Molecular Dynamic Simulation Study of Cold Spray Process ______

MOLECULAR DYNAMIC SIMULATION STUDY OF COLD SPRAY PROCESS ______

A Thesis

Presented to the

Faculty of

California State University, Fullerton ______

In Partial Fulfillment

of the Requirements for the Degree

Master of Science

Mechanical Engineering ______

Aneesh Abhay Joshi

Thesis Committee Approval:

Sagil James, Department of Mechanical Engineering Salvador Mayoral, Department of Mechanical Engineering Darren Banks, Department of Mechanical Engineering

Spring, 2017

ABSTRACT

Cold Spray (CS) process is deposition of solid particles over a substrate above a certain critical impact velocity. 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 extremely complex considering the dynamic nature of the process. Though CS process offers great promise, the realization of its full potential is limited by the lack of understanding of the complex mechanisms. The focus of this research is to understand the complex nanoscale mechanisms involved in CS process. The study uses Molecular Dynamics (MD) simulation technique to comprehend the material deposition phenomenon during the CS process. Impact of a single crystalline copper nanoparticle on copper substrate is modelled under varying process conditions.

The study finds that the flattening ratio and hence the quality of deposition was highest for velocity of impact of 700 m/s, with particle size 20 Å and an impact angle of 90°. The stress and strain analysis revealed regions of shear instabilities in the periphery of impact and revealed plastic deformation of the particles after the impact. The results of this study can be used to augment our existing knowledge in the field of CS process.

TABLE OF CONTENTS

ABSTRACT ...... ii

LIST OF TABLES ...... v

LIST OF FIGURES ...... vi

ACKNOWLEDGMENTS ...... ix

Chapter 1. INTRODUCTION ...... 1

Background of Cold Spray Process ...... 2 Types of Cold Spray Process ...... 3 High Pressure Cold Spray Process...... 4 Low Pressure Cold Spray Process ...... 4 Other Thermal Spray Process ...... 6 Advantages...... 9 Disadvantages ...... 10

2. LITERATURE REVIEW ...... 11

Research Goals and Objectives...... 15 Numerical Simulation Technique ...... 15 Atomic Scale Numerical Simulation Technique ...... 19 Monte Carlo Method ...... 20 Molecular Dynamic Simulation ...... 20

3. RESEARCH METHODOLOGY ...... 22

Development of Simulation Model...... 23 The Velocity-Verlet Algorithm ...... 25

4. RESULTS AND DISCUSSION ...... 27

Effect of Impact velocity on Material Deposition ...... 28 Effect of Angle of Impact on Material Deposition ...... 33 Effect of Particle Size on Material Deposition ...... 36

iii von Mises Stresses Distribution acting on particle during Impact in Cold Spray Process ...... 39 Strain acting on particle during Impact in Cold Spray Process ...... 42

5. CONCLUSION ...... 47

APPENDIX: THESIS DISSEMINATION ...... 48

REFERENCES ...... 49

LIST OF TABLES

Table Page

1. Cold Spray Process Used for Different Powder Materials ...... 5

2. Simulation Parameters Used for the Molecular Dynamics Simulation of Cold Spray Process ...... 24

LIST OF FIGURES

Figure Page

1. Schematic of Cold Spray process ...... 2

2. Schematic of high pressure Cold Spray process ...... 4

3. Schematic of low pressure Cold Spray process ...... 5

4. In-process working of Thermal Spray Process ...... 7

5. Temperature versus velocity regimes for TS processes compared to CGDS ...... 8

6. Comparison of copper coatings by CS process and Air Plasma process ...... 8

7. Snapshots of same or different material coatings in Cold Spray Process ...... 10

8 . Impact velocity necessary for different materials ...... 11

9. Effective bonding of copper on aluminum substrate ...... 12

10. Representation of the relationship between simulation, theory and experiment . 17

11. Approximate time and length scales accessible for different modelling ...... 18

12. Schematic of Molecular Dynamic Simulation model of Cold Spray process ..... 24

13. Various systems of the Verlet algorithm ...... 25

14. a) Representative 3D snapshot of MD Simulation after nanoparticle impact on surface of substrate during CS Process ...... 27 b) Representative front view snapshot of MD Simulation after nanoparticle impact on substrate surface during Cold Spray process ...... 28

15. Impact of particle on a solid surface ...... 28

vi 16. a) Impact velocity 400 m/s...... 30 b) Impact velocity 500 m/s ...... 30 c) Impact velocity 600 m/s ...... 30 d) Impact velocity 800 m/s ...... 31

17. a) Effect of impact velocity on deposition height ...... 32 b) Effect of impact velocity on flattening ratio ...... 33

18. a) Side view and top view during MD simulations showing effect of 60° Impact angle on material deposition of CS process ...... 33 b) Side view and top view during MD simulations showing effect of 70° Impact angle on material deposition of CS process ...... 34 c) Side view and top view during MD simulations showing effect of 80° Impact angle on material deposition of CS process ...... 34

19. a) Effect of change angle of impact on deposition height during Cold Spray process ...... 35 b) Effect of change angle of impact on flattening ratio during Cold Spray process ...... 36

20. a) MD Simulation snapshots showing effect of 10 Å particle size on Material Deposition during Cold Spray process ...... 37 b) MD Simulation snapshots showing effect of 15 Å particle size on Material Deposition during Cold Spray process ...... 37 c) MD Simulation snapshots showing effect of 20 Å particle size on Material Deposition during Cold Spray process ...... 37

21. a) Effect of particle size vs deposition height during Cold Spray process ...... 38 b) Effect of particle size on flattening ratio during Cold Spray process ...... 39

22. a) von Mises Stress acting on particle for an impact velocity of 300 m/s ...... 40 b) von Mises Stress acting on particle for an impact velocity of 800 m/s ...... 40

23. Distribution of von Mises Stress with respect to approach distance for varying impact velocities during Cold Spray process ...... 41

24. Variation in particle travel velocity during CS Process for different initial velocities ...... 42

25. a) Strain acting on particle and substrate with an impact velocity of 300 m/s .... 42 b) Strain acting on particle and substrate with an impact velocity of 800 m/s .... 43

26. a) Variation in plastic shear strain with respect to time during Cold Spray process ...... 44 b) Variation in plastic shear strain with respect to distance during Cold Spray process ...... 44

vii 27. Snapshots of particle at different timesteps during CS process for impact velocities of 300 m/s and 800 m/s ...... 45

28. a) MD Simulation snapshot of particle impact for an impact velocity of 300 m/s ...... 46 b) MD Simulation snapshot of particle impact for a velocity of impact of 800 m/s ...... 46

viii

ACKNOWLEDGMENTS

I would like to convey my heartfelt thanks to Dr. Susamma Barua, Dean, and Dr.

