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Numerical simulation of coating growth and pore formation in rapid plasma spray tooling
Thin Solid Films 390 Ž2001. 13᎐19
Numerical simulation of coating growth and pore formation in rapid plasma spray tooling Yanxiang Chen, Guilan Wang, Haiou ZhangU State Key Laboratory of Plastic Forming Simulation and Die & Mold Tech., Huazhong Uni¨ ersity of Science and Technology, Wuhan, 430074, PR China
Abstract Rapid plasma spray tooling ŽRPST. is a process that can quickly make molds from rapid prototyping or nature patterns without limitation of pattern’s size or material. In this paper, the process of coating growth and pore formation in RPST has been analyzed by numerical simulation. The objective of this work was to determine the porosity in plasma sprayed coatings and verify the developed computer model, which might serve for future thermal residual stress studies of plasma sprayed coatings. The analysis was divided into two steps: particle flattening and coating growth. In the analysis, a ballistic model was used for modeling the in-flight powder particles. The method allows for the calculation of off-normal spray angle, which is common in plasma spraying of engineering components. Also, a set of rules for coating growth as well as pore formation in the coating has been proposed. Based on these works, a computer program was developed to calculate the effects of process parameters, such as gun scanning velocity, spray angle, etc., on the porosity of the coating. Finally, an experiment was carried out to verify the effects of spray parameters on the porosity. The results agree with the prediction of the model. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Rapid tooling; Plasma spray; Coating; Porosity
1. Introduction As a quick tooling method, rapid plasma spray tooling, which is not limited by pattern’s size or material, has received much attention. It can quickly make molds from rapid prototyping or nature patterns w1,2x. There are two technical development areas that must be addressed for its widespread success of application. The first is control of residual stresses accumulated in tools. The second is investigation of porosity. The presence of some porosity in the plasma sprayed coating is inevitable. During compression loading of the type experienced by injection molding or stamping tools, these pores may act as crack initiation sites. The evolution of porosity in spray formation is not fully understood, research is being carried out to obtain a better U
Corresponding author. Tel.: q86-27-87543493r; fax: q86-2787554405. E-mail address: [email protected] ŽH. Zhang..
understanding of the porosity formation in order to control and minimize the porosity. During the process of rapid spray tooling, the quality of coatings, including mechanical and physical properties, determines the quality of the final mold. So, it is important to know the effects of process parameters on the coating quality. In rapid plasma spray tooling, the quality of the coating is mainly dependent on such parameters: the power of the torch, its position relative to the substrate, spray angle, scanning velocity of the gun, type of powder used, and morphology of the substrate. Traditionally, these parameters have been optimized empirically in order to obtain good coatings. As this wastes time and money, recently, many researchers have employed numerical modeling methods. Knotek and Elsing w3x and Cirolini et al. w4x have researched the coating deposition process in plasma spray, given the porosity of the coating. In their model, they did not consider the off-normal spray angle as the engineering component, however, sometimes it was re-
0040-6090r01r$ - see front matter 䊚 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 1 . 0 0 9 3 3 - 6
14
Y. Chen et al. r Thin Solid Films 390 (2001) 13᎐19
quired to spray at angles other than 90⬚, so it should enhance the coating deposition model to consider such situations. In the present work, we used a ballistic deposition model to track individual powder particles as they form a coating structure. Ballistic deposition was originally proposed by Vold w5x and Sutherland w6x as a model for colloidal aggregation. Later this work was extended and analyzed to simulate the process of vapor deposition w7x. The simulation is usually done in the following way: particles are assumed to drop along straight lines on the deposit and attach to the substrate or the deposited material. This apparently simple rule produces a structure that is complex. In the present work, we have attempted to use this method to construct a model for the simulation of coating growth and pore formation, and use this model to analyze the effects of process parameters, 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 apply coatings on surfaces for providing enhanced properties. Fig. 1 is a schematic illustration of the plasma spray process. The formation of plasma sprayed coatings is a complicated procedure including the stochastic deposition of a large number of droplets. In plasma plume, individual powder particles are heated up, melted and accelerated. Then molten droplets hit against the substrate, are splashed and quenched to the substrate temperature within a very short time, and form a lamellar-structured coating, as illustrated in Fig. 2. The freezing time of the particle is very short. It takes a few milliseconds or even shorter. But the time between two consecutive collisions is much longer than the freezing time, thus the liquid droplets are not likely to encounter a liquid surface w8x. We can therefore split the modeling of coating deposition into two steps. First, we should provide a model to explain the behavior of the droplet on arrival at the coating. Second, we require a set of rules for the growth of the coating and the generation of pores in the coating.
