger strains. In the Z loading direction, dislocation lines start to be gener- ated at 11.3 % strain, and they have a longer length. Ini- tially, the dislocation lines have a more orderly distribu- tion with increasing strain. However, as the dislocations continue to occur, the dislocation lines grow, intertwine, and eventually show an overall irregular and locally more regular distribution. It can be observed that in the X loading direction, there are fewer dislocation lines, but their distribution is regular. In the Y loading direction, there are more dislo- cation lines compared to the X loading direction, and they have longer lengths. However, the distribution of these dislocation lines is overall disordered with some local order. In the Z loading direction, there are more dis- location lines than in both the X and Y loading directions. These lines are long and interwoven, resulting in an overall disorder with a relatively more orderly local or- der. 4 CONCLUSIONS In this paper, the changes in the properties of magne- sium single crystals under different loadings at 300 K are investigated using molecular dynamics. The following results are obtained by discussing the stress strain, poten- tial energy strain, dislocation line changes and crystal structure changes: 1) The strain values corresponding to the generation of dislocation lines in magnesium single crystals under different loading directions are different, with the small- est strain value corresponding to the X direction, fol- lowed by the Y direction, and Z direction with the largest strain value. 2) Under different loading directions, the arrange- ment of dislocation lines and the conversion and distribu- tion of the crystal structure vary. When loaded in the X direction, dislocation lines are regularly distributed, and most of the HCP structure converts into the BCC struc- ture. When loaded in the Y direction, the overall distribu- tion of dislocation lines is irregular with some local regu- larity, and the crystal structure undergoes conversion primarily into the BCC structure, along with some OTHER structure. When loaded in the Z direction, the overall distribution of dislocation lines is irregular with some local regularity, and the HCP structure mainly con- verts into an unknown structure. 3) Under different loading directions, the number and length of dislocation lines are different. In the X direc- tion, the number of dislocation lines is small and the lines are short. In the Y direction, there are more and lon- ger dislocation lines accompanied by a small amount of interweaving. In the Z direction, the number of disloca- tion lines is large, the lines become longer and there is a lot of interweaving. 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