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Molecular dynamics simulation study of cold spray process
Journal of Manufacturing Processes 33 (2018) 136–143
Contents lists available at ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Molecular dynamics simulation study of cold spray process Aneesh Joshi, Sagil James
⁎
T
Department of Mechanical Engineering, California State University Fullerton, CA 92831, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Cold spray process Molecular dynamics simulation Nanoparticles Particle impact
Cold Spray (CS) process is a deposition process in which micron-to-nano sized solid particles are deposited on a substrate using high-velocity impacts. Unlike thermal spray processes, CS process does not melt the particles thus retaining their original physical and chemical properties. These characteristics make CS process ideal for various engineering applications. The bonding mechanism involved in CS process is hugely complicated considering the dynamic nature of the process. Even though CS process offers great promises, the realization of its full potential is limited by lack of understanding of the complex mechanisms involved. The study focuses on understanding the complex nanoscale mechanisms involved in CS process. The study uses Molecular Dynamics (MD) simulation technique to understand the material deposition phenomenon during the CS process. For the simulation conditions used, the study finds that the quality of deposition is highest for an impact velocity of 700 m/s, the particle size of 20 Å and an impact angle of 90°. The von Mises stress and plastic strain analysis revealed that bonding mechanism in CS process could be attributed to adiabatic softening, adiabatic shear instabilities followed by interfacial jetting of particle materials resulting in a uniform coating. The findings of this study can further the scope and applications of CS process.
1. Introduction Cold Spray (CS) is an emerging solid-state deposition process, where micron-to-nano sized particles bond to a substrate due to high-velocity impact. Unlike thermal spray processes, chemical and physical properties of deposited particles are retained in CS process considering the solid-state low-oxidized nature of the coating. These characteristics make CS process ideal for several critical engineering applications in industries such as defense and aerospace sectors [1]. During CS process, the acceleration of particles is achieved by the expansion of hot pressurized gases through a converging-diverging nozzle [2]. The high-velocity impact of the accelerating particles causes plastic deformation of the particles and the substrate surface resulting in a uniform coating. The schematic of CS process is shown in Fig. 1. The quality of the coating during the CS process is influenced by the incident velocity of the particles [1]. The successful bonding of powder particles on the substrate occurs only when the velocity of sprayed material exceeds a critical value that is specific to the material [1]. For instance, the critical velocity is found to be approximately 570 m/s for copper particles having a size of 5–25 μm [3]. The material suitability for CS process depends on the mechanical and physical properties including material hardness, melting temperature and density [4]. Materials with relatively low yield strength such as copper, aluminum, and zinc are considered ideal for the CS process
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as they exhibit relatively high softening at elevated temperatures [5]. High strength materials are not ideal for CS process as they do not provide enough energy for deposition [6]. Experimental study on CS process of metal particles on polymer reveals that no metal particles can be coated on soft polymer due to lack of plastic deformation of particles [7]. Other factors influencing the quality of deposition during CS process include angle of impact, gas flow rate and stand-off distance between the nozzle tip and target surface [8]. Study on variations in stand-off distances (range 10 mm–110 mm) for particles of aluminum, titanium and copper powders showed deposition efficiency decreases with increase in stand-off distance [9]. Most of the studies reported on CS process is performed through experimentation [10]. While experimental techniques reveal the quality of material deposition and the microstructural characteristics, the use of experimentation in understanding dynamic mechanisms involved in the CS process is often limited. Simulation tools such as finite element (FE) simulation techniques and numerical methods have often been used as an alternative way in these cases. FE simulation have been used to understand the effect of process parameters during CS and other thermal spray processes at macroscales. The impact dynamics, bonding mechanism, and critical velocities during the CS process were studied using FE simulation tool ABAQUS [6]. The study found that the critical velocity depends on several parameters including the type of spray material, powder
Corresponding author. E-mail address: [email protected] (S. James).
https://doi.org/10.1016/j.jmapro.2018.05.005 Received 19 August 2017; Received in revised form 15 April 2018; Accepted 6 May 2018 1526-6125/ © 2018 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
Journal of Manufacturing Processes 33 (2018) 136–143
A. Joshi, S. James
Fig. 1. Schematic of Cold Spray Process.
“Large-scale atomic/molecular massively parallel simulator” (LAMMPS) [15]. The study considers the impact of nanoparticle impact on the surface of a metal substrate in three-dimension (3D). The simulation system consists of copper (Cu) atoms as a substrate, and a nanoparticle also made of Cu atoms. The substrate is made of 30,000 atoms of Cu, and the nanoparticle is made of 100 Cu atoms in fcc lattice structure. The shape of the substrate is a rectangular block having dimensions of 100 Å × 100 Å × 20 Å with face-centered cubic (fcc) lattice structure having a lattice spacing of 3.61 Å. The nanoparticle is spherical having a diameter of 10 Å with Cu atoms arranged in (fcc) lattice structure having a lattice spacing of 3.61 Å. The schematic of the model used for CS process simulation is shown in Fig. 2. The conditions used for CS process simulation study are given in Table 1. The interatomic forces between the Cu-Cu atoms are calculated using Embedded Atom Method (EAM), a suitable potential for the simulations of structural, mechanical, and thermal properties of metallic systems including Cu [16]. The Velocity-Verlet algorithm is employed to calculate the position and velocity of the atoms. In the actual working of CS, particles of varying shapes and sizes strike randomly on the substrate surface. The present MD simulation study considers only a single impact of a particle on the substrate under varying operational conditions. It is assumed that a single impact of a particle can explain the complex bonding mechanism involved in the CS process. Embedded Atom Method model function for the fcc of copper and its alloys [16]. In the computational simulation, the potential energy of an atom, i is given by
quality, particle size and the particle impact temperature. Splat formation during the thermal process was studied by numerical simulation method which revealed that increase in substrate temperature reduces the formation of splats [11]. FE tool ABAQUS/Explicit used for simulation study on CS process showed that a minimal impact particle velocity needed to produce shear localization [12]. It is known that the feed powder particles and the substrate and deposited material (after the first layer of particle impact) suffer a full localized distortion during impact. It causes disturbance of the thin surface films forming an adiabatic shear band which enables a conformal interaction between the particles and the substrate/deposited material. Formation of high strain rates during impact along with continuous deformation on the shear band leads to instability which causes the material to behave as a liquid material although in a solid-state. This close interaction of clean surfaces combined with high contact pressures is supposed to be the necessary circumstances for particles/substrate and particle/particle bonding. This phenomenon is unique and leads to a strong bond between parent material and the impacting particle. It is agreed that the actual mechanism when solid particles deform and bond onto the substrate during cold spray is still not well understood [12]. FE simulation studies are not capable of explaining the bonding process accurately. Because bonding during the CS process happens at molecular scale, Molecular Dynamics (MD) simulation technique is considered as the ideal tool. During MD simulation, the movements and interactions of atoms or molecules are determined based on the classical equations of motion. However, very few studies have reported on the use of MD simulation on CS process thus far [13]. One such study has used MD simulation to understand the effect of impact velocity on coating process of titanium and nickel particles on titanium substrate during CS process [13]. The study revealed that higher impact velocities result in the stronger interface between the particle and substrate. MD simulation has also been used to investigate structure-property relation during thermal spray processes [14]. The study found that maximum diameter after the impact and the height of the splat increases with increasing Reynolds number of the flow stream until a critical value is reached. From the literature review, it is evident that the effect of critical process parameters on the bonding and the real complex phenomenon of particle/substrate and particle/particle bonding during the CS process is not understood at the nanoscale. This study focusses on the use of molecular dynamics simulation investigate the bonding mechanism in CS process and to understand the effect of critical parameters including impact velocity, particle size and angle of impact on the material deposition phenomenon during the CS process of copper nanoparticles on the copper substrate. The effect of parameters including particle shape, material type and properties, and particle concentration are not considered in this study.