Fig. 1. Plasma spray process.
ratio when a molten droplet hits on a planar substrate Žas illustrated in Fig. 4.. s Drd
Ž1.
In analytical research, the most prevalent approach is based on macroscopic mechanical energy balance, and described mathematically as: d Ž E q Ep q Lf . s 0 dt k
Ž2.
where E k , Ep and Lf are the kinetic energy, the potential energy and the work due to frictional forces, respectively, and t is the time w11x. Taking the viscosity and surface tension effects into consideration, and neglecting the solidifying effect, the typical theory was given by Madejski w12x. Based on his work, by using a better velocity field and a correct derivation of the viscous energy, Delplanque and Rangle w13x gave an improved model for droplet deformation: 3 2 1 q We Re 1.1625
ž
5
/ s 1,
Re ) 140, We ) 670 Ž 3 .
2.1. Splat formation In a typical plasma spray process, the deformation and solidification of a single droplet plays a fairly important role, Fig. 3a illustrates the morphology of an individual powder splat when the spray angle is 90⬚. Many researchers have examined the procedure of splat formation Ža recent general review can be seen in w9,10x.. As a result of these efforts during the past decades, a series of experimental and analytical formulas have been derived to calculate the splat flattening
Fig. 2. Fractured cross-section of plasma sprayed coating.
Y. Chen et al. r Thin Solid Films 390 (2001) 13᎐19
15
where Re s
Vd V 2d , We s
McPherson has pointed out that for plasma spraying the term 3 2rWe is negligible w14x. Thus Eq. Ž3. can be rewritten as: s 1.1625Re1r5 , Re) 140, We ) 670
Ž4.
When the spray angle is not 90⬚, the impact results in a clear elongation of the splat in the direction of the component of the droplet velocity parallel to the target, such that the splat has more of an oval shape. Fig. 3b illustrates the morphology of an individual powder splat when the spray angle is 30⬚. The ‘pancake shape’ indicates a relatively homogeneous molten state of the impinging particles before the impact. A modified
Fig. 4. Schematic illustration of the normal angle impact of a molten droplet on a flat substrate.
spread coefficient defined as: ⬘ s LrD
Ž5.
Data in Kanouff w15x is taken to account for the elongation effect that non-perpendicular impacts have on the shape of the splats. 2.2. Coating growth Materials deposited by the plasma-spraying process exhibit a mass distribution on the substrate. This distribution can be approximated by a Gaussian distribution w3x, which can be determined according to the morphology of the spray deposited object on the substrate. In this model, it is assumed that the powder feed rate is constant and the spray pattern is only a function of the spatial location Ži.e. independent of time.. So the spray pattern is conical and symmetrical with the centerline of the torch Žsee Fig. 5.. The Gaussian probability distribution function pŽ x, y . is expressed as: p Ž x, y . s
1 x2 qy2 exp y , 2 22
ž
/
y ⬁ - x- q⬁,y⬁ - y - q⬁
Ž6.
A random hit location of the droplet is given by random coordinates X random and Yrandom . On the basis of this location, the cross-section of the new generated lamella is integrated into the coating cross-section. In this paper, the Monte Carlo method is used to simulate the stochastic deposition of molten droplets. A polar method proposed by Marsaglia et al. w16x is employed to generate the random number. The programming procedure of the polar method is: Ž1. First, two independent random numbers r 1 and r 2 are generated, and transferred to section wy1,1x Fig. 3. Morphologies of individual splats for 90⬚ and 30⬚ spray angle.
¨ 1 s 2 r 1 y 1,
¨ 2 s 2 r2 y 1
Y. Chen et al. r Thin Solid Films 390 (2001) 13᎐19
16
Fig. 5. Schematic illustration of off-normal spray.
