assadi 2011

8/11/2019 assadi 2011

1/16

8/11/2019 assadi 2011

2/16

simple relationships in view of the existing experimentaldata (Ref 8, 9, 19, 22-25). To facilitate the analysis, vpi andvcr are expressed explicitly in terms of primary keyparameters, namely, the particle size and the process gaspressure and temperature. In this way, coating propertiesare linked directly to primary material and processparameters.

The manuscript starts with a description of thenumerical model, through which the particle velocity isworked out for a range of process and materials parame-ters. Subsequently, tting functions for vpi and vcr arepresented. Correlations between coating properties andparticle velocity are presented and discussed next. Finally,examples of parameter selection maps are presented,

including a note on possible implications of these maps inthe development of cold spray technology.

2. Numerical Calculation of ParticleVelocity

Particle acceleration and deceleration in the nozzle isdue to the drag force on the particle. The particle velocityfor a spherical particle can be calculated from this forcebalance (Ref 26):

vpdvpdz

34

C dqv vpjv vpj

qp dp Eq 1

1162Volume 20(6) December 2011 Journal of Thermal Spray Technology

P e e r R e v i e w e d Nomenclature

a Gas sound velocity A Nozzle area A* Nozzle area at the throata* Sound velocity in the throat of the nozzlea ref Reference particle velocityC d Drag coefcientc1-6 Fitting parameterscp Specic heat of particleD * Nozzle diameter at the throatD e Nozzle diameter at the exitD i Nozzle diameter at the inletdp Particle diameterdpref Reference particle diameter f Calibration coefcienthp Height of the splatparticle attened due to

impactk Gas specic heat ratiok1 A particle-size-dependent tting parameter, used

in vcr formulaL c Length of the converging (subsonic) part of thenozzle

L d Length of the diverging (supersonic) part of thenozzle

M Mach numberm t Mass ow rate of the process gasn Fitting parameterP Gas heating powerP ref Reference gas heating powerP Gas pressure p0 Gas stagnation pressure p0* Critical process gas pressure for cold sprayingR Universal gas constant

r e Expansion ratioT Gas temperatureT 0 Gas stagnation temperatureT 0

ref Reference gas stagnation temperatureT 0* Critical process gas temperature for cold sprayingT m Melting temperature of particleT p Particle temperatureT pi Particle impact temperature

t Characteristic process time for adiabatic strainphenomena

V t Rate of gas consumptionV t ref Reference rate of gas consumptionV Gas velocityv1 Approximated gas velocityv2 Approximated particle velocity at the nozzle exitv3 Approximated particle velocity upon impactvcr Critical particle velocity for bondingvcrref Reference critical particle velocityvcr

min Critical particle velocity for fully adiabaticdeformation

verosion Impact velocity causing erosion by hydrodynamicpenetration

vm Impact velocity causing a rise of T p up to T mvmax Maximum particle velocity achievable at a nite

p0vp In-ight particle velocity

vpi Impact velocity of particlevpi0 Characteristic impact velocity ( vpi to induce 1 Krise in T p)

x Characteristic system dimension for adiabaticstrain phenomena

z Axial distance from nozzle throatz0 Location of particle injection on the axial

coordinatea Heat diffusivity of particleb Adiabaticity of particle deformationd Characteristic thickness of the bow shock

boundary layerg Particle impact velocity quotient; coating quality

parameterg f g under failure conditionsl Mean particle sizeq Gas densityq0 Gas stagnation densityqp Particle densityr Tensile strength of particle at 293 Kr c Cohesive strengthr u Ultimate tensile strength

8/11/2019 assadi 2011

3/16

Generally, the above differential equation is solvednumerically to obtain vp , while the gas velocity, v, isobtained from a 1D isentropic model of gas ow through a

convergent-divergent nozzle (Appendix A ). In the presentanalysis, the nozzle is assumed to have a linear prole, i.e.,it is conical in both subsonic and supersonic parts. Forsuch a prole, d z can be substituted by d M (Appendix B),so that Eq 1 can be rewritten (for M 1) as follows:

dvp 38

a2ref R T 0

DD e D v vpj

v vpjvp

f 0AM f qM ffiffiffiffiffiffiffiffiffiffiffiffiffi f AM p

dM

Eq 2 where

a2ref C d L d p0

qp dp Eq 3 The parameter aref (with the dimension m/s) is regardedhere as the reference particle velocity . This parameter canbe perceived as a product of three factors, each of whichscale with the magnitude of particle velocity at the exit of the nozzle. The rst factor C d =qp dp is a combination of particle characteristics that represents susceptibility of theparticle to gain velocity; a lower value of C d =qp dpimplies higher resistance to acceleration, and vice versa.The second factor L d is a key dimension of the nozzle,relating to the time period during which the particle isaccelerated by the process gas. The driving force foracceleration scales with the density of the process gas,which is represented by the third factor, p0. Thus, aref

encapsulates the intrinsic susceptibility of particle toaccelerate, the duration of acceleration, and the drivingforce for acceleration. Consequently, higher values of a ref lead naturally to higher particle velocities at the nozzleexit. A more detailed interpretation of aref will be pre-sented in section 3.

For a specic nozzle, gas, upstream stagnation tem-perature and pressure of the gas (see Table 2 for thecurrent example) the gas dynamics equations and the dragequation are solved numerically, using an explicit nitedifference method. In the present analysis, M is taken asthe primary variable, which is varied between M jzz0 and

M jzL d by a xed increment of d M = 0.01. Subsequently,Eq 1 is used to obtain d vp , and hence, vp . Figure 1 showsan example of the obtained results (for the parametersgiven in Table 2, with C d = 0.65), where particle velocity,gas velocity, and gas temperature are plotted as a functionof the axial distance z .

