gradient method

Materials Science Forum Vols. 414-415 (2003) pp. 385-393 online at http://www.scientific.net © (2003) Trans Tech Publications, Switzerland

A Simplified Semi-Empirical Method to Select the Processing Parameters for Laser Clad Coatings Lino Costa1, Imre Felde2, Tamás Réti3, Zoltán Kálazi2, Rogerio Colaço1, Rui Vilar1, Balázs Ver 2 1

Instituto Superior Técnico, DEMat, Av. Rovisco Pais, 1049-001 Lisboa, Portugal 2

Bay Zoltán Institute for Materials Science and Technology, Fehérvári u. 130, H-1116 Budapest, Hungary 3

Budapest Polytechnic, Népszínház u. 8., H-1081 Budapest, Hungary

Keywords: Laser cladding, gradient technique, processing parameter selection

Abstract A semi-empirical method for selecting the processing parameters of laser cladding is proposed. This phenomenological approach uses simple mathematical formulae, derived from a statistical analysis of measured data, to relate the laser cladding parameters with the geometric features of the clad track. Given the prescribed clad height and available laser beam power, the proposed method allows to calculate values of the scanning speed and powder feed rate which are required to obtain low dilution, pore free coatings, fusion bonded to the substrate. To illustrate the application of this method, variable powder feed rate laser cladding experiments were carried out with Stellite 6 powder on mild steel substrates. In this technique the laser beam power and radius and the processing speed are kept constant, while the powder feed rate is varied along a single track length according to a specified linear function. The expressions derived from the model allowed to plot the experimental data in a coherent manner, revealing the combined role of the different processing parameters. Introduction Laser cladding by powder injection is a method of producing good quality, metallurgically bonded coatings with minimal heat input into the work piece (Fig. 1). Frequently, the aim of laser cladding is to improve the wear and corrosion resistance of surfaces, by generating a protective layer of a different material [1, 2, 3]. The laser cladding operating window is defined in terms of laser beam power (P) and spot diameter (D), scanning speed (S) and powder feed rate (F). However, not all combinations of the processing parameters will produce good quality coatings. Only values within limited ranges can be applied to generate tracks meeting the geometrical requirements to produce adherent and pore free coatings by overlapping single tracks [2, 4, 5]. Methods to select adequate values of the processing parameters must be simple and reliable. Several approaches exist, based either on physico-computational models of the process or on empirical equations derived from statistical analysis of experimental data. Modelling of laser cladding requires taking into consideration phenomena such as mass and heat transfer, fluid flow and phase transformations, leading to a complex set of coupled equations [6, 7, 8, 9, 10, 11, 12]. In general these physical models are useful to investigate the influence of the processing parameters on the characteristics of the clad, but solving these equations usually requires numerical techniques and considerable computation time.

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a)

b)

Figure 1 a) Schematic view of laser cladding by powder injection and b) cross section of a laser clad coating. Due to the wide range of temperatures involved, the material properties must be described as temperature dependent, but such data is not always readily available. Therefore, complex numerical models have limited use for practical process optimisation. Several authors [3, 4, 5, 13, 14, 15, 16] have attempted to directly relate the shape of the cross section of single tracks (that defines the cladding quality) with the processing parameters, in general by fitting simple functions of individual processing parameters to large sets of experimental data. However, the effect of processing parameters on a particular cladding characteristic is, in general, combined and this is not considered in those models, making the selection of the process window a difficult task. In this paper a simple method to choose values of the processing parameters that allow to obtain low dilution, pore free coatings, fusion bonded to the substrate is proposed. This method relates accurately the processing parameters with the main single track geometric features, reducing the need for extensive and time consuming experiments. In order to establish mathematical formulae which can be used for process design, variable powder feed rate laser cladding experiments [17, 18] were performed to deposit Stellite 6 in powder form on mild steel substrates. In this procedure single clad tracks are produced using constant laser beam power, processing speed and beam radius, while varying the powder feed rate along the tracks length according to a specified linear function. The clad quality was characterised quantitatively by several geometrical parameters measured on the cross-section of the tracks. The relations between the processing parameters and the geometrical parameters of the transverse cross section were evaluated using multi-variable statistical analysis. As a result, a phenomenological method for the selection of the processing window for laser cladding has been proposed. Application of the method based on the use of simple mathematical formulae is demonstrated by a practical example. Experimental A. Preparation of the test samples The laser cladding tests were performed using a computer controlled laser cladding system, consisting of a 5kW continuous wave CO2 laser, a XY table and a powder feeder [17]. The cladding experiments were carried out with commercially available Stellite 6 powder (25-65 mm) on DIN Ck45 plain carbon steel substrates (0.45 wt.% C, 0.35 wt.% Si and 0.6 wt.% Mn). The three substrates, with dimension of 10x100x200 mm3, were normalised, then cleaned using a jet of glass spheres before laser cladding treatments. In order to reduce the number of experiments, the gradient technique (Fig. 2) was used to evaluate the effect of the processing parameters on the clad geometry. The powder feeder was calibrated for Stellite 6 and programmed to deliver into the melt pool a flow of powder which