Ei = Fα
⎛ ⎞ 1 ρ (r ) + ∑ Φαβrij ⎜∑ β ij ⎟ 2 j≠i ≠ j i ⎝ ⎠
(1)
where i and j (i ≠ j ) label the atoms in the solid, rij is the distance between atoms i and j , and ρβ is the electron density at the position of atom i due to all other atoms in the solid. It is supposed that this density can be given as a sum of individual atomic densities f (rij ) where rij is the distance between i atoms j , Φαβ and is a potential function, ρβ is the
2. MD simulation Fig. 2. Schematic of MD Simulation Model of Cold Spray Process.
In the current study, the simulation of CS process is performed using 137
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observed. As the impact velocity is 800 m/s, the particles show signs of penetration into the substrate surface as shown in Fig. 4d. It suggests that maintaining the impact velocity within an optimal range is critical in achieving uniform coating. The effect of impact velocity on the deposition height during the MD simulation study of cold spray process is shown in Fig. 5a. The results show that as the impact velocity increases the deposition height decreases. The effect of impact velocity on the flattening ratio during the MD simulation study of cold spray process is shown in Fig. 5b. Flattening ratio is the ratio of the maximum diameter of splat (particle after impact) to original diameter of the particle before impact. In this study, flattening ratio is used to measure the uniformity of deposition of particles on the substrate during the CS process. According to this study, highest flattening ratio is achieved at an impact velocity of 700 m/s. It is also observed that flattening ratio decreases significantly after impact velocity of 750 m/s due to penetration of particles into the substrate.
Table 1 Simulation Conditions used in the MD Simulation of CS process. Materials
Substrate Material Nanoparticle Material
Operating Conditions
Bulk Temperature Potential Used Initial Stand-off Distance Impact Velocity Particle Size Angle of Impact Time step Duration of Simulation
Cu (100 Å × 100 Å × 20 Å) Approx. 30,000 Atoms Cu Sphere (Diameter 5–20 Å) Approx. 50–400 Atoms 300 K Embedded Atom Method (EAM) 15 Å 300–850 m/s 5 Å–25 Å 60°–90° 0.001 ps (picoseconds) 10 ps
electron charge density from atom j of type β at the location of atom i and F is an embedding function that represents the energy required to place atom i of type α into the electron cloud.
ρi =
3.2. Effect of angle of impact on material deposition
∑ f (rij) j
(2)
The angle of impact is another important parameter in CS process. Fig. 6 shows the screenshots of MD simulation study on the effect of angle of impact on particle bonding during the CS process at 500 m/s impact velocity and 10 Å particle size. Fig. 7a shows that as the angle of impact increases the deposition height increases. Highest deposition height is achieved at 90° revealing that jet of particles perpendicular to the substrate will have thicker coating compared to 60° angle of impact. The result of the angle of impact on the flattening ratio during the MD simulation study of cold spray process is shown in Fig. 7b. According to the study, highest flattening ratio is achieved at an angle of impact of 60° as the particles spread over larger area resulting in uniform and less dense coatings as shown in Fig. 6c. It is also observed that flattening ratio is least in 90° due to a concentrated jet of particles forming a non-uniform coating as shown in Fig. 6d. However, it must be noted that at 60° impact angle particles tend to rebound from the substrate more compared to at 90° angle of impact.
Eq. (3) is stress state at a point in a body be given by the three normal stresses σx , σy , σz and the tangential stresses σxy, σyz , σxz based upon a rectangular coordinate system [17]
((0.5 × (σx −σy )2 + (σy−σz )2 + (σx −σz )2 + (3 × (σxy )2 + (σyz )2 + (σxz )2)) (3) The MD simulation of CS process is conducted for duration of 10 ps (ps). In this study, it is assumed that the simulation converges when the relative change in kinetic energies between two successive iterations is less than 10−12. For all the simulations, the convergence occur before 10 ps according to this criterion. 3. Results and discussions All the results reported in this work refer to data obtained after 10 ps (ps) of simulation. A typical atomic configuration of copper nanoparticle deposition on the copper substrate during the CS process for impact velocity of 500 m/s and 90°angle of impact is shown in Fig. 3. The effect of critical process parameters – a) impact velocity b) angle of impact and c) particle size is evaluated by measuring the deposition height and flattening ratio of the bonded nanoparticle.