3. Parametric Expression of the ParticleVelocity

The following expression ts the numerically calculatedvalues of gas velocity, for any T 0, and for a wide range of k(1.1-2.1) and expansion ratio (3.0-16.0):

v v1 c1 D c1D

D e n

a Eq 4 where c1 and n are tting parameters given as c1 exp0355k 1162k2 and n 0:85k 3. Note that these

Table 1 Effect of key materials and process parameterson v pi and v cr

Parameter Effect on v pi Effect on v cr

ParticleMelting temperature Specic heat Hardness

Density Size Gas

Temperature (a)Pressure

NozzleLength

(a) Presuming that particle temperature increases with increasing gastemperature

Table 2 Parameters used for the numerical calculations(Fig. 1)

Parameter Value

Particle (copper)C d 0.65-0.85dp 20 9 10 6, mq p 8960, kg/m3

cp 384, J/kg per KT m 1357, Kr 2.2 9 108, Pa

Gas (nitrogen)R 297, J/kg per Kk 1.4T 0 600, K p0 4 9 106, Pa

NozzleD i, D *, D e 15, 2.7, 6.4, 9 10 3 mL c, L d 30, 130, 9 10 3 mz0 30, 9 10 3 m

Fig. 1 A parametric plot of v, vp , T , and p versus z, the axialdistance from the nozzle throat, calculated using the isentropicow model, and the data given in Table 2

Journal of Thermal Spray Technology Volume 20(6) December 20111163

P e er R evi ew e d

8/11/2019 assadi 2011

4/16

tting parameters depend only on the type of the pro-cess gas, and that v1 (as expected) is independent of pressure.

The form of the tting function for particle velocity ischosen in view of the following considerations: First, thenal gas velocity is taken as an upper bound for the nalparticle velocity at the exit of the nozzle. This implies thatv

p does not exceed v during particle acceleration within

the nozzle. Noting that v depends on T 0 and not on p0, thegas velocity also represents the highest achievable particlevelocity as obtained for a nite T 0 and innitely large p 0.Likewise, it is assumed that there exists a second limitingvelocity, vmax , which represents the highest achievableparticle velocity as obtained for a nite p0 and innitelylarge T 0. The particle velocity at the exit of the nozzle isconsidered as a convolution of vmax and v1, as follows:

vp v2 f 1vmax

1v1

1

Eq 5a where f is a calibration coefcient close to unity, consid-ered here to compensate for the deviation of the abovetting function from the real solution. It is clear that f would equal unity at extremely large p 0 or T 0, i.e., wherevmax or v1 approach innity, respectively.

An examination of the numerically calculated values of vp , as obtained for extremely large values of T 0, demon-strate that vmax does indeed exist, and that it scales withthe reference particle velocity, a ref , as follows:

vmax 1:3 r 0:21e a ref Eq 5b where r e is the expansion ratio of the nozzle. It is inter-esting to note that for typical values of expansion ratio(4.0-9.0) the prefactor 13r 0:21e is close to unity (0.8 to1.0). This implies that a ref and vmax are roughly equal, andhence, convey a similar physical meaning. Therefore, a ref as dened by Eq 3 can be viewed as an estimate of themaximum particle velocity, achievable for a given set of particle characteristics, nozzle length and pressure,regardless of the magnitude of the gas stagnation tem-perature. For the parameters given in Table 2, a ref is about1500 m/s.

By choosing f =1.09, Eq. 5a ts well the numericallycalculated values of particle velocity over a relatively widerange of process and materials parameters (Fig. 2). For anozzle with an expansion ratio of 5.6 (corresponding to theparameters given in Table 2), Eq 5a, b can be rewritten interms of primary materials and process parameters as

follows:

vp c2

ffiffiffiffiffiffiffiffiffiffiR T 0p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiqp dp

C d L d p0s !1

Eq 6 where c2 is 0.42 for nitrogen, and 0.45 for helium as pro-cess gas. Note that Eq 6 ts the results of the employedone-dimensional isentropic model, as applied to a nozzlewith a linear prole, assuming constant C d . In reality,ow is inuenced by friction at the nozzle interior, thenozzle has often a non-linear prole, and C d is notconstant (Appendix C). Therefore, Eq 6 should be used

with reservation, especially for very small or very largeparticles. Equation 6 is also not applicable to low-pressurecold-spray systems, where powder is injected into thesupersonic part of the nozzle.

The following example shows how the above ttingfunction may be used to provide a quick overview on theinuence of process parameters on vp . Differentiation of Eq 6 with respect to p

0 and T

0, with the parameters given

in Table 2, results in:

dvpvp ffi

0:21d p0 p0 0:29

dT 0T 0 Eq 7

According to this relation, for the conditions specied inTable 2, 10% increase in p0 and/or T 0, results in 2.1% and/or 2.9% increase in vp , respectively.

Because of the bow shock that forms in front of thesubstrate, the velocity of particles upon impact would inpractice be lower than that given by Eq 6. This effect canbe taken into account by solving Eq 1 once more for thedeceleration of particles in the bow-shock region. Theresult of modelling, considering the bow-shock effect, hasbeen found to t the following expression:

vpi v3 v2 1 q0dqp dp !

1

Eq 8 where d is a tting parameter of about 0.0007 m for thecurrent example. Figure 3 shows the results of thenumerical model as compared to Eq 6 and 8.

It should be noted that similar approximations havebeen used by different authors (Ref 10, 14). The presentapproximation, however, appears to be applicable to awider range of parameters, partly because it relaxes thecondition vp v. Moreover, postulation of the maximumparticle velocity, vmax , in this study is considered to pro-vide further insight to the problem of particle accelerationin cold spray.

