Cold Spray (CS) process is a solid-phase metal deposition technique, where micron to nanoscale solid particles of a material are deposited on the substrate. In this process, the powder particles of the metal material accelerate towards the substrate through a supersonic jet of pressurized hightemperature gases. This process consists of the convergingdiverging type nozzle, and the high impact velocities are achieved due to the expansion of gases through the nozzle [1] . The impact velocities used in the CS process are in the range of 300 m/s to 1000 m/s [2] . The gas used in this process to accelerate the powder particles through the nozzle is usually Nitrogen or inert gases such as Helium. These gases are preferred as they prevent any unintended chemical reactions on the surface of the substrate [3] . The CS process is beneficial as it does not include phase change or melting of the powder particles sprayed on the substrate. Thermal spray coating processes, on the other hand, involve melting of sprayed particles, which cause phase change of the material. The studies show that phase change of metals alters the mechanical properties of material to some extent [4] . The CS technology is capable of coating a wide range of materials including metals, alloys, and so on [5] . It is also capable of coating dissimilar metals and metals on ceramics or glass [6] . However, it is preferred to use lower impact velocities for some of the dissimilar metals and brittle materials to avoid fracture [6] . The powder materials used for the deposition are selected according to the operational requirements of the parts to be coated [7] . The mechanical and physical properties of metals and alloys are the key to the selection of the deposition materials. The bonding process in CS depends on the high impact velocities and kinetic energy of the particles [8] . The schematic of the CS process is shown in Figure 1 . In the CS process, a gas heater passes the high-temperature gas to the mixing chamber and the powder particles to be deposited are fed from the powder 
Cold Spray (CS) process is a solid-phase metal deposition technique, where micron to nanoscale solid particles of a material are deposited on the substrate. In this process, the powder particles of the metal material accelerate towards the substrate through a supersonic jet of pressurized hightemperature gases. This process consists of the convergingdiverging type nozzle, and the high impact velocities are achieved due to the expansion of gases through the nozzle [1] . The impact velocities used in the CS process are in the range of 300 m/s to 1000 m/s [2] . The gas used in this process to accelerate the powder particles through the nozzle is usually Nitrogen or inert gases such as Helium. These gases are preferred as they prevent any unintended chemical reactions on the surface of the substrate [3] . The CS process is beneficial as it does not include phase change or melting of the powder particles sprayed on the substrate. Thermal spray coating processes, on the other hand, involve melting of sprayed particles, which cause phase change of the material. The studies show that phase change of metals alters the mechanical properties of material to some extent [4] . The CS technology is capable of coating a wide range of materials including metals, alloys, and so on [5] . It is also capable of coating dissimilar metals and metals on ceramics or glass [6] . However, it is preferred to use lower impact velocities for some of the dissimilar metals and brittle materials to avoid fracture [6] . The powder materials used for the deposition are selected according to the operational requirements of the parts to be coated [7] . The mechanical and physical properties of metals and alloys are the key to the selection of the deposition materials. The bonding process in CS depends on the high impact velocities and kinetic energy of the particles [8] . The schematic of the CS process is shown in Figure 1 . In the CS process, a gas heater passes the high-temperature gas to the mixing chamber and the powder particles to be deposited are fed from the powder 
Cold Spray (CS) process is a solid-phase metal deposition technique, where micron to nanoscale solid particles of a material are deposited on the substrate. In this process, the powder particles of the metal material accelerate towards the substrate through a supersonic jet of pressurized hightemperature gases. This process consists of the convergingdiverging type nozzle, and the high impact velocities are achieved due to the expansion of gases through the nozzle [1] . The impact velocities used in the CS process are in the range of 300 m/s to 1000 m/s [2] . The gas used in this process to accelerate the powder particles through the nozzle is usually Nitrogen or inert gases such as Helium. These gases are preferred as they prevent any unintended chemical reactions on the surface of the substrate [3] . The CS process is beneficial as it does not include phase change or melting of the powder particles sprayed on the substrate. Thermal spray coating processes, on the other hand, involve melting of sprayed particles, which cause phase change of the material. The studies show that phase change of metals alters the mechanical properties of material to some extent [4] . The CS technology is capable of coating a wide range of materials including metals, alloys, and so on [5] . It is also capable of coating dissimilar metals and metals on ceramics or glass [6] . However, it is preferred to use lower impact velocities for some of the dissimilar metals and brittle materials to avoid fracture [6] . The powder materials used for the deposition are selected according to the operational requirements of the parts to be coated [7] . The mechanical and physical properties of metals and alloys are the key to the selection of the deposition materials. The bonding process in CS depends on the high impact velocities and kinetic energy of the particles [8] . The schematic of the CS process is shown in Figure 1 . In the CS process, a gas heater passes the high-temperature gas to the mixing chamber and the powder particles to be deposited are fed from the powder 48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to feeder. From the mixing chamber, the gas along with the powder particles is accelerated towards the substrate through a supersonic jet. Upon deposition of these particles on the substrate, they form a thick uniform coating on the surface of the substrate. The impact caused by the spraying particles on the substrate surface results in adiabatic shear instabilities and subsequent adhesion [1, 8] . The bonding happens through the plastic deformation of the particles [1] . CS processes are known to impart higher strengths and quality to the coatings compared to its thermal spray counterparts [1] . The residual stress development in the substrate has a profound role while studying the subsurface condition and integrity of the coatings [9] [10] [11] . Residual stresses are the stresses which are locked inside the body or substrate in the absence of any external forces. Residual stresses are developed invariably in all the manufacturing or fabrication operations, including thermal spraying, welding, casting, grinding, milling, rolling, and particularly forging and shot-peening processes [12] [13] [14] .