3.3. Effect of particle size on material deposition Particle Size is another critical parameter for optimum coatings in CS process. Fig. 8 shows the result obtained by varying size of particles at 500 m/s impact velocity with 90° angle of impact. According to the result, the size of particles should not be less than 10 Å as it fails to coat the substrate uniformly. Uniform and thick coatings can be observed at 20 Å. Deposition height increases with increase in particle size up to 20 Å size as shown in Fig. 9a. Above a particle size of 20 Å, deposition does not show any visible changes, which suggests that optimal coating is obtained with particle sizes ranging from 10 to 20 Å for the conditions used in this study. Fig. 9b shows the effect of particle size on flattening ratio during the CS process. From the Fig. 9b, it is observed that the flattening ratio increases with particle size. Moreover, it can be seen that there is no significant change in flattening ratio above a particle size of 20 Å.
3.1. Effect of impact velocity on material deposition Impact velocity is one of the essential parameters in CS process. Critical impact velocity range must be achieved for uniform and efficient bonding of the particles [8]. Fig. 4 shows the screenshot of MD simulation study on the effect of impact velocity on particle bonding during the CS process at 90° angle of impact and 10 Å particle size. The results revealed that an impact velocity of fewer than 500 m/s does not bond the particles efficiently to the surface as shown in Fig. 4a. As the velocity increases above 500 m/s, a uniform coating phenomenon is
Fig. 3. Representative Snapshot of MD Simulation after Nanoparticle Impact on Substrate Surface during Cold Spray Process a) 3D view and b) Side View. 138
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Fig. 4. MD Simulation Snapshots Showing Effect of Variation in Impact Velocity on Material Deposition during Cold Spray Process for a) 400 m/s, b) 500 m/s, c) 600 m/s and d) 800 m/s.
Fig. 5. (a) Effect of Impact Velocity on Deposition Height during Cold Spray Process. (b) Effect of Impact Velocity on Flattening Ratio during Cold Spray Process.
Fig. 6. MD Simulation Snapshots Showing Effect of Variation in Angle of Impact on Material Deposition during Cold Spray Process – (a), (c) Impact angle of 60° and (b), (d) Impact angle of 90°.
Fig. 7. (a) Effect of Angle of Impact on Deposition Height during Cold Spray Process. (b) Effect of Angle of Impact on Flattening Ratio during Cold Spray Process. 139
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Fig. 8. MD Simulation Snapshots Showing Effect of Variation in Particle Size on Material Deposition during Cold Spray Process a) 10 Å particle and b) 20 Å particle.
Fig. 9. (a) Effect of Particle Size on Deposition Height during Cold Spray Process. (b) Effect of Particle Size on Flattening Ratio during Cold Spray Process. Fig. 10. von Mises Stress Acting on Particle for Impact Velocity of a) 300 m/s and b) 800 m/s. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
3.4. von Mises stress distribution during CS process The deformation pattern and the arrangements of particle and substrate molecules/atoms in CS process were examined throughout the simulation. The strain and stress profiles along a particle edge are examined to understand the localization of plastic deformation. The corresponding variation of the equivalent or von Mises stress along particle edge is shown in Fig. 10a and b. Higher stress is induced on the particle and subsequently on to the substrate, which is visible in the red shade on the particle and substrate in case of impact velocity of 800 m/ s. This highly induced stress results in the formation of shear adiabatic instability around the edge of the substrate. Adiabatic shear instability in the substrate and plastic deformation into the particle helps the particle with high strength bonding. It is the reason behind effective, heat-free and dense coatings by CS process. Fig. 11 shows the effect of von Mises stress along the path followed by the particle during the CS process from initial state to the final state after coating for impact velocities of 300 m/s and 800 m/s respectively. From the figure, it is seen there is a no drastic change in equivalent stress for an impact velocity of 300 m/s when it approaches near the interface. As the velocity increases, the von Mises stress is seen to increase during the impact process suggesting material hardening. It is followed by a sudden drop in the equivalent von Mises stress eventually approaching zero stress value. It could be explained by the fact that particle undergoes softening immediately after the impact. Fig. 12 represents variation in velocity as the particle approaches on to the substrate during the cold spray process. From the figure, it is observed that sudden decrease in velocity immediately after its impact.
Fig. 11. Distribution of von Mises Stress with respect to Approach Distance for Varying Impact Velocities during Cold Spray Process.
3.5. Strain acting on the particle during impact in cold spray process Fig. 12. Variation in Particle Travel Velocity During CS Process for Different Initial Velocities.
Fig. 13a and b shows the shear strain distribution on the particle and the substrate after the beginning of the impact for velocities of 300 m/s and 800 m/s respectively. From the figure, it is seen that there is a 140
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Fig. 13. Plastic Strain Distribution During CS Process for Impact velocity of a) 300 m/s and b) 800 m/s.
Fig. 14. (a) Variation in Plastic Shear Strain with respect to Time during Cold Spray Process. (b) Variation in Plastic Shear Strain with respect to Distance during Cold Spray Process.
Fig. 15. Snapshots of Particle at Different Timesteps During CS Process for Impact Velocities of 300 m/s and 800 m/s.
Fig. 16. MD Simulation Snapshot of Particle Impact during the CS process for a) 300 m/s showing no jet formation and b) 800 m/s showing the formation of interfacial jets.
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over time during the CS process is consistent with the findings of the FE simulation study reported by Grujicic et al. [12]. In both the studies, the strains values for impact velocities above a critical value undergo an abrupt owing to material softening and high plastic shear strain-rate deformation. The variation in stress with respect to approach distance showed a similar trend in the MD simulation in this study and results reported on thermos-mechanical finite element simulation of CS process [21].
significant increase in plastic strain on the particle and at the particle/ substrate interface for higher impact velocities. Fig. 14a reveals the variation in particle shear strain with respect to time as it approaches the final coating on to the substrate for impact velocities of 400 m/s, 500 m/s, 600 m/s, 700 m/s and 800 m/s respectively. There is a steady increase in the strain values for impact velocity of 300 m/s, 400 m/s, and 500 m/s. However, there is an abrupt increase in plastic strain values for 600 m/s, 700 m/s and 800 m/s after the impact on the substrate surface. This change in strain values from about 120–160 femtoseconds indicates material softening due to high plastic shear strain-rate deformation and reduction in equivalent von Mises stress. Fig. 14b shows the variation in plastic strain as the particle travels from an initial height of 15 Å towards the substrate. It can be seen that for higher impact velocities (500 m/s or higher), there is a sudden increase in plastic strain during the impact process which suggests high plastic strain rate deformation. Fig. 15 shows the top view of the particles during the CS process for impact velocities of 300 m/s and 800 m/s respectively. For higher impact velocities, it is evident that the impact of the particle on the substrate produces adiabatic shear instability in the shear bands resulting in adiabatic softening of the materials. Both the particle and substrate tend to behave like viscous material resulting in almost free flowing of particles. This unique phenomenon produces interfacial jets when the particle impacts the substrate. This jet formation holds the particle strongly preventing it from escaping from the surface which results in a uniform coating. The formation of jets is evident for higher impact velocities as compared to low impact velocities as shown in Fig. 16. This adiabatic shear instability leads to high strength bonding between particles and substrate and later by particle on the particle. It shows that adiabatic softening and adiabatic shear localization particle/substrate bonding during the cold-spray deposition process. This result is in agreement with the findings of experimental studies done by other researchers which suggested a similar bonding mechanism [1]. This study shows the particle-substrate bonding mechanism at an atomic scale which involves the interplay between adiabatic softening and adiabatic shear localization on one hand and particle/ substrate bonding on the other.