4. Parametric Expression of the CriticalVelocity

The critical impact velocity can be expressed in termsof materials properties and particle temperature as follows(Ref 8):

vcr k1 ffiffiffiffiffiffiffifficpT m T p 16

r

qp

T m T pT m 293 s Eq 9 where k 1 is a dimensionless tting parameter typically in

the range from 0.5 to 0.6. The effect of particle size can beincorporated into the above relation by taking k1 as afunction of dp . This has been done for copper. By ttingthe existing experimental data for particle sizes within therange 10-105 l m, one obtains (Ref 9):

k1 0:64dp =d ref p 0:18 Eq 10a and


P e e r R e v i e w e d

8/11/2019 assadi 2011

5/16

vcr vref cr dp =d ref p 0:18 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 T p =T mq Eq 10b where dp

ref

is a reference particle size, and vcrref

is a refer-ence critical velocity, which are for the current exampleequal to 10 l m and 650 m/s, respectively. Apart from themathematical form of the vcr -dp variation, it is wellestablished that in cold spraying smaller particles exhibithigher critical velocities as compared to larger particles.This can be attributed, among all possible factors, to largerdeviation from the condition of adiabaticityi.e., to moreeffective heat diffusion from the surface of the parti-clefor smaller particles (Ref 8).

Note that Eq 10a, b is valid only for copper and for alimited range of particle size; for innitely large or small

particles, the critical velocity as obtained from this equa-tion becomes zero or innity, respectively. To proceedfrom this point, a more general expression for vcr can be

obtained under the following considerations: First, in viewof the results of large-scale impact tests (Ref 8), one canpresume that the critical velocity approaches asymptoti-cally a non-zero minimum, vcrmin , as the particle sizebecomes extremely largei.e., where particle deforma-tion can be considered to become fully adiabatic. Like-wise, considering that temperature gradient in very smallparticles is negligible, it is assumed that the criticalvelocity for bonding coincides with another characteristicimpact velocity, vm , signifying the kinetic energy thatcauses the particle to reach its melting point. That is toassume, in other words, that bonding would be inevitable

Fig. 2 Numerically calculated particle velocity at the nozzle exit, vp , as compared to the values obtained from the t-function, Eq 5a, b,for copper as a reference spray material, nozzle type 24 (D24), nitrogen (a) or helium (b) as process gas, and temperatures from 30 to1300 K. (c) and (d) illustrate the correlations for nozzle types 24 and 40 (D24 and D40), obtained for copper, aluminum, and tantalum asspray materials, and nitrogen (900 K) as process gas. Small scattering of the data points from the diagonal (dashed) line demonstrates agood correlation between vp and v2, for a wide range of gas pressure (10-100 bar) and temperature (300-1300 K), and for different typesof process gas, material and nozzle geometry. Different data points of the same group (identied by the same marker/symbol) correspondto different values of pressure, i.e., the lowest and the highest points correspond to p0 = 10 and 100 bars, respectively. Particle size is xedat 20 l m in all calculations. Dimensions of the nozzle type 24 are the same as in the previous example (Table 2), whereas nozzle type 40has an expansion ratio of 7.6 and L d of 180 mm (nozzle type names are used according to the notation of the Helmut Schmidt University,Hamburg, Germany and CGT GmbH, Ampng, Germany)


P e er R evi ew e d

8/11/2019 assadi 2011

6/16

when the entire particle is at T m . Based on theseassumptions, vm and vcrmin would become the upper and thelower bounds of the critical velocity, respectively. In a rstapproximation, the critical velocity is formulated as asimple mathematical interpolation between these twolimits, using the following expression:

vcr vm c4bn vmincr

1 c4bn Eq 11a

where vm ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2cpT m T =c3p , in which c3 is the fractionof the kinetic energy that dissipates into heat within theparticle, c4 and n are tting constants, and b is a dimen-sionless parameter representing adiabaticity of particledeformationi.e., the degree to which the process of deformation can be considered to be adiabatic. The adi-abaticity is dened here as:

b dp v0pi

a Eq 11b in which a is the thermal diffusivity of the particle underconsideration, and v0pi ffiffiffiffiffiffiffiffi2 cpp is a characteristic impactvelocity, corresponding to 1 K rise in average particletemperature due to the dissipation of kinetic energy. Theabove denition of adiabaticity is based on that usedpreviously in the simulation of adiabatic shear instability

during particle impact (Ref 7). In the analysis of highstrain-rate phenomena, adiabaticity is represented by thedimensionless parameter x2/a t , in which x is a character-istic system dimension, and t is a characteristic processtime (Ref 27). In the present analysis, x and t are substi-tuted by dp and dp /vpi0 , respectively. Thus, the twoextremes of fully-isothermal and fully adiabatic deforma-tion are signied by b =0 and , respectively. The form of the interpolation function in Eq 11a , b is chosen in view of the following considerations: (a) Assuming that the ther-mal condition at the interacting interfaces plays a mostdetermining role in particle bonding, the adiabaticity

parameter (which incorporates both particle size and heatdiffusivity) should be the main argument of this function.(b) The interpolation function should satisfy the limitingconditions, vcr = vm and vcrmin , corresponding to b = 0 and ,respectively. (c) The function should be capable of pro-viding a good t to the existing experimental data oncopper, and (d) this should preferably be achieved via aminimum number of tting parameters. Note that theabove analysis is based on a heat-conduction view of thesize-dependence of critical velocity; other possible factors,such as surface oxidation, which may play a role in size-dependence of the critical velocity, are not consideredhere. Equation 11a , b should therefore be conceived onlyas a slightly improved version of Eq 10a, b. Also, furtherexperimental data will be needed to assess applicability of Eq 11a, b to materials other than copper. For this reason,size-dependence of the critical velocity is considered onlyfor the case of copper in the present analysis.

