Ž .Thin Solid Films 390 2001 13�19

Numerical simulation of coating growth and pore formation inrapid plasma spray tooling

Yanxiang Chen, Guilan Wang, Haiou Zhang�

State Key Laboratory of Plastic Forming Simulation and Die & Mold Tech., Huazhong Uni�ersity of Science and Technology, Wuhan,430074, PR China

Abstract

Ž .Rapid plasma spray tooling RPST is a process that can quickly make molds from rapid prototyping or nature patterns withoutlimitation of pattern’s size or material. In this paper, the process of coating growth and pore formation in RPST has beenanalyzed by numerical simulation. The objective of this work was to determine the porosity in plasma sprayed coatings and verifythe developed computer model, which might serve for future thermal residual stress studies of plasma sprayed coatings. Theanalysis was divided into two steps: particle flattening and coating growth. In the analysis, a ballistic model was used for modelingthe in-flight powder particles. The method allows for the calculation of off-normal spray angle, which is common in plasmaspraying of engineering components. Also, a set of rules for coating growth as well as pore formation in the coating has beenproposed. Based on these works, a computer program was developed to calculate the effects of process parameters, such as gunscanning velocity, spray angle, etc., on the porosity of the coating. Finally, an experiment was carried out to verify the effects ofspray parameters on the porosity. The results agree with the prediction of the model. � 2001 Elsevier Science B.V. All rightsreserved.

Keywords: Rapid tooling; Plasma spray; Coating; Porosity

1. Introduction

As a quick tooling method, rapid plasma spraytooling, which is not limited by pattern’s size or mate-rial, has received much attention. It can quickly make

� �molds from rapid prototyping or nature patterns 1,2 .There are two technical development areas that mustbe addressed for its widespread success of application.The first is control of residual stresses accumulated intools. The second is investigation of porosity. The pres-ence of some porosity in the plasma sprayed coating isinevitable. During compression loading of the typeexperienced by injection molding or stamping tools,these pores may act as crack initiation sites. The evolu-tion of porosity in spray formation is not fully under-stood, research is being carried out to obtain a better

� Corresponding author. Tel.: �86-27-87543493�; fax: �86-27-87554405.

Ž .E-mail address: zholab@mail.hust.edu.cn H. Zhang .

understanding of the porosity formation in order tocontrol and minimize the porosity.

During the process of rapid spray tooling, the qualityof coatings, including mechanical and physical proper-ties, determines the quality of the final mold. So, it isimportant to know the effects of process parameters onthe coating quality. In rapid plasma spray tooling, thequality of the coating is mainly dependent on suchparameters: the power of the torch, its position relativeto the substrate, spray angle, scanning velocity of thegun, type of powder used, and morphology of thesubstrate. Traditionally, these parameters have beenoptimized empirically in order to obtain good coatings.As this wastes time and money, recently, many re-searchers have employed numerical modeling methods.

� � � �Knotek and Elsing 3 and Cirolini et al. 4 haveresearched the coating deposition process in plasmaspray, given the porosity of the coating. In their model,they did not consider the off-normal spray angle as theengineering component, however, sometimes it was re-

0040-6090�01�$ - see front matter � 2001 Elsevier Science B.V. All rights reserved.Ž .PII: S 0 0 4 0 - 6 0 9 0 0 1 0 0 9 3 3 - 6

( )Y. Chen et al. � Thin Solid Films 390 2001 13�1914

quired to spray at angles other than 90�, so it shouldenhance the coating deposition model to consider suchsituations.

In the present work, we used a ballistic depositionmodel to track individual powder particles as they forma coating structure. Ballistic deposition was originally

� � � �proposed by Vold 5 and Sutherland 6 as a model forcolloidal aggregation. Later this work was extended andanalyzed to simulate the process of vapor deposition� �7 . The simulation is usually done in the following way:particles are assumed to drop along straight lines onthe deposit and attach to the substrate or the depositedmaterial. This apparently simple rule produces a struc-ture that is complex. In the present work, we haveattempted to use this method to construct a model forthe simulation of coating growth and pore formation,and use this model to analyze the effects of processparameters, such as gun scanning velocity, spray angle,etc., on the porosity of the coating.

2. Modeling

Plasma spray is a type of process used to applycoatings on surfaces for providing enhanced properties.Fig. 1 is a schematic illustration of the plasma sprayprocess. The formation of plasma sprayed coatings is acomplicated procedure including the stochastic deposi-tion of a large number of droplets. In plasma plume,individual powder particles are heated up, melted andaccelerated. Then molten droplets hit against the sub-strate, are splashed and quenched to the substratetemperature within a very short time, and form alamellar-structured coating, as illustrated in Fig. 2. Thefreezing time of the particle is very short. It takes a fewmilliseconds or even shorter. But the time between twoconsecutive collisions is much longer than the freezingtime, thus the liquid droplets are not likely to en-

� �counter a liquid surface 8 . We can therefore split themodeling of coating deposition into two steps. First, weshould provide a model to explain the behavior of thedroplet on arrival at the coating. Second, we require aset of rules for the growth of the coating and thegeneration of pores in the coating.

