8
Numerical simulation of cold spray coating R. Ghelichi a , S. Bagherifard a , M. Guagliano a, , M. Verani b a Politecnico di Milano, Dipartimento di Meccanica, Via La Masa, 1, 20156 Milano, Italy b Politecnico di Milano, Dipartimento di Matematica, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy abstract article info Article history: Received 30 June 2010 Accepted in revised form 23 May 2011 Available online 30 May 2011 Keywords: Cold spray coating Critical velocity FEM Wavelet transform In cold spray coating, bonding happens when the velocity of the particles exceeds a certain so called critical velocity(CV). The CV is affected by many process parameters. Therefore it serves as a representative parameter for verication of coating quality. Formerly, researchers have demonstrated that lower CV for a process leads to a better coating quality and demands less energy consumption. In this study, based on the well-recognized hypotheses that CV is related to adiabatic shear instability induced by high strain rate deformation during the impact, a numerical model of cold spray process is developed aimed to calculate the CV. The challenging problem of detecting the CV using the discrete output of numerical simulation has been solved applying Wavelet transformation and the second derivative of the physical parameters in Sobolev space. The results are compared with the other numerical models and the experimental results available in the literature. © 2011 Elsevier B.V. All rights reserved. 1. Introduction Cold spraying is an emerging coating process in which in contrast to the well-known thermal spray processes such as ame, arc, and plasma spraying, the powders do not melt before impacting the substrate [1]. This character makes cold spray process commendable for many different coating applications dealing with various materials, not only metals but also polymers, composites, etc. Bonding of the particles in this process occurs due to the high kinetic energy upon impact; therefore, the velocity of the particle plays the most important role in material deposition. During the process, powders are accelerated by injection into a high velocity stream of gas. The high velocity stream is generated through a convergingdiverging nozzle. As the process continues, the particles impact the substrate and form bonds with it, resulting in a uniform almost porosity-free coating with high bonding strength [1]. Low temperature also aids in retaining the original powder chemistry and phases in the coating, with changes only due to deformation and cold-working. Bonding of particles in cold gas spraying is presumed to be the result of extensive plastic deformation and related phenomena at the interface [2]. It is to be underlined that the particles remain in the solid state and are relatively cold, so the bulk reaction on impact and the cohesion of the deposited material is accomplished in solid state. Schematic diagram of the cold spray equipment is shown in Fig. 1. As mentioned, it is well-recognized that particle velocity prior to impact is a key parameter in cold spray process [2]. It determines what phenomenon occurs upon the impact of spray particles, whether it would be the deposition of the particle or the erosion of the substrate. CV for a given powder is dened as the velocity that an individual particle must attain in order to deposit after impacting the substrate [1]. In other words, for a given material, the CV is the velocity at which the transition from erosion of the substrate to deposition of the particle takes place. Experimental investigations also reveal that successful bonding is achieved only above this certain amount of particle velocity, the value of which is associated with temperature and thermo-mechanical properties of the sprayed material [3,4] as well as the characteristics of the substrate [59]. Different researches have been performed on CV characterization. Theoretical estimation of CV is based on the detection of adiabatic shear instability occurrence upon particle impact [10]. Adiabatic shear instability and the resultant plastic ow localization are the phenomena that are believed to play the major role in the particle/substrate bonding during cold spray process [3,10]. The instability observed on the trend of different physical param- eters including strain, temperature, and stress can lead to numerical estimation of the CV. The obtained particle deformation shapes predicted by different authors are almost equal in all the literature [3,10,11]; however it is curious that their results in the case of the predicted CV are different not only due to different methods but also to the dissimilar interpretations used for detection of the shear instability. Commonly the shear instability appears as a singularity in the parameters such as equivalent plastic strain (PEEQ) while dened as a function of time. Different criteria have been used for recognition of shear stability occurrence in the literature. For example, Grujicic et al. [10] presented the shear instability parameter establishing the idea that plastic ow localization in an Surface & Coatings Technology 205 (2011) 52945301 Corresponding author. Tel.: + 39 02 23998206; fax: + 39 02 23998202. E-mail address: [email protected] (M. Guagliano). 0257-8972/$ see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2011.05.038 Contents lists available at ScienceDirect Surface & Coatings Technology journal homepage: www.elsevier.com/locate/surfcoat