Equation 10a, b and 11a, b can provide almost identicalresults for copper powder (with particle size of 5-105 l m).The agreement between these two equationsas well as

the best t to the experimental datais achieved whenc3 =2/3, c4 = 1, n = 1/2, and vcrmin is calculated using Eq 9with k1 = 0.27. Note that all these constants are taken hereas adjustable tting parameters, with the exception of c3(fraction of the kinetic energy that dissipates into theparticle) which should in principle be consistent with thethermomechanical aspects of particle/substrate interac-tion. Preliminary simulations of particle impact suggestthat c3 is indeed in the range between 0.5 and 0.8. Usingthese parameters, Eq. 11a, b can be rewritten as:

vcr vref cr0:42dp =d ref p 0:5 ffiffiffiffiffiffi1 T p =T mp 1:19 ffiffiffi1 0:73T p =T mp 0:65dp =d ref p 0:5

Eq12 where dpref = 10 l m, and vcrref = 650 m/s, as before. Note thatunlike Eq 10a, b, the above equation results in nite val-ues of critical velocity for innitely large or small d p . Forthe example of copper, Fig. 4 shows plots of vcr versus d paccording to Eq 12, as compared to values of the criticalvelocity as obtained from experiments and FEM simula-tions. Figure 4 also provides an overview on the degree of adiabaticity in cold sprayas signied by the gap betweenvm and vcr .

5. Inuence of Particle Impact Velocityon Deposition Characteristics

The condition for successful cold spray deposition ismet as soon as vpi > vcr . However, obtaining cold-sprayedcoatings of favorable properties requires that vpi becomesnoticeably larger than vcr . On the other hand, higher vpimeans higher operation costs. Also, exceeding vcr by toolarge an amount may lead to unfavorable effects such aserosion. Therefore, the question of how coating propertiesare inuenced by the magnitude of vpi becomes of centralimportance in cold spray. This section examines the

Fig. 3 Variation of the particle impact velocity for copperparticles of different sizes (data points, numerically calculated),as compared to values obtained from the t-functions, Eq 6 and8. The calculation parameters are the same as in the previousexample (Table 2)



8/11/2019 assadi 2011

7/16

inuence of particle impact velocity on some of thesecharacteristics.

5.1 Flattening Ratio

The attening ratio, dened here as 1 h p /dp (Fig. 5),represents the severity of particle deformation as a resultof impact (Ref 5, 7). Deposits with severely deformed

particles are likely to exhibit minimal porosity, highamounts of bonded area, and relatively high values of cohesive strength. Therefore, the attening ratio can beconsidered as a diagnostic microstructural property,which serves as a general measure of the overall quality of cold-sprayed coatings.

The effect of particle impact velocity on the atteningratio is investigated through nite element modelling of plastic deformation during impact, using ABAQUS/Explicit (Ref 28). The calculation settings and the pre-sumed material properties were similar to those usedpreviously in Ref 7, 8. For simplicity, and to alleviate theeffect of particle size and that of excessive mesh distortionon the deformed shape, simulations were performed foradiabatic deformation of large particles (20 mm indiameter) impacting on a rigid substrate. Further atten-ing due to subsequent impingements was not considered.Moreover, a friction coefcient of 0.5 was chosen betweenthe surfaces of the particle and the substrate. Figure 6shows the results of modelling for different initial condi-tions, corresponding to aluminum and copper as example

feedstock materials.As shown in Fig. 6(a), the attening ratio always

increases with increasing particle impact velocity, thoughthe rate of this increase depends strongly on materialproperties, as well as on T pi . Interestingly, the atteningratio exhibits little dependence on material properties ortemperature, when it is plotted against the ratio of theparticle impact velocity to the critical particle impactvelocity ( Fig. 6b). In this case, all variations collapse ontoa single quasi-linear curve. Consequently, the atteningratio appears to be a unique function of vpi /vcr , regardlessof the values of materials and process parameters.

5.2 Deposition Efciency It is well established that higher pressures and tem-

peratures result in higher particle velocities, and hence,lead to higher deposition efciencies (DEs). Interest-ingly, the deposition efciency alsoin analogy withthe attening ratioappears to be a unique function of vpi /vcr . This can be demonstrated based on the existing

Fig. 4 Variation of the critical impact velocity with particle sizefor copper. The solid lines correspond to Eq 12, while the dottedlines show the upper limit of the critical velocity, correspondingto zero adiabaticity. The particle temperature upon impact isassumed to be 300 K

Fig. 5 An example of attening of a particle due to impact on arigid substrate, as obtained from FEM simulation

Fig. 6 Calculated attening ratios of copper and aluminum as a function of (a) particle impact velocity, and (b) the ratio of particleimpact velocity to critical velocity. The dashed line in (b) shows the relation: y =0.46 x


P e er R evi ew e d

8/11/2019 assadi 2011

8/16

experimental data (Ref 9). As illustrated in Fig. 7, vari-ation of DE with vpi /vcr (considering size-dependence of the critical velocity) is the same for cold spraying of different copper powders. It should be noted, however,that the characteristic smooth variation of DE withtemperature or pressure, as often observed in cold sprayexperiments, is also a consequence of particle size vari-ance. Under idealized conditions, the DE variation incold spraying of a mono-size powder would be expectedto resemble a step function. As the size distributionbecomes wider, the increase of DE with increasing anycharacteristic parametersuch as temperature, pressure,vpi of the mean particle size, or even the vpi /vcr ratiowill become more gradual. In view of these consider-ations, plots of DE versus vpi /vcr should be interpretedwith caution. For typical powders, on the other hand, the

effect of particle size variance is normally not signicant.Moreover, there is always a particle velocity variance dueto uid-dynamic effects (even for a mono-size powder)which masks the inuence of the particle-size variance.Therefore, it would still be safe to consider vpi /vcr as amost inuential factor in the prediction of DE. As ageneral rule for typically ductile materials, DE reaches asaturation limit at vpi /vcr = 1.2, and remains unchangeduntil erosive effects (due to hydrodynamic penetration)kick in at vpi /vcr = 1.5-3.0.