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increases linearly along the length of the tracks. Six clad tracks were deposited using different values of laser beam power on each substrate. Prior to the cladding experiments, individual tracks were separated by gaps produced by laser cutting in order to reduce the thermal build-up (by bulk heat conduction) between adjacent tracks. This assures that all tracks are deposited under similar thermal conditions and simplifies the final separation of individual tracks. The samples were produced using the following processing parameters: - laser cladding was performed using processing speeds 5, 10 and 15 mm/s, respectively. - for each clad track, the powder feed rate was increased linearly from 0.1 up to 0.6 g/s over a track length of 150 mm (Fig. 2). - on each specimen, tracks were deposited using a laser beam power of 1.0, 1.5, 2.0, 2.5, 3.0 and 3.5 kW, respectively (Fig. 3). - a constant laser spot diameter of 2 mm was used. The clad tracks were cross sectioned at regular intervals and the resulting samples polished and chemically etched for metallographic observation. Figure 3 shows the increase of the height of a clad track produced with P = 2.5 kW and S = 10 mm/s, due to the increase of the powder feed rate. The cross sections in the figure correspond to powder feed rates of 0.2, 0.3, 0.4 and 0.5 g/s. All cross sections show good adherence, but dilution decreases as the powder feed rate increases. The geometrical parameters defined in Fig. 4 were determined by image analysis of the micrographs. B. Characterisation of the clad geometry -

The geometrical characteristics measured on the cross-sections of the tracks were (Fig. 4): clad height, H (in mm), clad width, W (in mm), clad area, ACLAD (in mm2), area of the dilution zone, ADIL (in mm2).

Figure 2. Concept of the gradient technique, based on a linearly increasing powder feed rate.

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Figure 3. A work piece with clad tracks deposited using a processing speed of S = 10 mm/s.

Figure 4. Schematic cross-section of a laser clad track. On the bases of these values two parameters that characterise dilution and the probability of occurrence of porosity can be calculated [4]. Dilution was evaluated by the dilution factor, Df , defined as: Df =

A DIL A CLAD + A DIL

× 100 % .

(1)

In laser cladding, some dilution between the coating and the substrate is required to ensure a metallurgical bond [3]. However, dilution must be kept small (between 3 and 5 %) to limit the degradation of the coating properties. Also, to avoid porosity, while overlapping individual clad tracks, the a angle (Fig. 4), must exceed 90º. In practice, a > 100 °. This angle was not determined by direct measurements performed on the photographs of the cross sections of the samples, because this method leads to systematic errors and to considerable dispersion of data. Instead, it was calculated from the measured H and W data, by assuming that the cross section of the track is an arc of circumference [5]:




=

180 2

- ATAN

4´ H 2 - W 2 4´ H ´ W

.

(2)

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Results and Discussion In order to derive simple formulae which can be applied to the determination of the laser cladding processing window, the relations between geometrical features and processing parameters were analysed by statistical methods. In a first step, a number of "complex process parameters", defined by combining the individual processing parameters {P, S, F}, were correlated with the main geometric features of the clad cross section, namely the clad height, dilution factor and a angle. The best correlation factors were obtained for the following parameters: 1

= PF/S 2 .

(3)

2

= PS/F .

(4)

3

= S/F .

(5)

In a second step, using regression analysis, mathematical formulae were established describing the relations between the parameters F1, F2 and F3 and the geometrical characteristics of the clad. The formulas derived have the general form:

G p,i = A i + Bi i ,


(6)

where Gp,i represents the i-th geometrical parameter, while Ai and Bi are fitting constants. The results obtained are shown in Figs. 5 to 7. The gradient technique is a non-stationary process: increasing the powder feed rate along the track length reduces the amount of energy reaching the substrate, since more energy is used in melting the injected powder [19]. Therefore, to assure local near - stationary deposition conditions, a small F gradient (DF / Dx = 1 / 300 g / mm.s) was used. Due to the differences in the scanning speed, the powder feed rate time derivative was not equal for all the samples (Table 1) and the process generated distinct thermal fields in different tracks, which may contribute to some experimental data dispersion. Nevertheless, it is clear from the results presented in Figs. 5 to 7 that the complex process parameters F1, F2 and F3 describe correctly the main dependencies of the clad features and can be used for preliminary process planning. The corresponding equations are summarised below (for P in kW, S in mm/s and F in g/s): H (mm) = -0.24 + 6.33 × F1, Df (%) = -12.69 + 0.37 × F2, a (º) = 29.22 + 2.59 × F3.