Numerical simulation of cold spray coating

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Page 1: Numerical simulation of cold spray coating

Surface & Coatings Technology 205 (2011) 5294–5301

Contents lists available at ScienceDirect

Surface & Coatings Technology

j ourna l homepage: www.e lsev ie r.com/ locate /sur fcoat

Numerical simulation of cold spray coating

R. Ghelichi a, S. Bagherifard a, M. Guagliano a,⁎, M. Verani b

a Politecnico di Milano, Dipartimento di Meccanica, Via La Masa, 1, 20156 Milano, Italyb Politecnico di Milano, Dipartimento di Matematica, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy

⁎ Corresponding author. Tel.: +39 02 23998206; fax:E-mail address: [email protected] (M. Guag

0257-8972/$ – see front matter © 2011 Elsevier B.V. Adoi:10.1016/j.surfcoat.2011.05.038

a b s t r a c t

a r t i c l e i n f o

Article history:Received 30 June 2010Accepted in revised form 23 May 2011Available online 30 May 2011

Keywords:Cold spray coatingCritical velocityFEMWavelet transform

In cold spray coating, bonding happens when the velocity of the particles exceeds a certain so called ‘criticalvelocity’ (CV). The CV is affected by many process parameters. Therefore it serves as a representativeparameter for verification of coating quality. Formerly, researchers have demonstrated that lower CV for aprocess leads to a better coating quality and demands less energy consumption. In this study, based on thewell-recognized hypotheses that CV is related to adiabatic shear instability induced by high strain ratedeformation during the impact, a numerical model of cold spray process is developed aimed to calculate theCV. The challenging problem of detecting the CV using the discrete output of numerical simulation has beensolved applying Wavelet transformation and the second derivative of the physical parameters in Sobolevspace. The results are compared with the other numerical models and the experimental results available inthe literature.

+39 02 23998202.liano).

ll rights reserved.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Cold spraying is an emerging coating process in which in contrastto the well-known thermal spray processes such as flame, arc, andplasma spraying, the powders do not melt before impacting thesubstrate [1]. This character makes cold spray process commendableformany different coating applications dealingwith variousmaterials,not only metals but also polymers, composites, etc. Bonding of theparticles in this process occurs due to the high kinetic energy uponimpact; therefore, the velocity of the particle plays the mostimportant role in material deposition. During the process, powdersare accelerated by injection into a high velocity stream of gas. The highvelocity stream is generated through a converging–diverging nozzle.As the process continues, the particles impact the substrate and formbonds with it, resulting in a uniform almost porosity-free coating withhigh bonding strength [1]. Low temperature also aids in retaining theoriginal powder chemistry and phases in the coating, with changesonly due to deformation and cold-working. Bonding of particles incold gas spraying is presumed to be the result of extensive plasticdeformation and related phenomena at the interface [2]. It is to beunderlined that the particles remain in the solid state and arerelatively cold, so the bulk reaction on impact and the cohesion of thedeposited material is accomplished in solid state. Schematic diagramof the cold spray equipment is shown in Fig. 1. As mentioned, it iswell-recognized that particle velocity prior to impact is a keyparameter in cold spray process [2]. It determines what phenomenon

occurs upon the impact of spray particles, whether it would be thedeposition of the particle or the erosion of the substrate. CV for a givenpowder is defined as the velocity that an individual particle mustattain in order to deposit after impacting the substrate [1]. In otherwords, for a given material, the CV is the velocity at which thetransition from erosion of the substrate to deposition of the particletakes place. Experimental investigations also reveal that successfulbonding is achieved only above this certain amount of particlevelocity, the value of which is associated with temperature andthermo-mechanical properties of the sprayed material [3,4] as well asthe characteristics of the substrate [5–9]. Different researches havebeen performed on CV characterization. Theoretical estimation of CVis based on the detection of adiabatic shear instability occurrenceupon particle impact [10]. Adiabatic shear instability and the resultantplastic flow localization are the phenomena that are believed to playthe major role in the particle/substrate bonding during cold sprayprocess [3,10].

