Effect of Co Distribution on Plastic Deformation of Nanocrystalline Al-10 . 2 at . % Co Alloy

Molecular dynamics is employed to study stress-strain curves obtained during high strain rate deformation of nanocrystalline Al10.2 at.%Co alloy with (i) randomly distributedCo atoms (Al-Co substitutional solid solution) and (ii) Co atoms segregated in grain boundaries (GBs) of the alloy. The effect of Co distribution, deformation temperature, and the presence of hydrostatic pressure on the stress-strain relation is analyzed. The results are compared to that for nanocrystalline pure Al. It is found that the strength of the Al-Co solid solution is lower than that of the pure Al, while GB segregations of Co increase its strength.The alloys, regardless of the type of Co distribution, under shear loading with no hydrostatic pressure demonstrate higher ductility in comparison with the pure Al. The shear modulus of the Al-Co alloy with the GB segregations is noticeably larger than that of the pure Al and the Al-Co solid solution in a wide range of temperatures. The results of the study show that the GB segregations of Co can have a positive effect on the mechanical properties of nanocrystalline Al.

The limitations of the metallic bulk nanomaterials are low ductility, thermal stability, and deformability at ambient conditions [1,2].Mechanical and functional properties of bulk nanocrystalline Al and other metals can be further improved via alloying with other elements.As a result, not only structures but also physical and mechanical properties such as strength and ductility of bulk nanomaterials can be affected [8,[17][18][19][20][21][22][23][24].Mechanical and functional characteristics of metallic materials depend on many factors, for instance, the average grain size [1,2], the nature of interatomic bonding [18], crystallographic orientation [19], porosity [20,25,26], presence of lattice defects [27], or amorphous phase [28].It was observed that the elastic moduli of polycrystalline metals decrease with the reduction of their average grain size [29][30][31][32].
The effect of alloying elements on the mechanical properties of a bulk nanomaterial depends on their solubilities, concentrations [33], and distribution within it.During thermomechanical treatment of Al alloys, some of the alloying elements prefer to segregate on grain boundaries (GBs) [34], some are distributed randomly in the form of a solute [35], while others form second-phase precipitates or intermetallic compounds [36].In a coarse-grained Al alloy, SPD can redistribute its alloying elements and lead to formation of their GB segregations [21-24, 37, 38] or it can result in dissolution of the second-phase precipitates or fragmentation of the intermetallic compounds [39,40].In addition, it is believed that SPD through high pressure torsion and subsequent short annealing can result not only in the bulk but also in the GB phase transformations, for example, in partial or complete wetting of GB [41][42][43].The wetting phase can be either liquid or solid.Experimentally, it is a great challenge to determine the locations of atoms and compounds of a certain element in the nanocrystalline material [21][22][23][24].However, this challenge can be overcome through atomistic simulations.
The GB segregation energies and the embrittlement potencies for a substitutional Co impurity atom at different atomic positions in the tilt and twist GBs of Al bicrystals were calculated in our recent work [44].It was shown that the Co impurity atoms tend to remain in these GBs and increase their strength because both the GB segregation energies and the embrittlement potencies are negative for the Co atoms at most of the irreducible positions in the GBs.Having these results in mind it is tempting to study the effect of the GB segregations of Co on the yield stress and thermal stability of the shear modulus of nanocrystalline Al-Co alloy at different deformation temperatures.The present study focuses on the comparison of these results with those obtained for the nanocrystalline pure Al and its alloy with random distribution of the Co atoms.