Ž2. Let s s r 12 q r 22 Ž3. If s G 1, then go to Ž1., otherwise; xs ¨ 1
(
y2ln s , y s¨ 2 s
(
y2ln s s
when the angle between the spray direction and the substrate is not 90⬚ Žsee Fig. 5.. Supposing that ⌫ is the operator transforming from coordinate system x⬘ y⬘z⬘ to coordinate system xyz, we can obtain the coordinate of p⬘ in the xyz coordinate system by: x y z
¡x⬘¦ ¢z⬘§
~ y⬘¥
½5 0 s⌫
p⬘
s
p⬘
sin␣ 0 ycos␣
¡¦ ¢§
x⬘ = y⬘ z⬘
~ ¥
0 1 0
cos␣ 0 sin␣
x q y z p⬘
½5
Ž7. o⬘
Supposing that the deposition efficiency does not change with the angle, the deposition point coordinate of the droplet on the real plane P2 can be obtained by solving a simple line equation: x g y x p⬘ x p s x p⬘ y z p⬘ z g y z p⬘ y g y y p⬘ y p s y p⬘ y z p⬘ z g y z p⬘
¢
1. The splat follows exactly the shape of the underlying layer, which is under the impact region of the droplet. If the splat comes to a vertical drop, it falls straight down until it finds the top surface. When the splat hits a step on the surface, a pore is generated, as illustrated in the fractured cross-section of coating in Fig. 2. 2. The void that cannot be ‘seen’ by a splat will not be filled. 3. A gap in the surface narrower than twice the height of the splat will not be filled, but forms a pore.
3. Results and discussion
¡ ~
shrinkage w17x. Experimentally obtained data suggest that the distribution of pore size in plasma sprayed coatings is non-uniform. Summing up the results obtained by the methods of petrographic porosimetry and mercury intrusion porosimetry, it can be stated that plasma sprayed coatings are characterized by micropores or mesopores w18x. Pores of 1.0᎐5.0 m are the most typical, and are illustrated in Fig. 6. In the computer program, three criteria are employed for the growth of coating and the generation of pores w19x:
Ž8.
zp s0
The coating produced by the plasma spray is formed by splats in a complex fashion. Three likely mechanisms have been proposed for porosity formation: gas porosity, interstitial gas porosity, and solidification
The coating deposition process has been simulated with the program developed. The coating’s profile is divided into a mesh, and the lamellar structures are deposited layer-by-layer. It follows the deformation of a series of droplets. Fig. 7 shows the structure of coating produced by the program. This figure uses a 150 = 150 mesh. It is small enough to be printed out, while at the same time big enough to show the coating’s structure. The pores are added according to the criteria proposed above during the coating growth process. The
Y. Chen et al. r Thin Solid Films 390 (2001) 13᎐19
17
Table 1 Plasma spray parameters Plasma gun Input power ŽkW. Argon mass flow rate Žl miny1 . Nitrogen mass flow rate Žl miny1 . Powder Powder injection Powder feed rate Žg miny1 .
Fig. 6. Polished cross-section of plasma sprayed coating Žblack represent pores..
porosity of the coating is obtained by using the following equation: Ps
Area white = 100% Area total
Ž9.
A comparison with the illustration of a real plasma sprayed coating ŽFig. 6. shows agreement of pore sizes between the modeled and real coating structure. In the simulation process, a mesh up to 5000 = 600 is used to ensure that the coating structure is independent of the mesh numbers. Figs. 8 and 9 show the effects of spray angle and gun scanning velocity on the porosity of the coating. The porosity of the coating decreases with the spray angle,
Fig. 7. Typical coating structure produced by program Žwhite represent pores..
G781 14.6 20 3.5 Stainless steel Internal 40
and increases with the gun scanning velocity. In order to verify the calculation, an experiment was carried out. The experimental set-up can be seen in Fig. 10. The main experimental spray parameters are listed in Table 1. The feedstock material used in the experiment was a nickel-based stainless steel. The powder was characterized by near perfect spherical particles, as illustrated in Fig. 11, which is important in modeling the behavior of particles in plasma plume. Such a typical shape was obtained from the gas atomization process. The powder was plasma spray processed. The porosity of the coating according to different gun scanning velocities and spray angle is measured using an image analysis system ᎏ IBAS 2000. The system converts pictures of polished cross-sections of plasma sprayed coating into a whiteblack binary image, using operations such as noise reduction, low frequency cut-off filtering to clarify the pore’s image. After calculating the area of the white part and the total picture, the porosity of the coating is obtained by using Eq. Ž9.. Leigh et al. w20x researched the effects of the spray angle on the porosity. In their experiment, the porosity of the coating also decreased with the spray angle, which agrees with the prediction of the model. While decreasing the spray angle from 90⬚, there will be a phenomenon called shading effect in the spray process w15x. Large roughness is generated
Fig. 8. Variation of porosity with spray angle.
Y. Chen et al. r Thin Solid Films 390 (2001) 13᎐19
18
Fig. 11. SEM view of powder particles.