The instability observed on the trend of different physical param-eters including strain, temperature, and stress can lead to numericalestimation of the CV. The obtained particle deformation shapespredicted by different authors are almost equal in all the literature[3,10,11]; however it is curious that their results in the case of thepredicted CV are different not only due to different methods butalso to the dissimilar interpretations used for detection of the shearinstability. Commonly the shear instability appears as a singularity inthe parameters such as equivalent plastic strain (PEEQ) while definedas a function of time. Different criteria have been used for recognitionof shear stability occurrence in the literature.

For example, Grujicic et al. [10] presented the shear instabilityparameter establishing the idea that plastic flow localization in an

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Fig. 1. Schematic view of the cold spray coating machine [1].

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element at the particle/substrate interface occurs when the shearlocalization parameter goes beyond a certain value.

In the present study the shear instability is acknowledged usinga precise criterion based on a sensitive method for shear instabilitydetection. Admittedly, the outputs of the finite element commercialsoftware are discrete numbers. Finding the minimum velocity atwhich the shear instability occurs using these discrete data is muchtricky and challenging due to the discontinuity of the results. In orderto overcome this problem, a mathematical method which is able toobserve any small change in the smoothness of the result functionsis developed for identification of shear instability. The output datafor different physical and mechanical parameters have been elabo-rated using Wavelet transformation and the second derivative inSobolev space in order to identify the minimum velocity at whichshear stability occurs. In order to critically investigate the impact andparticle bonding phenomena, the interaction of the particles withsubstrate has been modeled using the commercial arbitrary Lagrang-ian finite element program ABAQUS/Explicit [12]. Using a 3D fullmodel, single particles are assumed to impact the substrate in normaldirection with given impact velocity and temperature. The Johnson–Cook constitutivematerialmodel [13,14] has been selected to describethe plastic flow of material, which takes strain hardening, strain ratehardening and thermal softening into account. Mesh convergencestudy has been performed analyzing element size influence. The “zeroelements” method is used to obtain mesh size independent results,due to the fact that the outcomes are found to be so sensitive toelement size that convergence cannot be obtained by decreasing theelement size. “Zero elements” method is the technique used in theliterature to obtain results independent from element size while thedependency cannot be easily omitted just by decreasing mesh size[3,11]. The obtained results are compared with the experimental dataavailable in the literature and numerical results obtained by otherresearchers [15]. Table 1 presents the nomenclature used in this paper.

Table 1Nomenclature.

σeq[MPa] equivalent normal plastic stressA [MPa] Yield stressB [MPa] Hardness modulus�p(�p0)[mm/mm] Equivalent plastic strain�̇p �̇p0�

mm=mm½ � Equivalent plastic strain raten Hardening exponentC and m ConstantT(Tinit) [K] TemperatureTmelt[K] Melting temperatureR Real numbersZ IntegersL2(Ω) Finite energy function ∫ | f(t)2dt|≤+∞‖ f ‖ Norm of function fdj,k Wavelet coefficientHm(Ω) Sobolev space with derivatives up to order m in L2(Ω)ψj, k Orthonormal basis of L2(Ω)f Filtered version of function f

2. Bonding mechanism

The adiabatic shear instability and its correlation with bondingwere first considered in appropriate details by Wright [16,17]. Wrighttried to model a rigid, work-hardening, plastic material with ratehardening and thermal softening in order to estimate the formation ofadiabatic shear bands. The results demonstrated that it is necessary tocontrol the defect which initiates the localized shear band. Generallyspeaking, increasing the stress level results in strain increase in typicalstress–strain curves of isothermal materials; however this is not thecase when adiabatic shear strain model is applied. This model ifconsidered under high strain rates causes localized softening behaviorin certain points.