2.1. Splat formation

In a typical plasma spray process, the deformationand solidification of a single droplet plays a fairlyimportant role, Fig. 3a illustrates the morphology of anindividual powder splat when the spray angle is 90�.Many researchers have examined the procedure of

Žsplat formation a recent general review can be seen in� �.9,10 . As a result of these efforts during the pastdecades, a series of experimental and analytical formu-las have been derived to calculate the splat flattening

Fig. 1. Plasma spray process.

ratio � when a molten droplet hits on a planar sub-Ž .strate as illustrated in Fig. 4 .

Ž .��D�d 1

In analytical research, the most prevalent approachis based on macroscopic mechanical energy balance,and described mathematically as:

d Ž . Ž .E �E �L �0 2k p fd t

where E , E and L are the kinetic energy, thek p fpotential energy and the work due to frictional forces,

� �respectively, and t is the time 11 .Taking the viscosity and surface tension effects into

consideration, and neglecting the solidifying effect, the� �typical theory was given by Madejski 12 . Based on his

work, by using a better velocity field and a correctderivation of the viscous energy, Delplanque and Ran-

� �gle 13 gave an improved model for droplet deforma-tion:

523� 1 � Ž .� �1, Re�140, We�670 3ž /We Re 1.1625

Fig. 2. Fractured cross-section of plasma sprayed coating.

( )Y. Chen et al. � Thin Solid Films 390 2001 13�19 15

where

Vd V 2dRe�� , We��

� �

McPherson has pointed out that for plasma spraying2 � � Ž .the term 3� �We is negligible 14 . Thus Eq. 3 can be

rewritten as:

1�5 Ž .��1.1625Re , Re�140, We�670 4

When the spray angle is not 90�, the impact results ina clear elongation of the splat in the direction of thecomponent of the droplet velocity parallel to the target,such that the splat has more of an oval shape. Fig. 3billustrates the morphology of an individual powder splatwhen the spray angle is 30�. The ‘pancake shape’ indi-cates a relatively homogeneous molten state of theimpinging particles before the impact. A modified

Fig. 3. Morphologies of individual splats for 90� and 30� spray angle.

Fig. 4. Schematic illustration of the normal angle impact of a moltendroplet on a flat substrate.

spread coefficient defined as:

Ž .���L�D 5

� �Data in Kanouff 15 is taken to account for theelongation effect that non-perpendicular impacts haveon the shape of the splats.

2.2. Coating growth

Materials deposited by the plasma-spraying processexhibit a mass distribution on the substrate. This dis-tribution can be approximated by a Gaussian distribu-

� �tion 3 , which can be determined according to themorphology of the spray deposited object on the sub-strate. In this model, it is assumed that the powder feedrate is constant and the spray pattern is only a function

Ž .of the spatial location i.e. independent of time . So thespray pattern is conical and symmetrical with the cen-

Ž .terline of the torch see Fig. 5 . The Gaussian probabil-Ž .ity distribution function p x, y is expressed as:

1 x 2 �y2Ž .p x , y � exp � ,2ž /2�� 2�

Ž .��x��,��y�� 6

A random hit location of the droplet is given byrandom coordinates X and Y . On the basisrandom randomof this location, the cross-section of the new generatedlamella is integrated into the coating cross-section. Inthis paper, the Monte Carlo method is used to simulatethe stochastic deposition of molten droplets. A polar

� �method proposed by Marsaglia et al. 16 is employedto generate the random number. The programmingprocedure of the polar method is:Ž .1 First, two independent random numbers r and1

� �r are generated, and transferred to section �1,12

� � 2 r �1, � � 2 r �11 1 2 2

( )Y. Chen et al. � Thin Solid Films 390 2001 13�1916

Fig. 5. Schematic illustration of off-normal spray.