Fig. 9. Variation of porosity with gun scanning velocity.
on the coating surface; portions of the coating surface downstream of this part can be shaded from the thermal spray mass flux. Big pores will be generated at these areas. This has resulted in a large increase of porosity. As the current model did not take this into consideration, there are some discrepancies between calculations and experiments in Fig. 8. 4. Conclusions We have shown how to model the coating growth and pore formation by using a few simple rules, which can give an insight into how a simple sequence of steps governed by stochastic or other algorithms may generate a structure with very specific characteristics. In the paper, the effects of process parameters, such as gun scanning velocity, spray angle, etc., on the
porosity of the coating have been investigated. The pattern deposited by the plasma-spraying process was assumed to be a Gaussian distribution. Based on the droplet deformation formula and the criteria for coating growth and pore generation, a computer program was developed to simulate the growth of the coating and the generation of the pores. The porosity of the coating decreases with the spray angle, but increases with the gun scanning velocity. The results of an experiment that was carried out to verify the effects of gun scanning velocity and spray angle on the porosity agreed with the prediction of the model. Because of shading effects, there are some discrepancies between calculation and experiments while changing the spray angle. The final structure of the coating depends on the detailed history of how it was deposited. The current two-dimensional model is based on the work of Delplanque with the assumptions noted. A model that takes shading effect and three-dimensional effects of droplet splash into consideration should be adopted in future research. At present, this is being undertaken in our current research. 5. Nomenclature d: D: H: L: T: Re: V: We: x,y,z: :
⬘: Fig. 10. Experimental set-up.
Initial droplet diameter Žm. Flattening disk diameter Žm. Flattening disk thickness Žm. Length of a splat Žm. Temperature Ž⬚. Reynolds number Žy. Droplet velocity Žm sy1 . Weber number Žy. x,y,z coordinate Žm. Spread coefficient for perpendicular droplet impact Žy. Spread coefficient for non-perpendicular droplet impact Žy.
Y. Chen et al. r Thin Solid Films 390 (2001) 13᎐19
: : :
Density of the material Žkg my3 . Surface tension Žkg sy2 . Viscosity Žkg my1 sy1 .
Acknowledgements This research was funded by the Ministry of Science and Technology and the Ministry of Education of the Chinese government through research grants 863-511943-017 and w1998x679, respectively. The authors would like to thank associate professor Zhiming Chen and graduate student Zhizhong Tang for experiment preparation. The authors are also grateful for the valuable comments of the referees which facilitated revision of this manuscript. References w1x H. Zhang, T. Nakagawa, J. Mater. Process. Technol. 63 Ž1997. 899. w2x H. Zhang, G. Wang, T. Nakagawa, in: T. Nakagawa ŽEd.., Proceedings of the 8th International Conference on Rapid Prototyping, June 12᎐13, Tokyo, Japan, 2000, p. 444.
19
w3x O. Knotek, R. Elsing, Surf. Coat. Technol. 32 Ž1987. 261. w4x S. Cirolini, J.H. Harding, G. Jacucci, Surf. Coat. Technol. 48 Ž1991. 137. w5x M.J. Vold, J. Colloid Interface Sci. 14 Ž1959. 168. w6x D.N. Sutherland, ibid 22 Ž1966. 300. w7x J.E. Yehoda, R. Messier, Appl. Surf. Sci. 22-23 Ž1984. 590. w8x R.B. Heimann, Plasma-Spray Coatings: Principles and Applications, Weinheim, New York, 1996. w9x V.V. Sobolev, J. Therm. Spray Technol. 8 Ž1999. 87. w10x V.V. Sobolev, J. Therm. Spray Technol. 8 Ž1999. 301. w11x H. Zhang, Int. J. Heat Mass Transfer 42 Ž1999. 2499. w12x J. Madejski, Int. J. Heat Mass Transfer 19 Ž1976. 1009. w13x J.-P. Delplanque, R.H. Rangle, J. Mater. Sci. 32 Ž1997. 1519. w14x R. McPherson, Thin Solid Films 83 Ž1981. 297. w15x M.P. Kanouff, R.A. Neiser Jr., T.J. Roemer, J. Therm. Spray Technol. 7 Ž1998. 219. w16x G. Marsaglia, B. Narasimhan, A. Zaman, Comput. Phys. Commun. 60 Ž1990. 345. w17x E.J. Lavernia, Y. Wu, Spray Atomization and Deposition, John Wiley & Sons, Inc, New York, 1996, p. 264. w18x P.Yu. Pekshev, I.G. Murzin, Surf. Coat. Technol. 56 Ž1993. 199. w19x Y. Chen, G. Wang, H. Zhang, J. Fang, in: T. Nakagawa ŽEd.., Proceedings of the 8th International Conference on Rapid Prototyping, June 12᎐13, Tokyo, Japan, 2000, p. 450. w20x S.H. Leigh, C.C. Berndt, Surf. Coat. Technol. 89 Ž1997. 213.