The plastic strain energy which is released as heat rises thetemperature and accounts for material softening. Indeed, fluctuationsin stress, strain, temperature or micro structure, and the inherentinstability of strain softening can give rise to plastic flow (shear)localization. Accordingly, material model plays an extremely impor-tant role in the accuracy of the numerical analysis output of suchphenomena. There are different types of material models which takethis issue into account among which the Johnson–Cook [13,14] modelhas been chosen to be implemented in this numerical simulation.Strain hardening, strain-rate sensitivity and thermal softening aredefined for the considered material model, the equivalent normalplastic deformation resistance of which is described by Eq. (1).

σeq = A + B �p

� �nh i1+ Cln �̇p = �̇p0

� �h i× 1− T−Tinit

Tmelt−Tinit

� �m� �ð1Þ

By using this material model, the evolution of equivalent shearstrain, strain rate, temperature, and stress can be investigated.

3. Numerical approach

3.1. FE model development

A 3D full model of particle impact on substrate has been simulatedusing ABAQUS/Explicit [12] with Lagrangian formulation. Differentpartitions shown in Fig. 2 are created to obtain an optimized meshdistribution in order to reduce the number of elements in non-impactzones. One of the demanding aspects of high velocity impactsimulations is the wave speed spread through the elements and

Fig. 2. Isometric view of the FEM 3D model.

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Table 2Material constants for Johnson–Cook model [13,14,18–20].

Parameters Cu Ni SS316

Johnson–CookParameters

A [MPa] 90 163 388B [MPa] 292 648 1728C 0.025 0.006 0.02494m 1.09 1.44 0.6567n 0.31 0.33 0.8722�̇0 [1/s] 1 1 1e-5

General and thermalproperties

Density [kg/m3] 8960 8900 8031Conductivity [W/Km2] 386 90.9 16Specific heat [J/kgK] 383 435–446 457Melting point [K] 1356 1728–1726 1643Poisson ration 0.34 0.31 0.3Module of elasticity [GPa] 124 200 193

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the fluctuations of this wave which remain in the model preventingthe possibility of having stable results. The half infinite bottom-upelements [12] have been used in the boundaries of the model in orderto damp the wave fluctuations. Fig. 2 shows the developed finiteelement model with the annotations to describe its different parts.It is to be mentioned that similar to all other cold spray simulations,the physical bonding has not been modeled and the particles aredetached after impacting the substrate. However the deformation ofthe particles and the consequent substrate profile is quite equal towhat happens in real process as it is specifically verified in the nextsections. Different analyses have been performed varying the velocityof the particles in the range of 200–1000 m/s. In all cases, the durationof numerical analysis has been set to provide enough time for the

Fig. 3. Flowchart of CV ca

particle to detach from the substrate and therefore, to fully completethe considered process. General contact without friction has beenregarded as the interaction model between the particle and thesubstrate [12]. All the dimensions in the model for instance thesubstrate dimensions, size of the elements, etc. have been chosen asratios of the particle diameter. The particle temperature is set to150 °C and the temperature of the substrate is the ambient tem-perature, both chosen according to the experimental setup in [15].

3.2. Material

Different material types have been considered for the particle andthe substrate. Copper (Cu) and nickel (Ni) have been used for particlemodeling and copper and SS316 for the substrate. The Johnson–Cookplasticity model [13,14] has been used both for the particle andthe substrate. The considered material constants are presented inTable 2 [13,14,18–20]. According to [11] the Johnson–Cook damageparameters shall be defined in order to control the distortion of theelements due to large deformations attributed to the high velocity ofthe particles.

3.3. Mesh convergence study

It is well-known that element size strongly affects the results ofnumerical simulations. A very dense mesh has been generated on theimpact area and the element sizes have been gradually increasedgetting far from the impact zone. “C3D8R” linear hexahedron 8 nodereduced integration elements have been used tomesh the particle andthe substrate. Half infinite “CIND8” elements have been used to cover

lculation algorithm.

