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Temperature-dependent mechanical properties of Al/Cu nanocomposites under tensile loading via molecular dynamics method

Temperature-dependent mechanical properties of Al/Cu nanocomposites under tensile loading via... Curved and Layer. Struct. 2022; 9:96–104 Research Article Mohammed Ali Abdulrehman*, Mohammed Ali Mahmood Hussein, and Ismail Ibrahim Marhoon Temperature-dependent mechanical properties of Al/Cu nanocomposites under tensile loading via molecular dynamics method https://doi.org/10.1515/cls-2022-0009 1 Introduction Received Oct 13, 2021; accepted Nov 29, 2021 Abstract: Al-Cu Nanocomposites (NCs) are widely used in In recent years, metal matrix composites have received con- industrial applications for their high ductility, light weight, siderable attention to their availability, low production cost, excellent thermal conductivity, and low-cost production. and superior properties compared to pure metals [1]. With The mechanical properties and deformation mechanisms of an assortment of industrial applications, from aerospace to Metal Matrix NCs (MMNCs) strongly depend on the matrix automotive and military, Al-Cu NCs are no exception thanks microstructure and the interface between the matrix and to their light weight and high specific strength, toughness, the second phase. The present study relies on Molecular and thermal conductivity [2, 3]. Several methods have been Dynamics (MD) to investigate the effects of temperature on proposed to improve the mechanical properties of Al-Cu the mechanical properties and elastic and plastic behav- NCs and make them more ductile with a focus on improv- ior of the Al-Cu NC with single-crystal and polycrystalline ing the bond strength at the matrix/reinforcement interface. matrices. The effects of heating on microstructural defects Many studies [4, 5] have addressed the issue in an attempt in the aluminum matrix and the Al/Cu interface were also to increase these composites’ yield strength, elastic mod- addressed in the following. It was found that the density ulus, and wear resistance. Despite being a macroscopic of defects such as dislocations and stacking fault areas are phenomenon, nanocomposite fracture is a consequence much higher in samples with polycrystalline matrices than of structural changes at the atomic scale. Accordingly, to those with single-crystal ones. Further, by triggering ther- characterize the fracture mechanisms and investigate the mally activated mechanisms, increasing the temperature structural evolutions during deformation, we need tools to reduces the density of crystal defects. Heating also facili- track atomic movements across the crystal structure. The tates atomic migration and compromises the yield strength best approach to simulating the mechanical properties and and the elastic modulus as a result of the increased energy investigating changes in the atomic structure is modeling of atoms in the grain boundaries and in the Al-Cu interface. on the atomic scale by molecular dynamics simulation [6]. The results showed that the flow stress decreased in all On the macroscopic scale, several factors, including the samples by increasing the temperature, making them less geometry of the specimen, strain rate, temperature, and the resistant to the plastic deformation. crystal structure, affect the material’s behavior. Meanwhile, on the microscopic scale, plastic deformation in nanocrys- Keywords: Al-Cu nanocomposite; molecular dynamics tals often takes place as a result of either dislocation slip or method; mechanical properties; temperature; tensile load- twinning [7]. Previous studies [8, 9] showed that dislocation ing; dislocations glide in the crystal lattice is a major factor in the deforma- tion of FCC crystals. As notable defects in the crystalline microstructure, dislocations can nucleate through the ma- terial from free surfaces, grain boundaries, voids, or atomic *Corresponding Author: Mohammed Ali Abdulrehman: Materi- impurities. Given that both aluminum and copper have an als Engineering Department, College of Engineering, Mustansiriyah FCC crystal structure, their slip planes and directions are University, Baghdad, Iraq; expected to be compatible. Balaram et al. [10] showed that Email: mohammed_ali_mat@uomustansiriyah.edu.iq Mohammed Ali Mahmood Hussein: Al Rafidain University Col- Al–Cu alloy precipitation can create effective obstacles for lage, Department of Air-Conditioning and Refrigeration Eng.Tech, dislocation slip. In another study, Mojmoder [11] showed Baghdad 10, Iraq that the mechanical properties of alloy structures strongly Ismail Ibrahim Marhoon: Materials Engineering Department, depend on the loading direction. Regardless, NC deforma- College of Engineering, Mustansiriyah University, Baghdad, Iraq Open Access. © 2022 M. Ali Abdulrehman et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License Temperature-dependent mechanical properties of Al/Cu nanocomposites | 97 tion has stark differences from deformation in alloys. It the deformation mechanisms at ambient temperature, the has been shown that crystal defects can also form the in- results were supported by previous studies of [33–39]. terface of the matrix and the second phase. For example, Temperature as one of the most important factors af- Pagerleco et al. [12] carried out a microstructural investiga- fecting the deformation mechanisms through changes in tion of an Al-Cu NC with single-crystal matrix at different the density of structural defects, is highly regarded by re- strain rates and high temperature by molecular dynam- searchers. In this regard, in order to investigate the effect ics simulation. The study suggests that atomic mismatch of temperature on the deformation process of structural in the interface of the copper nanoparticle with the alu- defects such as dislocations and stacking faults areas, ac- minum matrix promotes the formation of voids that grow cording to previous studies of [40–49], the values of HCP and compromise the mechanical properties of the sample. atoms and dislocations for both nanocomposite samples In another study, Tian et al. [13] investigated plastic defor- with single crystal matrix and polycrystalline matrix were mation in multi-layered aluminum–copper composites by calculated and the results were compared and discussed. Molecular Dynamics (MD). It was found that dislocations Based on the previous discussion, present MD simu- nucleate in the copper layer and move into the aluminum lation investigates the mechanical properties and defor- layer, deforming it