Ž . 2 22 Let s� r � r1 2

Ž . Ž .3 If s�1, then go to 1 , otherwise;

�2ln s �2ln sx�� , y��( (1 2s s

when the angle between the spray direction and theŽ .substrate is not 90� see Fig. 5 . Supposing that is the

operator transforming from coordinate system x�y�z�to coordinate system xyz, we can obtain the coordinateof p� in the xyz coordinate system by:

x� sin� 0 cos�x � �y�� � 0 1 0y½ 5 �� 0z �cos� 0 sin�z�p� p�

x� x� � Ž .y�� � 7y½ 5 � zz� o�p�

Supposing that the deposition efficiency does notchange with the angle, the deposition point coordinateof the droplet on the real plane P can be obtained by2solving a simple line equation:

x �xg p�x �x �zp p� p� z �zg p�

y �y� g p� Ž .8y �y �zp p� p� z �zg p� z �0p

The coating produced by the plasma spray is formedby splats in a complex fashion. Three likely mecha-nisms have been proposed for porosity formation: gasporosity, interstitial gas porosity, and solidification

� �shrinkage 17 . Experimentally obtained data suggestthat the distribution of pore size in plasma sprayedcoatings is non-uniform. Summing up the results ob-tained by the methods of petrographic porosimetry andmercury intrusion porosimetry, it can be stated thatplasma sprayed coatings are characterized by micro-

� �pores or mesopores 18 . Pores of 1.0�5.0 �m are themost typical, and are illustrated in Fig. 6. In the com-puter program, three criteria are employed for the

� �growth of coating and the generation of pores 19 :

1. The splat follows exactly the shape of the underly-ing layer, which is under the impact region of thedroplet. If the splat comes to a vertical drop, it fallsstraight down until it finds the top surface. Whenthe splat hits a step on the surface, a pore isgenerated, as illustrated in the fractured cross-sec-tion of coating in Fig. 2.

2. The void that cannot be ‘seen’ by a splat will not befilled.

3. A gap in the surface narrower than twice theheight of the splat will not be filled, but forms apore.

3. Results and discussion

The coating deposition process has been simulatedwith the program developed. The coating’s profile isdivided into a mesh, and the lamellar structures aredeposited layer-by-layer. It follows the deformation ofa series of droplets. Fig. 7 shows the structure ofcoating produced by the program. This figure uses a150�150 mesh. It is small enough to be printed out,while at the same time big enough to show the coating’sstructure. The pores are added according to the criteriaproposed above during the coating growth process. The

( )Y. Chen et al. � Thin Solid Films 390 2001 13�19 17

ŽFig. 6. Polished cross-section of plasma sprayed coating black repre-.sent pores .

porosity of the coating is obtained by using the fol-lowing equation:

Area white Ž .P� �100% 9Areatotal

A comparison with the illustration of a real plasmaŽ .sprayed coating Fig. 6 shows agreement of pore sizes

between the modeled and real coating structure. In thesimulation process, a mesh up to 5000�600 is used toensure that the coating structure is independent of themesh numbers.

Figs. 8 and 9 show the effects of spray angle and gunscanning velocity on the porosity of the coating. Theporosity of the coating decreases with the spray angle,

ŽFig. 7. Typical coating structure produced by program white repre-.sent pores .

Table 1Plasma spray parameters

Plasma gun G781Ž .Input power kW 14.6

�1Ž .Argon mass flow rate l min 20�1Ž .Nitrogen mass flow rate l min 3.5

Powder Stainless steelPowder injection Internal

�1Ž .Powder feed rate g min 40

and increases with the gun scanning velocity. In orderto verify the calculation, an experiment was carried out.The experimental set-up can be seen in Fig. 10. Themain experimental spray parameters are listed in Table1. The feedstock material used in the experiment was anickel-based stainless steel. The powder was character-ized by near perfect spherical particles, as illustrated inFig. 11, which is important in modeling the behavior ofparticles in plasma plume. Such a typical shape wasobtained from the gas atomization process. The powderwas plasma spray processed. The porosity of the coat-ing according to different gun scanning velocities andspray angle is measured using an image analysis system� IBAS 2000. The system converts pictures of polishedcross-sections of plasma sprayed coating into a white-black binary image, using operations such as noisereduction, low frequency cut-off filtering to clarify thepore’s image. After calculating the area of the whitepart and the total picture, the porosity of the coating is

Ž . � �obtained by using Eq. 9 . Leigh et al. 20 researchedthe effects of the spray angle on the porosity. In theirexperiment, the porosity of the coating also decreasedwith the spray angle, which agrees with the predictionof the model. While decreasing the spray angle from90�, there will be a phenomenon called shading effect

� �in the spray process 15 . Large roughness is generated

Fig. 8. Variation of porosity with spray angle.

( )Y. Chen et al. � Thin Solid Films 390 2001 13�1918

Fig. 9. Variation of porosity with gun scanning velocity.

on the coating surface; portions of the coating surfacedownstream of this part can be shaded from the ther-mal spray mass flux. Big pores will be generated atthese areas. This has resulted in a large increase ofporosity. As the current model did not take this intoconsideration, there are some discrepancies betweencalculations and experiments in Fig. 8.

4. Conclusions

We have shown how to model the coating growthand pore formation by using a few simple rules, whichcan give an insight into how a simple sequence of stepsgoverned by stochastic or other algorithms may gener-ate a structure with very specific characteristics.