4. Conclusion In this study, molecular dynamics (MD) simulation technique is used to investigate the bonding mechanism involved in cold spray process of copper nanoparticles on the copper substrate. The study also understands the effect of critical process parameters including impact velocity, particle size and angle of impact on the material deposition during the CS process. The critical findings of this study are as follows: a) Impact velocity study revealed that a medium range (500–700 m/s in this study) of impact velocity is found to be optimal for achieving uniform and dense coating. Maintaining impact velocity within an optimal range is critical in achieving a good quality deposition during the cold spray process. b) The angle of impact study revealed that highest deposition height is achieved at angles closer to normal revealing that jet of particles at or near perpendicular to the substrate will have thicker coatings compared to low angles of impact. However, more uniform coatings are observed when the angle of impact is low. c) Particle size study showed that the deposition height and uniformity increase with increasing particle size. However, there is no significant increase in deposition height and uniformity above a particle size of 20 Å for the conditions used in this study. The bonding mechanism study revealed that adiabatic softening, adiabatic shear instabilities and interfacial jet formation occurs at the particle/substrate interface at high velocities resulting in a uniform coating. The von Mises stress and plastic strain analysis further confirmed shear instabilities at higher impact velocities. The results of the MD simulation study are consistent with findings of previously reported experimental and finite element simulation studies. The findings of this study can be used to advance our existing knowledge in the field of cold spray processes.
3.6. Comparison of MD simulation results with past experimental findings The MD simulation results obtained in this study are consistent with the experimental study results previously published [8,18,19]. The MD study found that the flattening ratio increases as the impact velocity increases. The flattening ratio reaches a maximum and then start decreasing suggesting an optimal impact velocity for good quality deposition. This result is consistent with the experimental study results reported by Assadi et al., in which copper particles are deposited on the copper substrate using the CS process [18]. Also, the results of the MD simulation results on variation in von Mises Stress and plastic shear strain with respect to approach distance is consistent with the previously reported experimental results [18]. Both MD simulation and experimental studies suggested that both stress and strain have an inverse relationship with the approach distance. The experimental study reported by Gilmore et al. and Li et al. suggested that the deposition efficiency is higher at normal angles of impact and the efficiency decreases significantly as the angle of impact is approximately 60° [8,19]. It is in agreement with the finding of the current MD simulation study.
Acknowledgment We would like to thank the College of Engineering and Computer Science at California State University Fullerton for providing the financial support for this research. References [1] Assadi H, Kreye H, Gärtner F, Klassen T. Cold spraying–a materials perspective. Acta Mater 2016;116:382–407. [2] A.P. Alkhimov, A.N. Papyrin, V.F. Kosarev, N.I. Nesterovich, M.M. Shushpanov, Gas-dynamic spraying method for applying a coating, in, Google Patents (1994). [3] Stoltenhoff T, Kreye H, Richter H. An analysis of the cold spray process and its coatings. J Therm Spray Technol 2002;11:542–50. [4] Vlcek J, Gimeno L, Huber H, Lugscheider E. A systematic approach to material eligibility for the cold-spray process. J Therm Spray Technol 2005;14:125–33. [5] Moridi A, Hassani-Gangaraj S, Guagliano M, Dao M. Cold spray coating: review of material systems and future perspectives. Surf Eng 2014;30:369–95. [6] Schmidt T, Gärtner F, Assadi H, Kreye H. Development of a generalized parameter window for cold spray deposition. Acta Mater 2006;54:729–42. [7] Lupoi R, O’Neill W. Deposition of metallic coatings on polymer surfaces using cold spray. Surf Coat Technol 2010;205:2167–73. [8] Gilmore D, Dykhuizen R, Neiser R, Smith M, Roemer T. Particle velocity and deposition efficiency in the cold spray process. J Therm Spray Technol 1999;8:576–82. [9] Li W-Y, Zhang C, Guo X, Zhang G, Liao H, Li C-J, et al. Effect of standoff distance on coating deposition characteristics in cold spraying. Mater Des 2008;29:297–304. [10] Lima R, Karthikeyan J, Kay C, Lindemann J, Berndt C. Microstructural
3.7. Comparison of MD simulation results with past finite element simulation findings The MD simulation results obtained in this study are compared with previously reported numerical and finite element simulations. The MD simulation results obtained in this study are consistent with the findings of numerical reported by Ghelichi et al. for CS process of Cu-Cu coating [20]. The predictions of MD simulation of the variation in plastic strain 142
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Phys 1995;117:1–19. [16] Foiles S, Baskes M, Daw M. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys Rev B 1986;33:7983. [17] Von Mises R. Mechanics of solid bodies in the plastically-deformable state, German. Nachr Ges Wiss Goettingen Math-Phys Kl 1913;1:582–92. [18] Assadi H, Gärtner F, Stoltenhoff T, Kreye H. Bonding mechanism in cold gas spraying. Acta Mater 2003;51:4379–94. [19] Li C, Li W, Wang Y, Fukanuma H. Effect of spray angle on deposition characteristics in cold spraying. Therm Spray 2003:91–6. [20] Ghelichi R, Bagherifard S, Guagliano M, Verani M. Numerical simulation of cold spray coating. Surf Coat Technol 2011;205:5294–301. [21] Ju D, Nishida M, Hanabusa T. Simulation of the thermo-mechanical behavior and residual stresses in the spray coating process. J Mater Process Technol 1999;92:243–50.
