3-D finite element modeling of laser cladding by powder injection: effects of laser pulse shaping on the process

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Optics and Lasers in Engineering 41 (2004) 849–867

3-D finite element modeling of laser cladding by powder injection: effects of laser pulse shaping on the process Ehsan Toyserkani, Amir Khajepour*, Steve Corbin Department of Mechanical Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ont., Canada, N2L 3G1 Received 3 February 2003; accepted 25 May 2003

Abstract This paper introduces a 3-D transient finite element model of laser cladding by powder injection to investigate the effects of laser pulse shaping on the process. The proposed model can predict the clad geometry as a function of time and process parameters including laser pulse shaping, travel velocity, laser pulse energy, powder jet geometry, and material properties. In the proposed strategy, the interaction between powder and melt pool is assumed to be decoupled and as a result, the melt pool boundary is first obtained in the absence of powder spray. Once the melt pool boundary is obtained, it is assumed that a layer of coating material is deposited on the intersection of the melt pool and powder stream in the absence of the laser beam in which its thickness is calculated based on the powder feedrate and elapsed time. The new melt pool boundary is then calculated by thermal analysis of the deposited powder layer, substrate and laser heat flux. The process is simulated for different laser pulse frequencies and energies. The results are presented and compared with experimental data. The quality of clad bead for different parameter sets is experimentally evaluated and shown as a function of effective powder deposition density and effective energy density. The comparisons show excellent agreement between the modeling and experimental results for cases in which a high quality clad bead is expected. r 2003 Elsevier Ltd. All rights reserved. Keywords: Laser cladding by powder injection; Laser powder deposition; Laser pulse shaping; 3D transient finite element; Moving heat source; Experimental analysis

*Corresponding author. Tel.: +1-519-888-4567; fax: +1-519-888-6197. E-mail address: [email protected] (A. Khajepour). 0143-8166/03/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0143-8166(03)00063-0

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1. Introduction Laser cladding by powder injection is an advanced laser material processing technique, which is used in manufacturing, part repair, coating, and metallic rapid prototyping. In this process, a laser beam melts powder particles and a thin layer of the substrate to create a bulk layer on the substrate. A great variety of materials can be deposited on a substrate to form a layer with a thickness of 0.1–2 mm: This technique can produce much better coatings than other techniques such as arc welding and thermal spray, with the production of minimal dilution, minimal distortion, and good surface quality. These advantages are very attractive for part manufacturing and metallic rapid prototyping [1]. To improve and understand the underlying process and theory, several models have been developed in the literature. These models can be used in predicting the process for different parameters as well as controller design. An accurate model can significantly reduce the development cost of automated laser cladding systems. Several analytical and numerical models have been developed to show the dependency of the process on the important parameters involved. They address several important physical phenomena such as thermal conduction, thermocapilary (Marangoni) flow, powder and shield gas forces on melt pool, mass transport, diffusion, laser/powder interaction, melt pool/powder interaction, and laser/ substrate interaction in the process zone. Kar and Mazumder [2] considered the dissolution of powder and mixing of the clad in a one-dimensional study. Hoadley and Rappaz [3] developed a pure two-dimensional heat transfer model in which the powder was assumed to mix rapidly and uniformly in the molten region. Weerasinghe and Steen [4] proposed a finite difference model for calculating the heat flux in the process. They considered the effects of shadowing of the particle cloud, heat absorption of particles, and overlapping of traces on the heat flux. Chande and Mazumder [5] developed a numerical model which solves a twodimensional, transient equation of convection diffusion in the melt pool using the alternate-diagonal implicit method. The model developed by Jouvard et al. [6] predicts the power limits for generating good quality clad. Their model takes into account the interaction between the powder and laser beam. Picasso and Hoadley [7] developed a two-dimensional, stationary, finite element model for laser cladding by considering heat transfer, fluid motion, and deformation of the liquid–gas interface. They solved a stationary Stephan equation and found the shape of the melt pool in a known clad height. Picasso et al. [8] also developed a simple geometrical model for laser cladding. Their model calculates the laser-beam velocity and the powder feedrate when the laser power, beam radius, powder jet geometry and clad height and width are known. The work done by Kim and Peng [9] modeled the melt pool of the laser cladding by wire feeding using a two-dimensional, transient finite element technique. Bamberger et al. [10] found a simplified theoretical model for parameters estimation of laser surface cladding by direct injection. They used the Mie theory in the model to show the influence of the injected particles on the heat flux and temperature distribution.