due to the semi-coherent Cu/Al inter- mation mechanisms of the Al-Cu NCs by uniaxial tensile face. The study showed that the aluminum layer deformed tests for samples with single-crystal and polycrystalline to a greater extent than the copper layer and that rupture matrices at ambient temperature. Then, in order to capture began from the aluminum as voids began to develop. In a temperature affects, the sample was stretched at different study of the effects of grain boundaries on crystal defects temperatures. Accordingly, the second part of the study and the mechanical properties of Al-Cu alloys, Mahta et goes through the details of molecular dynamics parame- al. [14] the structures were melted in MD simulations to ters and sample construction techniques. The third section compare the mechanical properties of the samples as grain presents the uniaxial tensile test results at different tem- boundaries formed. The grain boundaries were shown to peratures and discusses the deformation mechanisms. The be critical factors when it comes to the formation of dislo- fourth and final section summarizes the study results and cations and stacking faults. A review of past studies on the presents the conclusions. subject shows that the important role of grain boundaries in plastic deformation and the mechanical properties of Al-Cu nanocomposites are yet to be investigated in detail. 2 MD setup Moreover, in light of the high-temperature applications of these nanocomposites [15], the temperature-based plastic The present study aims to molecular dynamics simulation deformation mechanisms of these materials need to be ad- to probe temperature effects on the deformation mecha- dressed in more detail. nisms of the Al-Cu NCs in uniaxial tensile tests and evalu- In the present study, in order to fabricate the polycrys- ate its mechanical properties. In the following, this section talline samples according to the method presented by [16], discusses how the samples are prepared, the interaction samples were made, then using the software and details of potential, and the analysis tools. molecular dynamics simulation presented by authors [17– 25], the samples experienced the uniaxial tensile. These details are fully discussed in the next section. The results 2.1 Sample construction were also analyzed using atomic geometry-based tools in- troduced in [26]. In the case of sample with single crystal matrix, NCs sam- To do a quantitative validation the obtained outcomes, ples were constructed by considering a 10×10×10 nm alu- first, the results were extracted from the stress–strain minum cube having copper nanoparticle in the center. The curves of the samples were first compared with the studies copper nanoparticle with 4 nm diameter accounted for 2.6 such as [27–29]. Then the results were discussed from the of the entire nanocomposite volume. The polycrystalline perspective of differences in the values of mechanical prop- Al-Cu nanocomposite samples were built by the Voronoi erties for both single crystal and polycrystalline samples tessellation method [16]. The nanocomposite matrix com- based on previous observations [30, 32]. Due to the fact prised four aluminum grains with average grain size of 2 that the most important factors in plastic deformation in nm. Figure 1 depicts the mentioned samples. nanomaterials are microstructural defects such as dislo- cations and twins, in order to provide a better picture of 98 | M. Ali Abdulrehman et al. 3 Results and discussion This section delves into the temperature effects on mechan- ical properties, crystal defects, and plastic deformation of Al/Cu nanocomposites with single-crystal and polycrys- talline matrices. 3.1 Temperature-based mechanical Figure 1: Al/Cu nanocomposite samples: (a) cross-section of single- characteristics of the Al-Cu crystalline matrix having Cu NP, (b) cross-section of poly-crystalline nanocomposite matrix having Cu NP The effects of temperature on the mechanical properties of nanocomposite samples were investigated by annealing 2.2 Parameters of molecular dynamics the specimens at 300, 400, 500, and 600 K before uniaxial tensile test. Figure 2 plots the tensile stress–strain curve of The simulations were implemented using LAMMPS [17]. the nanocomposite samples with single-crystal and poly- Aluminum–aluminum, copper–copper, and aluminum– crystalline matrices at different temperatures. The graph copper interactions were modeled using the angular- shows a linear-elastic region with the stress dropping after dependent potential function [18]. The potential function the yield. In the plastic region, the stress follows a zig-zag has been successfully used by other researchers to simu- pattern that is also found in the stress–strain graph of pure late the aluminum–copper system to characterise the me- aluminum [27]. It is evident that increasing the temperature chanical properties by identifying and examining disloca- tions and stacking faults [12, 19–21]. In the present simu- lations, the initial velocities were set using the Maxwell– Boltzmann distribution at given temperatures. Moreover, the equations of motion were integrated by the velocity Verlet algorithm [22]. Before the simulation tensile test, the single-crystal samples were relaxed for 200 ps using the NPT ensemble at zero pressure, and the desired temperature with 1 fs time- steps. It’s worth mentioning that all polycrystalline sam- ples were annealed at 300 K for 100 ps to improve grain boundary stability. It must also be noted that, the grain size was calculated again after this stage, showing no sign of grain growth. Then, the polycrystalline samples relaxed at desired temperature. Periodic boundary conditions were considered in all three directions. Similar to previous stud- ies [23, 24], after relaxation, the samples were subjected 8 −1 to tension at 0.01 A/ps. The strain rate was 10 s and the test continued up to 15% strain along the x-axis. Zero pressure was maintained in the lateral directions using the Nosé–Hoover barostat during tension. Stress concentration was measured around crystal de- fects, the Al/Cu interface, and grain boundaries by the von Mises analysis. The dislocations were characterized by the Dislocation Extraction Algorithm (DXA) [26]. Moreover, im- ages and other analyses were produced by OVITO. Figure 2: Stress–strain curves of nanocomposite samples for ten- sion at different temperatures: (a) nanocomposite samples having single-crystalline matrix, (b) nanocomposite samples having poly- crystalline matrix Temperature-dependent mechanical properties of Al/Cu nanocomposites | 99 