Processing rate (mm/s) Dt – deposition time (sec) DF / Dt (g / sec2)

5 30 0.0167

10 15 0.0334

(7) (8) (9)

15 10 0.05

Table 1. Comparison of the powder feed rate time derivative for each scanning speed.

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H (mm) = - 0.24 + 6.33 F1

1.5

Df (%) = - 12.69 + 0.37 F2

70

Dilution factor, Df (%)

Clad height, H (mm)

60 1.0

0.5 R = 0.961

3% < Df < 5% 42.4 < P S / F < 47.8

50

R = 0.908

40 30 20 10 0

0.0 0.00

0.05

0.10

0.15

0.20

0.25

0

0.30

25

50

75

100

125

150

175

Complex parameter F2 = P S / F

Complex parameter F1 = Ö(P F / S^2)

Figure 5. Dependence of the clad height.

Figure 6. Dependence of the dilution factor.

Equation 7 shows that the clad height is proportional to the product of the mass of powder delivered per unit length of clad (F/S) times the available energy per unit length of clad (P/S). F3 represents the track length that accommodates one mass unit of injected powder material. A larger F3 means a lower clad height, implying therefore a higher a angle. Finally, F2 = P × F3 defines the fraction of addition material diluted in the base material. Application of the Method Equations 7 to 9 can be used to select the processing parameters. The choice of the adequate {P,S,F} combination will be exemplified by analysing the problem of coating a plain carbon steel substrate with Stellite 6. Bearing in mind that a constant laser beam spot diameter of 2 mm was used, the clad cross sectional quality criteria (dilution factor and a angle) determine the maximum laser power allowed: - using Eq. 8 one finds that 3% < Df < 5% is satisfied if 42.4 < P * S / F < 47.8. (10) - as to the a angle, Eq. 9 determines that a > 100º is assured if S / F > 27. (11)

a (º) = 29.22 + 2.59 F3

180 160 140 a angle, (º)

120 100 80

a > 100º

60

S / F > 27

40 20

R = 0.923

0 0

10

20

30

40

Complex parameter F3 = S / F

Figure 7. Evolution of the a angle.

50

60

These two conditions can only be simultaneously satisfied if P < 1.8 kW. This general limitation, resulting from the need to limit the materials dilution, can be avoided and larger laser beam power used if the laser spot size is increased. Using Eqs. 7 to 9, a general processing map can be plotted, describing the evolution of the clad height as a function of the powder feed rate and scanning speed. For a certain laser beam power, the complex parameter F1 can be decomposed into the form F = c(H) ´ S2 , defined for each clad height H.

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Dimensional analysis helps to clarify the physical meaning of the complex process parameters (F1, F2, F3):

Energy P´ F P F Mass = ´ ®[ ´ ], 2 S S Distance Distance S Energy Distance S F2 = P´ ® [ ´ ], F Time Mass S Distance F3 = ® [ ]. F Mass

F 12 =

(12) (13) (14)

The limits of operation are imposed by the quality criteria. Figure 8 presents the processing map for P = 1.5 kW. It shows that only a limited set of processing parameters lead to coatings satisfying the specifications. The continuous curves are based on the results presented in Figs. 5 to 7, while the dashed ones are obtained by extrapolation to higher scanning speeds. Colaço et al. [5] derived a theoretical condition for avoiding interrun porosity: 

F
a / (3×b) it predicts a cutoff in the range of possible Figure 8. General process map for selection of the {S, F} powder feed rates due to the combination for a constant laser power of 1.5 kW and a spot reduction of the melt pool width diameter of 2 mm, as a function of the clad height H. W (see Fig. 4) with increasing processing speed. Above this limit, it is not possible to deposit clad tracks that exhibit simultaneously a low dilution factor and a high a angle value. Table 2 contains the limiting values of {S, F} for several values of the clad height, calculated using Eqs. 7 and 8, in accordance with the processing map presented in Fig. 8. It should be noted that the expressions presented in Figs. 5 to 7 are based on experimental data produced in the ranges of processing parameters P Î [1.0; 3.5] kW; S Î [5; 15] mm/s; F Î [0.1; 0.6] g/s. The extension of these results to a broader interval of operation requires experimental validation.

