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Schematic diagram (a) MD simulation model of the nanoindentation, (b) volume of material (1 nm  1 nm  1 nm) considered for stress computation (only 2D representation is shown here).
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Unlike other BCC metals, the plastic deformation of nanocrystalline Ta during compression
is regulated by deformation twinning. Whether or not this twinning exhibits anisotropy was
investigated through simulation of displacement-controlled nanoindentation test using molecular
dynamics simulation. MD data was found to correlate well with the experim...
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... automated identification of crystal defects, dislocation lines and their Burgers Vector from the output of the MD data. DXA and CAT in conjunction with OVITO provides unique flexibility to measure the length of dislocations in a fully automated fashion, an example may be seen elsewhere [20]. The MD simulation model after equilibration is shown in Fig. 2a. The atoms in the Newton region directly affected by the chemical interactions were allowed to follow Newtonian dynamics (LAMMPS NVE dynamics), while atoms in a thin boundary layer were subjected to a thermostat (LAMMPS NVT dynamics) to dissipate the heat generated in the artificial volume which would have otherwise taken away by the ...
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... (in cutting). Normally, pyramidal indenters, such as Berkovich or cube corner, are classified as "sharp" indenters while spherical indenters are referred to as "blunt" indenters [3]. In practice, almost all indenters have some finite edge radius (despite being referred to as extremely sharp) and therefore a spherical shaped indenter was deployed (Fig. 2a) during the simulation to mimic an indenter with a finite edge radius. However, the atoms in the indenter were kept fixed (the indenter was assumed to be an infinitely rigid body). In the literature, there was not any robust interaction potential energy function between carbon and tanta- lum (to the best of our knowledge) and hence, ...
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... fluctuations and thermal vibrations), a low temperature of 10 K was used to equilibrate the sample and to perform the nanoindentation. Choi et al. [22] have discussed some implications of the boundary conditions for such a simula- tion model and accordingly the model in this work assumed periodic boundary conditions along X and Z directions (Fig. ...
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... analysis of maximum shear stress or Tresca stress in the deformation zone calls for quantifying the atomic stresses and for this reason, the atomic stress tensor 1 during the simulation was calculated by considering an elemental atomic volume (1 nm  1 nm  1 nm) in the deformation zone right underneath the indenter as shown in Fig. 2b. During the simulation, the summation of the total stresses acting on this small volume was divided by the pre-calculated total volume of the element to obtain the physical stress tensor. The physical stress tensor was then used to assess the yielding criteria of tantalum using Tresca stress, von Mises stress, Octahedral stresses, ...
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In this work, the interaction between dislocation loop (DL) and coherent twin boundary (CTB) in a body-centered cubic (BCC) tantalum (Ta) film during nanoindentation was investigated with molecular dynamics (MD) simulation. The formation and propagation of <111> full DLs in the nanotwinned (nt) Ta film during the indentation was observed, and it wa...
Citations
... To prevent boundary effects on simulation results, periodic boundary conditions are applied in the X and Y directions, while a free boundary condition is set in the Z direction. [21][22][23][24] Before the nanoindentation and scratch, the indenter was placed 1.0 nm above the workpiece, as shown in Fig. 1. In the indentation process, the indenter was moved downwards in the Z direction at a constant speed of 20 m s −1 , reaching a specified depth 0.5 nm. ...
This study investigates the effects of the indenter on nickel coated by MoS2 during nanoindentation and nanoscratch through molecular dynamics (MD) simulations. The effects of indenter size, indenter shape, and scratch angle on the deformation and wear mechanisms of the material were studied. The results show that the size and shape of the indenter have significant effects under nanoindentation and scratching. A larger indenter size can lead to a larger deformation zone and more dislocations inside the workpiece, and the friction coefficient also decreases as the radius of the indenter increases. The friction coefficient at different scratch angles is not significant difference, which indicates that in the case of the monolayer of MoS2 coating has weakly dependent on the lattice orientation. In addition, different indenter shapes will cause differences in stress concentration and penetration depth inside the workpiece. The trapezoidal indenter also shows a higher friction coefficient and wear rate.