Having the particle size distribution function, f (dp), fora given powder, DE can be worked out quantitatively as afunction of process and materials parameters as follows:

DE Z 10 g f dp ddp Eq 13a where d d p is the differential of dp and g is a size-depen-dent function, which is obtained in terms of the charac-teristic particle velocities as follows:

g 1 if vcr

8/11/2019 assadi 2011

9/16

strength would be expected at vpi /vcr = 1. Alternatively, thedifference between these impact velocities can beaccounted for by adjusting the vpi /vcr ratio in such a waythat the cohesive strength drops to zero at vpi /vcr =1. Forthe case of copper, this is achieved by applying a correc-tion factor of f =1.05 to the vpi /vcr ratio; implying 5%underestimation of vpi with reference to vcr . The result of this modication is shown in Fig. 8(c), where the cohesivestrength is normalized with respect to a reference value of 300 MPa. The reference value represents the value of strength at vpi /vcr = 2. Considering the special stress con-dition in the TCT test, this value coincides roughly withthe ultimate tensile strength of 450 MPa as obtained for

(highly deformed) copper (Ref 8, 19, 20). In view of theseresults, the real cohesive strength of cold-sprayed coatingsmay be expressed generally, for typical powders and idealspraying conditions, as follows:

r c r u f vpivcr

1 Eq 14 where r u is the ultimate tensile strength, and f is a cali-bration factor as explained above.

A similar behavior was observed for titanium, forwhich various impact conditions were obtained using awide range of process gas temperature at p0 =40 bar

(Fig. 9). As illustrated in Fig. 9(b), again, the normalizedcohesive strength shows a unique linear correlation withvpi /vcr for both types of the titanium powder used in thisstudy. In this case, however, size-dependence of thecritical velocity is not considered when calculating thevpi /vcr ratio. In analogy with the results of the copperpowders ( Fig. 8b), there is non-zero strength at vpi /vcr =1. Figure 8(c) shows the alternative relation, which isobtained by applying a correction coefcient of f =1.08,and considering a reference (TCT) strength of 420 MPa,corresponding to an ultimate tensile strength of 630 MPa.

Preliminary analysis of the experimental data for tita-

nium sprayed on aluminum suggests that the adhesivestrength between the titanium coating and the substrate,also, depends only on vpi /vcr . However, a general quanti-tative relationship as in Eq 14 cannot be derived for theadhesion strength because of the inuence of differentsubstrate materials involved.

Despite the arguable deviations from Eq 14, the overallresults as obtained for copper and titanium suggest thatthe coating strength, too, can be considered as a uniquefunction of vpi /vcr . This further supports the notion thatthe ratio vpi /vcr might be used as a universal and simplemeasure of the general quality of cold-sprayed deposits.

Fig. 8 Measured values of the cohesive strength of cold-sprayed copper coatings, as plotted against (a) particle impact velocity, and (b)the ratio of particle impact velocity to critical velocity, and (c) the adjusted velocity ratio using a correction factor of f = 1.05. The dashedline in (c) shows the relation: y = x 1, where y (on the vertical axis) indicates the cohesive strength normalized with respect to areference value of 300 MPa, representing the tensile strength of highly deformed bulk copper in a TCT test


P e er R evi ew e d

8/11/2019 assadi 2011

10/16

6. Parameter Selection MapsThe above results (section 5) suggest that coating

characteristics may be conceived as a function of adimensionless parameter, dened as the ratio of particleimpact velocity to critical particle impact velocity:

g vpivcr Eq 15

Considering the correlations obtained for vpi and vcr(sections 3 and 4), g can be expressed directly in terms of primary materials and process parameters, namely, parti-cle size, gas temperature, and gas pressure. For the specicmaterial, spraying conditions and nozzle geometry asconsidered in this study (Table 2), g can be expressed asfollows:

g ffi"vref cra ref dpd ref p !0:18

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 T piT mr 10:32 ffiffiffiffiffiffiffiffiffiffiffiffiffiC d L d p01 kqp dp k R T 0s ! 1

p0dRT 0dp #

1

(Eq 16)

where vcrref = 650 m/s, dpref = 10 l m, and d = 0.0007 m. Notethat the above equation incorporates size-dependence of

the critical velocity according to Eq 10a, b. Equation 16provides a basis for the construction of parameter selectionmaps for cold spraying of copper, as described next.

6.1 Constructing the Maps

An important feature of Eq 16 is that, apart from T pi , itdoes not contain any intermediate variable; note thatvelocity variables vpi and vcr are replaced by primaryprocess parameters in this equation. Elimination of T pifrom Eq 16 may in principle be pursued through numeri-cal modelling combined with a tting procedure, similar tothat performed for vpi (section 3). However, nding ageneral expression for T pi might be comparatively less

straightforward. In addition to the parameters consideredin this analysis, T pi is expected to be inuenced by factorssuch as the length of the pre-chamber and the stand-off distance (Ref 9-14). Apart from these complexities, par-ticle bonding is expected to be inuenced by the temper-ature difference between the substrate and the particle,especially at higher values of T 0. This means that even anaccurately estimated T pi may not solve the issue com-pletely. Clearly, further experimental and theoreticalstudies will be needed on this front. Nevertheless, toobtain a preliminary overview on the variation of g withprimary process parameters, T pi is considered here to

Fig. 9 Measured values of the cohesive strength of cold-sprayed titanium coatings, as plotted against (a) particle impact velocity, and (b)the ratio of particle impact velocity to critical velocity, and (c) the adjusted velocity ratio using a correction factor of f = 1.08. The dashedline in (c) shows the relation: y = x 1, where y is the cohesive strength normalized with respect to 420 MPa, representing the tensilestrength of a highly deformed material in a TCT test



8/11/2019 assadi 2011

11/16

increase linearly with increasing T 0, according to: T pi =c5 + c6 T 0, where c5 and c6 are tting parameters. Thislinear approximation is based on the results of numericalmodelling (Appendix D).