Sang June Oh, Associate Dean Engineering and Computer Science, California State

University, Fullerton (CSUF) for giving me an opportunity to take up our thesis work in this well- reputed organization.

My deep sense of gratitude and sincere thanks to Dr. Chean Chin Ngo, Chair,

Department of Mechanical Department, CSUF for granting me permission and giving us an opportunity to pursue my thesis in Advanced Manufacturing.

I sincerely convey my profound sense of thankfulness to my guide Dr. Sagil

James, Assistant Professor, CSUF. His immense depth of knowledge and his meticulous and precise research attitude has certainly been infectious and has very much shaped the course of this research. His constant input of time, patience, valuable guidance, encouragement, and moral support has guided me through this journey.

I also want to thank Mr. Thao Nguyen, Laboratory Technician, CSUF for his continuous support in setting up our computers. I extend my gratitude to Mr. Mayur

Parmar and Mr. Abhishek Ganesh Sonate and Mr. Mayur Narkhede for their valuable help, guidance and support.

I would like to thank Sandia National Laboratories for their LAMMPS software which was instrumental in simulating the cold spray process.

ix 1

CHAPTER 1

INTRODUCTION

Cold Spray (CS) is a solid-state coating and additive manufacturing procedure, where micron-to-nano sized particles bond to a substrate owing to impact by high velocity and linked thermos-plastic shear instability. Acceleration of the particle is achieved by expansion of pressurized hot gases through a converging – diverging nozzle

(Alfa-de Laval nozzle) thereby facilitating particle deformation through thermal softening

(Hamid Assadi, Gärtner, Stoltenhoff, & Kreye, 2003). Unlike thermal spray processes,

CS process do not melt the particles thus retaining their initial physical and chemical properties. This characteristic make CS process ideal for various engineering applications involving metals, polymers, ceramics and composites. During CS process, the particles to be deposited are stored in a pressurized powder feeder from where they are accelerated in a supersonic jet or a converging-diverging nozzle. When the jet of particles impact on the target surface, they plastically deform forming a uniform coating. The graphic of CS process is shown in Figure 1. The attachment of powder particles on to the base surface happens just when the speed of splashed material surpasses the basic critical speed under the specific operating conditions (Hamid Assadi et al., 2003). The material suitability for

CS process depends on their mechanical and physical properties, for example, material hardness, liquefying point, melting temperatures and density (Hamid Assadi, Kreye,

Gärtner, & Klassen, 2016). Relatively low yield strength materials such as copper,

2 aluminum and zinc are considered ideal for CS as they exhibit relatively higher softening at high temperatures (Vlcek, Gimeno, Huber, & Lugscheider, 2005), while high strength materials are not ideal for CS as they fail to provide enough energy for deposition.

Figure 1. Schematic of Cold Spray process

The temperature stream of gas is dependably underneath the liquefying temperature of particle in CS process and the resultant is self-supporting additive structure is solid state which are less oxidized.

Critical velocity of particles is the main concept of CS Process. An ideal velocity for a specific powder is the speed that given particle must reach to stick to the substrate after impact. Generally, particles of about 10 – 20 µm are most efficient to coat the substrate but the powder contains mixture of particles some of which coat while other bounce off (Klassen et al., 2010).

Background of Cold Spray Process

Cold Spray Process uses low temperature of material to efficiently add material on to the substrate without change in phase. Due to the use of Kinetic energy instead of temperature as the driving force the thermal stresses, undesired chemical reactions,

3 oxidized fumes, porosity and many more undesirable phenomenon are avoided. Cold

Spray process is a solid-state material deposition procedure means the adhesion of metal particles and cohesion of substrate is accomplished in solid state, this phenomenon induces unique characteristics in the deposited coatings. Residual stresses are most harmful effects that can be observed at high temperature at substrate-coating interface when the substrate and particle are dissimilar materials. But, Cold Spray process minimizes or eliminates these adverse effects. These advantages make CS process an ideal process for coating and additive manufacturing in fields of Aeronautical, bio- medical, automotive and other fields where avoiding the thermal stresses and phase changes are of prime importance.

Institute of Theoretical and Applied Mechanics originally developed the CS coatings during the period of 1985 by Anatolli Papyrin and team in Russian Science

Academy (Papyrin, Kosarev, Klinkov, Alkhimov, & Fomin, 2006). This team from

Russia effectively deposited a extensive variety of metals, metal mixtures, and even composites on different substrates by CS process. During the early period of 21th century, research studies associated with Cold Spray step up. Currently, many government, educational and industrial institutions are working on Cold Spray Process to improvise it.

Types of Cold Spray Process

Cold Spray process deals with high or low pressure based on the application of the process. So CS process is divided into a) High Pressure Cold Spray process and b)

Low Pressure Cold Spray Process.

High Pressure Cold Spray Process

High-pressure CS system is shown in Figure 2 where the core stream of heated gas and the pressurized stream of powder are together mixed uniformly and sent into the inlet compartment of the nozzle. Such system is generally used for coatings of hard particles on to the substrate. This arrangement is mostly used in stationary cold spray systems. High-pressure CS systems uses higher pressure gases above 1.5 to 4 MPa and usually have a dedicated gas compressor for enhancing gas pressure. Helium is generally used as the carrier gas due to its low molecular weight for high end applications

Figure 2. Schematic of high pressure Cold Spray process

Low Pressure Cold Spray Process

Graphic representation of Low Pressure CS Process is revealed below in Figure 3.

Pressurized powder stream is introduced at the point where the gas expands in converging-diverging nozzle. Atmospheric pressure is used to transport pressurized powder from the feeder. Low Pressure CS process generally uses compressed air or nitrogen for coating according to the material used.

Figure 3. Schematic of low pressure Cold Spray process

Types of Cold Spray Process used for different materials. Table 1 Displays types of CS process used for dissimilar powder materials. The provided figure clearly shows that the composites are hard in nature and cannot be coated with Low pressure CS process so only High Pressure CS system must be used for uniform and thick layers of coating. But, a low-pressure CS system is easy for portable CS for non-ductile materials like copper, aluminum, and others.

Other Thermal Spray Process

CS process is an additive manufacturing and coating process from the family of

Thermal Spray Process. But, the main difference between CS process and other thermal process is that CS process does not rely on temperature for coatings but uses K.E for it.

Other thermal process uses molten particles for coating or to repair worn out substrate.

Figure 4 shows actual in process image of Thermal Spray Process.