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Although the literature contains several laser cladding models, there is a significant lack in more accurate numerical models which take into account the effects of power attenuation due to the powder particles, absorption factor deviation during the process (Brewster effect), temperature dependencies of material properties, melt pool geometry and laser pulse characteristics. The literature also shows the absence of a model for the prediction of the clad geometry in the transient and dynamic period of the process. In this paper, we use the finite element technique to develop a 3-D transient model for laser cladding by a powder injection process. In this study, we use the model to understand the correlation between the clad geometry and laser pulse shaping parameters (laser pulse frequency and energy) when the other process parameters such as travel speed, laser pulse width, powder jet geometry and powder feedrate are constant. In this analysis, the material properties are assumed to be functions of temperature and the effects of Marangoni phenomena and hydrodynamic of the liquid metal are considered in the material properties by increasing the thermal conductivity. The model also takes into account the power attenuation and Brewster effects to include the changes in absorption factor due to the clad geometry. In the following, the modeling approach is first discussed and then the assumptions for the numerical solution are presented. Finally, the numerical results obtained at different laser pulse setting are compared with experimental data.

2. Thermal mathematical model For a laser cladding process, a moving laser beam with a Gaussian distribution intensity strikes on the substrate at t ¼ 0 as shown in Fig. 1. Due to additive material, the clad forms on the substrate as shown in the figure. The transient

Fig. 1. Schematic of the associated physical domains of the laser cladding process.

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temperature distribution Tðx; y; z; tÞ is obtained from the three-dimensional heat conduction in the substrate as [11] @ðrcp TÞ þ r  ðrcp UTÞ  r  ðKrTÞ ¼ Q; ð1Þ @t where Q is power generation per unit volume of the substrate ðW=m3 Þ; K is thermal conductivity ðW=m KÞ; cp is specific heat capacity ðJ=kg KÞ; r is density ðkg=m3 Þ; t is time (s), and U is the travel velocity of workpiece (process speed) (m/s). The essential boundary condition is ( bIðx; y; z; tÞ  hc ðT  T0 Þ  et sðT 4  T04 Þ if OAG; KðrT  nÞ j O ¼ ð2Þ hc ðT  T0 Þ  et sðT 4  T04 Þ if OeG; where n is the normal vector of the surface, Iðx; y; z; tÞ is the laser energy distribution on the workpiece ðW=m2 Þ; b is the absorption factor, hc is heat convection coefficient ðW=m2 KÞ; et is emissivity, s is Stefan–Boltzman constant ð5:67 108 W=m2 K4 Þ; O is the workpiece surfaces ðm2 ), G is the surface area irradiated by the laser beam ðm2 Þ and T0 is the ambient or reference temperature (K). The following conditions should also be satisfied: Tðx; y; z; 0Þ ¼ T0

ð3Þ

Tðx; y; z; NÞ ¼ T0 :

ð4Þ

and In order to incorporate the effects of the laser beam shaping, latent heat of fusion, Marangoni phenomena, geometry growing (changing geometry), and Brewster effect the following adjustments are combined: *

A pulsed Gaussian laser beam with a circular modes (TEM00 ) [12] is considered for the beam distribution. The laser beam intensity profile I ðW=m2 Þ is [13] 2 pffiffiffi!2 3 2 IðrÞ ¼ dI0 exp4 ð5Þ r2 5; rl where r¼

*

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x 2 þ y2

and

I0 ¼

2 Pl ; Pl ¼ EF pr2l

ð6Þ

and rl is the beam radius (m), I0 is intensity scale factor ðW=m2 Þ; Pl is the laser average power (W), E is the energy per pulse (J), and F is the laser pulse frequency (Hz). When the laser beam is on d ¼ 1 and when it is off d ¼ 0: The parameter d is changed based on the laser pulse shaping parameters such as frequency F and width W that is the time that the laser beam is on in one period. The effect of latent heat of fusion on the temperature distribution can be approximated by increasing the specific heat capacity [14], as Lf cp ¼ þ cp ð7Þ Tm  T0

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*

where cp is modified heat capacity ðJ=kg KÞ; Lf is latent heat of fusion ðJ=kgÞ; Tm is melting temperature (K), and T0 is ambient temperature (K). The effect of fluid motion due to the thermocapilary phenomena can be taken into account using a modified thermal conductivity for calculating the melt pool boundaries. Experimental work and estimations in the literature [15] suggest that the effective thermal conductivity in the presence of thermocapilary flow is at least twice the stationary melt conductivity. This increase can be generally presented by K  ðTÞ ¼ aKðT Þ if T > T ; ð8Þ m

*

853

m

where a is the correction factor and K  is modified thermal conductivity ðW=m KÞ: Power attenuation is considered using the method developed by Picasso et al. [8] with some minor modifications. Fig. 2 shows the proposed geometrical characteristics in the process zone which is used in the development of the following equations. Based on their work

 Pat P1 ¼ Pl bw ðyÞ 1  ; ð9Þ Pl

 Pat Pat P2 ¼ Pl Zp bp 1 þ ð1  bw ðyÞÞ 1  ; ð10Þ Pl Pl

Fig. 2. The proposed geometrical characteristics.