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H (mm) 0.1 0.2 0.3 0.4 0.5

Df (%) 5 3 5 3 5 3 5 3 5 3

S (mm/s) 16.3 18.4 9.7 11.0 6.5 7.3 4.6 5.2 3.4 3.9

F (g/s) 0.51 0.65 0.31 0.39 0.20 0.26 0.14 0.18 0.11 0.14

Table 2 - Process parameter {S, F} limits for a laser power of P = 1.5 kW and a spot diameter of 2 mm, for different clad heights. Conclusions A phenomenological method for the selection of the processing window for laser cladding has been proposed, based on the multivariable statistical analysis of a large set of laser cladding samples. To allow a wide range of processing parameters to be tested with promptness and flexibility the gradient method was used. Using this method empirical relations between the processing parameters and the clad geometrical features were obtained. These expressions allowed to plot the comprehensive experimental data in a coherent manner, revealing the combined role of the different processing parameters. The simple mathematical formulae obtained by regression analysis of the experimental data, can easily be used by engineers, as an aid in the optimisation of cladding conditions simplifying the use of this technology in industrial applications. Acknowledgements The authors would like to acknowledge ICCTI and OMFB for the financial support to this investigation under the Bilateral Cooperation Program Portugal/Hungary (Project 3D Cladding 2000 - 423/OMFB). References [1] R. Vilar: Inter. J. Powder Metall. Vol. 37 (2001), p. 31. [2] R. Vilar: Mater. Sci. Forum Vol. 301 (1999), p. 229. [3] R. Colaço, T. Carvalho and R. Vilar: High Temp. Chem. Processes Vol. 3 (1994), p. 21. [4] V.M. Weerasinghe and W.M. Steen: Laser cladding by powder injection, in 1st International Conference on Lasers in Manufacturing, M.F. Kimmitt, Ed. (IFS Ltd. and North-Holland Publishing Company, 1983), p. 125. [5] R. Colaço, L. Costa, R. Guerra and R. Vilar: A simple correlation between the geometry of laser cladding tracks and the process parameters, in Laser Processing: surface treatment and film deposition, J. Mazumder, O. Conde, R. Vilar and W. Steen, Eds. (Kluwer Academic Publishers, 1996), p. 421. [6] A.M. Deus and J. Mazumder: Two-dimensional thermo-mechanical finite element model for laser cladding, in ICALEO'96, W. Duley, K. Shibata and R. Poprawe, Eds. (Laser Institute of America, Orlando, Florida 1996), p. B/174.

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[7] A.F.A. Hoadley, C.F. Marsden and M. Rappaz: A computer study of the laser cladding process, in Modeling of casting, welding and advanced solidification processes, M. Rappaz, M. Ozgu and K. Mahin, Eds. (TMS, Davos, Switzerland 1990), p. 123. [8] M. Picasso and M. Rappaz: J. Phys. IV Vol. 4 (1994), p. C4/27. [9] M. Picasso, C.F. Marsden, J.D. Wagniere, A. Frenk and M. Rappaz: Metall. Mater. Trans. Vol. 25B (1994), p. 281. [10] F. Lemoine, D.F. Grevey and A.B. Vannes: Cross-section modelling laser cladding, in ICALEO'93, P. Denney, I. Miyamoto and B.L. Mordike, Eds. (Laser Institute of America, Orlando, Florida 1993), p. 203. [11] A.F.A. Hoadley and M. Rappaz: Metall. Trans. Vol. 23B (1992), p. 631. [12] J.M. Jouvard, D.F. Grevey, F. Lemoine and A.B. Vannes: J. Laser Appl. Vol. 9 (1997), p. 43. [13] V.M. Weerasinghe and W.M. Steen: Metal Construction Vol. (1987), p. 581. [14] A. Frenk, M. Vandyoussefi, J.D. Wagniere, A. Zryd and W. Kurz: Metall. Mater. Trans. Vol. 28B (1997), p. 501. [15] C.F. Marsden, A.F.A. Houdley and J.D. Wagnière: Characterisation of the laser cladding process, in ECLAT'90, H.W. Bergman and R. Kupfer, Eds. (Sprechsaal Publ. Group, Erlangen, Germany 1990), p. 543. [16] D.C. Xiao, M. Ellis, W.M. Steen, C. Lee, K.G. Watkins and W.P. Brown: Laser Cladding of Lead Bronze, in ICALEO'93, P. Denney, I. Miyamoto and B.L. Mordike, Eds. (Laser Institute of America, Orlando, Florida 1993), p. 913. [17] P.A. Carvalho, N. Braz, M.M. Pontinha, M.G.S. Ferreira, W.M. Steen, R. Vilar and K.G. Watkins: Surf. Coat. Tech. Vol. 72 (1995), p. 62. [18] I. Felde, Z. Kálazi, B. Vero, T. Reti, G. Králik and O. Szabados: An experimental design technique for the approximation of process parameters in laser surface hardening, in Surface Modification Technologies XIV, T.S. Sudarshan and M. Jeandin, Eds. (ASM International, Paris 2000), p. 360. [19] O. O. Neto and R. Vilar: Interaction between the laser beam and the powder jet in blown powder laser alloying and cladding, in ICALEO'98, E. Beyer, X. Chen and I. Miyamoto, Eds. (Laser Institute of America, Orlando, Florida 1998), p. 180.