Table 1: Comparison of obtained mechanical properties in this study with the literature Study Case Yield strength (GPa) Elastic modulus (GPa) Pogorelko [12] Al and Cu inclusion 5.6 — Mahata [14] Al-11% at Cu 3.1 — Pogorelko [28] Al-Cu composite 5 — Present work Al single crystal and Cu NP 4.4 61.91 Hocker [29] Polycrystalline Al-4% at Cu 2.3 — Present work Polycrystalline Al and Cu NP 1.8 51.39 Figure 3: Comparison of the elastic modulus variations of the sam- Figure 4: Average flow strength as a function of temperature ples at different temperatures the average flow stress for different specimens. Accordingly, reduces the samples’ yield strength. The elastic modulus the average flow stress reduces as temperature rises. In fact, was also calculated based on the slope in the linear region. heating reduces the required stress to continue plastic defor- Table 1 compares the yield strength results at 300 K with mation. Elevated temperatures promote the energy states the literature. of atoms, facilitating their displacement, which translates According to Figure 3, the elastic modulus declines in to lower elastic and plastic strength. The values of calcu- all samples as the temperature rises. In fact, high tempera- lated flow stress for nanocomposites with a polycrystalline ture promotes the energy state of the atoms, compromising matrix is lower than those with a single-crystal matrix at their elastic strength. The yield stress and elastic modu- all temperatures. The reason lies in the fact that the inverse lus of nanocomposite samples with polycrystalline matrix Hall–Petch relation holds for the deformation mechanism were found to be inferior to those of samples with a single- of samples with grains smaller than 10 nm and that grain crystal matrix. This outcome is due to the fact that atoms boundary sliding reduces the mechanical properties of sam- in grain boundaries are more able to move than the atoms ples [31]. inside grains. Therefore, the elastic strength is reduced as According to Zhou [32], potential energy variations in grain boundaries increases. This phenomenon has been composite structures are excellent indicators of the role observed by Rajaram et al. [30]. they found that the elas- of the second phase and its interface with the matrix on tic modulus of polycrystalline nickel samples dramatically structural changes. As such, the potential energy of atoms decreased with decreasing grain sizes. located at the Al/Cu interface and aluminum grain bound- The effects of temperature on the plasticity of samples aries for samples with single-crystal and polycrystal matri- were investigated by calculating the average tensile stress ces at the yield point plotted at 300 and 600 K in Figure 5. It for a strain range of 0.7 to 0.15 in samples with a single- is, therefore, evident that increasing the temperature to 600 crystal matrix and strain range between 0.4 and 0.15 for K would increase the number of aluminum atoms having specimens with a polycrystalline matrix. This strain range high potential energy around the interfacial region. Fur- was considered to maintain steady-state stress and ensure thermore, besides atoms at the interface, atoms inside the the variations are independent of strain. Figure 4 shows 100 | M. Ali Abdulrehman et al. grain boundaries in the polycrystalline material are also in a higher potential state than those in a single-crystal mate- rial. With the temperature on the rise, the potential energy of atoms in these areas also increases, facilitating their dis- placement under loading. It is important to establish here that how the temperature affects the mechanical behav- ior of samples. In other words, how does the temperature change the plastic deformation mechanisms? Figure 6: DXA results representing the effects of Al/Cu interfacial region and grain boundaries on the emission of dislocations from the interfacial area of different Al/Cu NCs: (a-c) NC samples having single-crystalline matrix, (d-f) NC samples having poly-crystalline matrix Figure 5: Potential energy of atoms within the microstructure of Figure 7: von Mises stress distribution in the Al/Cu nanocomposite nanocomposite samples at the temperatures of 300 K and 600 K: samples: (a) nanocomposite samples having single-crystalline (a-b) nanocomposite samples having single-crystalline matrix, (c-d) matrix, (b) nanocomposite samples having poly-crystalline matrix nanocomposite samples having poly-crystalline matrix increases. According to the study carried out by Pagrelco et al. [12], in the interface of Al/Cu, the difference of atomic radius between aluminum and copper atoms leads to an 3.2 Deformation mechanisms of the Al-Cu NC atomic mismatch. Therefore, it seems that the atomic mis- at ambient temperature match can lead to defect formation from the interfacial area. In order to probe this issue more, we measured the stress This section goes through the structural changes of the values at the interface region. As such, the von Mises anal- Al-Cu NC in terms of crystal defects such as dislocations ysis of Figure 7 is suggestive of stress concentration on the and stacking fault to study the plastic deformation mech- interfacial atoms, which reduces the stress required for dis- anisms. According to previous studies [33, 34], in the sin- location nucleation in this area. Accordingly, it is evident gle crystals, dislocations can nucleate from the sources that the Al/Cu interface serves as a dislocation source. In inside the grains, from free surfaces, or from atomic impu- Figures 6d–6f, which correspond to nanocomposites with rities. In contrast, in the polycrystalline aluminum, these polycrystalline matrix, besides the interface area, disloca- defects are easily emitted into the grains through grain tions nucleate from the grain boundaries, too, resulting in boundaries [35]. In the case of our study, the Al-Cu samples many more dislocations than in the case of a single-crystal were compared at 300 K in different strain values to investi- matrix. It is, therefore, easy to understand that the smaller gate the trend of structural defect formation. According to flow stress in the case of a polycrystalline matrix (Figure 4) Figures 6a–6c, dislocations nucleate at the Al/Cu interface is a result of the considerable density of crystal defects in the nanocomposite with a single-crystal matrix, emitting in the structure. The dislocation density increases as the into the nanocomposite matrix. Moreover, the density of strain increases. In both samples, most of the dislocations dislocations emitting from the interface increases as strain