... Table 4 presents a comprehensive overview of the indentation force and hardness comparisons in both simulated and experimental indentation tests. Generally, the values obtained in this study fall within the range of values reported in other works utilizing MD simulation [12], [18], [20], [38], [48], [51][52], [62][63][64]. It is worth noting that certain studies [12], [20], [52] achieved the highest indentation force and hardness values through the implementation of a nanolaminate material design. ...
The molecular dynamics approach is utilized to examine the deformation mechanism and evolutionary patterns of mechanical behavior in the Alx(CuCrFeNi)1-x high-entropy alloy (HEA) during nanoindentation. A comprehensive investigation is carried out on how temperature, grain size, and alloy composition impact the mechanical attributes and structural changes in the Alx(CuCrFeNi)1-x HEA (with x representing the molar ratio, x = 0.04–0.3). Alterations in the proportion of aluminum within the alloy content reveal a correlation wherein an increase in the Al percentage leads to a reduction in the indentation force. In terms of plastic deformation, the interplay between Al concentration, grain size, and temperature influences the conversion of local stress and shear strain into the bulk of the substrate, as evidenced by the presence of diverse slip bands. Additionally, the concentration of aluminum and larger grain sizes facilitate the extension of shear bands into the substrate, thereby augmenting the overall ductility of the alloys. In the realm of microstructure development, the movement of mobile prismatic dislocations within the substrate significantly contributes to the deformation process. Notably, the aluminum content governs the displacement of these dislocation rings into the substrate, while the growth of these rings is hindered by the grain size.
... Atoms of the FCC phase, BCC phase, and diamond are hidden to clearly observe atomic dislocations and phase transitions. As shown in Fig. 4, the Burger vector of a dislocation includes five types: 1/2 < 110 > (blue, also known as "full dislocation"), 1/6 < 112 > (green, also known as "Shockley incomplete dislocation"), 1/3 < 001 > (yellow, also known as "Frank incomplete dislocation"), 1/3 < 111 > (light blue), and Disorder (red) [39,40]. The overall distribution characteristics of dislocations are that the total number of dislocations decreases with the increase in indentation rate. ...
The FeO/Fe bond in the oxide scale is very tight, and FeO fracture is complicated under external force. In this study, the deformation behavior and mechanical properties of single-crystal FeO/Fe under nanoindentation are analyzed by the molecular dynamics (MD) simulation method. The results show that: 1. loading stage: the load increases with the increase in the loading rate; unloading stage: the load drop rate increases with the increase in the unloading rate in the early stage, and the opposite in the middle and late stage. 2. The dislocation density and the phase transition of the HCP structure decrease with the increase in the indentation rate, and the total volume of defect atoms increases with the increase in the indentation rate. 3. When the indenter is in the FeO layer, the hardness and elastic modulus increase with the increase in the indentation rate. 4. The hydrostatic stress and Von Mises stress analysis show that the average stress value increases with the increase in the indentation rate, and coexistence of compressive and tensile stress inside the model. This study provides essential help for further exploration of the deformation behavior and mechanical properties of oxide scales.
... [111] uniaxial tensile tests for high-purity Ta [9]. Atomic simulations also support the findings of these experimental studies [10][11][12][13][14][15]. ...
In this study, anti-twinning and deformation twinning of body-centered-cubic (BCC) metals under shear loading in the anti-twin direction were examined. Molecular dynamics simulations of BCC Ta showed both the existence of anti-twinning and a novel two-layer-by-two-layer anti-twinning mechanism consisting of a staggered shuffle sliding of {112} atomic planes in the [111¯] and [1¯1¯1] directions, generating finite shear displacement along the anti-twin direction. The density functional theory multi-dimensional interlayer slipping energy landscape of the newly observed anti-twinning process has a lower energy barrier for both twin nucleation and growth than the recently proposed layer-by-layer anti-twinning process.