characteristics of cold-sprayed nanostructured WC–Co coatings. Thin Solid Films 2002;416:129–35. Pasandideh-Fard M, Pershin V, Chandra S, Mostaghimi J. Splat shapes in a thermal spray coating process: simulations and experiments. J Therm Spray Technol 2002;11:206–17. Grujicic M, Zhao C, DeRosset W, Helfritch D. Adiabatic shear instability based mechanism for particles/substrate bonding in the cold-gas dynamic-spray process. Mater Des 2004;25:681–8. Malama T, Hamweendo A, Botef I. Molecular dynamics simulation of Ti and Ni particles on Ti substrate in the cold gas dynamic spray (CGDS) process. Materials science forum. Trans Tech Publ.; 2015. p. 453–60. Goel S, Faisal NH, Ratia V, Agrawal A, Stukowski A. Atomistic investigation on the structure–property relationship during thermal spray nanoparticle impact. Comp Mater Sci 2014;84:163–74. Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J Comput
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Contents lists available at ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Molecular dynamics simulation study of cold spray process Aneesh Joshi, Sagil James
⁎
T
Department of Mechanical Engineering, California State University Fullerton, CA 92831, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Cold spray process Molecular dynamics simulation Nanoparticles Particle impact
Cold Spray (CS) process is a deposition process in which micron-to-nano sized solid particles are deposited on a substrate using high-velocity impacts. Unlike thermal spray processes, CS process does not melt the particles thus retaining their original physical and chemical properties. These characteristics make CS process ideal for various engineering applications. The bonding mechanism involved in CS process is hugely complicated considering the dynamic nature of the process. Even though CS process offers great promises, the realization of its full potential is limited by lack of understanding of the complex mechanisms involved. The study focuses on understanding the complex nanoscale mechanisms involved in CS process. The study uses Molecular Dynamics (MD) simulation technique to understand the material deposition phenomenon during the CS process. For the simulation conditions used, the study finds that the quality of deposition is highest for an impact velocity of 700 m/s, the particle size of 20 Å and an impact angle of 90°. The von Mises stress and plastic strain analysis revealed that bonding mechanism in CS process could be attributed to adiabatic softening, adiabatic shear instabilities followed by interfacial jetting of particle materials resulting in a uniform coating. The findings of this study can further the scope and applications of CS process.
1. Introduction Cold Spray (CS) is an emerging solid-state deposition process, where micron-to-nano sized particles bond to a substrate due to high-velocity impact. Unlike thermal spray processes, chemical and physical properties of deposited particles are retained in CS process considering the solid-state low-oxidized nature of the coating. These characteristics make CS process ideal for several critical engineering applications in industries such as defense and aerospace sectors [1]. During CS process, the acceleration of particles is achieved by the expansion of hot pressurized gases through a converging-diverging nozzle [2]. The high-velocity impact of the accelerating particles causes plastic deformation of the particles and the substrate surface resulting in a uniform coating. The schematic of CS process is shown in Fig. 1. The quality of the coating during the CS process is influenced by the incident velocity of the particles [1]. The successful bonding of powder particles on the substrate occurs only when the velocity of sprayed material exceeds a critical value that is specific to the material [1]. For instance, the critical velocity is found to be approximately 570 m/s for copper particles having a size of 5–25 μm [3]. The material suitability for CS process depends on the mechanical and physical properties including material hardness, melting temperature and density [4]. Materials with relatively low yield strength such as copper, aluminum, and zinc are considered ideal for the CS process
⁎
as they exhibit relatively high softening at elevated temperatures [5]. High strength materials are not ideal for CS process as they do not provide enough energy for deposition [6]. Experimental study on CS process of metal particles on polymer reveals that no metal particles can be coated on soft polymer due to lack of plastic deformation of particles [7]. Other factors influencing the quality of deposition during CS process include angle of impact, gas flow rate and stand-off distance between the nozzle tip and target surface [8]. Study on variations in stand-off distances (range 10 mm–110 mm) for particles of aluminum, titanium and copper powders showed deposition efficiency decreases with increase in stand-off distance [9]. Most of the studies reported on CS process is performed through experimentation [10]. While experimental techniques reveal the quality of material deposition and the microstructural characteristics, the use of experimentation in understanding dynamic mechanisms involved in the CS process is often limited. Simulation tools such as finite element (FE) simulation techniques and numerical methods have often been used as an alternative way in these cases. FE simulation have been used to understand the effect of process parameters during CS and other thermal spray processes at macroscales. The impact dynamics, bonding mechanism, and critical velocities during the CS process were studied using FE simulation tool ABAQUS [6]. The study found that the critical velocity depends on several parameters including the type of spray material, powder
Corresponding author. E-mail address: [email protected] (S. James).
https://doi.org/10.1016/j.jmapro.2018.05.005 Received 19 August 2017; Received in revised form 15 April 2018; Accepted 6 May 2018 1526-6125/ © 2018 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
Journal of Manufacturing Processes 33 (2018) 136–143
A. Joshi, S. James
Fig. 1. Schematic of Cold Spray Process.