forming are either Shockley partial dislocations or stair-rod Temperature-dependent mechanical properties of Al/Cu nanocomposites | 101 3.3 Temperature effects on crystal defects and deformation mechanisms of the Al-Cu NC The effects of temperature on crystal defects in the Al-Cu NCs were studied using DXA by investigating dislocations and stacking faults at 300 and 600 K for similar strain. Ac- cording to Figure 9, more dislocations formed at 300 K than 600 K in both types of nanocomposites. Since stacking fault regions are bound by two Shockley partial disloca- tions, the lower dislocation density at elevated tempera- tures translates to fewer stacking faults. This outcome can be attributed to the thermally activated mechanisms [40]. For example, edge dislocations can climb at high temper- atures, reducing the density of this type of dislocations under tension [41, 42]. Accordingly, more slip paths will be available to other dislocations, facilitating further defor- mation. In contrast, at ambient temperature, considerable Figure 8: Steps of grain boundary migration analyzed using vol- amounts of partial dislocations form that end up locking umetric strain at different strains: (a) ϵ = 0.08, (b) ϵ = 0.09, (c) ϵ = 0.10, (d) ϵ = 0.11, (e) ϵ = 0.12, (f) ϵ = 0.13 the slip paths. In this case, the material will require more considerable stress to continue its plastic deformation. The consequence is higher flow stress at low temperatures com- dislocations. Studies have shown that interactions between pared to high temperatures [43, 45]. these dislocations during the deformation can lock the dis- locations and prevent the slip of other dislocations [36, 37]. Dislocation locking has noticeable effects in cases where plastic deformation is driven by dislocation slip. Plastic deformation of the polycrystalline aluminum with a grain size of below 10 nm is governed by grain- boundary-induced mechanisms [38]. The phenomenon was investigated by calculating the volumetric strain at 300 K and monitoring grain boundary displacements in the nanocomposite with polycrystalline matrix at differ- ent strains. The red arrows in Figure 8 show the path the grain boundary takes in the next step of strain. It is evident from Figures 8a–8f that grain boundaries and the Al/Cu interface correspond to the highest strain. Moreover, grain boundaries move at any strains. Therefore, grain boundary sliding is the dominant plastic deformation mechanisms in nanocomposites with a polycrystalline matrix. In con- trast, plastic deformation in nanocomposites with a single- Figure 9: Snapshots of the nanocomposite samples at the temper- crystal matrix is governed by dislocation slip. According atures of 300 K and 600 K at the same strain: (a-b) ϵ = 0.12, (c-d) to Figures 8e–8f, voids formed inside the grains at higher ϵ = 0.09 (Configurations were characterized by DXA) strains. Vacancy and void formation are significant factors that make the material less resistant to plastic deformation For a quantitative analysis of the effects of temperature and accelerate failure. Void formation in high-plasticity on the density of dislocations and stacking faults, all sam- materials such as aluminum, copper, and nickel has been ples were compared in terms of the number of these defects studied by Walt et al. [39]. What remains to be addressed in during tension. According to Figure 10, nanocomposites the following is whether raising the temperature can affect with a polycrystalline matrix had more dislocations than the nature and density of these crystal defects. those with a single-crystal matrix. As discussed earlier, this 102 | M. Ali Abdulrehman et al. outcome is a result of more grain boundaries and nucle- 4 Conclusion ation sites available for dislocations. With the temperature increasing, the dislocation density is reduced as the recov- Aiming to probe the effects of temperature on mechanical ery process activates. The dislocation density decreased characteristics and plastic deformation mechanisms of the to a larger extent in the specimens with polycrystalline Al-Cu nanocomposite, samples with single-crystal and poly- matrices than those with a single-crystal matrix when the crystalline matrices were subjected to uniaxial tensile tests temperature was increased from 300 to 600 K. This phe- at different temperatures. It was shown that, by increasing nomenon is due to the much higher dislocation density the energy levels of the atoms, an increase in temperature in the polycrystalline matrix, which makes interactions would reduce their elastic and plastic strength. Accordingly, between dislocations with opposite signs more likely. In the yield strength and elastic modulus of the samples were Figure 11, the total number of atoms in an HCP structure, reduced as the temperature increased. Observations were representing the stacking fault, is calculated for the spec- also suggestive of the emission of dislocations and stack- imens throughout the tension process. Accordingly, the ing faults from the Al/Cu interface into the nanocomposite density of stacking faults decreases as Shockley partial matrix due to stress concentration in this area. Moreover, dislocations neutralize each other with the temperature due to stress concentration around them, grain boundaries dropping. This observation is consistent with the graph are critical for dislocation nucleation in nanocomposite plotting dislocation density [46–49]. samples with a polycrystalline matrix. It was shown in this study that as the temperature increases, the density of dis- locations and stacking faults is reduced as thermally acti- vated mechanisms are triggered. It was also observed that, in both types of nanocomposites, the flow stress decreases as temperature increases, suggesting that the samples will require smaller stress to continue plastic deformation. Acknowledgement: The authors would like to thank Mus- tansiriyah University (http://www.uomustansiriyah.edu.iq) Baghdad – Iraq for support the present work Funding information: The authors state no funding in- Figure 10: Dislocation analysis outcomes revealing the impacts of volved. temperature on the dislocation length in the Al/Cu nanocomposite samples Author contributions: All authors have accepted responsi- bility for the entire content of this manuscript and approved its submission. Conflict of interest: The authors state no conflict of inter- est. References [1] Sozhamannan GG, Prabu SB, Paskaramoorthy R. 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Temperature-dependent mechanical properties of Al/Cu nanocomposites under tensile loading via molecular dynamics method