Modeling
A three-dimensional cuboidal computational cell with the edge of 42 nm contains about 4.6 million atoms.Using the Voronoi procedure [10,25,[44][45][46], the cell volume is divided into 100 randomly oriented face-centered cubic (fcc) Al grains with the average size of about 11 nm.The Al (Co) atom has the radius of 143 (125) pm [47].Two types of the Al-Co alloys are obtained through the substitution of the Al atoms by the Co atoms.Random substitution of 10.2% of the Al atoms of the computational cell, regardless their coordination numbers, results in the Al-10.2at.%Co substitutional solid solution (Figure 1 The molecular dynamics (MD) simulations are performed using the atomic/molecular massively parallel simulator (LAMMPS) program package [48].The interatomic forces are modeled with the many-body embedded-atom method potentials [49].Periodic boundary conditions are applied along the three orthogonal directions of the cuboidal computational cell.The simulations of a shear deformation of the pure Al and its alloys are performed with the NPT ensemble (constant number of atoms, pressure, and temperature).
Initially, the nanocrystalline Al and the Al-Co alloys are relaxed at zero temperature to obtain the state of the minimum potential energy.Then the shear deformation up to shear strain of   = 0.2 is applied at a constant strain rate of 10 8 s −1 .The simulations of plastic deformation of the pure Al and its alloys are performed at two different temperatures (300 and 600 K) and the concurrent presence of the hydrostatic pressure of 0 and 6 GPa, while the shear modulus at different temperatures (0, 150, 300, 450, and 600 K) is calculated as the tangent of the stress-strain curves obtained at their shear elastic deformation up to   = 0.005 and zero hydrostatic pressure.hydrostatic pressure, while in (b, d) the hydrostatic pressure is equal to 6 GPa.Notice that at all the considered conditions of plastic deformation, the Al-Co alloy with the GB segregations of Co demonstrates higher strength compared to that of the pure Al, while the strength of the Al-Co solid solution is always lower.Naturally, the increase of temperature results in the reduction of the yield stress, while the increase in the hydrostatic pressure leads to the opposite effect.Among these deformation conditions, the highest yield stress of the pure Al and its alloys can be observed for the temperature of 300 K and the hydrostatic pressure of 6 GPa (Figure 2(b)).Note that such value of the hydrostatic pressure is typically realized during SPD through high-pressure torsion [2].As expected, the yield stresses are the lowest for the pure Al and the Al-Co alloys after the shear deformation at 600 K and zero hydrostatic pressure (Figure 2(c)).All the curves after reaching a maximum demonstrate slow decrease in stresses with further deformation.This can be explained by the deformation-induced grain growth by means of GB migration and grain rotation, according to the Hall-Petch law [50].In order to analyze the stress-strain relations of the studied materials, their microstructures at shear deformation of   = 0.2 are studied.

Microstructure at 20% Shear Deformation.
The atom common neighbor analysis of the studied materials' structures at 20% shear strain in the x-y-plane is carried out.The obtained results for the pure Al, Al-Co solid solution, and Al-Co alloy with the GB segregations of Co are shown in the left, middle, and right columns of Figure 3, respectively.The analysis for the nanocrystalline pure Al (Figure 3, left column) reveals that at the shear strain of 20% the fcc coordination of atoms prevails inside the grains, especially at the deformation temperature of 300 K.At 600 K, due to large thermal fluctuations the crystal structure in some regions inside grains is indefinite.It is noticeable that the width of GBs is larger at the deformation temperature of 600 K as compared to 300 K.The red regions which correspond to the hcp lattice in the structures reveal the appearance of stacking faults and indicate some dislocation activity which is highest at 300 K and the hydrostatic pressure of 6 GPa.The deformation at 600 K, regardless of the presence of the hydrostatic pressure, results in the change of GBs' positions with respect to those for the structure after the low temperature deformation meaning that the pure Al undergoes the GB migraton and has low thermal stability.
The Al-Co solid solution undergoes strong amorphization during the shear plastic deformation (Figure 3, middle column) [51].Indeed, a large portion of the atoms is colored in grey with the indefinite crystal structure.Interestingly, the presence of hydrostatic pressure somewhat decreases the areas with the amorphous structure.
The Al-Co alloy with the Co atoms located in GBs (Figure 3, right column) undergoes the amorphization only in the regions close to GBs which are rich in Co.The dislocation activity can be noticed inside grains but it is weaker than that in the case of the pure Al.Unlike the pure Al, the Al-Co alloy with the GB segregations does not undergo any GB motion during high temperature deformation implying that the GB segregations increase the thermal stability of the alloy.Structures presented in the right column of Figure 3 confirm the possibility of the GB phase transformations discussed, for example, in a series of works by Straumal et al. [41][42][43].
Due to the formation of voids (Figure 3, shown in black), the nanocrystalline pure Al has smaller ductility than the Al-Co alloys.It should be noticed that the voids appear only in the pure Al deformed in the absence of the hydrostatic pressure.The void formation is more intensive in the case of lower deformation temperature.
Figure 4 shows   shear stress distribution at   = 0.2 in (a) the nanocrystalline pure Al, (b) Al-Co solid solution, and (c) Al-Co alloy with the GB segregations of Co.The deformation conditions are 300 K and no hydrostatic pressure.The voids in Figure 4(a) are highlighted in black.In Figures 4(a) and 4(c), the high shear stresses can be seen

Shear Modulus.
Figure 5 shows the shear modulus  as the function of temperature at zero hydrostatic pressure for the nanocrystalline pure Al (solid line with no symbols), Al-Co solid solution (open dots), and Al-Co alloy with GB segregations of Co (filled dots).At 0 K, both the alloys have  higher than that for the pure Al.For the Al-Co solid solution the increase in the rigidity is about 4%, while for the Al-Co alloy with the GB segregations of Co, it is about 16%.For all the three materials, as expected, the shear modulus decreases with temperature.For elevated temperatures, the Al-Co solid solution has the lowest , while for the Al-Co alloy with the GB segregations, it remains the highest.At 600 K, the shear modulus of the Al-Co alloy with the GB segregations is 51% larger than that of the pure Al demonstrating the highest thermal stability of .