“Large-scale atomic/molecular massively parallel simulator” (LAMMPS) [15]. The study considers the impact of nanoparticle impact on the surface of a metal substrate in three-dimension (3D). The simulation system consists of copper (Cu) atoms as a substrate, and a nanoparticle also made of Cu atoms. The substrate is made of 30,000 atoms of Cu, and the nanoparticle is made of 100 Cu atoms in fcc lattice structure. The shape of the substrate is a rectangular block having dimensions of 100 Å × 100 Å × 20 Å with face-centered cubic (fcc) lattice structure having a lattice spacing of 3.61 Å. The nanoparticle is spherical having a diameter of 10 Å with Cu atoms arranged in (fcc) lattice structure having a lattice spacing of 3.61 Å. The schematic of the model used for CS process simulation is shown in Fig. 2. The conditions used for CS process simulation study are given in Table 1. The interatomic forces between the Cu-Cu atoms are calculated using Embedded Atom Method (EAM), a suitable potential for the simulations of structural, mechanical, and thermal properties of metallic systems including Cu [16]. The Velocity-Verlet algorithm is employed to calculate the position and velocity of the atoms. In the actual working of CS, particles of varying shapes and sizes strike randomly on the substrate surface. The present MD simulation study considers only a single impact of a particle on the substrate under varying operational conditions. It is assumed that a single impact of a particle can explain the complex bonding mechanism involved in the CS process. Embedded Atom Method model function for the fcc of copper and its alloys [16]. In the computational simulation, the potential energy of an atom, i is given by
quality, particle size and the particle impact temperature. Splat formation during the thermal process was studied by numerical simulation method which revealed that increase in substrate temperature reduces the formation of splats [11]. FE tool ABAQUS/Explicit used for simulation study on CS process showed that a minimal impact particle velocity needed to produce shear localization [12]. It is known that the feed powder particles and the substrate and deposited material (after the first layer of particle impact) suffer a full localized distortion during impact. It causes disturbance of the thin surface films forming an adiabatic shear band which enables a conformal interaction between the particles and the substrate/deposited material. Formation of high strain rates during impact along with continuous deformation on the shear band leads to instability which causes the material to behave as a liquid material although in a solid-state. This close interaction of clean surfaces combined with high contact pressures is supposed to be the necessary circumstances for particles/substrate and particle/particle bonding. This phenomenon is unique and leads to a strong bond between parent material and the impacting particle. It is agreed that the actual mechanism when solid particles deform and bond onto the substrate during cold spray is still not well understood [12]. FE simulation studies are not capable of explaining the bonding process accurately. Because bonding during the CS process happens at molecular scale, Molecular Dynamics (MD) simulation technique is considered as the ideal tool. During MD simulation, the movements and interactions of atoms or molecules are determined based on the classical equations of motion. However, very few studies have reported on the use of MD simulation on CS process thus far [13]. One such study has used MD simulation to understand the effect of impact velocity on coating process of titanium and nickel particles on titanium substrate during CS process [13]. The study revealed that higher impact velocities result in the stronger interface between the particle and substrate. MD simulation has also been used to investigate structure-property relation during thermal spray processes [14]. The study found that maximum diameter after the impact and the height of the splat increases with increasing Reynolds number of the flow stream until a critical value is reached. From the literature review, it is evident that the effect of critical process parameters on the bonding and the real complex phenomenon of particle/substrate and particle/particle bonding during the CS process is not understood at the nanoscale. This study focusses on the use of molecular dynamics simulation investigate the bonding mechanism in CS process and to understand the effect of critical parameters including impact velocity, particle size and angle of impact on the material deposition phenomenon during the CS process of copper nanoparticles on the copper substrate. The effect of parameters including particle shape, material type and properties, and particle concentration are not considered in this study.
Ei = Fα
⎛ ⎞ 1 ρ (r ) + ∑ Φαβrij ⎜∑ β ij ⎟ 2 j≠i ≠ j i ⎝ ⎠
(1)
where i and j (i ≠ j ) label the atoms in the solid, rij is the distance between atoms i and j , and ρβ is the electron density at the position of atom i due to all other atoms in the solid. It is supposed that this density can be given as a sum of individual atomic densities f (rij ) where rij is the distance between i atoms j , Φαβ and is a potential function, ρβ is the
2. MD simulation Fig. 2. Schematic of MD Simulation Model of Cold Spray Process.
In the current study, the simulation of CS process is performed using 137
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observed. As the impact velocity is 800 m/s, the particles show signs of penetration into the substrate surface as shown in Fig. 4d. It suggests that maintaining the impact velocity within an optimal range is critical in achieving uniform coating. The effect of impact velocity on the deposition height during the MD simulation study of cold spray process is shown in Fig. 5a. The results show that as the impact velocity increases the deposition height decreases. The effect of impact velocity on the flattening ratio during the MD simulation study of cold spray process is shown in Fig. 5b. Flattening ratio is the ratio of the maximum diameter of splat (particle after impact) to original diameter of the particle before impact. In this study, flattening ratio is used to measure the uniformity of deposition of particles on the substrate during the CS process. According to this study, highest flattening ratio is achieved at an impact velocity of 700 m/s. It is also observed that flattening ratio decreases significantly after impact velocity of 750 m/s due to penetration of particles into the substrate.
Table 1 Simulation Conditions used in the MD Simulation of CS process. Materials
Substrate Material Nanoparticle Material
Operating Conditions
Bulk Temperature Potential Used Initial Stand-off Distance Impact Velocity Particle Size Angle of Impact Time step Duration of Simulation
Cu (100 Å × 100 Å × 20 Å) Approx. 30,000 Atoms Cu Sphere (Diameter 5–20 Å) Approx. 50–400 Atoms 300 K Embedded Atom Method (EAM) 15 Å 300–850 m/s 5 Å–25 Å 60°–90° 0.001 ps (picoseconds) 10 ps
electron charge density from atom j of type β at the location of atom i and F is an embedding function that represents the energy required to place atom i of type α into the electron cloud.
ρi =
3.2. Effect of angle of impact on material deposition
∑ f (rij) j
(2)
The angle of impact is another important parameter in CS process. Fig. 6 shows the screenshots of MD simulation study on the effect of angle of impact on particle bonding during the CS process at 500 m/s impact velocity and 10 Å particle size. Fig. 7a shows that as the angle of impact increases the deposition height increases. Highest deposition height is achieved at 90° revealing that jet of particles perpendicular to the substrate will have thicker coating compared to 60° angle of impact. The result of the angle of impact on the flattening ratio during the MD simulation study of cold spray process is shown in Fig. 7b. According to the study, highest flattening ratio is achieved at an angle of impact of 60° as the particles spread over larger area resulting in uniform and less dense coatings as shown in Fig. 6c. It is also observed that flattening ratio is least in 90° due to a concentrated jet of particles forming a non-uniform coating as shown in Fig. 6d. However, it must be noted that at 60° impact angle particles tend to rebound from the substrate more compared to at 90° angle of impact.