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Curved and Layer. Struct. 2022; 9:96–104 Research Article Mohammed Ali Abdulrehman*, Mohammed Ali Mahmood Hussein, and Ismail Ibrahim Marhoon Temperature-dependent mechanical properties of Al/Cu nanocomposites under tensile loading via molecular dynamics method https://doi.org/10.1515/cls-2022-0009 1 Introduction Received Oct 13, 2021; accepted Nov 29, 2021 Abstract: Al-Cu Nanocomposites (NCs) are widely used in In recent years, metal matrix composites have received con- industrial applications for their high ductility, light weight, siderable attention to their availability, low production cost, excellent thermal conductivity, and low-cost production. and superior properties compared to pure metals [1]. With The mechanical properties and deformation mechanisms of an assortment of industrial applications, from aerospace to Metal Matrix NCs (MMNCs) strongly depend on the matrix automotive and military, Al-Cu NCs are no exception thanks microstructure and the interface between the matrix and to their light weight and high specific strength, toughness, the second phase. The present study relies on Molecular and thermal conductivity [2, 3]. Several methods have been Dynamics (MD) to investigate the effects of temperature on proposed to improve the mechanical properties of Al-Cu the mechanical properties and elastic and plastic behav- NCs and make them more ductile with a focus on improv- ior of the Al-Cu NC with single-crystal and polycrystalline ing the bond strength at the matrix/reinforcement interface. matrices. The effects of heating on microstructural defects Many studies [4, 5] have addressed the issue in an attempt in the aluminum matrix and the Al/Cu interface were also to increase these composites’ yield strength, elastic mod- addressed in the following. It was found that the density ulus, and wear resistance. Despite being a macroscopic of defects such as dislocations and stacking fault areas are phenomenon, nanocomposite fracture is a consequence much higher in samples with polycrystalline matrices than of structural changes at the atomic scale. Accordingly, to those with single-crystal ones. Further, by triggering ther- characterize the fracture mechanisms and investigate the mally activated mechanisms, increasing the temperature structural evolutions during deformation, we need tools to reduces the density of crystal defects. Heating also facili- track atomic movements across the crystal structure. The tates atomic migration and compromises the yield strength best approach to simulating the mechanical properties and and the elastic modulus as a result of the increased energy investigating changes in the atomic structure is modeling of atoms in the grain boundaries and in the Al-Cu interface. on the atomic scale by molecular dynamics simulation [6]. The results showed that the flow stress decreased in all On the macroscopic scale, several factors, including the samples by increasing the temperature, making them less geometry of the specimen, strain rate, temperature, and the resistant to the plastic deformation. crystal structure, affect the material’s behavior. Meanwhile, on the microscopic scale, plastic deformation in nanocrys- Keywords: Al-Cu nanocomposite; molecular dynamics tals often takes place as a result of either dislocation slip or method; mechanical properties; temperature; tensile load- twinning [7]. Previous studies [8, 9] showed that dislocation ing; dislocations glide in the crystal lattice is a major factor in the deforma- tion of FCC crystals. As notable defects in the crystalline microstructure, dislocations can nucleate through the ma- terial from free surfaces, grain boundaries, voids, or atomic *Corresponding Author: Mohammed Ali Abdulrehman: Materi- impurities. Given that both aluminum and copper have an als Engineering Department, College of Engineering, Mustansiriyah FCC crystal structure, their slip planes and directions are University, Baghdad, Iraq; expected to be compatible. Balaram et al. [10] showed that Email: mohammed_ali_mat@uomustansiriyah.edu.iq Mohammed Ali Mahmood Hussein: Al Rafidain University Col- Al–Cu alloy precipitation can create effective obstacles for lage, Department of Air-Conditioning and Refrigeration Eng.Tech, dislocation slip. In another study, Mojmoder [11] showed Baghdad 10, Iraq that the mechanical properties of alloy structures strongly Ismail Ibrahim Marhoon: Materials Engineering Department, depend on the loading direction. Regardless, NC deforma- College of Engineering, Mustansiriyah University, Baghdad, Iraq Open Access. © 2022 M. Ali Abdulrehman et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License Temperature-dependent mechanical properties of Al/Cu nanocomposites | 97 tion has stark differences from deformation in alloys. It the deformation mechanisms at ambient temperature, the has been shown that crystal defects can also form the in- results were supported by previous studies of [33–39]. terface of the matrix and the second phase. For example, Temperature as one of the most important factors af- Pagerleco et al. [12] carried out a microstructural investiga- fecting the deformation mechanisms through changes in tion of an Al-Cu NC with single-crystal matrix at different the density of structural defects, is highly regarded by re- strain rates and high temperature by molecular dynam- searchers. In this regard, in order to investigate the effect ics simulation. The study suggests that atomic mismatch of temperature on the deformation process of structural in the interface of the copper nanoparticle with the alu- defects such as dislocations and stacking faults areas, ac- minum matrix promotes the formation of voids that grow cording to previous studies of [40–49], the values of HCP and compromise the mechanical properties of the sample. atoms and dislocations for both nanocomposite samples In another study, Tian et al. [13] investigated plastic defor- with single crystal matrix and polycrystalline matrix were mation in multi-layered aluminum–copper composites by calculated and the results were compared and discussed. Molecular Dynamics (MD). It was found that dislocations Based on the previous discussion, present MD simu- nucleate in the copper layer and move into the aluminum lation investigates the mechanical properties and defor- layer, deforming it due to the semi-coherent Cu/Al inter- mation mechanisms of the Al-Cu NCs by uniaxial tensile face. The study showed that the aluminum layer deformed tests for samples with