... More importantly, researchers can easily track the structural evolution process of materials under various external loads, which is convenient to reveal the fundamental mechanism of relevant properties from atomic scale. For instance, through molecular dynamic simulations, the nanoindentations have been done for different types of materials, including metals (like tantalum [42], titanium [43], tungsten [44], etc.), semiconductors (like silicon [45], gallium nitride [46], etc.) and insulators (like diamond [47], cubic boron nitride [48], etc.).The mechanical responses as well as the microstructure evolutions of the indented materials can be obtained. Inspired by these studies, we will study the mechanical properties of CdTe under indentations through molecular dynamics. ...
... The corresponding calculated results still agree well with the experimental results, which has a good reference value. Before our simulation, we refer to the system size of different works [42,[72][73][74]. In addition, we also considered the computing power of our computer. ...
... The dimensions and number of atoms for the simulated CdTe samples are listed in Table 1. In our simulations, the dimension of the sample is about 466 Å × 466 Å × 466 Å, which is larger than all the models in the studies [42,[72][73][74]. For such a large sample, the influence of its size and boundary conditions on the simulation results should be very limited. ...
Molecular dynamic simulations were performed to investigate the indentations of CdTe crystal on (100), (110) and (111) surfaces. We found that the incipient plasticity, hardness, elastic recovery ratio and the structural evolution of CdTe during the indenting process depend strongly on the orientation of the indented surfaces due to the anisotropic nature of CdTe. The obtained load–displacement curves showed abrupt drops at critical indentation depths, indicating the occurrence of incipient plasticity. We found that the (001) plane yields first during the indenting process, followed by (110) plane, and the (111) plane yields last. For all the indented planes of CdTe, the incipient plasticity should be resulted from the nucleation and propagation of 1/2 < 110 > dislocations, which is consistent with the results from both experiments and the calculations of the generalized stacking fault energy. We found that the dislocation distribution under the indented (110) plane shows a twofold rotation symmetry, while those under the indented (111) and (001) planes show three- and fourfold rotation symmetry, respectively. The temperature effect on the indentation responses and structural evolution were also studied. This paper will not only answer the question about the orientation-dependent indentation responses of CdTe crystals, but also reveal the dislocation activities under the indentations in real time. The results of this paper are generally applicable to CdTe single-crystal systems and may provide reference data to improve the design and ultimately performance of the related CdTe-based devices.
... Before the indentation procedure, the temperature of the Si substrate was equilibrated at either 1 K or 300 K. To equilibrate the temperature of the substrate, an NVE ensemble with a velocity rescaling method was used in the Newtonian layer [22,23]. Subsequently, the indentation load was applied by displacing the conical indenter into the substrate. ...
The influence of the indenter angle on the deformation mechanisms of single-crystal Si was analyzed via molecular dynamics simulations of the nanoindentation process. Three different types of diamond conical indenters with semi-angles of 45°, 60°, and 70° were used. The load–indentation depth curves were obtained by varying the indenter angles, and the structural phase transformations of single-crystal Si were observed from an atomistic view. In addition, the hardness and elastic modulus with varying indenter angles were evaluated based on the Oliver–Pharr method and Sneddon’s solution. The simulation results showed that the indenter angle had a significant effect on the load–indentation depth curves, which resulted from the strong dependence of the elastic and plastic deformation ratios on the indenter angle during indentations.
... At the lattice scale, dislocation slip and deformation twinning are widely regarded as two of the most important deformation mechanisms and play an important role in accommodating plastic deformation [7][8][9][10][11]. Despite tremendous experimental [12][13][14][15][16][17][18][19][20][21] and simulation [22][23][24][25][26][27][28][29][30][31] efforts, a complete understanding of the two competing mechanisms, dislocation slip and deformation twinning in tantalum, is still lacking, especially in high strain rate shock-induced plastic deformation. ...