Similarly, the CS process also develops residual stresses in the coated components [9] . Residual stresses in undesired amounts could lead to component breakage, surface cracks, corrosion, and strength reduction in the manufactured parts [15] . Most manufactured components could have a combination of both tensile and compressive residual stress components. Several studies show that the CS process generates tensile residual stress and compressive residual stresses [16] [17] [18] . The residual stress measurements are classified into three types namely Type I, Type II and Type III which are based on Macro, Micro and Nanoscale measurements [11, 19] . The Type I residual stresses are developed in several grains of a structure, Type II residual stresses are developed in single grain, and Type III is present within several atomic distances of a grain of the structure. Residual stresses in cold sprayed components are regarded as a critical factor that affects the quality and fatigue life of components [20] .
Both FEA and experimental studies have been used to measure the residual stresses in the CS process. However, these studies are limited to Type I and Type II classification of residual stresses in the measurements [9, 16, 20] . However, there are no significant studies done to investigate the Type III residual stresses in the CS process. A preliminary study by our research group briefly described the presence of Type III residual stresses in the substrate after the impact of the nanoparticles. However the preliminary study did not consider the surface behavior when a single particle impacts and variation of process parameters, which affects the residual stress generation. The goal of this research is to investigate the effects of impact velocity and angle on the generation of Type III residual stresses during the CS process.
The present study uses the Molecular Dynamics (MD) simulation to investigate the generation of residual stresses in the CS process. The MD approach is taken as it could unveil different parameters and results which are currently out of reach for other simulation and experimental methods. The tool used for MD simulation is Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [21] . The simulation model used consists of a nanoparticle impacting on a substrate at different angles and velocities. The material selected for the substrate and the sprayed particle is Copper (Cu). The substrate is rectangular and contains approximately 100,000 atoms having a size of 140 Å x 140 Å x 60 Å. The particles used for the simulation are assumed to be spherical, having a size of 20 Å. The lattice constant of both the substrate and the sprayed nanoparticles is 3.615 Å. It has a face-centered cubic (FCC) lattice structure. Figure 2 shows the MD simulation model of the CS process, where particle impacts the substrate at an angle. The impact angles used for the study are 60° and 90°. The oblique angle is chosen to understand the influence of impact angle on the particle deformation during the nanoparticle impact. A fixed boundary layer (140 Å x 140 Å x 5 Å) of atoms is provided at the base of the substrate to hold its position in space, and a thermal layer (140 Å x 140 Å x 5 Å) is placed above the fixed boundary layer. This rectangular boundary layer and the thermal layer contains approximately 9000 atoms each.
The MD simulation uses two cases for the study of residual stress development inside the substrate. The first case consists of the study of residual stress distribution when the particle impacts at an angle of 60°, and the second case involves the residual stress distribution at an angle of 90°. These impact angles were selected from earlier studies with the combination of different process parameters [22] [23] [24] . In the simulation process of these two cases, the particle is equilibrated for one picosecond (ps), and the bulk temperature is kept in the range of 300 K. During equilibration, the particle does not gain velocity. In the next step, the particle is impacted by velocity, and the process goes on for 100 ps to observe the particle deformation. The process allows relaxation time after the highvelocity impact before we measure the residual stress of the system. Table 1 shows the conditions used for MD simulation in the CS process. 