single-crystal and polycrystalline to a greater extent than the copper layer and that rupture matrices at ambient temperature. Then, in order to capture began from the aluminum as voids began to develop. In a temperature affects, the sample was stretched at different study of the effects of grain boundaries on crystal defects temperatures. Accordingly, the second part of the study and the mechanical properties of Al-Cu alloys, Mahta et goes through the details of molecular dynamics parame- al. [14] the structures were melted in MD simulations to ters and sample construction techniques. The third section compare the mechanical properties of the samples as grain presents the uniaxial tensile test results at different tem- boundaries formed. The grain boundaries were shown to peratures and discusses the deformation mechanisms. The be critical factors when it comes to the formation of dislo- fourth and final section summarizes the study results and cations and stacking faults. A review of past studies on the presents the conclusions. subject shows that the important role of grain boundaries in plastic deformation and the mechanical properties of Al-Cu nanocomposites are yet to be investigated in detail. 2 MD setup Moreover, in light of the high-temperature applications of these nanocomposites [15], the temperature-based plastic The present study aims to molecular dynamics simulation deformation mechanisms of these materials need to be ad- to probe temperature effects on the deformation mecha- dressed in more detail. nisms of the Al-Cu NCs in uniaxial tensile tests and evalu- In the present study, in order to fabricate the polycrys- ate its mechanical properties. In the following, this section talline samples according to the method presented by [16], discusses how the samples are prepared, the interaction samples were made, then using the software and details of potential, and the analysis tools. molecular dynamics simulation presented by authors [17– 25], the samples experienced the uniaxial tensile. These details are fully discussed in the next section. The results 2.1 Sample construction were also analyzed using atomic geometry-based tools in- troduced in [26]. In the case of sample with single crystal matrix, NCs sam- To do a quantitative validation the obtained outcomes, ples were constructed by considering a 10×10×10 nm alu- first, the results were extracted from the stress–strain minum cube having copper nanoparticle in the center. The curves of the samples were first compared with the studies copper nanoparticle with 4 nm diameter accounted for 2.6 such as [27–29]. Then the results were discussed from the of the entire nanocomposite volume. The polycrystalline perspective of differences in the values of mechanical prop- Al-Cu nanocomposite samples were built by the Voronoi erties for both single crystal and polycrystalline samples tessellation method [16]. The nanocomposite matrix com- based on previous observations [30, 32]. Due to the fact prised four aluminum grains with average grain size of 2 that the most important factors in plastic deformation in nm. Figure 1 depicts the mentioned samples. nanomaterials are microstructural defects such as dislo- cations and twins, in order to provide a better picture of 98 | M. Ali Abdulrehman et al. 3 Results and discussion This section delves into the temperature effects on mechan- ical properties, crystal defects, and plastic deformation of Al/Cu nanocomposites with single-crystal and polycrys- talline matrices. 3.1 Temperature-based mechanical Figure 1: Al/Cu nanocomposite samples: (a) cross-section of single- characteristics of the Al-Cu crystalline matrix having Cu NP, (b) cross-section of poly-crystalline nanocomposite matrix having Cu NP The effects of temperature on the mechanical properties of nanocomposite samples were investigated by annealing 2.2 Parameters of molecular dynamics the specimens at 300, 400, 500, and 600 K before uniaxial tensile test. Figure 2 plots the tensile stress–strain curve of The simulations were implemented using LAMMPS [17]. the nanocomposite samples with single-crystal and poly- Aluminum–aluminum, copper–copper, and aluminum– crystalline matrices at different temperatures. The graph copper interactions were modeled using the angular- shows a linear-elastic region with the stress dropping after dependent potential function [18]. The potential function the yield. In the plastic region, the stress follows a zig-zag has been successfully used by other researchers to simu- pattern that is also found in the stress–strain graph of pure late the aluminum–copper system to characterise the me- aluminum [27]. It is evident that increasing the temperature chanical properties by identifying and examining disloca- tions and stacking faults [12, 19–21]. In the present simu- lations, the initial velocities were set using the Maxwell– Boltzmann distribution at given temperatures. Moreover, the equations of motion were integrated by the velocity Verlet algorithm [22]. Before the simulation tensile test, the single-crystal samples were relaxed for 200 ps using the NPT ensemble at zero pressure, and the desired temperature with 1 fs time- steps. It’s worth mentioning that all polycrystalline sam- ples were annealed at 300 K for 100 ps to improve grain boundary stability. It must also be noted that, the grain size was calculated again after this stage, showing no sign of grain growth. Then, the polycrystalline samples relaxed at desired temperature. Periodic boundary conditions were considered in all three directions. Similar to previous stud- ies [23, 24], after relaxation, the samples were subjected 8 −1 to tension at 0.01 A/ps. The strain rate was 10 s and the test continued up to 15% strain along the x-axis. Zero pressure was maintained in the lateral directions using the Nosé–Hoover barostat during tension. Stress concentration was measured around crystal de- fects, the Al/Cu interface, and grain boundaries by the von Mises analysis. The dislocations were characterized by the Dislocation Extraction Algorithm (DXA) [26]. Moreover, im- ages and other analyses were produced by OVITO. Figure 2: Stress–strain curves of nanocomposite samples for ten- sion at different temperatures: (a) nanocomposite samples having single-crystalline matrix, (b) nanocomposite samples having poly- crystalline matrix Temperature-dependent mechanical properties of Al/Cu nanocomposites | 99 Table 1: Comparison of obtained mechanical properties in this study with the literature Study Case Yield strength (GPa) Elastic modulus (GPa) Pogorelko [12] Al and Cu inclusion 