Using Eq 16 and the above approximation for T pi , thedeposition window may be dened in the p0-T 0-dp space asfollows:

1

8/11/2019 assadi 2011

12/16

p0 and T 0; a xed g value would impose a constraint oneither p0 or T 0 but not on both. At this stage, one mayconsider different criteria to dene the best choice of p0and T 0, and so, to pinpoint a specic processing conditionon the parameter selection map.

The cost of operation is likely to be a commonsensicalcriterion in most industrial applications. In this case, usingthe lowest possible gas pressure, or the highest possiblegas temperature, would constitute the most favorableprocess setting. This can be demonstrated by taking thecase of copper (Fig. 10) as a typical example. For sim-plicity, the operation cost is considered here to be gov-erned by gas consumption and heating power. These twofactors can be calculated from the mass ow rate of theprocess gas, m t , which is given as:

m t A p0 ffiffiffiffiffiffiffiffiffikRT 0s k 12 k12k 1

Eq 18 Assuming a constant heat capacity of 1200 J/kg fornitrogen, the gas consumption, V t , and the gas heatingpower, P , are obtained for the given nozzle ( Table 2) interms of p 0 and T 0 as follows:

V t V ref t p0 pref 0 ffiffiffiffiffiffiffiffiT

ref 0

T 0s Eq 19 P P ref

p0 pref 0

T 0T ref 0

1 ffiffiffiffiffiffiffiffiT ref 0

T 0s Eq 20 where V t ref =3.8 m3/h and P ref = 0.47 kW, for p0ref = 1 barand T 0ref = 298 K. Considering that g = 1 represents thethreshold of cold-spray deposition, p0 can be worked outin terms of T 0, and then, inserted into Eq 19 and 20 towork out the gas ow rate and the heating power as a solefunction of T 0. Figure 11 shows the corresponding resultsfor two cases of g =1 and g = 1.5, using the parametersgiven in Table 2, with C d = 0.85. As shown in Fig. 11, forboth cases the ow rate and the heating power decrease

with increasing gas temperature. The latter trend mayseem somewhat surprising, as higher gas temperatureswould intuitively be associated with higher heating pow-ers. This is clearly not the case in this example. Note thathigher temperatures on a given g -contour correspond tolower pressures and that, according to Eq 20, P scales with p0. As a result, the operation cost (gas consumption plusheating) will always decrease with increasing gas temper-ature, regardless of the price of gas or electricity. Thismeans that, as far as the operation cost is concerned, T 0should be set as high as it is technically feasibletakinginto account the capability of the system and the meltingtemperature of the feedstock materialand then, thecorresponding p 0 should be determined from the relevantg -contour on the given p0-T 0 diagram. Practical issues likenozzle clogging should also be taken into account whenselecting parameters along a desired g -contour. It shouldalso be noted that the absolute power consumption that isneeded in real spray equipment is normally higher thanthat estimated by Eq 20, since Eq 20 does not take intoaccount heat losses.

An alternative criterion to dene the best choice of p 0and T 0 can be devised with respect to homogeneity of thecoating microstructure. Figure 12 shows superimposedg -contours of 10 and 50 l m particles. The gray region isthe overlap of the respective windows of deposition. It isreasonable to assume that spraying within this regionwould ensure maximal deposition efciency when theparticle size is between 10 and 50 l m. It should be noted,however, that none of the respective g -contours of the twowindows match. Instead, they cross over at certain points(shown as dots in Fig. 12) within the gray region. Only atthese points g -values of different particles are equal;anywhere else within the gray region particles of differentsizes deposit with different g -values, and hence, exhibitdifferent attening ratios and bonding characteristics. Inthis respect, the locus of these crossovers signies theoptimum conditions for cold spraying, should a deposit of uniform bonding characteristics be desired. The lowestpoint of this locus, marked by p 0* and T 0*, represents the

Fig. 11 Calculated variations of the gas ow rate and the heating power with the gas temperature, (a) for the condition of g = 1 forcopper, i.e., where vpi = vcr , and (b) for g = 1.5, corresponding to the dark gray region in Fig. 10 (left)



8/11/2019 assadi 2011

13/16

critical process parameters for cold spraying of copper,when particles are between 10 and 50 l m, nitrogen is usedas process gas, and the nozzle has the dimensions asspecied in Table 2. The signicance of the point ( p0*, T 0*)is that it marks a minimal condition for efcient depositionof a structurally uniform coating. In this way, p0* and T 0*

might be conceived as main cold-spray attributes of agiven feedstock material, for a given type of gas andnozzle geometry. It would seem interesting to workoutusing the above procedureand report these attri-butes for various combinations of feedstock materials andcold spray systems.

A parameter selection map may also provide a guide-line for further development of cold spray systems. Asshown in Fig. 12, the threshold of deposition (as signiedby g = 1) for a 10 l m particle has a local minimum around40 bars. This implies that increasing pressure beyond 40bars would actually work against deposition of 10 l mparticles. This effect results from the deceleration of par-ticles by the bow shock, which would be more signicantfor smaller particles. In view of this consideration, it may

not be necessarily helpful, nor desirable, to develop coldspray systems that are capable of working at much higherpressures. Instead, it would be helpful to devise methodsto alleviate the bow shock effect, e.g., by spraying inpartial vacuum as in the so-called aerosol depositionmethod (Ref 29), or to spray at highest possible temper-atures. In contrast, for larger particle sizes (see theexample for a particle size of 50 l m in Fig. 12) increasingthe gas pressures to values higher than 40 bars would bebenecial for enhancing coating properties.