Eq. (3) is stress state at a point in a body be given by the three normal stresses σx , σy , σz and the tangential stresses σxy, σyz , σxz based upon a rectangular coordinate system [17]
((0.5 × (σx −σy )2 + (σy−σz )2 + (σx −σz )2 + (3 × (σxy )2 + (σyz )2 + (σxz )2)) (3) The MD simulation of CS process is conducted for duration of 10 ps (ps). In this study, it is assumed that the simulation converges when the relative change in kinetic energies between two successive iterations is less than 10−12. For all the simulations, the convergence occur before 10 ps according to this criterion. 3. Results and discussions All the results reported in this work refer to data obtained after 10 ps (ps) of simulation. A typical atomic configuration of copper nanoparticle deposition on the copper substrate during the CS process for impact velocity of 500 m/s and 90°angle of impact is shown in Fig. 3. The effect of critical process parameters – a) impact velocity b) angle of impact and c) particle size is evaluated by measuring the deposition height and flattening ratio of the bonded nanoparticle.
3.3. Effect of particle size on material deposition Particle Size is another critical parameter for optimum coatings in CS process. Fig. 8 shows the result obtained by varying size of particles at 500 m/s impact velocity with 90° angle of impact. According to the result, the size of particles should not be less than 10 Å as it fails to coat the substrate uniformly. Uniform and thick coatings can be observed at 20 Å. Deposition height increases with increase in particle size up to 20 Å size as shown in Fig. 9a. Above a particle size of 20 Å, deposition does not show any visible changes, which suggests that optimal coating is obtained with particle sizes ranging from 10 to 20 Å for the conditions used in this study. Fig. 9b shows the effect of particle size on flattening ratio during the CS process. From the Fig. 9b, it is observed that the flattening ratio increases with particle size. Moreover, it can be seen that there is no significant change in flattening ratio above a particle size of 20 Å.
3.1. Effect of impact velocity on material deposition Impact velocity is one of the essential parameters in CS process. Critical impact velocity range must be achieved for uniform and efficient bonding of the particles [8]. Fig. 4 shows the screenshot of MD simulation study on the effect of impact velocity on particle bonding during the CS process at 90° angle of impact and 10 Å particle size. The results revealed that an impact velocity of fewer than 500 m/s does not bond the particles efficiently to the surface as shown in Fig. 4a. As the velocity increases above 500 m/s, a uniform coating phenomenon is
Fig. 3. Representative Snapshot of MD Simulation after Nanoparticle Impact on Substrate Surface during Cold Spray Process a) 3D view and b) Side View. 138
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Fig. 4. MD Simulation Snapshots Showing Effect of Variation in Impact Velocity on Material Deposition during Cold Spray Process for a) 400 m/s, b) 500 m/s, c) 600 m/s and d) 800 m/s.
Fig. 5. (a) Effect of Impact Velocity on Deposition Height during Cold Spray Process. (b) Effect of Impact Velocity on Flattening Ratio during Cold Spray Process.
Fig. 6. MD Simulation Snapshots Showing Effect of Variation in Angle of Impact on Material Deposition during Cold Spray Process – (a), (c) Impact angle of 60° and (b), (d) Impact angle of 90°.
Fig. 7. (a) Effect of Angle of Impact on Deposition Height during Cold Spray Process. (b) Effect of Angle of Impact on Flattening Ratio during Cold Spray Process. 139
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Fig. 8. MD Simulation Snapshots Showing Effect of Variation in Particle Size on Material Deposition during Cold Spray Process a) 10 Å particle and b) 20 Å particle.
Fig. 9. (a) Effect of Particle Size on Deposition Height during Cold Spray Process. (b) Effect of Particle Size on Flattening Ratio during Cold Spray Process. Fig. 10. von Mises Stress Acting on Particle for Impact Velocity of a) 300 m/s and b) 800 m/s. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
3.4. von Mises stress distribution during CS process The deformation pattern and the arrangements of particle and substrate molecules/atoms in CS process were examined throughout the simulation. The strain and stress profiles along a particle edge are examined to understand the localization of plastic deformation. The corresponding variation of the equivalent or von Mises stress along particle edge is shown in Fig. 10a and b. Higher stress is induced on the particle and subsequently on to the substrate, which is visible in the red shade on the particle and substrate in case of impact velocity of 800 m/ s. This highly induced stress results in the formation of shear adiabatic instability around the edge of the substrate. Adiabatic shear instability in the substrate and plastic deformation into the particle helps the particle with high strength bonding. It is the reason behind effective, heat-free and dense coatings by CS process. Fig. 11 shows the effect of von Mises stress along the path followed by the particle during the CS process from initial state to the final state after coating for impact velocities of 300 m/s and 800 m/s respectively. From the figure, it is seen there is a no drastic change in equivalent stress for an impact velocity of 300 m/s when it approaches near the interface. As the velocity increases, the von Mises stress is seen to increase during the impact process suggesting material hardening. It is followed by a sudden drop in the equivalent von Mises stress eventually approaching zero stress value. It could be explained by the fact that particle undergoes softening immediately after the impact. Fig. 12 represents variation in velocity as the particle approaches on to the substrate during the cold spray process. From the figure, it is observed that sudden decrease in velocity immediately after its impact.
Fig. 11. Distribution of von Mises Stress with respect to Approach Distance for Varying Impact Velocities during Cold Spray Process.
3.5. Strain acting on the particle during impact in cold spray process Fig. 12. Variation in Particle Travel Velocity During CS Process for Different Initial Velocities.
Fig. 13a and b shows the shear strain distribution on the particle and the substrate after the beginning of the impact for velocities of 300 m/s and 800 m/s respectively. From the figure, it is seen that there is a 140
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Fig. 13. Plastic Strain Distribution During CS Process for Impact velocity of a) 300 m/s and b) 800 m/s.
Fig. 14. (a) Variation in Plastic Shear Strain with respect to Time during Cold Spray Process. (b) Variation in Plastic Shear Strain with respect to Distance during Cold Spray Process.
Fig. 15. Snapshots of Particle at Different Timesteps During CS Process for Impact Velocities of 300 m/s and 800 m/s.
Fig. 16. MD Simulation Snapshot of Particle Impact during the CS process for a) 300 m/s showing no jet formation and b) 800 m/s showing the formation of interfacial jets.