Numerical simulation of coating growth and pore formation in rapid plasma spray tooling Yanxiang Chen, Guilan Wang, Haiou ZhangU State Key Laboratory of Plastic Forming Simulation and Die & Mold Tech., Huazhong Uni¨ ersity of Science and Technology, Wuhan, 430074, PR China
Abstract Rapid plasma spray tooling ŽRPST. is a process that can quickly make molds from rapid prototyping or nature patterns without limitation of pattern’s size or material. In this paper, the process of coating growth and pore formation in RPST has been analyzed by numerical simulation. The objective of this work was to determine the porosity in plasma sprayed coatings and verify the developed computer model, which might serve for future thermal residual stress studies of plasma sprayed coatings. The analysis was divided into two steps: particle flattening and coating growth. In the analysis, a ballistic model was used for modeling the in-flight powder particles. The method allows for the calculation of off-normal spray angle, which is common in plasma spraying of engineering components. Also, a set of rules for coating growth as well as pore formation in the coating has been proposed. Based on these works, a computer program was developed to calculate the effects of process parameters, such as gun scanning velocity, spray angle, etc., on the porosity of the coating. Finally, an experiment was carried out to verify the effects of spray parameters on the porosity. The results agree with the prediction of the model. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Rapid tooling; Plasma spray; Coating; Porosity
1. Introduction As a quick tooling method, rapid plasma spray tooling, which is not limited by pattern’s size or material, has received much attention. It can quickly make molds from rapid prototyping or nature patterns w1,2x. There are two technical development areas that must be addressed for its widespread success of application. The first is control of residual stresses accumulated in tools. The second is investigation of porosity. The presence of some porosity in the plasma sprayed coating is inevitable. During compression loading of the type experienced by injection molding or stamping tools, these pores may act as crack initiation sites. The evolution of porosity in spray formation is not fully understood, research is being carried out to obtain a better U
Corresponding author. Tel.: q86-27-87543493r; fax: q86-2787554405. E-mail address: [email protected] ŽH. Zhang..
understanding of the porosity formation in order to control and minimize the porosity. During the process of rapid spray tooling, the quality of coatings, including mechanical and physical properties, determines the quality of the final mold. So, it is important to know the effects of process parameters on the coating quality. In rapid plasma spray tooling, the quality of the coating is mainly dependent on such parameters: the power of the torch, its position relative to the substrate, spray angle, scanning velocity of the gun, type of powder used, and morphology of the substrate. Traditionally, these parameters have been optimized empirically in order to obtain good coatings. As this wastes time and money, recently, many researchers have employed numerical modeling methods. Knotek and Elsing w3x and Cirolini et al. w4x have researched the coating deposition process in plasma spray, given the porosity of the coating. In their model, they did not consider the off-normal spray angle as the engineering component, however, sometimes it was re-
0040-6090r01r$ - see front matter 䊚 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 1 . 0 0 9 3 3 - 6
14
Y. Chen et al. r Thin Solid Films 390 (2001) 13᎐19
quired to spray at angles other than 90⬚, so it should enhance the coating deposition model to consider such situations. In the present work, we used a ballistic deposition model to track individual powder particles as they form a coating structure. Ballistic deposition was originally proposed by Vold w5x and Sutherland w6x as a model for colloidal aggregation. Later this work was extended and analyzed to simulate the process of vapor deposition w7x. The simulation is usually done in the following way: particles are assumed to drop along straight lines on the deposit and attach to the substrate or the deposited material. This apparently simple rule produces a structure that is complex. In the present work, we have attempted to use this method to construct a model for the simulation of coating growth and pore formation, and use this model to analyze the effects of process parameters, 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 apply coatings on surfaces for providing enhanced properties. Fig. 1 is a schematic illustration of the plasma spray process. The formation of plasma sprayed coatings is a complicated procedure including the stochastic deposition of a large number of droplets. In plasma plume, individual powder particles are heated up, melted and accelerated. Then molten droplets hit against the substrate, are splashed and quenched to the substrate temperature within a very short time, and form a lamellar-structured coating, as illustrated in Fig. 2. The freezing time of the particle is very short. It takes a few milliseconds or even shorter. But the time between two consecutive collisions is much longer than the freezing time, thus the liquid droplets are not likely to encounter a liquid surface w8x. We can therefore split the modeling of coating deposition into two steps. First, we should provide a model to explain the behavior of the droplet on arrival at the coating. Second, we require a set of rules for the growth of the coating and the generation of pores in the coating.