The presented method of analysis has also some limi-tations. A main limitation is that it does not take substrate

properties into account. Consequently, the method doesnot incorporate certain deposition characteristicssuch asthe adhesive strength of the coating/substratethat areadditionally inuenced by the properties of the substratematerial. On the other hand, preliminary analysis of theadhesive-strength data suggest that similar correlationscould be worked out between the measured data and thev

pi/v

cr ratio, with v

cr representing a weighted average of

the respective critical velocities for the feedstock andsubstrate materials. Further work is in progress on thisfront.

7. Conclusions

Particle velocity at the exit of the nozzle can beexpressed, with reasonable accuracy, as an explicit func-tion of pressure, temperature, and particle size. Thisfunction is obtained as a convolution of two limitingvelocities as follows: (a) the gas velocity at the exit, which

is a function of T 0 but not p0, and (b) a reference particlevelocity, which is a function of p0 but not T 0. The latterparameter signies the maximum particle velocityachievable for a given nozzle geometry, particle size, and p0. In combination with a parametric expression for thecritical particle velocity, the above tting function is usedto work out an explicit expression for the ratio of particlevelocity to critical velocity, referred to as g . Based on theexisting experimental data (for copper and titanium) andsimulations (for copper and aluminum), it is postulatedthat main coating and deposition characteristics can beexpressed as a unique function of this dimensionlessparameter. In this way, nal coating properties are linkeddirectly to primary process and material parameters forthe examined materials. To facilitate selection and opti-mization of cold spray parameters, parameter selectionmaps are constructed as contour plots of g on p0-T 0planes. These maps show not only the respective windowof deposition, but also the spraying parameters corre-sponding to the desired g -value, and hence, to the targetcoating property. Moreover, application of parameterselection maps in cold spray alleviates the need for athorough understanding of uid dynamics or solidmechanics by the end user. Finally, parameter selectionmaps can be used to pinpoint optimal spraying conditionswith respect to different criteria such as minimization of the process cost or maximization of the uniformity of the

coating properties. A future line of research in cold spraycould involve assessment of the proposed method in viewof further experimental data, and possibly, application of the method to work out the most favorable sprayingconditions for various feedstock materials.

Acknowledgments

The authors thank K. Onizawa and K. Donner forassistance with the numerical calculations. Also, technicalsupport from T. Breckwoldt, H. Hu bner, D. Mu ller,

Fig. 12 Parameter selection map as calculated for copper fortwo different values of particle size. The dots show the locus of the crossovers of the respective g -contours. The crossover atg = 1 is signied by the critical processing conditions p 0* and T 0*


P e er R evi ew e d

8/11/2019 assadi 2011

14/16

N. Nemeth, C. Schulze, M. Schulze, and U. Wagener isgratefully acknowledged. HA is much thankful toFo rderverein Metallkunde e.V. , Hamburg, Germany, for aresearch fellowship.

Appendix A: Gas Dynamic Equationsfor Flow in a Nozzle

The following well-known gas dynamic equations areused for isentropic ow of an ideal gas with constantthermodynamic properties through a convergent-diver-gent nozzle (Ref 10-14, 30):

A A f AM

1M

2 k 1M 2k 1

k12k 1Eq A1

T T 0 f TM 1

k 12

M 2

1

Eq A2 p p0 f pM 1

k 12

M 2 k

k 1

Eq A3 qq0 f qM 1

k 12

M 2 1

k 1

Eq A4 q0

p0R T 0 Eq A5

a ffiffiffiffiffiffiffiffiffiffiffiffik R T p ; a ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi2 k R T 0=1 kp Eq A6 v

a M

Eq A7

Appendix B: Nozzle Prole Equations

For a simplied geometry with linear proles in thesubsonic and the supersonic parts, the following relationsare obtained between the nozzle area and the axial dis-tance z , where z = 0 at the throat of the nozzle.

Supersonic part ( M 1):

z 2 ffiffiffiffiffiffiffiffiffi A=pp DD e D L d Eq B1

Subsonic part (M 150 l m) particles.

References

1. A.P. Alkimov, V.F. Kosarev, N.I. Nesterovich, and A.N. Papyrin,Method of Applying Coatings, Russian Patent No. 1618778, 1990

2. A. Papyrin, Cold Spray Technology , Elsevier, Amsterdam, 2007

3. V.K. Champagne, The Cold Spray Materials Deposition Process:Fundamentals and Applications , CRC Press, Cambridge, 2007

4. E. Irissou, J.-G. Legoux, A.N. Ryabinin, B. Jodoin, and C.Moreau, Review on Cold Spray Process and Technology: PartIIntellectual Property, J. Therm. Spray Technol. , 2008, 54,p 495-516

5. R.C. Dykhuizen, M.F. Smith, R.A. Neiser, D.L. Gilmore, X.Jiang, and S. Sampath, Impact of High Velocity Cold SprayParticles, J. Therm. Spray Technol , 1998, 8(4), p 559-564

6. S. Yin, X.-F. Wang, B.-P. Xu, and W.-Y. Li, Examination on theCalculation Method for Modeling the Multi-Particle ImpactProcess in Cold Spraying, J. Therm. Spray Technol , 2010, 19(5),p 1032-1041

7. H. Assadi, F. Ga rtner, T. Stoltenhoff, and H. Kreye, BondingMechanism in Cold Gas Spraying, Acta Mater. , 2003, 51, p 4379-4394

Fig. D1 Temperature of copper particles, as a function of (a) process gas temperature and (b) particle diameter, calculated using anisentropic model, for nozzle type 24 (Table 2), injection 20 mm/135 mm upstream of the nozzle throat

Fig. C1 Drag coefcient (a) and corresponding Reynolds numbers of particles (b) as a function of Mach number, calculated for differentparticle sizes. For this calculation a supersonic nitrogen gas stream of Mach 3 is taken. The stagnation conditions are 30 bar 600 C fornitrogen as process gas. The approximation of Walsh is used in a similar way in the uid dynamics software FLUENT (Ref 33)