5.6 — Mahata [14] Al-11% at Cu 3.1 — Pogorelko [28] Al-Cu composite 5 — Present work Al single crystal and Cu NP 4.4 61.91 Hocker [29] Polycrystalline Al-4% at Cu 2.3 — Present work Polycrystalline Al and Cu NP 1.8 51.39 Figure 3: Comparison of the elastic modulus variations of the sam- Figure 4: Average flow strength as a function of temperature ples at different temperatures the average flow stress for different specimens. Accordingly, reduces the samples’ yield strength. The elastic modulus the average flow stress reduces as temperature rises. In fact, was also calculated based on the slope in the linear region. heating reduces the required stress to continue plastic defor- Table 1 compares the yield strength results at 300 K with mation. Elevated temperatures promote the energy states the literature. of atoms, facilitating their displacement, which translates According to Figure 3, the elastic modulus declines in to lower elastic and plastic strength. The values of calcu- all samples as the temperature rises. In fact, high tempera- lated flow stress for nanocomposites with a polycrystalline ture promotes the energy state of the atoms, compromising matrix is lower than those with a single-crystal matrix at their elastic strength. The yield stress and elastic modu- all temperatures. The reason lies in the fact that the inverse lus of nanocomposite samples with polycrystalline matrix Hall–Petch relation holds for the deformation mechanism were found to be inferior to those of samples with a single- of samples with grains smaller than 10 nm and that grain crystal matrix. This outcome is due to the fact that atoms boundary sliding reduces the mechanical properties of sam- in grain boundaries are more able to move than the atoms ples [31]. inside grains. Therefore, the elastic strength is reduced as According to Zhou [32], potential energy variations in grain boundaries increases. This phenomenon has been composite structures are excellent indicators of the role observed by Rajaram et al. [30]. they found that the elas- of the second phase and its interface with the matrix on tic modulus of polycrystalline nickel samples dramatically structural changes. As such, the potential energy of atoms decreased with decreasing grain sizes. located at the Al/Cu interface and aluminum grain bound- The effects of temperature on the plasticity of samples aries for samples with single-crystal and polycrystal matri- were investigated by calculating the average tensile stress ces at the yield point plotted at 300 and 600 K in Figure 5. It for a strain range of 0.7 to 0.15 in samples with a single- is, therefore, evident that increasing the temperature to 600 crystal matrix and strain range between 0.4 and 0.15 for K would increase the number of aluminum atoms having specimens with a polycrystalline matrix. This strain range high potential energy around the interfacial region. Fur- was considered to maintain steady-state stress and ensure thermore, besides atoms at the interface, atoms inside the the variations are independent of strain. Figure 4 shows 100 | M. Ali Abdulrehman et al. grain boundaries in the polycrystalline material are also in a higher potential state than those in a single-crystal mate- rial. With the temperature on the rise, the potential energy of atoms in these areas also increases, facilitating their dis- placement under loading. It is important to establish here that how the temperature affects the mechanical behav- ior of samples. In other words, how does the temperature change the plastic deformation mechanisms? Figure 6: DXA results representing the effects of Al/Cu interfacial region and grain boundaries on the emission of dislocations from the interfacial area of different Al/Cu NCs: (a-c) NC samples having single-crystalline matrix, (d-f) NC samples having poly-crystalline matrix Figure 5: Potential energy of atoms within the microstructure of Figure 7: von Mises stress distribution in the Al/Cu nanocomposite nanocomposite samples at the temperatures of 300 K and 600 K: samples: (a) nanocomposite samples having single-crystalline (a-b) nanocomposite samples having single-crystalline matrix, (c-d) matrix, (b) nanocomposite samples having poly-crystalline matrix nanocomposite samples having poly-crystalline matrix increases. According to the study carried out by Pagrelco et al. [12], in the interface of Al/Cu, the difference of atomic radius between aluminum and copper atoms leads to an 3.2 Deformation mechanisms of the Al-Cu NC atomic mismatch. Therefore, it seems that the atomic mis- at ambient temperature match can lead to defect formation from the interfacial area. In order to probe this issue more, we measured the stress This section goes through the structural changes of the values at the interface region. As such, the von Mises anal- Al-Cu NC in terms of crystal defects such as dislocations ysis of Figure 7 is suggestive of stress concentration on the and stacking fault to study the plastic deformation mech- interfacial atoms, which reduces the stress required for dis- anisms. According to previous studies [33, 34], in the sin- location nucleation in this area. Accordingly, it is evident gle crystals, dislocations can nucleate from the sources that the Al/Cu interface serves as a dislocation source. In inside the grains, from free surfaces, or from atomic impu- Figures 6d–6f, which correspond to nanocomposites with rities. In contrast, in the polycrystalline aluminum, these polycrystalline matrix, besides the interface area, disloca- defects are easily emitted into the grains through grain tions nucleate from the grain boundaries, too, resulting in boundaries [35]. In the case of our study, the Al-Cu samples many more dislocations than in the case of a single-crystal were compared at 300 K in different strain values to investi- matrix. It is, therefore, easy to understand that the smaller gate the trend of structural defect formation. According to flow stress in the case of a polycrystalline matrix (Figure 4) Figures 6a–6c, dislocations nucleate at the Al/Cu interface is a result of the considerable density of crystal defects in the nanocomposite with a single-crystal matrix, emitting in the structure. The dislocation density increases as the into the nanocomposite matrix. Moreover, the density of strain increases. In both samples, most of the dislocations dislocations emitting from the interface increases as strain forming are either Shockley partial dislocations or stair-rod Temperature-dependent mechanical properties of Al/Cu nanocomposites | 101 3.3 Temperature effects on crystal