Table 1. Cold Spray Process Used for Different Powder Materials

High Pressure Cold Spray Low Pressure Cold Spray Powders Process Process

Aluminium ✔ ✔

Copper ✔ ✔

Nickel ✔ ✔

Zinc ✔ ✔

Tin ✔ ✔

Metal Matrix ✔ ✔ Composites

Brass ✔

Bronze ✔

Silver ✔

Aluminium Alloy ✔

Titanium ✔

Tantalum ✔

Niobium ✔

Ti-6Al-4V ✔

Inconel 625, 718 ✔

SS 316 L ✔

SS 403 ✔

SS 430 ✔

Ni-Cr ✔

Ni-Al ✔

Figure 4. In-process working of Thermal Spray process (Technologies)

Figure 5 clearly shows gas temperature used by CS Process is lowest compared with other members of thermal spray family but CS utilizes high velocity of particles than other thermal spray process. The prime difference which separates other thermal processes from CS process is that these processes heat the particle which changes the phase of particles that are to be coated on to the substrate and this also induces thermal stress and degrades quality of coating. These thermal stresses are completely avoided in

CS process as the particles are not heated up to melting point and actual coating takes place due to plastic deformation (Grujicic, Zhao, DeRosset, & Helfritch, 2004), but this phenomenon is still unclear

Figure 5. Temperature versus velocity regimes for TS processes compared to CGDS (Grigoriev, Okunkova, Sova, Bertrand, & Smurov, 2015)

Cold Spray process has high particle deformation rate along with product shaping reliability compared with other Thermal Spray processes (Champagne, 2007). Figure 6 reveals that Cold Spray process provides less oxidized uniform coatings with higher density while high oxidized and less dense coatings are produced by other thermal spray process.

a. Copper coatings by Cold Spray process b. Copper coatings by Air Plasma process (Papyrin et al., 2006) (Van Steenkiste et al., 1999) Figure 6. Comparison of Copper Coatings by CS process and Air Plasma Process

Advantages

Figure 7 shows patterns of coatings of different materials by Cold Spray process.

CS process allows a broader range of industrial alloys to be coated more quickly, accurately, and with higher material integrity due to the high velocity approach rather than non-thermal method. Due to this technique, bonding is obtained through plastic deformation upon impact (Grujicic et al., 2004), this phenomenon has a number of advantages over other thermal processes that deal with high temperature defects. Below are few of the important advantages of Cold Spray process (Champagne, 2007; Maev &

Leshchynsky, 2009)

• High deposition efficiency without considerable material degradation to

oxygen and thermal sensitive materials like Cu and Ti (Titanium).

• Dense coatings obtained without porous coatings are obtained.

• Original mechanical, thermal, and chemical properties of the material is

retained due to no phase change.

• Used as additive manufacturing for developing prototypes at low cost.

• CS process offers alternative to low temperature welding

• CS process is generally safe compared to other high temperature thermal

spray process

• CS process which is an environmentally safe process offers new possibilities

for cost effective alternative for electroplating, painting and soldering

technologies.

Figure 7. Snapshots of same or different material coatings in Cold Spray Process (Gärtner, Stoltenhoff, Schmidt, & Kreye, 2006; Klassen et al., 2010; Schmidt, Gärtner, Assadi, & Kreye, 2006; Watanabe & Kumai, 2009)

Disadvantages

• It is still unclear if CS process can coat ceramics effectively. There are studies

which show bonding of ceramics but these deposits have low bonding strength

• If Helium is used as a carrier gas then coatings produced are expensive.

CHAPTER 2

LITERATURE REVIEW

The particle in Cold Spray Process is deposited initially on the bare substrate and then coating of new particles over formerly deposited particles. These method is highly relied upon critical velocity of particle (푣) and, parent base and also the material properties of particle (Grujicic et al., 2004). The particles moving below the critical impact velocity bounce or reflect through the substrate. Figure 8 displays the impact of critical velocity for numerous materials with 25 µm as particle size. The grey shades show a series of vulnerability as for the range of existing materials information.

Figure 8. Impact velocity necessary for different materials (Schmidt et al., 2006)

Experimental studies on the CS process and coatings achieved CS process revealed that that attachment only takes place when particles of powder surpass a basic speed which required for impact particular to the every material (Hamid Assadi et al.,

2003) .This paper reveals the importance of process parameters for effective bonding.

Figure 9 from this paper shows coating of copper on aluminum substrate.

Figure 9. Effective bonding of Copper on aluminum substrate (Hamid Assadi et al., 2003)

The conditional velocity is experimentally found as 570 m/s for copper particles having a size of 5-25 µm (Moridi, Hassani-Gangaraj, Guagliano, & Dao, 2014). An experimental study of velocity of particle and deposition effectiveness in the CS method on 20 µm copper powder on aluminum substrate with jet of 640 m/s found that the particle velocity drops as the mass ratio of powder of particles to the gas flow rate was exceeded by 3% (Stoltenhoff, Kreye, & Richter, 2002). Study on variations in stand-off distances (range 10 mm-110 mm) for particles of aluminum, titanium and copper powders showed that a 30 mm stand-off distance gives maximum efficiency for copper while it decreases for aluminum and titanium as the range moves higher (Gilmore,

Dykhuizen, Neiser, Smith, & Roemer, 1999). Experimental study of metal particles on polymer reveal that no metal particles can be coated on soft nature polymer due to lack of

13 plastic deformation of particles. Study also revealed that pure limited fracture is experienced on the parent material where no particles were devoted firmly on the substrate (Li et al., 2008)

Complexity of bonding mechanism in CS process and accurate understanding of structural and dynamic aspects in atomic level cannot be understood through experimental studies. Simulation tools such as finite element techniques, numerical methods have often been used as an alternative tool in these cases. Finite element techniques have also been extensively used to understand the effect of process variables during CS and further thermal spray processes at macroscales. Critical process variables such as impact dynamics, mechanism of bonding and ideal velocities were studied to understand their effect on the coating process using finite element tool ABAQUS

(Ganesan, Affi, Yamada, & Fukumoto, 2012). Finite element tool ABAQUS/Explicit was used for simulation study on CS process displayed that the nominal impact particle velocity is necessary to produce a shear localization at the particle/surface of parent material boundary correlate with the ideal impact velocity (Pasandideh-Fard, Pershin,

Chandra, & Mostaghimi, 2002). Splat formation during the thermal process is studied by numerical simulation method which revealed that increase in substrate temperature reduces formation of splats (Schmidt et al., 2006).