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over time during the CS process is consistent with the findings of the FE simulation study reported by Grujicic et al. [12]. In both the studies, the strains values for impact velocities above a critical value undergo an abrupt owing to material softening and high plastic shear strain-rate deformation. The variation in stress with respect to approach distance showed a similar trend in the MD simulation in this study and results reported on thermos-mechanical finite element simulation of CS process [21].
significant increase in plastic strain on the particle and at the particle/ substrate interface for higher impact velocities. Fig. 14a reveals the variation in particle shear strain with respect to time as it approaches the final coating on to the substrate for impact velocities of 400 m/s, 500 m/s, 600 m/s, 700 m/s and 800 m/s respectively. There is a steady increase in the strain values for impact velocity of 300 m/s, 400 m/s, and 500 m/s. However, there is an abrupt increase in plastic strain values for 600 m/s, 700 m/s and 800 m/s after the impact on the substrate surface. This change in strain values from about 120–160 femtoseconds indicates material softening due to high plastic shear strain-rate deformation and reduction in equivalent von Mises stress. Fig. 14b shows the variation in plastic strain as the particle travels from an initial height of 15 Å towards the substrate. It can be seen that for higher impact velocities (500 m/s or higher), there is a sudden increase in plastic strain during the impact process which suggests high plastic strain rate deformation. Fig. 15 shows the top view of the particles during the CS process for impact velocities of 300 m/s and 800 m/s respectively. For higher impact velocities, it is evident that the impact of the particle on the substrate produces adiabatic shear instability in the shear bands resulting in adiabatic softening of the materials. Both the particle and substrate tend to behave like viscous material resulting in almost free flowing of particles. This unique phenomenon produces interfacial jets when the particle impacts the substrate. This jet formation holds the particle strongly preventing it from escaping from the surface which results in a uniform coating. The formation of jets is evident for higher impact velocities as compared to low impact velocities as shown in Fig. 16. This adiabatic shear instability leads to high strength bonding between particles and substrate and later by particle on the particle. It shows that adiabatic softening and adiabatic shear localization particle/substrate bonding during the cold-spray deposition process. This result is in agreement with the findings of experimental studies done by other researchers which suggested a similar bonding mechanism [1]. This study shows the particle-substrate bonding mechanism at an atomic scale which involves the interplay between adiabatic softening and adiabatic shear localization on one hand and particle/ substrate bonding on the other.
4. Conclusion In this study, molecular dynamics (MD) simulation technique is used to investigate the bonding mechanism involved in cold spray process of copper nanoparticles on the copper substrate. The study also understands the effect of critical process parameters including impact velocity, particle size and angle of impact on the material deposition during the CS process. The critical findings of this study are as follows: a) Impact velocity study revealed that a medium range (500–700 m/s in this study) of impact velocity is found to be optimal for achieving uniform and dense coating. Maintaining impact velocity within an optimal range is critical in achieving a good quality deposition during the cold spray process. b) The angle of impact study revealed that highest deposition height is achieved at angles closer to normal revealing that jet of particles at or near perpendicular to the substrate will have thicker coatings compared to low angles of impact. However, more uniform coatings are observed when the angle of impact is low. c) Particle size study showed that the deposition height and uniformity increase with increasing particle size. However, there is no significant increase in deposition height and uniformity above a particle size of 20 Å for the conditions used in this study. The bonding mechanism study revealed that adiabatic softening, adiabatic shear instabilities and interfacial jet formation occurs at the particle/substrate interface at high velocities resulting in a uniform coating. The von Mises stress and plastic strain analysis further confirmed shear instabilities at higher impact velocities. The results of the MD simulation study are consistent with findings of previously reported experimental and finite element simulation studies. The findings of this study can be used to advance our existing knowledge in the field of cold spray processes.
3.6. Comparison of MD simulation results with past experimental findings The MD simulation results obtained in this study are consistent with the experimental study results previously published [8,18,19]. The MD study found that the flattening ratio increases as the impact velocity increases. The flattening ratio reaches a maximum and then start decreasing suggesting an optimal impact velocity for good quality deposition. This result is consistent with the experimental study results reported by Assadi et al., in which copper particles are deposited on the copper substrate using the CS process [18]. Also, the results of the MD simulation results on variation in von Mises Stress and plastic shear strain with respect to approach distance is consistent with the previously reported experimental results [18]. Both MD simulation and experimental studies suggested that both stress and strain have an inverse relationship with the approach distance. The experimental study reported by Gilmore et al. and Li et al. suggested that the deposition efficiency is higher at normal angles of impact and the efficiency decreases significantly as the angle of impact is approximately 60° [8,19]. It is in agreement with the finding of the current MD simulation study.
Acknowledgment We would like to thank the College of Engineering and Computer Science at California State University Fullerton for providing the financial support for this research. References [1] Assadi H, Kreye H, Gärtner F, Klassen T. Cold spraying–a materials perspective. Acta Mater 2016;116:382–407. [2] A.P. Alkhimov, A.N. Papyrin, V.F. Kosarev, N.I. Nesterovich, M.M. Shushpanov, Gas-dynamic spraying method for applying a coating, in, Google Patents (1994). [3] Stoltenhoff T, Kreye H, Richter H. An analysis of the cold spray process and its coatings. J Therm Spray Technol 2002;11:542–50. [4] Vlcek J, Gimeno L, Huber H, Lugscheider E. A systematic approach to material eligibility for the cold-spray process. J Therm Spray Technol 2005;14:125–33. [5] Moridi A, Hassani-Gangaraj S, Guagliano M, Dao M. Cold spray coating: review of material systems and future perspectives. Surf Eng 2014;30:369–95. [6] Schmidt T, Gärtner F, Assadi H, Kreye H. Development of a generalized parameter window for cold spray deposition. Acta Mater 2006;54:729–42. [7] Lupoi R, O’Neill W. Deposition of metallic coatings on polymer surfaces using cold spray. Surf Coat Technol 2010;205:2167–73. [8] Gilmore D, Dykhuizen R, Neiser R, Smith M, Roemer T. Particle velocity and deposition efficiency in the cold spray process. J Therm Spray Technol 1999;8:576–82. [9] Li W-Y, Zhang C, Guo X, Zhang G, Liao H, Li C-J, et al. Effect of standoff distance on coating deposition characteristics in cold spraying. Mater Des 2008;29:297–304. [10] Lima R, Karthikeyan J, Kay C, Lindemann J, Berndt C. Microstructural
3.7. Comparison of MD simulation results with past finite element simulation findings The MD simulation results obtained in this study are compared with previously reported numerical and finite element simulations. The MD simulation results obtained in this study are consistent with the findings of numerical reported by Ghelichi et al. for CS process of Cu-Cu coating [20]. The predictions of MD simulation of the variation in plastic strain 142
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