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the substrate side faces. The size of the elements in the impact zonehas been chosen as ratios of the particle diameter which are 1/10th,1/15th, and 1/20th. Similar size of elements has been chosen in eachanalysis for the particle and the impact zone. As mentioned in theliterature [11] in case of particle impact numerical simulation theresults of critical velocity do not converge by decreasing the elementsize. Since as the mesh size is decreased, variations of instableparameters are almost linear, the extrapolation of instable results to ameshing size of zero has been used to stand for the real one. This socalled “zero elements” method provides the final result independentfrom element size [3,11].

As mentioned before, evolution of the four physical parameterswhich are presented in Johnson–Cook model should be investigatedduring the impact time. Thus, a series of elements are chosen asshown in Fig. 2 as monitor elements, to survey the variation of theseparameters during the particle impact.

3.4. Wavelet, Sobolev spaces and denoising

As mentioned before Wavelet transformation and the secondderivative in Sobolev space have been implemented on discreteoutput of different physical and mechanical parameters to accuratelydetect the minimum velocity at which shear stability occurs. In thissection a concise description of these mathematical definitions is

Fig. 4. Different parameters' results for one monitored element a) equivalent plastic strainequivalent plastic strain and Von-Mises stress.

presented. For ΩpR, L2(Ω) is defined to be the space of functionsf:Ω→R such that:

‖ϑ‖L2 Ωð Þ = ∫Ω ϑ xð Þj j2dxn o1

2 b∞: ð2Þ

In order to measure the smoothness properties of a function in anaverage sense it is common to introduce Sobolev spaces Hm(Ω)consisting of all functions f∈L2(Ω), with derivatives up to order m inL2(Ω), i.e.

‖ f ‖Hm Ωð Þ = ‖ f ‖L2 Ωð Þ+ ∑m

α=1‖ fα‖L2 Ωð Þb∞: ð3Þ

Characterizing smoothness properties of a function is briefly recalledthrough Wavelet coefficients as the following [21]. Let {ψj,k(x)}j≥0,k∈Z

be anorthonormal basis of L2(Ω) (see e.g. [21] for a detailed discussion),then a function f∈L2(Ω) belongs to the Sobolev spaceHm(Ω) if and onlyif

Em fð Þ = ∑j≥0

∑k∈Z

22jm dj;k 2

!12

b∞ ð4Þ

where dj, k=∫Ω f(x)ψj, k(x)dx are the Wavelet coefficients of thefunction f. It is important to remark that the quantity Em( f) is

b) Von-Mises stress c) equivalent plastic strain rate d) calculating J2 for an element in

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equivalent to the Sobolev norm ‖f‖Hm(Ω). In the sequel, the quantity E2will be used to monitor the behavior of the average regularity of thesecond derivative of a given sequence f = fn xð Þf gNn = 0 of functions. Inparticular computing the following quantity is of interest:

J2 f� �

= max0≤n≤N−1

E2 fn+1�

−E2 fnð Þ : ð5Þ

J2 f� �

measures the maximum variation of the H2-Sobolev norm of agiven sequence of functions. The reliability of the quantity J2 as anindicator to identify the CV is well validated in Section 6.

TheWavelet bases are also suitable to be used in a straightforwardway to perform compression (or denoising) of a given signal. Letf=∑ j, kdj, kψj, k be the Wavelet decomposition of a given signal f(x)and TN0 be a threshold parameter. The filtered version f̃ of the signal fcan be computed in the following way [21]:

f = ∑dj;kj j≥T

dj;kψj;k: ð6Þ

This procedure, which retains the main features (i.e. the largestwavelet coefficients) of thegiven signal,will be employed in Section 5 todenoise the plastic equivalent strain rate and Von-Mises stress resultsfor the monitored elements.