P e er R evi ew e d

8/11/2019 assadi 2011

16/16

8. T. Schmidt, F. Ga rtner, H. Assadi, and H. Kreye, Developmentof a Generalized Parameter Window for Cold Spray Deposition, Acta Mater. , 2006, 54, p 729-742

9. T. Schmidt, H. Assadi, F. Ga rtner, H. Richter, T. Stoltenhoff,H. Kreye, and T. Klassen, From Particle Acceleration to Impactand Bonding in Cold Spraying, J. Therm. Spray Technol. , 2009,18, p 794-808

10. R.C. Dykhuizen and M.F. Smith, Gas Dynamic Principles of ColdSpray, J. Therm. Spray Technol. , 1998, 7, p 205-212

11. T. Stoltenhoff, H. Kreye, and H.J. Richter, An Analysis of theCold Spray Process and its Coatings, J. Therm. Spray Technol. ,2002, 11, p 542-550

12. T. Stoltenhoff, J. Voyer, and H. Kreye, Cold SprayingState of the Art and Applicability, International Thermal Spray Confer-ence 2002 , Essen, E.F. Lugscheider, C.C. Berndt, Eds., DVS-Verlag, Du sseldorf, Germany, 2002, p 366-374

13. V.F. Kosarev, S.V. Klinkov, A.P. Alkimov, and A.N. Papyrin,On Some Aspects of Gas Dynamics of the Cold Spray Process, J. Therm. Spray Technol , 2003, 12(2), p 265-281

14. M. Grujicic, C.L. Zhao, C. Tong, W.S. DeRosset, and D.Helfritch, Analysis of the Impact Velocity of Powder Particles inthe Cold-Gas Dynamic-Spray Process, Materials science andEngineering , 2004, A368 , p 222-230

15. S.V. Klinkov, V.F. Kosarev, and M. Rein, Cold Spray Deposition,Signicance of Particle Impact Phenomena, Aerospace Scienceand Technology , 2005, 9, p 582-591

16. C.J. Li, W.Y. Li, and H. Liao, Examination of the CriticalVelocity for deposition of Particles in Cold Spraying, J. Therm.Spray Technol , 2006, 15(2), p 212-222

17. K. Kim, M. Watanabe, J. Kawakita, and S. Kuroda, Effects of Temperature of In-ight Particle on Bonding and Microstructurein Warm-Sprayed Titanium Deposity, J. Therm. Spray Technol ,2009, 18(3), p 392-400

18. C. Borchers, T. Schmidt, F. Ga rtner, and H. Kreye, High StrainRate Deformation Microstructures of Stainless Steel 316L byCold Spraying and Explosive Powder Compaction, AppliedPhysics A , 2008, 90, p 517-526

19. K. Binder, J. Gottschalk, M. Kollenda, F. Ga rtner, and T.Klassen, Inuence of Impact Angle and Gas Temperatureon Mechanical Properties of Titanium Cold Spray Deposits, J. Therm. Spray Technol. , 2010, 20, p 234-242

20. T. Schmidt, F. Ga rtner, and H. Kreye, New Developments inCold Spray Based on Higher Gas- and Particle Temperatures, J. Therm. Spray Technol , 2006, 15(4), p 488-494

21. G. Bae, K. Kang, H. Na, J.-J. Kim, and C.H. Lee, Effect of Particle Size on the Microstructure and Properties of KineticSprayed Nickel Coatings, Surface & Coatings Technology , 2010,204, p 3326-3335

22. R.C. McCune, W.T. Donlon, O.O. Popola, and E.L. Cartwright,Characterization of Copper Layers Produced by Cold Gas-

Dynamic Spraying, J. Therm. Spray Technol , 2000, 9(1), p 73-8223. F. Ga rtner, T. Stoltenhoff, J. Voyer, H. Kreye, S. Riekehr, andM. Kocak, Mechanical Properties of Cold-Sprayed and Ther-mally Sprayed Copper Coatings, Surface & Coatings Technology ,2006, 200, p 6770-6782

24. W.Y. Li, C.J. Li, and H. Liao, Effect of Annealing treatment onthe Microstructure and Properties of Cold-Sprayed Cu Coatings, J. Therm. Spray Technol , 2006, 15(2), p 206-211

25. E. Calla, D.G. McCartney, and P.H. Shipway, Effect of deposi-tion Conditions on the Properties and Annealing Behavior of Cold-Sprayed Copper, J. Therm. Spray Technol , 2006, 15(2),p 255-262

26. G.B. Wallis, One Dimensional Two Phase Flow , McGraw Hill,New York, 1969

27. G.G.B. Olson, J.F. Mescall, and M. Azrin, Adiabatic Deforma-tion and Strain Localization, Shock Waves and High-Strain-RatePhenomena in Metals , M.A. Meyers and L.E. Murr, Ed., PlenumPress, New York, 1981, p 22-23

28. ABAQUS FEA, DS Simulia, Dassault Syste `mes, 2004,2010

29. J. Akedo, Room Temperature Impact Consolidation (RTIC) of Fine Ceramic Powder by Aerosol Deposition Method andApplications to Microdevices, J. Therm. Spray Technol. , 2008, 17,p 181-198

30. M.A. Saad, Compressible Fluid Flow , Prentice Hall, EnglewoodCliffs, NJ, 1985

31. D.J. Carlson and R.F. Hoglund, Particle Drag and Heat Transferin Rocket Nozzles, AIAA Journal , 1964, 2, p 1980-1984

32. M.J. Walsh, Drag Coefcient Equations for Small Particles inHigh Speed Flows, AIAA Journal , 1975, 13(11), p 1526-1528

33. ANSYS FLUENT Flow Modeling Software, release13.0,ANSYS, Inc. Canonsburg, PA 15317, USA. 2010



Documents

assadi 2011