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where P1 is total energy directly absorbed by the substrate (W), P2 is energy that is carried into the melt pool by powder particles (W), and Pat is attenuated laser power by powder particles (W). Consequently, the total energy absorbed by workpiece Pw is Pw ¼ P1 þ P2 ¼ bPl ;

ð11Þ

where b is the modified absorption factor. The ratio between the attenuated and average laser power can be obtained by [8] 8 m ’ > > if rjet orl ; < 2rc rl rp vp cosðyjet Þ Pat ð12Þ ¼ m ’ > Pl > : if rjet Xrl : 2rc rjet rp vp cosðyjet Þ In these equations, m ’ is powder feedrate ðkg=sÞ; rc is powder density ðkg=m3 Þ; rl is radius of the laser beam on the substrate (m), rp is radius of powder particles (m), vp is powder particles velocity (m/s), yjet is the angle between powder jet and substrate (deg), rjet is radius of powder spray jet (m), bw ðyÞ is workpiece absorption factor, bp is particle absorption factor, and y is angle of top surface of melt pool with respect to horizontal line as shown in Fig. 2 (deg). The powder efficiency Zp can be considered as the ratio between the melt pool surface and the powder stream’s area (Fig. 2) as Zp ¼

Aliq jet Ajet

;

ð13Þ

where Aliq jet is the intersection between the melt pool area on the workpiece and powder stream, and Ajet is the cross-sectional area of the powder stream on the workpiece. If we assume, the absorption of a flat plane inclined to a circular laser beam depends linearly on the angle of inclination y as shown in Fig. 2 and bw ð0Þ is the workpiece absorption of a flat surface, bw ðyÞ can be calculated from bw ðyÞ ¼ bw ð0Þð1 þ aw yÞ;

*

*

ð14Þ

where y is the angle shown in Fig. 2 and aw is a constant coefficient obtained experimentally for each material [8,12]. The temperature dependency of material properties and absorption coefficients on the temperature are taken into account in the model. In order to reduce the computational time, a combined heat transfer coefficient for the radiative and convective boundary conditions is calculated based on the relationship given by Goldak [16] and Yang et al. [17]: hc ¼ 24:1 104 et T 1:61 :

ð15Þ

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Using (15), (5), and (11) the boundary condition in (2) is simplified to 8 pffiffi > < 2 dbP exp½ð 2Þ2 r2   h ðT  T Þ if OAG; l c 0 rl KðrT  nÞ j O ¼ pr2l > : hc ðT  T0 Þ if OeG:

855

ð16Þ

3. Prediction of clad geometry Eq. (1) along with the adjustments presented in the previous section is for thermal analysis of the cladding process. In this section, we use the thermal equation and introduce a method to predict the clad geometry. This method is based upon calculation of the melt pool boundary on the substrate and the addition of a layer of powder to the melt pool area. In the following, we explain the proposed algorithm: *

*

Step 1: We assume that the laser impinges the moving substrate in the absence of a powder stream (see Fig. 3a). Using Eq. (1), the temperature distribution is obtained, and consequently, the melt pool boundary is obtained. Step 2: Once the melt pool boundary is calculated, it is assumed that a layer of coating material based on the powder feedrate, elapsed time, and intersection of

Fig. 3. Sequence of calculation in the proposed numerical model.