Fig. 5. Examples of denoising the data a) denoising the equivalent Von-Mises stress for200 m/s and 1000 m/s initial velocity of particle b) denoising the strain rate for 500 m/sinitial velocity of particle.

4. Critical velocity detection procedure

Based on the second derivative of the physical parameters for eachvelocity in Sobolev space, the biggest jump is considered as aninstability which has not been introduced in previous velocities. Inthis regard, as can be observed also in the flowchart and algorithm,the value of J2 which is the scalar value of the second derivative of

Fig. 6. Rc as a function of time and particle velocity after impact for different materialsa) Rc for Ni on Cu b) Rc for Cu on Cu c) Rc for Cu on SS316.

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different physical parameters such as strain rate in each velocity, hasto be considered and compared to that of other velocities in order tofind the range of critical velocity based on the biggest jump in J2 value.

The algorithm developed for finding CV requires performing aseries of numerical tests in Abaqus and evaluating the secondderivative of different physical parameters which are practicallyaffected by shear instability in the Johnson–Cook material model. Inthis regard, Python [22] is used to develop a subroutine to beimplemented in Abaqus for performing the numerical tests automat-ically. The developed algorithm is described as following:

1. Based on the experimental results, no material bounding occurs incold spray coatingwith velocities less than200 m/s andalmost all thetested materials bound with a velocity lower than 1000 m/s. Thus,the first step has been set to perform 8 sets of analysis with differentvelocities in the practical range of 200–1000 m/s, in order to obtainan approximation of the CV for the considered material types.

2. Then for each parameter, the maximum jump in the secondderivative in the Sobolev space based on Wavelet transform hasbeen located. Having performed this step, the CV for the consideredshot and substrate material type is achieved in the range of 100(due to the step of velocity change set to 100 m/s). In order to reacha better assessment of the material behavior, the evaluation isperformed for different parameters such as PEEQ, equivalent Von-Mises stress, temperature of the particle and equivalent plasticstrain rate. These properties all appear in the Johnson–Cook [13,14]material model.

3. In the view of the results obtained in previous step, another seriesof analyses are performed using a smaller pace in order to obtain anarrower range of the CV approximation. For example, if in thesecond step the CV is found to be between 500 m/s and 600 m/s, inthis level, the analysis are performed changing the particlevelocities from 500 m/s to 600 m/s with the pace of 10 m/s.

4. The3rd step is repeated over to obtain anaccurate enoughevaluationof the CV.

5. After having detected the CV, the whole process should bereproduced with three different sizes of the mesh in order toassess the linear variation trend and then apply the zero elementsize extrapolating method and eventually obtain the mesh sizeindependent CV value.

Fig. 3 shows the flowchart of the CV detection algorithm based onthe second derivative of the physical parameters. It is worthy to notethat due to many numerical limitations such as the minimum number

Fig. 7.Deformation of the particle after 5 and 10 ns considering different particle velocities a)10 ns f) 200 m/s at 10 ns.

of increments in Abaqus and analysis time and also the numericalsensitivity of the chosen procedure, it is hardly practical to obtain anabsolute value for the CV. Thus the results will be stated in a delicaterange for CV.

5. Results and discussion

The developed procedure mostly studies the evolution of differentphysical parameters attributed to the particle velocity in order toestimate the CV of the process. In this section different outcomes ofthe process are presented; in particular the displacement and thedeformation of the particles are discussed. Fig. 4 shows the changesand also the distinctions between different physical parametersnumerically calculated during the process. The evolution of PEEQ,Von-Mises stress and equivalent strain rate are respectively presentedin Fig. 4a–c for a monitored element. As it is observed the criticalchange cannot be easily located in the presented graphs. Thus it isrequired to elaborate the data using the second derivative in Sobolevspace in order to perform a more perceptive monitoring of thechanges. Fig. 4d shows the evolution of J2 which has been used forfinding the CV for each of the examined parameters. The maximumjump in the second derivative in Sobolev space observed in Fig. 4dshows the position of CV in this range of speed. In Fig. 4d, J2 isnormalized in each step.