Fig. 1. Plasma spray process.
ratio when a molten droplet hits on a planar substrate Žas illustrated in Fig. 4.. s Drd
Ž1.
In analytical research, the most prevalent approach is based on macroscopic mechanical energy balance, and described mathematically as: d Ž E q Ep q Lf . s 0 dt k
Ž2.
where E k , Ep and Lf are the kinetic energy, the potential energy and the work due to frictional forces, respectively, and t is the time w11x. Taking the viscosity and surface tension effects into consideration, and neglecting the solidifying effect, the typical theory was given by Madejski w12x. Based on his work, by using a better velocity field and a correct derivation of the viscous energy, Delplanque and Rangle w13x gave an improved model for droplet deformation: 3 2 1 q We Re 1.1625
ž
5
/ s 1,
Re ) 140, We ) 670 Ž 3 .
2.1. Splat formation In a typical plasma spray process, the deformation and solidification of a single droplet plays a fairly important role, Fig. 3a illustrates the morphology of an individual powder splat when the spray angle is 90⬚. Many researchers have examined the procedure of splat formation Ža recent general review can be seen in w9,10x.. As a result of these efforts during the past decades, a series of experimental and analytical formulas have been derived to calculate the splat flattening
Fig. 2. Fractured cross-section of plasma sprayed coating.
Y. Chen et al. r Thin Solid Films 390 (2001) 13᎐19
15
where Re s
Vd V 2d , We s
McPherson has pointed out that for plasma spraying the term 3 2rWe is negligible w14x. Thus Eq. Ž3. can be rewritten as: s 1.1625Re1r5 , Re) 140, We ) 670
Ž4.
When the spray angle is not 90⬚, the impact results in a clear elongation of the splat in the direction of the component of the droplet velocity parallel to the target, such that the splat has more of an oval shape. Fig. 3b illustrates the morphology of an individual powder splat when the spray angle is 30⬚. The ‘pancake shape’ indicates a relatively homogeneous molten state of the impinging particles before the impact. A modified
Fig. 4. Schematic illustration of the normal angle impact of a molten droplet on a flat substrate.
spread coefficient defined as: ⬘ s LrD
Ž5.
Data in Kanouff w15x is taken to account for the elongation effect that non-perpendicular impacts have on the shape of the splats. 2.2. Coating growth Materials deposited by the plasma-spraying process exhibit a mass distribution on the substrate. This distribution can be approximated by a Gaussian distribution w3x, which can be determined according to the morphology of the spray deposited object on the substrate. In this model, it is assumed that the powder feed rate is constant and the spray pattern is only a function of the spatial location Ži.e. independent of time.. So the spray pattern is conical and symmetrical with the centerline of the torch Žsee Fig. 5.. The Gaussian probability distribution function pŽ x, y . is expressed as: p Ž x, y . s
1 x2 qy2 exp y , 2 22
ž
/
y ⬁ - x- q⬁,y⬁ - y - q⬁
Ž6.
A random hit location of the droplet is given by random coordinates X random and Yrandom . On the basis of this location, the cross-section of the new generated lamella is integrated into the coating cross-section. In this paper, the Monte Carlo method is used to simulate the stochastic deposition of molten droplets. A polar method proposed by Marsaglia et al. w16x is employed to generate the random number. The programming procedure of the polar method is: Ž1. First, two independent random numbers r 1 and r 2 are generated, and transferred to section wy1,1x Fig. 3. Morphologies of individual splats for 90⬚ and 30⬚ spray angle.
¨ 1 s 2 r 1 y 1,
¨ 2 s 2 r2 y 1
Y. Chen et al. r Thin Solid Films 390 (2001) 13᎐19
16
Fig. 5. Schematic illustration of off-normal spray.
Ž2. Let s s r 12 q r 22 Ž3. If s G 1, then go to Ž1., otherwise; xs ¨ 1
(
y2ln s , y s¨ 2 s
(
y2ln s s
when the angle between the spray direction and the substrate is not 90⬚ Žsee Fig. 5.. Supposing that ⌫ is the operator transforming from coordinate system x⬘ y⬘z⬘ to coordinate system xyz, we can obtain the coordinate of p⬘ in the xyz coordinate system by: x y z
¡x⬘¦ ¢z⬘§
~ y⬘¥
½5 0 s⌫
p⬘
s
p⬘
sin␣ 0 ycos␣
¡¦ ¢§
x⬘ = y⬘ z⬘
~ ¥
0 1 0
cos␣ 0 sin␣
x q y z p⬘
½5
Ž7. o⬘
Supposing that the deposition efficiency does not change with the angle, the deposition point coordinate of the droplet on the real plane P2 can be obtained by solving a simple line equation: x g y x p⬘ x p s x p⬘ y z p⬘ z g y z p⬘ y g y y p⬘ y p s y p⬘ y z p⬘ z g y z p⬘
¢
1. The splat follows exactly the shape of the underlying layer, which is under the impact region of the droplet. If the splat comes to a vertical drop, it falls straight down until it finds the top surface. When the splat hits a step on the surface, a pore is generated, as illustrated in the fractured cross-section of coating in Fig. 2. 2. The void that cannot be ‘seen’ by a splat will not be filled. 3. A gap in the surface narrower than twice the height of the splat will not be filled, but forms a pore.