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melt pool/powder jet is deposited on the melt pool area (see Figs. 2 and 3b). The new deposited layer builds a tiny clad on the previous domain which is limited to the intersection of powder stream and melt pool where its height is given by Dh ¼

mDt ’ ; pr2jet rc

ð17Þ

where Dh is the thickness of deposited layer (m), rjet is the radius of the powder stream (m) and Dt is the elapsed time (s). The temperature profile of the added layer is assumed to be the same as the temperature of underneath layer due to the numerical convergence which will be discussed later. The new temperature profile of the combined workpiece and the layer of powder is then obtained by repeating Step 1. As illustrated in Fig. 3, Steps 1 and 2 are repeated with an identical concepts (Sequences 3, 4 , 5, 6, etc. as seen in Fig. 3). The numerical solution is carried out in two different time steps. The first one is the time between two deposition steps and the second one is the time step for calculating the melt pool area. After performing Step 2 and before repeating Step 1, the following corrections are applied: *

*

* *

All thermo-physical properties and absorption factor bw ð0Þ are updated based on the new temperature distribution. The new bw ðyÞ is calculated based on the updated y and Eq. (14). y is obtained from the developed geometry at any time based on the proposed triangle, which connects the tip of melt pool to the highest melted point on the clad as shown in Fig. 2. The new Zp is obtained based on the new melt pool geometry using Eq. (13). The new Pw is calculated using Eq. (11).

Many numerical methods for solving Eq. (1) have been reported since 1940. Finite element methods (FEM) are one of the reliable and efficient numerical techniques which have been used for many years. The FEM can solve different form of partial differential equations with different boundary conditions. In this work, the governing PDE Eq. (1) is highly nonlinear due to material properties with dependency on temperature and a moving heat source with a Gaussian distribution. To implement the strategy for predicting the clad geometry, a code was developed using the MATLAB (www.mathworks.com) and FEMLAB (www.femlab.com) software. The code discretizes the substrate and generates the initial mesh. By solving Eq. (1) and calculating the melt pool, the geometry of the domain is modified to incorporate the clad into the substrate. For meshing, the domain is partitioned into tetrahedrons (mesh elements) as shown in Fig. 6. Due to the deposited layer and changes in the substrate geometry, an adaptive meshing strategy is used. As it is seen, the mesh is finer for the portion of the domain in which the clad is generated. A time-dependent solver is used to solve the nonlinear time-dependent heat transfer equation. It is an implicit differential-algebraic

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equation (DAE) solver with automatic step size control [18]. The solver is suitable for solving equations with singular and nonlinear terms. As it was mentioned in Step 2 of the solution strategy, a layer is deposited to the workpiece with the same temperature of the underneath layer. Since in Eq. (11), the energy transferred to the workpiece by the powder particles is considered, the temperature of the deposited layer should be assumed as that of the ambient temperature. However, due to large temperature gradient between the added and the underneath layers, the numerical solution does not converge with the selected solver. As a result, it is assumed that the temperature of profile of the added layer is the same as the temperature of underneath layer in the second step of solution algorithm. Although this assumption violates the balance of energy and adds some extra energy to the numerical procedure, however it is not more than 1% of the total energy absorbed by the workpiece in Eq. (11), and it does not have a considerable contribution in the overall results.

4. Numerical results A 50 10 5 mm3 block was selected for the initial substrate in a Cartesian coordinates as shown in Fig. 6. The thermo-physical properties of iron were considered for both substrate and powder. All thermo-physical properties such as thermal conductivity, specific thermal heat, emissivity and density were considered to be temperature dependent and were obtained from Ref. [19]. The thermo-physical properties for temperatures higher than vapor temperature Tv were fixed to the amount of thermo-physical properties in Tv : Also, bw ð0Þ; as a function of temperature, was considered for pure iron when a Nd:YAG laser is used [20]. The other process parameters are listed in Table 1. In order to evaluate the contribution of the laser pulse frequency F and the laser pulse energy E on the clad geometry, two separate conditions were considered as follows: 1. The laser pulse energy was stepped up in increments of 0:5 J from 2.5 to 4 J as shown in Fig. 4a. 2. The laser pulse frequency was stepped up in increments of 10 Hz from 70 to 100 Hz as shown in Fig. 4b.

Table 1 Process parameters selected for the numerical modeling m ’ ðkg=sÞ rl (m) U (m/s) Laser pulse width (ms) rp (m) rjet (m) a

1:67e  5 7:0e  4 0.001 3 22:5e  6 7:5e  4 1:67e  2 [8]

T0 ðKÞ Tv (K) Tm (K) vp (m/s) yjet (deg.) bp (%) for Nd:YAG a

293 3313 1811 26 55 34 2.5 [15]

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Average laser power (W)

Laser pulse energy (J)

858

4 3.5 3 2.5 2

0

2

4

6

8

0

2

4

6

8

12

14

16

18

20

12

14

16

18

20

400 300 200 100

10 Time (s)

(a)

100

Average laser power (W)

Laser pulse frequency (Hz)

10 Time (s)

80 60 0

2

4

6

8

10 Time (s)

12

14

16

18

20

2

4

6

8

10 Time (s)

12

14

16

18

20

300 200 100

0

(b) Fig. 4. Comparison between the calculated temperature at a desired point in different nodes number to investigate the independency of solutions on the number of grid.