The actual mechanism when particles are distorted and coat onto the substrate during CS process is yet not surely known. It is identified that the particles of the selected powder and the substrate and then the deposited powder later on (i.e., after first layer of particle impact) suffer a wide localized distortion through impact. This leads to disturbance of the thin films on the surface which localizes the shear material known as

14 adiabatic shear band and this band enables a conformal interaction among the depositing particles and the substrate or the deposited material. Formation of high strain rates during impact causes this shear adiabatic band is formed, constant deformation on this band leads to instability which causes the material to behave as a material which is in liquid state although in solid state. This close interaction of renewed surfaces joint where high interacting pressures are supposed to be the essential circumstances for particles/substrate and particle/particle bonding. This phenomenon is unique and leads to strong bonds between parent material and the high velocity particle. The given theory can be explained on the basis of some experimental findings like: (a) an extensive variety of metallic and polymer ductile materials can be effectively cold-sprayed brittle materials like ceramics can be deposited successfully by CS process after they are mixed with ductile materials

(b) the particle must surpass a minimum (dependent on material) impact speed to attain effective deposition which proposes that adequate kinetic energy (K.E) should be produced to plastically deform the particle by disturbing the surface film and (c) the solid material at impact is thought to be less than the velocity needed to soften the material signifying that particle on the base material and then particle on particle is basically a complete solid-state process. This phenomenon is confirmed through microscopic observation of the cold sprayed materials

Finite element studies find it difficult to explain the bonding process accurately considering the molecular scale of bonding during the CS process. Molecular Dynamics

(MD) simulation technique is considered as the ideal tool for understanding molecular scale phenomena such as bonding in CS processes. Classical equations of motion are

15 used during MD simulation to understand the movements and interactions of atoms or molecules.

Though, very limited work is found on the use of Molecular Dynamic simulation on CS process thus far. One such study has used MD simulation to know the effect of only limited process parameters such as velocity of impact on coating process of titanium and nickel particles on titanium substrate during CS process (Malama, Hamweendo, &

Botef, 2015). The study revealed that higher impact speeds result in more robust interface between the particle and substrate. MD simulation has also been used to investigate structure-property relation during thermal spray processes (Goel, Faisal, Ratia, Agrawal,

& Stukowski, 2014). The study found that maximum span of the splat after the impact and the tallness of it rises with expanding Reynolds number of the flow stream until a critical value is reached.

Research Goals and Objective

From the literature review, it is noticeable that the result of critical process variables of actual complex phenomenon of particle/substrate and particle/particle bonding during the CS process is not clearly understood at nanoscale. This thesis focusses on use of molecular dynamics simulation investigate the bonding methodology in Cold Spray process and to recognize the result of critical variables including velocity of impact, size of particle and impact angle on the material deposition phenomenon during the CS process of copper nanoparticles on copper substrate.

Numerical Simulation Techniques

Generally, multifaceted physical experiments are developed on support of pre- reviewed conventional theoretical works, study on Cold Spray process has much deep scope. Within the context Cold Spray process for example, there exist ultimate physical association of particles/particles or particles/substrate bonding which present models are not able to predict it accurately as expected (Hamid Assadi et al., 2003). Investigational study methods propose high amount analogy to display the experimental works in the information available, but it many times it is not up to mark to collect actual physical data. There is high possibility that physical phenomena are beyond the naked eye capabilities to view the underlying complex mechanisms. This problem which cannot be solved at physical level has to take support of atomic level simulations. Utilizing the material accessible in a database at Micron/Nano scales many times proves hard that other traditional techniques are able to note down some physical properties. So, to overcome traditional techniques drawback it is advisable to apply a simulation method that precisely discloses the behavior which is not defined by experiments such as knowing the complex bonding mechanisms of coating by Molecular Dynamics.

Simulations should be carefully parameterized with data available in the arrangement, while the provided information should be derived from trusted sources and/or successfully performed tests. Simulation has the original base of experimental findings, as the model developed out of these experiments forms the basic criteria for similar system simulations. Simulations are generally used to predict the possible results of experiments moreover it also validates the theoretic derivations. Figure 10 gives the graphic image of the relation between simulation dependency on experiments while

17 experiment theory. The study of particles impacts and changes in material deposition by variation in critical parameters.

Figure 10. Representation of the relationship between simulation, theory, and experiment (Tildesley & Allen, 1987).

Figure 11 shows a time and length scales available for different simulation techniques.

Figure 11. Approximate time and length scales accessible for different modelling (Sutmann, 2002)

In Figure 11, Brownian dynamics works efficiently near to 1010 atoms with 10-7 seconds. Though it works a thigh number of atoms the BD is difficult to express in equation. The present way about this obstacle can be done by making the equation simpler equation 1 of motion and removing quickly varying degrees of freedom.

푝 ξ 푝 (푡) 푝 (푡) (1)

The classical Brownian motion is anticipated for a given particle which is hit arbitrarily and rapidly by neighbouring particles in fluid. To explain the dynamics of this for a high time scale particle displacements given by Equation (1) imitate to Einstein's relation

1 2푡퐷 = (푟 (푡) − 푟 (표)) (2) 3 where ξ is connected to the D known as diffusion coefficient as

푘 푇 휉 = (3) 푚퐷

Thus, BD is presented as a particle-based method wherever the fluid is implicitly presented (Tildesley & Allen, 1987). So, it is observed that the BD cannot be suited for studying high temperature behavior

Atomic Scale Numerical Simulation Technique

As it was shown before, simulations which are working at atomistic scale might offer much needed complex understandings which might be difficult by other simulation techniques. The appropriate understanding of complexity and mechanism is difficult to be obtained by BD or continuum models. When working at atomic scales simulations there is high pressure on the computation systems as diverse degrees of freedom are worked simultaneously. Two important simulating tools with multiple-body arrangements which work at Nano scale are standard Monte Carlo (MC) and Molecular Dynamics (MD) simulations. The two systems of simulations where MC works on stochastic process while MD covers the deterministic replication way. These imitations are not used to clearly consider for automated freedom of work. So, the simulations go over the precise difficulty to solve Schrödinger particle ensemble work (Sutmann, 2002). Chemical identities are represented implicitly to describe the interaction of potential energy (P.E) between fine geometry of particles. Modelling the inner physical and chemical connections of different materials will be observed in later units. Though traditional method is to provide mathematical need of the P.E. interaction among a couple of atoms by considering their atomic arrangement. With an interacting potential energy function, energy of an atomic ensemble can be easily computed.

Monte Carlo Method

Monte Carlo simulations focuses on finding the lowest possible allowed energy of ensemble of particle. MC simulations tracks modification in energy of structure of molecules or its atoms particles by searching for all degrees of freedom of every other particle by only trails. For example, these trial steps might comprise the internal molecular moments, location change or displacement among different atoms, and even considered if there is change in volume of system. A trial which is run is acknowledged if it helps in lowering the energy of system. The trial is accepted for increased energy of system only when the probability is specified by a Boltzmann statistical distribution,

푁 푔 푒 = (4) 푁 푍 (푇)

Where, Ni / N is particles portion at i condition with Ei is part of energy of the whole number of particles, gi is the degradation in the energy state, Boltzmann constant is given as kB, and temperature T. Partition function is given as Z(T),

푍 (푇) = 푔푒 (5)

This equation shows the probability of a particle ensemble which will receive the energy state (Sutmann, 2002).