defects and deformation mechanisms of the Al-Cu NC The effects of temperature on crystal defects in the Al-Cu NCs were studied using DXA by investigating dislocations and stacking faults at 300 and 600 K for similar strain. Ac- cording to Figure 9, more dislocations formed at 300 K than 600 K in both types of nanocomposites. Since stacking fault regions are bound by two Shockley partial disloca- tions, the lower dislocation density at elevated tempera- tures translates to fewer stacking faults. This outcome can be attributed to the thermally activated mechanisms [40]. For example, edge dislocations can climb at high temper- atures, reducing the density of this type of dislocations under tension [41, 42]. Accordingly, more slip paths will be available to other dislocations, facilitating further defor- mation. In contrast, at ambient temperature, considerable Figure 8: Steps of grain boundary migration analyzed using vol- amounts of partial dislocations form that end up locking umetric strain at different strains: (a) ϵ = 0.08, (b) ϵ = 0.09, (c) ϵ = 0.10, (d) ϵ = 0.11, (e) ϵ = 0.12, (f) ϵ = 0.13 the slip paths. In this case, the material will require more considerable stress to continue its plastic deformation. The consequence is higher flow stress at low temperatures com- dislocations. Studies have shown that interactions between pared to high temperatures [43, 45]. these dislocations during the deformation can lock the dis- locations and prevent the slip of other dislocations [36, 37]. Dislocation locking has noticeable effects in cases where plastic deformation is driven by dislocation slip. Plastic deformation of the polycrystalline aluminum with a grain size of below 10 nm is governed by grain- boundary-induced mechanisms [38]. The phenomenon was investigated by calculating the volumetric strain at 300 K and monitoring grain boundary displacements in the nanocomposite with polycrystalline matrix at differ- ent strains. The red arrows in Figure 8 show the path the grain boundary takes in the next step of strain. It is evident from Figures 8a–8f that grain boundaries and the Al/Cu interface correspond to the highest strain. Moreover, grain boundaries move at any strains. Therefore, grain boundary sliding is the dominant plastic deformation mechanisms in nanocomposites with a polycrystalline matrix. In con- trast, plastic deformation in nanocomposites with a single- Figure 9: Snapshots of the nanocomposite samples at the temper- crystal matrix is governed by dislocation slip. According atures of 300 K and 600 K at the same strain: (a-b) ϵ = 0.12, (c-d) to Figures 8e–8f, voids formed inside the grains at higher ϵ = 0.09 (Configurations were characterized by DXA) strains. Vacancy and void formation are significant factors that make the material less resistant to plastic deformation For a quantitative analysis of the effects of temperature and accelerate failure. Void formation in high-plasticity on the density of dislocations and stacking faults, all sam- materials such as aluminum, copper, and nickel has been ples were compared in terms of the number of these defects studied by Walt et al. [39]. What remains to be addressed in during tension. According to Figure 10, nanocomposites the following is whether raising the temperature can affect with a polycrystalline matrix had more dislocations than the nature and density of these crystal defects. those with a single-crystal matrix. As discussed earlier, this 102 | M. Ali Abdulrehman et al. outcome is a result of more grain boundaries and nucle- 4 Conclusion ation sites available for dislocations. With the temperature increasing, the dislocation density is reduced as the recov- Aiming to probe the effects of temperature on mechanical ery process activates. The dislocation density decreased characteristics and plastic deformation mechanisms of the to a larger extent in the specimens with polycrystalline Al-Cu nanocomposite, samples with single-crystal and poly- matrices than those with a single-crystal matrix when the crystalline matrices were subjected to uniaxial tensile tests temperature was increased from 300 to 600 K. This phe- at different temperatures. It was shown that, by increasing nomenon is due to the much higher dislocation density the energy levels of the atoms, an increase in temperature in the polycrystalline matrix, which makes interactions would reduce their elastic and plastic strength. Accordingly, between dislocations with opposite signs more likely. In the yield strength and elastic modulus of the samples were Figure 11, the total number of atoms in an HCP structure, reduced as the temperature increased. Observations were representing the stacking fault, is calculated for the spec- also suggestive of the emission of dislocations and stack- imens throughout the tension process. Accordingly, the ing faults from the Al/Cu interface into the nanocomposite density of stacking faults decreases as Shockley partial matrix due to stress concentration in this area. Moreover, dislocations neutralize each other with the temperature due to stress concentration around them, grain boundaries dropping. This observation is consistent with the graph are critical for dislocation nucleation in nanocomposite plotting dislocation density [46–49]. samples with a polycrystalline matrix. It was shown in this study that as the temperature increases, the density of dis- locations and stacking faults is reduced as thermally acti- vated mechanisms are triggered. It was also observed that, in both types of nanocomposites, the flow stress decreases as temperature increases, suggesting that the samples will require smaller stress to continue plastic deformation. Acknowledgement: The authors would like to thank Mus- tansiriyah University (http://www.uomustansiriyah.edu.iq) Baghdad – Iraq for support the present work Funding information: The authors state no funding in- Figure 10: Dislocation analysis outcomes revealing the impacts of volved. temperature on the dislocation length in the Al/Cu nanocomposite samples Author contributions: All authors have accepted responsi- bility for the entire content of this manuscript and approved its submission. Conflict of interest: The authors state no conflict of inter- est. References [1] Sozhamannan GG, Prabu SB, Paskaramoorthy R. 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Journal

Curved and Layered Structuresde Gruyter

Published: Jan 1, 2022

Keywords: Al-Cu nanocomposite; molecular dynamics method; mechanical properties; temperature; tensile loading; dislocations

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