In both cases all other conditions were fixed. The average laser power for both cases are also shown in Figs. 4a and b. In all numerical simulation, it was assumed that the laser was turned on at t ¼ 0 and beaming at position x ¼ 10; y ¼ 0 and z ¼ 5 mm: In order to investigate the independency of the solutions on the number of nodes, simulations were performed in the different number of nodes. The computational results are shown in Fig. 5. As seen, with increase of number of nods, the curve shown at the calculated temperatures at x ¼ 0:03 m; y ¼ 0:0 m; z ¼ 0:005 m and at t ¼ 20 s becomes flat such that the difference between the calculated temperatures with 8,100 and 10,203 nodes is 8 K: As a result, the number of elements was initialized with 10,203 nodes and 43,577 elements which were mostly concentrated on

ARTICLE IN PRESS Tempearture (K) at x=0.03 m, y=0.0 m, z=0.005 m

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2400 2300 2200 2100 2000 1900 1800 1700 1600 1500 1000

2000

3000

4000

5000

6000

7000

8000

9000

10000 11000

Number of nodes Fig. 5. A typical mesh in the proposed domain.

Fig. 6. (a) Multistep laser pulse energy along with corresponding average laser power. (b) Multistep laser pulse frequency along with corresponding average laser power.

the top of the surface as seen in Fig. 6. The simulation was performed for 20 s: The time step between the layer deposition segment was set to 20 ms and the other time step was controlled by the solver, however it was not greater than 0:2 ms: In the next section, several aspects of the modeling results will be discussed. 4.1. Temperature distribution and clad creation Fig. 7 shows the temperature distribution of the workpiece at t ¼ 20 s in different views for a multistep laser pulse energy. The figure illustrates the isothermal lines in

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Fig. 7. Temperature distribution at t ¼ 20 s for a multistep laser pulse energy.

the domain where the maximal temperature is 2388 K: The figure also shows a rapid cooling in the domain due to the concentrated moving heat source. Behind the moving heat source, the isothermal lines expand whereas the condensed isothermal lines exist in the area close to the laser source. Fig. 8 shows the generated clad after 20 s for a multistep laser pulse energy. In order to have a better view of the generated clad on the substrate, a light source to illuminate the domain was considered. The ripples on the generated clad was discovered to be dependent on the size, shape and number of the elements used to mesh the domain. Increasing the number of meshes can reduce the ripples, however the average height remains the same. As seen in Figs. 7 and 8, the clad height and width increase with increasing the laser pulse energy as expected. The results also show that when the ratio between the pulse energies E1 ¼ 3 and E2 ¼ 4 J is 1.33, the ratio between the corresponding

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Fig. 8. Generated clad after 20 s for a multistep laser pulse energy.

average clad heights is about 2.278, whereas for the energy ratio of 1.167, the clad height ratio becomes 1.28. This is an indication of the nonlinearities in the process. In order to compare the numerical and experiential results, we will next explore an experimental analysis for the evaluation of the clad quality. Then, we will use the experimental analysis along with numerical results to interpret the modeling results.

5. Experimental and numerical analysis 5.1. Experimental setup The experiments were performed using 1000 W LASAG FLS 1042N Nd:YAG pulsed laser, a 9MP-CL Sulzer Metco powder feeder unit, and a 4-axis CNC table. The laser pulse energy and laser pulse frequency were changed based on those which are shown in Figs. 4a and b when the pulse width was set to 3 ms: The process speed was set to 1 mm=s for all experiments similar to the numerical simulation. The diameter of the laser beam spot size on the workpiece was set to 1:4 mm where the laser intensity was Gaussian. The laser beam was shrouded by argon shield gas. In the experiments, the powder feed rate was set to 1 g=min ð1:67e  5 kg=sÞ with argon as the shield gas at a rate of 2:35e  5 m3 =s (3 SCFH). The laser shield gas (inert gas) was set to 1:56e  5 m3 =s (2 SCFH). The angle of the nozzle spray was set to 55 from the horizontal line and the size of powder stream profile was approximately 1:5 mm on the workpiece. The powder used in the experiments was iron with a purity