Molecular Dynamics Simulation

MD is a simulating tool that has started to gain speed in the last couple of years because of the development of highly extensive, successful computational work, but its origin spreads back to 1950-60. B. J. Alder and T. E. Wainright had done imitations on change in phase before 1960s. Their work involved a system which comprised hard solid

21 particles colliding on each other like snooker balls. Atomic interactions were simulated by A. Rahman using a continuous interatomic potential of Lennard-Jones energy before

1965. This work became famous due to its work on combination of the equations of motion with a finite difference method for the first time, which was not employed by

Alder and Wainright in their former study (Schmidt et al., 2006). MD does not have an imaginary upper boundary on the time and length scales which help in making this system very proficient. This is unique characteristic of MD. So, system under consideration by MD is only limited by the computational capacity on which the simulations are being worked on and not the MD tool. So MD is considered as most operative tool in reduction the breach between nano and macro physical bodies(Frank

Gärtner et al., 2006). It should be known that realism cannot be still depicted of the physical bodies according to the size and time scale in MD simulations. It might be difficult to simulate the actual body of macro scale with the use of MD. To allow such high-end simulations, we have chosen MD calculations. LAMMPS is a MD simulating tool, which is an brought by Sandia Labs that is used in this work (Plimpton, 1995). As in the Monte Carlo simulations, Molecular Dynamic simulations also entail to define assembly of particle connections, or the potential function (pf) of potential energy. In short, this system can be defined as potential function (pf), as it can produce the experimentally observed behavior.

CHAPTER 3

RESEARCH METHODOLOGY

Monte Carlo (MC), Phase Field, Molecular Dynamic (MD), Volume of Fluid

(VOF), and Computational Fluid Dynamics (CFD) are among the simulation techniques used to study coating and additive manufacturing tools. MD, which basically works at molecular level scale, is assumed to prove useful in simulating particle impact and bonding mechanisms for CS process. The success of MD basically revolves around its microscopic scale three-dimensional determination together with constant periodic scales of a nuclear ensemble over the experimental or other numerical techniques. Other advantage of MD is that, it works on limited assumptions to build a physical process model. The important step to bridge the gap between possibility of getting a valid solution in MD and through experiment is still a significant step for scientists to completely clarify work of particle impact, high pressure and temperature, bouncing off particles, phase change, and bonding mechanism (Tildesley & Allen, 1987). The dependency of the precision of MD simulations of the study of critical parameter and behavior of particles in CS process using MD is on high configuration machines.

Important mechanisms are observed from these atomistic simulations, and mesoscale equivalences help to cover the breach of time scale explanations can be used to apply the knowledge to definite engineering developments. This work shows an atomic model which works on optimization of critical impact parameters and the complex bonding

23 mechanism of CS process. Goal of this study using MD is on model development of CS process and to obtain results of working parameters with the simulations.

Development of Simulation Model

This research work employs a pre-existing molecular dynamics (MD) suite called

LAMMPS. LAMMPS software is open end working module provided by Sandia National

Laboratories. It stands for Large-scale Atomic/Molecular Massively Parallel Simulator.

EAM i.e Embedded Atom Method is used for simulation of metals and metal alloys, is an established model (Bonn & Ross, 2001; Foiles, Baskes, & Daw, 1986; Marion, 2013;

Plimpton, 1995). The study considers impact of effect on to the outer surface of a metal substrate. The imitation model includes copper (Cu) atoms as a substrate and a nanoparticle made also 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 substrate is a rectangular block having dimensions of 100 Å x 100 Å x 20 Å with structure of face- centered cubic (fcc) lattice having 3.61 Å as lattice spacing. The nanoparticle is spherical having a diameter of 10 Å with Cu atoms organized in (fcc) lattice assembly having 3.61

Å as its lattice arrangement. The schematic simulation model of copper nanoparticle into copper substrate by CS process is shown in Figure 12. The parameters used for simulation of CS process study are shown in Table 1. Embedded Atom Method (EAM) is used to calculate the interatomic forces between the atoms of Cu-Cu, an appropriate potential for the imitations of structural, mechanical, and thermal properties of metallic systems including Cu (Ajdelsztajn, Zuniga, Jodoin, & Lavernia, 2006). Velocity-Verlet procedure is used to compute the atom velocity and its position. In 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 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 (Ajdelsztajn et al., 2006).

Figure 12. Schematic of Molecular Dynamic simulation model of Cold Spray process

Table 2. Simulation parameters used for the Molecular Dynamics simulation of Cold Spray process.

Cu (100 Å x 100 Å x 20 Å) Substrate Material Approx. 30,000 Atoms Materials Cu Sphere (Diameter 5-20 Å) Nanoparticle Material Approx. 50-400 Atoms Bulk Temperature 300 K Potential Used Embedded Atom Model (EAM) Initial Stand-off Distance 15 Å Impact Velocity 300-750 m/s Operating Conditions Particle Size 5 Å -25 Å Angle of Impact 60°-90° Time step 0.001 ps (picoseconds) Duration of Simulation 10 ps

The Velocity Verlet Algorithm

Typical Verlet algorithm can be clarified as compacted and easy to program integrator which is totally time adjustable and which proves having exceptional low energy utilizing properties over a high series of sizes (Figure 12). Varied systems of the

Verlet algorithm where (1) is attributed to the Verlet technique, (2) slight jump (can be explained as frog leap) variation, and (3) form of velocity Verlet. Sequential stages for different algorithms are shown in the figure. The color boxes signify stowed variables

(Tildesley & Allen, 1987).

Figure 13. Various systems of the Verlet algorithm (Tildesley & Allen, 1987)

The velocity Verlet algorithm helps in storing the complete information about position of particle, particle velocity, and acceleration with time t while diminishing any remaining error (Tildesley & Allen, 1987) LAMMPS MD simulations run on velocity

Verlet integration.

CHAPTER 4

RESULTS AND DISCUSSION

The outcomes stated during this course of thesis refer to information which is attained after 10 picoseconds (ps) of MD simulation. An illustrative atomic configuration of copper nanoparticle deposition on copper substrate throughout the CS process for a velocity of impact of 500 m/s and 90° impact angle which shown in Figure 14. The result of change in critical process parameters – a) velocity of impact b) impact angle and c) particle size is evaluated by measuring the deposition height and flattening ratio of the bonded nanoparticle.

Figure 14a. Representative 3D snapshot of MD simulation after nanoparticle impact on surface of substrate during CS process

Figure 14b. Representative front view snapshot of MD simulation after nanoparticle impact on substrate surface during CS process

Effect of Impact Velocity on Material Deposition

Figure. 15 indicates how particle diameter and impact velocity play an ideal role in deposition efficiency of CS process. Figure indicates that minimum velocity of particles needed for cold spray process should be more than supersonic velocity up to

1200 m/s, beyond that velocity there are changes in the physical orientation of the substrate and even in particles.

Figure 15. Impact of Particle on a solid surface (Klinkov, Kosarev, & Rein, 2005).