Conclusions and Future Problems
The paper studies the effect of deformation temperature and the hydrostatic pressure on stress-strain responses of the nanocrystalline pure Al, Al-10.2 at.%Co solid solution, and Al-10.2 at.%Co alloy with the Co atoms segregated along the GBs during their shear plastic deformation via the MD simulations.Evolution of the microstructure during shear deformation was analyzed and the temperature dependence of the shear modulus was calculated for all the three studied materials.
In contrast to the Al-Co solid solution, the Al-Co alloy with the Co distributed along GBs has an enhanced strength as well as the structure thermal stability in comparison with the pure Al.In particular, the Al-Co alloy with the GB segregation of Co (Al-Co solid solution) at the low temperature shear deformation (300 K) with the concurrent presence of the hydrostatic pressure of 6 GPa demonstrates the maximal shear stress which is 27% higher (28% lower) than that for the nanocrystalline pure Al.
Unlike the Al-Co alloys, regardless of the Co atom distribution, in the nanocrystalline pure Al deformed in the absence of the hydrostatic pressure at shear strain of   = 0.2 the voids formation can be observed.The void nucleation is more intensive in the case of the low temperature deformation.Thus, the pure Al has smaller ductility than for the considered alloys.
The GB segregations of the Co atoms in the Al-Co alloy increase the shear modulus at 0 K and its thermal stability.
The presence of the Co atoms leads to the amorphization of the Al-Co alloys and can result in the GB phase transformations [41][42][43] (see Figure 3, right column).
To the best of our knowledge, the effect of GB wetting has not been yet addressed in MD study.It is tempting to apply this powerful method to the analysis of GB transformations in such alloys as Al-Zn [41,43] or Cu-Co [42].
Notice that in this study, the shear deformation is applied to the nanocrystalline structures that are free of internal stresses.In practice, however, bulk nanocrystalline materials obtained by SPD and disperse metallic nanomaterials containing defects, such as dislocations and disclinations, are characterized by the presence of high residual stresses [52][53][54][55][56].The study of mechanical characteristics of Al alloys with the residual stresses and comparison of the results with those presented here is another interesting direction for a future work.

Figure 1 :
Figure 1: Nanocrystalline Al-10.2 at.%Co alloys with (a) randomly distributed Co atoms and (b) those segregated in the GBs.Al atoms are represented in light grey, while Co atoms in black.
(a)).Atoms in the ideal fcc lattice have 12 neighbors but in the vicinity of GBs some atoms have different number of neighbors.Replacement of all the Al atoms having 11 or 10 neighbors by Co atoms results in the Al-10.2at.%Co alloy with the GB segregations of Co (see Figure 1(b)).Note that the discussion of how such solubility and distributions of the Co atoms can be achieved experimentally is out of the scope of the present study.

3. 1 .
Stress-Strain Curves.The calculated stress-strain curves   (  ) for the pure nanocrystalline Al (solid line), the Al-Co solid solution (dotted line), and the Al-Co alloy with the GB segregations of Co (dashed line) are presented in Figure2.Figures2(a) and 2(b) show the results for the shear deformation at 300 K, and Figures 2(c) and 2(d) for 600 K.The curves plotted in (a, c) are obtained in the absence of

Figure 2 :
Figure 2: Stress-strain curves for the nanocrystalline pure Al (blue line), Al-Co solid solution (red line), and Al-Co alloy with the GB segregations of Co (green line).For (a, b), the deformation temperature is 300 K, while for (c, d), it is 600 K.The hydrostatic pressure in (a, c) is 0 GPa, while in (b, d), it is 6 GPa.

Figure 3 :
Figure 3: Common neighbor analysis of the structures for the pure Al and its alloys in the x-y-plane at 20% shear deformation.The regions with the fcc, hexagonal close packed (hcp), body-centered cubic (bcc), and other (undetermined) areas are colored in green, red, blue, and grey, respectively.The left, middle, and right columns show the results for the pure Al, Al-Co solid solution, and Al-Co alloy with the GB segregations, respectively.For each row, the deformation conditions are shown on the left of the structures.Voids are colored in black.

Figure 4 :
Figure 4: Shear stress distribution at   = 0.2 in (a) the nanocrystalline pure Al, (b) Al-Co solid solution, and (c) Al-Co alloy with the GB segregations of Co. Black regions in (a) show the voids.

Figure 5 :
Figure 5: Shear modulus  as a function of temperature for the nanocrystalline pure Al (solid line with no symbols), Al-Co solid solution (open dots), and Al-Co alloy with the GB segregations of Co (filled dots).