The deformation twinning to dislocation slip transition is observed in large-scale molecular dynamics simulations of single-crystal tantalum under dynamic loading, along with double plastic zones during the transition. The transition is accompanied by temperature rise and fast stress relaxation. Rapid nucleation and propagation of twins at the shock front give rise to a plastic precursor, followed by a dislocation-mediated plastic wave during the transition. These transient double plastic zones can be resolved via ultrafast x-ray or electron diffraction measurements and can help to improve time-dependent deformation models.
Graphical abstract
... To further study the ability of the material to locally resist the hard objects pressed into its surface under the three conditions, we have calculated their hardness H separately. The hardness H can be given by [22,44]: ...
Nickel-based single crystal alloys have excellent mechanical properties due to its unique two-phase structure and interface. Therefore, molecular dynamics methods were used to simulate nanoindentation and microstructural evolution. We found the indenter reaction force and hardness of the Ni3Al phase is the largest. The pop-in event in Ni3Al phase is more obvious than that in the Ni phase and Ni/Ni3Al phase. Because lots of dislocations in the Ni3Al phase break through the barrier of the interface and cut into the Ni phase, while dislocations in the Ni phase only slip inside the Ni phase. Moreover, we found that the position of the starting point of the adhesion force recovery is mainly related to the elastic recovery of the material. The stronger the elastic recovery of the phase, the smaller the depth value corresponding to the starting point of the recovery. We further studied the variation of potential energy with indentation depth and found that the change of wave trough of the load-displacement (P-h) curve is related to stacking fault energy. This study has important theoretical guiding significance for the in-depth understanding and engineering application of the mechanical properties of nickel-based single crystal alloys.
... To further explore effects of crystallographic orientations on the mechanical properties during nanoindentation, the atomic shear strain and stress are calculated. The von Mises stress (VMS) is determined as follows [36,37]: ...
Using molecular dynamics (MD) simulation, the influence of crystallographic orientation on the mechanical properties and microstructure evolution of the single-crystal CoCrFeMnNi high-entropy alloy as a face-centered cubic (FCC) metal is explored and quantified by nanoindentation. At the elastic stage of P-h curve, the results of MD-simulation are almost consistent with that of Hertz contact theory fitting, which ensures the accuracy of our results. The plastic deformation is studied by correlating the P-h curve with the instantaneous defect structure, and dominated by nucleation of Shockley partial dislocations or the movements of stacking faults. Furthermore, we discuss the effects of crystallographic orientations[001],[110], and [111] on the mechanical response of materials and the microstructure evolution. The slip mode and the stress-concentrated region are controlled by the crystallographic orientations, and an obvious pop-in behaviors are viewed in [111]-oriented sample, without appearing in other samples. The microstructure evolution exhibits distinct anisotropy causing the discrepancy of dislocation density and hardness. By analyzing the evolution of dislocation density and hardness, the linear relationship between the square root of dislocations density and hardness is revealed, and in good agreement with the classic Taylor hardening expression where the pre-factor is strongly dependent on the crystallographic orientation. In the study, the atomistic results are consistent with those predicted by the classic continuum mechanical theory, which contributes to the application of classic mechanical theory in molecular dynamics simulation.
... Tantalum added to Ni-based superalloys gives them important mechanical properties at higher temperatures, better resistance to hot corrosion, and longer life. Tantalum forms solid solutions with other refractory metals, such as molybdenum, tungsten, and niobium [50,51]. ...
The paper is proposing a mini-review on the capability of the new complex concentrated alloys (CCAs) to substitute or reduce the use of critical raw materials in applications for extreme conditions. Aspects regarding the regulations and expectations formulated by the European Union in the most recent reports on the critical raw materials were presented concisely. A general evaluation was performed on the CCAs concept and the research directions. The advantages of using critical metals for particular applications were presented to acknowledge the difficulty in the substitution of such elements with other materials. In order to establish the level of involvement of CCAs in the reduction of critical metal in extreme environment applications, a presentation was made of the previous achievements in the field and the potential for the reduction of critical metal content through the use of multi-component compositions.