Velocity of particle to impact on base material is one of the important variable in

CS process. Critical impact velocity range must be achieved for uniform and efficient bonding of the particles (Ganesan et al., 2012). Impact velocity decides the intensity of plastic deformation which will be responsible for effecting coating. If the velocity of impact is less than the ideal range required for bonding then the particles bounce of the substrate or may even stick to the surface but the coat which will be produced would not be efficient or even its strength would be minimal.

Figure 16 shows the screenshot of Molecular Dynamic simulation study on the outcome of impact velocity on particle bonding during the CS process at 90° angle of impact and 10 Å particle size. The outcomes show that an impact velocity of less than

500 m/s does not bond the particles efficiently to the surface as shown in Figure 16a.

During an impact of Cu particles on Cu substrate the impact velocity less than 500 m/s bounced off the substrate and particles which coated the substrate produced very weak coatings. When the velocity was increased above 500 m/s, a uniform coating phenomenon was clearly observed. This phenomenon revealed that the Cu particles should be set at a velocity of more than 500 m/s to achieve perfectly dense and anti- oxidized coatings. When the impact speed is augmented to 800 m/s, the particles show signs of penetration into the substrate surface as shown in Figure 16d. This suggests that

Cu particles when coatings on Cu as a base material must not be increased more than 800 m/s, as it destroys the physical orientation of the substrate which is not acceptable. In short, this experiment reveals that maintaining the impact velocity within an optimal range is very critical in achieving uniform coating.

Figure 16a. Impact velocity 400 m/s

As seen in Figure 16a, the Cu particles fairly stick to the Cu substrate but fail to coat the substrate effectively or efficiently. This indicates that according to (Schmidt et al., 2006)

Cu has a critical impact velocity of more than 400 m/s

Figure 16b. Impact velocity 500 m/s

Figure 16b, reveals that when the impact velocity is increased to 500 m/s, Cu particles start to coat the substrate efficiently. But the efficiency obtained by velocity of impact as

500 m/s is much less than efficiency achieved by the impact velocity of 600 m/s. Though the efficiency of 500 m/s is less but it is the starting range of Cu particles over Cu substrate to get coating by Cold Spray Process.

Figure 16c. Impact velocity 600 m/s

Figure 16 c gives clear understanding of high efficiency of coatings of Cu particles over Cu substrate when the impact velocity is 600 m/s. It is visible that the penetration of Cu particles inside the substrate is at optimized height and the strength of bonding between particle and substrate is maximum giving uniformity to coating.

Figure 16d. Impact velocity 800 m/s

Figure 16d gives clear idea than beyond impact velocity of 700 m/s for Cu particles over Cu substrate the particles penetrate deep inside the substrate and instead of coating the substrate they drill hole inside it. This is unacceptable phenomenon and it must be avoided. So, the critical impact velocity range for Cu over Cu should be between

500 m/s to 700 m/s to achieve thick, efficient and anti-oxidized coatings

The outcome of change in impact velocity on the splat height during the MD simulation study of cold spray process is shown in Figure 17a. The results reveal that as the velocity of impact increases the deposition height decreases. It is common practice that when you increase the impact force the particle or object tending to stick or move inside the substrate will keep on moving inside. But, this phenomenon is not completely advisable for coatings in cold spray as we want to avoid the penetration of particles inside the substrate and only have dense and thick coatings.

Figure 17a. Effect of impact velocity on deposition height

The result of change in flattening ratio due to change in impact velocity during the

MD simulation study of cold spray process is shown in Figure 17b. Flattening ratio is the ratio of maximum diameter of splat (particle after impact) to original diameter of particle before impact. In this study, flattening ratio is used to measure the uniformity of deposition of particles on the base material during the CS process. According to this study, highest flattening ratio is achieved at velocity of impact of 700 m/s. It is also observed that flattening ratio drops down significantly after impact velocity of 750 m/s due to penetration of particles into the substrate

Figure 17b. Effect of impact velocity on flattening ratio

Effect of Angle of Impact on Material Deposition

Angle of impact is another important parameter in CS process. Figure 18 shows the screenshot 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. Figure

19a 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 substrate will have thicker coating compared to 60° angle of impact.

Figure 18a. Side view and top view during MD simulations showing effect of 60° Impact angle on material deposition of CS process.

Figure 18a shows the impact of 60° angle of impact on material deposition. The figure reveals that the uniformity of coating produced on Cu substrate is very high as compared to Figure 18c. but the efficiency of particles coating the substrate is very less.

This theory is explained by ball bouncing theory. When a ball is thrown on the floor in an incline motion the ball tends to go away from the thrower, same way particles impacting at 60° mostly move away that is bounce off from the substrate rather than giving dense coating. This phenomenon applies to all other impact angles other than angle of impact perpendicular to the substrate.

Figure 18b. Side view and top view during MD simulations showing effect of 70° Impact angle on material deposition of CS process

As shown in figure 18b, efficiency achieved by impacting jet of particles at 70° is more than efficiency obtained by 60°, but still most of the particles are seen to bounce off the substrate rather than giving a dense thick coating.

Figure 18c. Side view and top view during MD simulations showing effect of 80° Impact angle on material deposition of CS process

The result of angle of impact on deposition height of particles during the MD simulation study of cold spray process is shown in Figure 19a. According to the study, highest

34 deposition height is achieved at an angle of impact of 90° as the particles, with impact angle less than 90° spread over larger area resulting reduced deposition height and less dense coatings. It can be clearly observed that there is a drastic change in deposition height after an impact angle of 85°. Deposition height given by jet of particles moving at

60° is least to most spreading of atoms over the substrate instead concentrating a fixed given point.

Figure 19a. Effect of change angle of impact on deposition height during Cold Spray process

The result of angle of impact on the flattening ratio during the MD simulation study of cold spray process is shown in Figure 19b. 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 Figure 18a. It is also observed that flattening ratio is least in 90° due to concentrated jet of particles forming non-uniform coating as shown in Figure 18b. However, it must be noted that at 60°

35 impact angle particles tend to rebound from the substrate more compared to at 90° angle of impact.

Figure 19b. Result of change angle of Impact on flattening ratio during Cold Spray process

Effect of Particle Size on Material Deposition

Particle Size is another important parameter for economical and optimum coatings in CS process. Figure 20 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 Figure 21a. 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 – 20 Å for the conditions used in this study. Figure 21b shows the effect of particle size on flattening ratio during the CS process. From Figure

21b it is clearly observed that the flattening ratio increases with particle size. Moreover, it can be observed that there is no significant change in flattening ratio above a particle size of 20 Å.

Figure 20a. MD simulation snapshots showing effect of 10 Å particle size on material deposition during Cold Spray process

As shown in Figure 20a, atoms combining to form a size of 10 Å is an optimized value to study effect of particle impact on the substrate. Lesser the number of atoms it becomes easy for the evaluator to observe the studying parameters.