In the paper, the effects of process parameters, suchas gun scanning velocity, spray angle, etc., on the

Fig. 10. Experimental set-up.

Fig. 11. SEM view of powder particles.

porosity of the coating have been investigated. Thepattern deposited by the plasma-spraying process wasassumed to be a Gaussian distribution. Based on thedroplet deformation formula and the criteria for coat-ing growth and pore generation, a computer programwas developed to simulate the growth of the coatingand the generation of the pores. The porosity of thecoating decreases with the spray angle, but increaseswith the gun scanning velocity. The results of an exper-iment that was carried out to verify the effects of gunscanning velocity and spray angle on the porosity agreedwith the prediction of the model. Because of shadingeffects, there are some discrepancies between calcula-tion and experiments while changing the spray angle.The final structure of the coating depends on thedetailed history of how it was deposited. The currenttwo-dimensional model is based on the work ofDelplanque with the assumptions noted. A model thattakes shading effect and three-dimensional effects ofdroplet splash into consideration should be adopted infuture research. At present, this is being undertaken inour current research.

5. Nomenclature

Ž .d: Initial droplet diameter mŽ .D: Flattening disk diameter mŽ .H: Flattening disk thickness m

Ž .L: Length of a splat mŽ .T : Temperature �

Ž .Re: Reynolds number �Ž �1 .V: Droplet velocity m sŽ .We: Weber number �Ž .x,y,z: x,y,z coordinate m

� : Spread coefficient for perpendicular droplet im-Ž .pact �

� �: Spread coefficient for non-perpendicular dropletŽ .impact �

( )Y. Chen et al. � Thin Solid Films 390 2001 13�19 19

Ž �3 .� : Density of the material kg mŽ �2 .� : Surface tension kg s

Ž �1 �1.�: Viscosity kg m s

Acknowledgements

This research was funded by the Ministry of Scienceand Technology and the Ministry of Education of theChinese government through research grants 863-511-

� �943-017 and 1998 679, respectively. The authors wouldlike to thank associate professor Zhiming Chen andgraduate student Zhizhong Tang for experiment prepa-ration. The authors are also grateful for the valuablecomments of the referees which facilitated revision ofthis manuscript.

References

� � Ž .1 H. Zhang, T. Nakagawa, J. Mater. Process. Technol. 63 1997899.

� � Ž .2 H. Zhang, G. Wang, T. Nakagawa, in: T. Nakagawa Ed. ,Proceedings of the 8th International Conference on RapidPrototyping, June 12�13, Tokyo, Japan, 2000, p. 444.

� � Ž .3 O. Knotek, R. Elsing, Surf. Coat. Technol. 32 1987 261.� �4 S. Cirolini, J.H. Harding, G. Jacucci, Surf. Coat. Technol. 48

Ž .1991 137.� � Ž .5 M.J. Vold, J. Colloid Interface Sci. 14 1959 168.� � Ž .6 D.N. Sutherland, ibid 22 1966 300.� � Ž .7 J.E. Yehoda, R. Messier, Appl. Surf. Sci. 22-23 1984 590.� �8 R.B. Heimann, Plasma-Spray Coatings: Principles and Applica-

tions, Weinheim, New York, 1996.� � Ž .9 V.V. Sobolev, J. Therm. Spray Technol. 8 1999 87.

� � Ž .10 V.V. Sobolev, J. Therm. Spray Technol. 8 1999 301.� � Ž .11 H. Zhang, Int. J. Heat Mass Transfer 42 1999 2499.� � Ž .12 J. Madejski, Int. J. Heat Mass Transfer 19 1976 1009.� � Ž .13 J.-P. Delplanque, R.H. Rangle, J. Mater. Sci. 32 1997 1519.� � Ž .14 R. McPherson, Thin Solid Films 83 1981 297.� �15 M.P. Kanouff, R.A. Neiser Jr., T.J. Roemer, J. Therm. Spray

Ž .Technol. 7 1998 219.� �16 G. Marsaglia, B. Narasimhan, A. Zaman, Comput. Phys. Com-

Ž .mun. 60 1990 345.� �17 E.J. Lavernia, Y. Wu, Spray Atomization and Deposition, John

Wiley & Sons, Inc, New York, 1996, p. 264.� � Ž .18 P.Yu. Pekshev, I.G. Murzin, Surf. Coat. Technol. 56 1993 199.� � Ž .19 Y. Chen, G. Wang, H. Zhang, J. Fang, in: T. Nakagawa Ed. ,

Proceedings of the 8th International Conference on RapidPrototyping, June 12�13, Tokyo, Japan, 2000, p. 450.

� � Ž .20 S.H. Leigh, C.C. Berndt, Surf. Coat. Technol. 89 1997 213.