3. Results and discussion
¡ ~
shrinkage w17x. Experimentally obtained data suggest that the distribution of pore size in plasma sprayed coatings is non-uniform. Summing up the results obtained by the methods of petrographic porosimetry and mercury intrusion porosimetry, it can be stated that plasma sprayed coatings are characterized by micropores or mesopores w18x. Pores of 1.0᎐5.0 m are the most typical, and are illustrated in Fig. 6. In the computer program, three criteria are employed for the growth of coating and the generation of pores w19x:
Ž8.
zp s0
The coating produced by the plasma spray is formed by splats in a complex fashion. Three likely mechanisms have been proposed for porosity formation: gas porosity, interstitial gas porosity, and solidification
The coating deposition process has been simulated with the program developed. The coating’s profile is divided into a mesh, and the lamellar structures are deposited layer-by-layer. It follows the deformation of a series of droplets. Fig. 7 shows the structure of coating produced by the program. This figure uses a 150 = 150 mesh. It is small enough to be printed out, while at the same time big enough to show the coating’s structure. The pores are added according to the criteria proposed above during the coating growth process. The
Y. Chen et al. r Thin Solid Films 390 (2001) 13᎐19
17
Table 1 Plasma spray parameters Plasma gun Input power ŽkW. Argon mass flow rate Žl miny1 . Nitrogen mass flow rate Žl miny1 . Powder Powder injection Powder feed rate Žg miny1 .
Fig. 6. Polished cross-section of plasma sprayed coating Žblack represent pores..
porosity of the coating is obtained by using the following equation: Ps
Area white = 100% Area total
Ž9.
A comparison with the illustration of a real plasma sprayed coating ŽFig. 6. shows agreement of pore sizes between the modeled and real coating structure. In the simulation process, a mesh up to 5000 = 600 is used to ensure that the coating structure is independent of the mesh numbers. Figs. 8 and 9 show the effects of spray angle and gun scanning velocity on the porosity of the coating. The porosity of the coating decreases with the spray angle,
Fig. 7. Typical coating structure produced by program Žwhite represent pores..
G781 14.6 20 3.5 Stainless steel Internal 40
and increases with the gun scanning velocity. In order to verify the calculation, an experiment was carried out. The experimental set-up can be seen in Fig. 10. The main experimental spray parameters are listed in Table 1. The feedstock material used in the experiment was a nickel-based stainless steel. The powder was characterized by near perfect spherical particles, as illustrated in Fig. 11, which is important in modeling the behavior of particles in plasma plume. Such a typical shape was obtained from the gas atomization process. The powder was plasma spray processed. The porosity of the coating according to different gun scanning velocities and spray angle is measured using an image analysis system ᎏ IBAS 2000. The system converts pictures of polished cross-sections of plasma sprayed coating into a whiteblack binary image, using operations such as noise reduction, low frequency cut-off filtering to clarify the pore’s image. After calculating the area of the white part and the total picture, the porosity of the coating is obtained by using Eq. Ž9.. Leigh et al. w20x researched the effects of the spray angle on the porosity. In their experiment, the porosity of the coating also decreased with the spray angle, which agrees with the prediction of the model. While decreasing the spray angle from 90⬚, there will be a phenomenon called shading effect in the spray process w15x. Large roughness is generated
Fig. 8. Variation of porosity with spray angle.
Y. Chen et al. r Thin Solid Films 390 (2001) 13᎐19
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Fig. 11. SEM view of powder particles.