Figure 20b. MD simulation snapshots showing effect of 15Å particle size on material deposition during Cold Spray process

Figure 20b reveals the deposition of Cu particles of size 15 Å on Cu substrate.

From the findings during this study it is revealed that this particle size might be an ideal size which achieves maximum efficiency after particle size of 20 Å

Figure 20c. MD Simulation Snapshots Showing Effect of 20Å Particle size on Material Deposition during Cold Spray Process

Figure 20c shows deposition of 20 Å particles on the Cu substrate. The efficiency of coating obtained by this particle size is maximum. But however, it becomes difficult to study stresses and strain acting on the particles during CS process with this particle size.

But, this difficulty level is solely dependent upon computational ability

Figure 21a reveals the effect of change in particle size on deposition height. It is clear that, more than the size of particles, highest is the deposition height, but when the particle size increases above 25 Å there is not much change in deposition height, so it is advisable in order to reduce the cost of complete process, particles can be kept in 10 Å –

25 Å range.

Figure 21b illustrates the effect of change in particle size to flattening ratio. The same observation is noted in Figure 21a. There is no drastic change in flattening ratio even though the particle size is increased further from 20 Å to 25 Å.

Figure 21a. Effect of particle size vs deposition height during Cold Spray process

Figure 21b. Effect of particle size on flattening ratio during Cold Spray process

von Mises Stresses Distribution Acting on Particle During Impact in Cold Spray Process

The deformation pattern and the arrangements of particle and substrate molecules/atoms in CS process were examined throughout the simulation. To understand the plastic deformation at localized point, the stress and strain outlines along a particle edge can be examined. The variation in von Mises stresses along particle edge is revealed in Figures 10a and 10b.

Figure 22a shows von Mises stress acting on particle with a velocity of impact of

300 m/s. Higher stress are not visible during this impact and hence no shear stress instabilities are performed which in other words reveal no bonding occurs between particle and substrate at an impact velocity of 300 m/s.

Figure 22a. von Mises Stress acting on particle for an impact velocity of 300 m/s

Figure 22b shows higher stress is induced on the particle and subsequently on to the substrate, which is visible in red shade on the particle and substrate in case of impact velocity of 800 m/s. This highly induced stress affects in formation of shear adiabatic instability around the edge of substrate. Adiabatic shear instability in the substrate and plastic deformation into the particle helps the particle with high strength bonding. This is the reason behind effective, heat-free and dense coatings by CS process.

Figure 22b. von Mises Stress acting on particle for an impact velocity of 800 m/s

Figures 23 show 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 velocity of impact of 300 m/s when the particle approaches near the interface. As the velocity increases the von Mises stress is seen to increase during the impact process suggesting material hardening. This is followed by a sudden drop in the equivalent von Mises stress eventually approaching to zero stress value. This could be explained by the fact that particle undergoes softening immediately after the impact.

Figure 23. Distribution of von Mises Stress with respect to approach distance for varying impact velocities during Cold Spray process

Figure 24 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.

Figure 24. Variation in particle travel velocity during CS process for different initial velocities

Strain Acting on particle during Impact in Cold Spray Process

Figures 25a and 25b shows particle shear strain on the substrate and particle after the start of the effect for different impact velocities with 300 m/s and 800 m/s respectively. From the figure, it is observed that there is a noteworthy upsurge in plastic strain on the particle and at the substrate/ particle boundary for higher impact speeds.

Figure 25a. Strain acting on particle and substrate with an impact velocity of 300 m/s

Figure 25a. reveals strain acting on the particle after particle impact with 400 m/s as an impact velocity. As the color scale suggest, red shade describes highest strain which also covers substrate particles due to impact. As, the impact velocity is less than the critical range of impact, the strain produced is quietly less than expected.

Figure 25b. Strain acting on particle and substrate with an impact velocity of 800 m/s

Figure 25b. reveals the maximum strain observed after particle impact of 800 m/s.

This figure is evident showing the coverage of maximum strain due to impact velocity above optimized range.

Figure 26a 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 monotonous 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.

Figure 26a. Variation in plastic shear strain with respect to time during Cold Spray process

Figure 26b shows the variation in plastic strain as the particle travels from an initial height of 15Å towards the substrate. It can be seen that for higher impact velocities (500 m/s or

44 higher), there is a sudden increase in plastic strain when particle impacts the substrate which suggest high plastic strain rate deformation.

Figure 26b. Variation in plastic shear strain with respect to distance during Cold Spray process

Figure 27 displays the top view of the particles during the CS process for an 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 parent material produces adiabatic shear instability in the shear bands resulting in adiabatic thermal softening of the materials.

Both the substrate and particle tend to behave like viscous material resulting in almost free flowing of particles. This unique phenomenon produces interfacial jets when the particle impact the substrate. This jet formation holds the particle strongly preventing it from escaping from the surface which results in uniform coating.

Timestep of Particle Top view of Particle for an Top view of Particle for an during CS process Impact Velocity of 300 m/s Impact Velocity of 800 m/s

At Impact

1 ps after Impact

5 ps after Impact

Figure 27. Snapshots of particle at different timesteps during CS process for impact velocities of 300 m/s and 800 m/s

The formation of jets is evident for higher impact velocities as compared to low impact velocities as shown in Figure 28. This formation of jets are is evident due to substrate behaving as a liquid though in solid state. Now the particles hits the substrate and are trapped inside this adiabatic instability provided by the substrate surface, this phenomenon explains the bonding mechanism of CS process. This adiabatic shear instability leads to high strength bonding between particles and substrate and later by particle on particle. Figure 28a shows no formation of interfacial jets which led to bonding in CS process. Figure 28b shows formation of interfacial jets due to an impact velocity of 800 m/s

Figure 28a. MD simulation snapshot of particle impact for an impact velocity of 300 m/s

Figure 28b. MD simulation snapshot of particle impact for a velocity of impact of 800 m/s

CHAPTER 5

CONCLUSION

In this study, molecular dynamics (MD) simulation technique is used to understand the effect of critical process parameters on the material deposition during the

CS process of copper nanoparticles on copper substrate. The findings of this study are as follows.

a) Impact velocity study revealed that a range of 500-700 m/s of impact velocity is found to be optimal for achieving uniform and dense coating for the conditions used in this simulation. Maintaining impact velocity within an optimal range is critical during the cold spray process

b) Angle of impact study revealed that highest deposition height is achieved at 90° revealing that jet of particles perpendicular to substrate will have thicker coatings compared to 60° angle of impact. However, more uniform coatings are observed when the angle of impact is 60°.

c) Particle size study showed that the deposition height and uniformity increases with increasing particle size. However, there is no significant increase in deposition height and uniformity above 20 Å.

Moreover, based on results obtained from stress and strain figures, the particle bonding mechanism can be attributed to thermal softening due to instability of shear band which happens at the edge of particle on to the substrate or particle on particle borders at

48 high velocities. There is variation in stress and strain at the particle edge suggested that particle bonding can be attributed to interrelating surfaces

The findings of this thesis can be utilized to enlarge our current learning in the field of cool spray process.