In this study, the MD simulation results are obtained when a particle is sprayed on the substrate with varying velocities of 300 m/s, 400 m/s, and 500 m/s at an angle of 60° and 90° respectively. It should be noted that the size and time scales limit the current simulation compared to the experimental studies. However, the results of this study are obtained using many combinations of process parameters, which shed light on the molecular scale mechanisms involved in the CS process. Figures 3 and 4 show the simulation screenshots of the particle impacting the substrate. It is observed from the figure that the particles achieve higher deformation when impacted with 500 m/s velocity. The deformation is lower for 300 m/s due to lower kinetic energy and the rebounding effect observed for lower velocity impacts. The higher impact velocities show higher flattening of the particle, which can be attributed to the fact that increasing impact velocities increase the flattening of the particle [25] . It is observed through the simulation screenshots that the particle undergoes higher flattening when the impact angle is 60°. However, the particle adhesion is higher when the impact angle is 90°. The higher flattening in the case of 60° can be attributed to the fact that the atoms of the particle slide on the surface for impact angle less than 90°. 
Angle of 60º Figure 5 shows the simulation screenshots of σz residual stress distribution when the particle is impacted at an angle of 60º for different particle impact velocities. For observing the stress distribution area, the substrate is sliced along Y-axis, and the results are observed in the direction of the XZ plane. The stress distribution is observed using three different impact velocities, including 300 m/s, 400 m/s, and 500 m/s. It can be seen that as the particle velocity increases, the stress distribution in the substrate is higher. Figure 5a shows moderate traces of compressive residual stresses and high tensile stresses on the right edge of the deformed particle. Figures 5b and 5c have a larger stress distribution area compared to Figure 5a . It is due to the high kinetic energy of the particle and deeper impact in case of increasing impact velocities. The study observes that the atoms in the stress distribution region of 400 m/s impact velocity show higher magnitudes of compressive residual stress than the stress distribution region of 500 m/s. From these observations, it can be considered that the particle having 400 m/s impact velocity is better than the 500 m/s impact velocity because higher compressive residual stresses are beneficial for the strength of the substrate [35] . Figure 6 shows the residual stress profile measured for 400 m/s impact velocity. The coating observes tensile residual stress, which changes to compressive residual stress in the depth of the substrate. The results shown in the figure are only plotted, considering the deformation and stress distribution region in the substrate rather than the complete depth of the substrate. 
Angle of 90º Figure 7 shows the simulation screenshots of σz residual stress distribution when the particle is impacted at an angle of 90º for different particle impact velocities. The simulation using normal impact shows that the stress distribution is uniform along the substrate, which means that the substrate can be sliced along any X or Y axis, and it will still show a similar stress distribution region. It is observed from the simulation that the magnitude of average compressive residual stress is highest when the impact velocity of the particle is 400 m/s. This observation is similar to the observation in the case of 60º impact angle. Thus, it can be concluded from the results that 400 m/s impact velocity gives higher compressive residual stress irrespective of the angle of impact. However, 500 m/s impact velocity observes more significant particle deformation and higher particle flattening for the process parameters considered in the simulation. Figure 8 shows the residual stress distribution for 400 m/s impact velocity and 90º impact angle. The stress profile in the coating region is tensile at the beginning but changes to compressive before the interface of the substrate. It shows that higher compressive residual stresses are observed in the coatings by the normal impact. It is also observed that the depth of coating, in this case, is higher than the 60º impact angle. 
Figures 9 and 10 show the deformation of the copper particle when the impact angles are 60º and 90º. The deformation is observed at various timesteps to understand the adhesion and bonding mechanism during and after the particle impact. Each simulation was carried out for the duration of 100 ps to allow sufficient after-impact relaxation time. The impact velocity used for the observations is 400 m/s, and the particle size is 20 Å. It is observed that the shape of the particle undergoes continuous deformation until the timestep of 20 ps for both 60º and 90º impact angle. This duration is known as the elastoplastic phase of particle deformation. While this phase extends to the duration until the atoms of the substrate stop dislocating, it is observed that the coated particle does not show significant shape deformation beyond 20 ps. 
This study is performed using the MD simulation technique to investigate the Type III residual stress distribution after highvelocity particle impacts in the CS process. The authors used a 3D model to simulate the impact of sprayed Cu particles on the surface of a rectangular Cu substrate. In this study, the impact velocities used were in the range of 300 m/s to 500 m/s, and the impact was varied between 60º and 90º. The study found that in the case of 60º impacts, the tensile residual stress generation observed on the surface of the coatings is higher than that observed in the case of 90° impacts. The study of impact velocity on residual stress found that the magnitude of average compressive residual stresses is highest in the case of 400 m/s impact velocity for both 60º and 90º impact angles. It is also found that 400 m/s is the optimum impact velocity, and 90º is the optimum impact angle with the combination of the process parameters considered in the simulation. The particle deformation study showed that the particle does not deform significantly after the elastoplastic phase of 20 ps.