Obviously, based on Fig. 4 the obtained numerical results for Von-Mises stress and strain rate, after a certain value, do not follow aregular expected path contrary to what is stated in the literature[3,10]. Thus a denoising method based on the Wavelet coefficient isapplied in order to obtain the clear path of parameter alterations. As itcan be observed in Fig. 5a, which represents the results for twodifferent particle velocities in Cu\Cu coating for equivalent Von-Mises stress, and in Fig. 5b, that shows the filtered data for 500 m/sparticle velocity for equivalent plastic strain rate, the filtered linesdemonstrate a significantly practical path of changes for the studiedparameters. Compression ratio is defined as a parameter related to theparticle geometry to keep track of the particle deformation during theimpact process. It is calculated based on Eq. (7):

Rp =D−hpD

× 100: ð7Þ

In which Rp is the compression ratio, hp is the smallest diameterafter deformation and D is the original particle diameter. Fig. 6a–c

1000 m/s at 5 ns b) 600 m/s at 5 ns c) 200 m/s at 5 ns d) 1000 m/s at 10 ns e) 600 m/s at

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5300 R. Ghelichi et al. / Surface & Coatings Technology 205 (2011) 5294–5301

show the compression ratio of the modeled particle in differentvelocities for Ni\Cu, Cu\Cu, and Cu–SS316 respectively. As it isdepicted in Fig. 6, the particle deformation varies with the substrateand particle material. Two peaks are observed for Cu\Cu and Cu–SS316 in velocities less than the CV. These peaks are attributed to thefact that under the considered condition the particle is deformedmoreseverely than the substrate and has resulted in the occurrence of thepeaks in the Rc graph. This phenomenon has been illustrated in Fig. 7which represents the deformation evolution of the particle for Cu\Cuwith different velocities at two different time intervals of the process.For example with a velocity of 600 m/s the particle continuesdeforming from 0.5 ns to 1 ns but the substrate retains its previousform and does not undergo further deformation; whereas with avelocity of 1000 m/s the substrate and the particle both deform inalmost the same rate during the process.

Fig. 9. Example of finding the final CV by the “zero elements” method for Ni on Cu.

Fig. 8. Velocity of the bottom point of the particle after impact a) Ni on Cu b) Cu on Cuc) SS316 on Cu.

In order to control the process duration and realize the entireprocedure, it is necessary to check the velocity of the particle. Fig. 8shows the evolution of particle velocity for its bottom point that is thefirst point of the particle that goes in contact with the substrate. Itrepresents the moment in which the velocity becomes zero underdifferent impact conditions. According to Fig. 8 in which the resultsobtained for different materials and different velocities are presented,the analyzing time is clearly enough for simulation of the impact aswell as the rebounding of the particle bottom point. Regardless of thefact that whether the bonding between particle and the substratehappens or not, the particle tries to detach from the substrate afterimpact due to the high impact velocity; the detaching velocity of theparticle is studied and presented in Fig. 8 which, as observed in theworst case, is about 100 m/s. Velocities in these graphs are presentedas vectors in the normal direction, thus positive/negative sign of thevelocity indicates the direction of the particle movement.

As discussed in previous sections and also confirmed by theliterature [3,11], the results of the finite element model does notconverge by decreasing the element size. Thus in order to find thefinal value independent from element size, the “zero elements”method has been used. Fig. 9 shows the implementation of the “zeroelements” method for Ni on Cu to obtain the final CV of the process.

6. Comparison with experimental and othernumerical simulations

The obtained numerical results are compared with the experi-mental data available in the literature and also with other referenceswhich have used numerical finite element approach for CV calcula-tion. In the present study, the CV has been calculated considering thesame process condition used in the experimental study of Raletz et al.[15]. In order to validate the comparison of the obtained results withthe experimental results of Raletz et al. [15], the condition of theirexperimental study is presented here briefly; in this regard, Table 3presents the laboratory condition of their tests [15]. The averageparticle size in their case is reported to be 20 μm [15].