APPENDIX

RESEARCH DISSEMINATION

1. Joshi, Aneesh and James, Sagil. “Optimization and Bonding Mechanism of Cold

Spray Process using Molecular Dynamics Simulation”, Journal of Thermal Spray

Technology (Under Review)

2. James, Sagil and Joshi, Aneesh. “Molecular Dynamics Simulation Study of Cold

Spray Process”, Poster, Manufacturing Science and Engineering Conference

(MSEC) by ASME, 2017 at University of Southern California

3. Joshi, Aneesh and James, Sagil. “A Molecular Dynamics Simulation Study of

Cold Spray Process”, Presentation, Student Research Competition (SRC) 2nd

place winner at California State University Fullerton

4. Joshi, Aneesh and James, Sagil. “Molecular Modeling Study of Cold Spray

Process of Nanocomposites”, American Society for Composites (ASC) Annual

Technical Conference, at Purdue University, Indiana, 2017 (In Preparation –

Abstract Accepted)

REFERENCES

Ajdelsztajn, L., Zuniga, A., Jodoin, B., & Lavernia, E. (2006). Cold gas dynamic spraying of a high temperature Al alloy. Surface and Coatings Technology, 201(6), 2109-2116.

Assadi, H., Gärtner, F., Stoltenhoff, T., & Kreye, H. (2003). Bonding mechanism in cold gas spraying. Acta Materialia, 51(15), 4379-4394.

Assadi, H., Kreye, H., Gärtner, F., & Klassen, T. (2016). Cold spraying–A materials perspective. Acta Materialia, 116, 382-407.

Bonn, D., & Ross, D. (2001). Wetting transitions. Reports on Progress in Physics, 64(9), 1085.

Champagne, V. K. (2007). The cold spray materials deposition process: Fundamentals and applications: Elsevier.

Foiles, S., Baskes, M., & Daw, M. (1986). Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Physical Review B, 33(12), 7983.

Ganesan, A., Affi, J., Yamada, M., & Fukumoto, M. (2012). Bonding behavior studies of cold sprayed copper coating on the PVC polymer substrate. Surface and Coatings Technology, 207, 262-269.

Gärtner, F., Schmidt, T., Stoltenhoff, T., & Kreye, H. (2006). Recent developments and potential applications of cold spraying. Advanced Engineering Materials, 8(7), 611-618.

Gärtner, F., Stoltenhoff, T., Schmidt, T., & Kreye, H. (2006). The cold spray process and its potential for industrial applications. Journal of thermal spray technology, 15(2), 223-232.

Gilmore, D., Dykhuizen, R., Neiser, R., Smith, M., & Roemer, T. (1999). Particle velocity and deposition efficiency in the cold spray process. Journal of thermal spray technology, 8(4), 576-582.

Goel, S., Faisal, N. H., Ratia, V., Agrawal, A., & Stukowski, A. (2014). Atomistic investigation on the structure–property relationship during thermal spray nanoparticle impact. Computational Materials Science, 84, 163-174.

Grigoriev, S., Okunkova, A., Sova, A., Bertrand, P., & Smurov, I. (2015). Cold spraying: from process fundamentals towards advanced applications. Surface and Coatings Technology, 268, 77-84.

Grujicic, M., Zhao, C., DeRosset, W., & Helfritch, D. (2004). Adiabatic shear instability based mechanism for particles/substrate bonding in the cold-gas dynamic-spray process. Materials & design, 25(8), 681-688.

Klassen, T., Gärtner, F., Schmidt, T., Kliemann, J. O., Onizawa, K., Donner, K. R., . . . Kreye, H. (2010). Basic principles and application potentials of cold gas spraying. Bindemechanismen und potenzielle Anwendungen des Kaltgasspritzens. Materialwissenschaft und Werkstofftechnik, 41(7), 575-584.

Klinkov, S. V., Kosarev, V. F., & Rein, M. (2005). Cold spray deposition: significance of particle impact phenomena. Aerospace Science and Technology, 9(7), 582-591.

Li, W.-Y., Zhang, C., Guo, X., Zhang, G., Liao, H., Li, C.-J., & Coddet, C. (2008). Effect of standoff distance on coating deposition characteristics in cold spraying. Materials & design, 29(2), 297-304.

Maev, R. G., & Leshchynsky, V. (2009). Introduction to low pressure gas dynamic spray: physics and technology: John Wiley & Sons.

Malama, T., Hamweendo, A., & Botef, I. (2015). Molecular Dynamics Simulation of Ti and Ni Particles on Ti Substrate in the Cold Gas Dynamic Spray (CGDS) Process. Paper presented at the Materials Science Forum.

Marion, J. B. (2013). Classical dynamics of particles and systems: Academic Press.

Moridi, A., Hassani-Gangaraj, S., Guagliano, M., & Dao, M. (2014). Cold spray coating: review of material systems and future perspectives. Surface Engineering, 30(6), 369-395.

Papyrin, A., Kosarev, V., Klinkov, S., Alkhimov, A., & Fomin, V. M. (2006). Cold spray technology: Elsevier.

Pasandideh-Fard, M., Pershin, V., Chandra, S., & Mostaghimi, J. (2002). Splat shapes in a thermal spray coating process: simulations and experiments. Journal of thermal spray technology, 11(2), 206-217.

Plimpton, S. (1995). Fast parallel algorithms for short-range molecular dynamics. Journal of computational physics, 117(1), 1-19.

Schmidt, T., Gärtner, F., Assadi, H., & Kreye, H. (2006). Development of a generalized parameter window for cold spray deposition. Acta Materialia, 54(3), 729-742.

Stoltenhoff, T., Kreye, H., & Richter, H. (2002). An analysis of the cold spray process and its coatings. Journal of thermal spray technology, 11(4), 542-550.

Sutmann, G. (2002). Classical molecular dynamics and parallel computing: FZJ-ZAM. Technologies, U. S. Retrieved from http://www.ust.com.au/thermal-spray.html

Tildesley, D., & Allen, M. (1987). Computer simulation of liquids. Clarendon, Oxford.

Van Steenkiste, T., Smith, J., Teets, R., Moleski, J., Gorkiewicz, D., Tison, R., . . . Zajchowski, P. (1999). Kinetic spray coatings. Surface and Coatings Technology, 111(1), 62-71.

Vlcek, J., Gimeno, L., Huber, H., & Lugscheider, E. (2005). A systematic approach to material eligibility for the cold-spray process. Journal of thermal spray technology, 14(1), 125-133.

Watanabe, M., & Kumai, S. (2009). High-speed deformation and collision behavior of pure aluminum plates in magnetic pulse welding. Materials Transactions, 50(8), 2035-2042.