Fig. 9. Variation of porosity with gun scanning velocity.
on the coating surface; portions of the coating surface downstream of this part can be shaded from the thermal spray mass flux. Big pores will be generated at these areas. This has resulted in a large increase of porosity. As the current model did not take this into consideration, there are some discrepancies between calculations and experiments in Fig. 8. 4. Conclusions We have shown how to model the coating growth and pore formation by using a few simple rules, which can give an insight into how a simple sequence of steps governed by stochastic or other algorithms may generate a structure with very specific characteristics. In the paper, the effects of process parameters, such as gun scanning velocity, spray angle, etc., on the
porosity of the coating have been investigated. The pattern deposited by the plasma-spraying process was assumed to be a Gaussian distribution. Based on the droplet deformation formula and the criteria for coating growth and pore generation, a computer program was developed to simulate the growth of the coating and the generation of the pores. The porosity of the coating decreases with the spray angle, but increases with the gun scanning velocity. The results of an experiment that was carried out to verify the effects of gun scanning velocity and spray angle on the porosity agreed with the prediction of the model. Because of shading effects, there are some discrepancies between calculation and experiments while changing the spray angle. The final structure of the coating depends on the detailed history of how it was deposited. The current two-dimensional model is based on the work of Delplanque with the assumptions noted. A model that takes shading effect and three-dimensional effects of droplet splash into consideration should be adopted in future research. At present, this is being undertaken in our current research. 5. Nomenclature d: D: H: L: T: Re: V: We: x,y,z: :
⬘: Fig. 10. Experimental set-up.
Initial droplet diameter Žm. Flattening disk diameter Žm. Flattening disk thickness Žm. Length of a splat Žm. Temperature Ž⬚. Reynolds number Žy. Droplet velocity Žm sy1 . Weber number Žy. x,y,z coordinate Žm. Spread coefficient for perpendicular droplet impact Žy. Spread coefficient for non-perpendicular droplet impact Žy.
Y. Chen et al. r Thin Solid Films 390 (2001) 13᎐19
: : :
Density of the material Žkg my3 . Surface tension Žkg sy2 . Viscosity Žkg my1 sy1 .
Acknowledgements This research was funded by the Ministry of Science and Technology and the Ministry of Education of the Chinese government through research grants 863-511943-017 and w1998x679, respectively. The authors would like to thank associate professor Zhiming Chen and graduate student Zhizhong Tang for experiment preparation. The authors are also grateful for the valuable comments of the referees which facilitated revision of this manuscript. References w1x H. Zhang, T. Nakagawa, J. Mater. Process. Technol. 63 Ž1997. 899. w2x H. Zhang, G. Wang, T. Nakagawa, in: T. Nakagawa ŽEd.., Proceedings of the 8th International Conference on Rapid Prototyping, June 12᎐13, Tokyo, Japan, 2000, p. 444.
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w3x O. Knotek, R. Elsing, Surf. Coat. Technol. 32 Ž1987. 261. w4x S. Cirolini, J.H. Harding, G. Jacucci, Surf. Coat. Technol. 48 Ž1991. 137. w5x M.J. Vold, J. Colloid Interface Sci. 14 Ž1959. 168. w6x D.N. Sutherland, ibid 22 Ž1966. 300. w7x J.E. Yehoda, R. Messier, Appl. Surf. Sci. 22-23 Ž1984. 590. w8x R.B. Heimann, Plasma-Spray Coatings: Principles and Applications, Weinheim, New York, 1996. w9x V.V. Sobolev, J. Therm. Spray Technol. 8 Ž1999. 87. w10x V.V. Sobolev, J. Therm. Spray Technol. 8 Ž1999. 301. w11x H. Zhang, Int. J. Heat Mass Transfer 42 Ž1999. 2499. w12x J. Madejski, Int. J. Heat Mass Transfer 19 Ž1976. 1009. w13x J.-P. Delplanque, R.H. Rangle, J. Mater. Sci. 32 Ž1997. 1519. w14x R. McPherson, Thin Solid Films 83 Ž1981. 297. w15x M.P. Kanouff, R.A. Neiser Jr., T.J. Roemer, J. Therm. Spray Technol. 7 Ž1998. 219. w16x G. Marsaglia, B. Narasimhan, A. Zaman, Comput. Phys. Commun. 60 Ž1990. 345. w17x E.J. Lavernia, Y. Wu, Spray Atomization and Deposition, John Wiley & Sons, Inc, New York, 1996, p. 264. w18x P.Yu. Pekshev, I.G. Murzin, Surf. Coat. Technol. 56 Ž1993. 199. w19x Y. Chen, G. Wang, H. Zhang, J. Fang, in: T. Nakagawa ŽEd.., Proceedings of the 8th International Conference on Rapid Prototyping, June 12᎐13, Tokyo, Japan, 2000, p. 450. w20x S.H. Leigh, C.C. Berndt, Surf. Coat. Technol. 89 Ž1997. 213.