Table 3Experimental condition presented in [15].

Nozzle diameter [mm] 2.6Feeding rate [g/min] 5 to 10Gas flow rate [Nlm] 1000–3300Standoff distance [mm] 30Gas pressure [MPa] 0.2, 0.5 and 1Gas temperature [°C] 150

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Table 4Final measured results for CV.

Powder Substrate Calculated Experimental Numerical results in literature

CV [m/s] Raltez [18]CV [m/s]

Grujicic [10]FEMCV [m/s]

Grujicic [10]SLCV [m/s]

Wen-Ya Li [11]CV [m/s]

Cu Cu 402–412 422±45 575–585 571 298–356Cu SS316 410–420 437±47 570–580 574 NANi Cu 454–464 512±59 570–580 576 NA

5301R. Ghelichi et al. / Surface & Coatings Technology 205 (2011) 5294–5301

The Kinetic 3000M system from CGT Gmbh has been used in orderto perform the cold spray process for three different materials for theparticle and substrate. In their work, the measurements of in-flightparticle parameters have been performed using SprayWatch equip-ment (Oseir, Osuusmyllynkatu13FIN-33700 Tampere Finla). Theexperimental process of measuring the particle velocity has beenexplained in detail in [15], in whichmeasuring the particles reboundingvelocity and investigating the first bounding of the particles aredescribed.

Table 4 shows the final calculated results for copper on copper,copper on SS316L, and nickel on copper. This table shows also theresults obtained from other numerical approaches developed in otherreferences. Grujicic et al. [10] have calculated the CV based on twodifferent approaches: FEM and SL. SL parameter is defined bySchoenfeld andWright [23], for quantification of the relative tendencyof material for shear localization. The tendency for strain localization(measured by inverse of the uniform plastic strain amount, takingplace past the strain at which the flow stress experiences a maximum,needed to obtain strain localization) scales with SL parametersdefined as:

SL = −∂2σe= ∂εp∂εp�

∂σe =∂ε̇p� �

σe

0@

1A

σe =σemax

ð8Þ

where σmaxe denotes the maximum value of the (adiabatic) flow stress

at a given impact particle velocity. Detailed computational analyses ofthe particle/substrate interactions carried out by Assadi et al. [3] andGrujicic et al. [10] established that plastic-flow localization in amaterial at particle/substrate interface occurs when SL parameter islarger than a threshold value of 1.6×10−4±0.2×10−4 s.

As presented in Table 4 the final obtained results by the proposedmethod in this article show a satisfactory correspondence with theexperimental results in [15].

7. Conclusion

A 3D finite elementmodel is developed in order to calculate the CVin the cold spray coating process. Abaqus 6.9-1 Explicit has been usedin order to perform the numerical analysis, and Python 2.4-1 is usedfor elaborating Abaqus discrete outputs and performing a series ofnumerical tests to accurately detect the shear instability and con-sequently the CV. Regarding the mesh convergence, the “zeroelements” method has been used to find the element size indepen-dent results. The obtained results from the software are converted toWavelet parameters in order to calculate the second derivative of thephysical parameters in Sobolev space. The results are compared with

different previously developed numerical approaches available in theliterature and also with the experimental tests of Raltez et al. [15]. Adifference of 12 to 20% is observed between previous numericalsimulations and Raletz experimental work [15], whereas thepresented results in this article show a very good correspondencewith the experimental measurements. This noteworthy differencewith other numerical models can be attributed to the sensitive andspecific mathematical approach developed for recognition of shearinstability. In view of the obtained results, the presented method is auseful tool to have better experimental setup and the sensitivity andaccuracy of the described method helps to survey the process and itsqualification in order to increase the functionality of the depositedmaterial with the optimum condition.

Acknowledgments

The authors would like to thank Dr. Simone Vezzu and Civen-NanoFab Association (Italy) for their support and useful suggestions.

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