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of 98% on metals basis. Sandblasted mild steel plates ð50 10 5 mm3 Þ were selected as the substrate. The laser was beamed at 10 mm away from the edge. The height of the clad was measured in real-time by the device discussed in [21]. 5.2. Experimental analysis In order to develop a methodology for evaluating the clad quality, two parameters the effective energy density Eeff ðJ=mm2 Þ and effective powder deposition density ceff ðg=mm2 Þ (discussed in [22,23]) are defined as Pl Eeff ¼ ; ð18Þ Aeff ceff ¼

mFW ’ ; Aeff

ð19Þ

where Aeff is the effective area irradiated by the laser beam per second ðmm2 =sÞ: This is determined not only by the substrate velocity but also by the pulse characteristics of the laser beam. The irradiated area per second is expressed as 8 2 for rl > 1FW pr þ 2Url  2F ½1FW > F Url 2F U; < l 1 y 1FW p  2F yU  2rl ð2  sin ðrl Þ Aeff ¼ ð20Þ > : 2 1FW for rl % 2F U; prl F þ 2Url WF where

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2 1  FW U y ¼ r2l  2F

ð21Þ

and U is the process velocity (mm/s). Calculated values for Eeff ; and Ceff for the processing conditions listed in Table 2 are plotted in Fig. 9. For these experiments, U ¼ 1 mm=s; rl ¼ 0:7 mm; W ¼ 3 ms and m ’ ¼ 1 g=min: By observation and mechanical and metallurgical tests, four regions are distinguishable for the generated clads as shown in Fig. 9. In the region called ‘‘Good quality clad’’, a good bond between the substrate and clad can be Table 2 Condition of experiments performed Condition

E (J)

F (Hz)

1 2 3 4 5 6 7 8

2.5 3 3.5 4 3.5 3.5 3.5 3.5

100 100 100 100 70 80 90 100

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240

4

220

Good quality clads

Effective energy density (J/mm 2)

200

3

8

180

7 160

2 High roughness

6 1

140

Brittle

5

120 100 80

No cladding 60 40 1.8

2

2.2

2.4

2.6

2.8

3

2

Effective powder deposition density (g/mm )

x 10

-3

Fig. 9. Effective energy versus effective powder deposition densities for Conditions 1–8.

clad height (mm)

2.5

Condition 1 E=2.5 J

2

Condition 3 E=3.5 J

Condition 2 E=3 J

Condition 4 E=4 J

Numerical model Experimental result

1.5 1

Laser on

Laser off

0.5 0 1

1.5

2

position (cm)

2.5

3

3.5

Clad is broken

Fig. 10. Comparison between the experimental and numerical results for Conditions 1–4.

generated where the clad has a smooth surface and good profile without cracks and pores. The region called ‘‘High roughness and porosity’’ indicates that the clad has some bonding with the substrate; however, the clad has many cracks and pores. The region called ‘‘Brittle clads’’ indicates that the clad has been generated without any bonds with the substrate. The clad in this region is easily removed by hand after the process. The region called ‘‘No cladding’’ indicates that no clad can be created in this region due to the lack of energy. The evidences for these regions are shown in Figs. 10 and 11.

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Clad height (mm)

2

Condition 5 F=70 Hz

Condition 6 F=80 Hz

Condition 8 F=100 Hz

Condition 7 F=90 Hz

1.5

Numerical model Experiment

1 0.5

Laser on

Laser off

0 1

1.5

2

2.5

3

3.5

position (cm)

Clad is broken

Fig. 11. Comparison between the experimental and numerical results for Conditions 5–8.

Table 3 Numerical and experimental average clad height Condition

E (J)

F (Hz)

Numerical average clad height (mm)

Experimental average clad height (mm)

Error (%)

2 3 4 7 8

3 3.5 4 3.5 3.5

100 100 100 90 100

0.77 1.45 1.73 1.2 1.43

0.89 1.42 1.57 1.1 1.23

15.5 2.1 9.2 8.3 13.9

5.3. Comparison between numerical and experimental results Fig. 10 shows the deviation between the numerical and experimental results for the change of laser pulse energy. As seen, the numerical modeling cannot predict the clad height for Condition 1 while for other Conditions 2–4 there is good agreement between the model and experimental results. Based on the quality analysis shown in Fig. 9, it can be concluded that the quality of Condition 1 listed in Table 2 is not acceptable due to weak bonding between the clad and substrate. The reason for this is the lack of sufficient energy to melt the powder and substrate. As a result, the clad is easily removed from substrate following the process as shown in Fig. 10. Reminding back to the numerical modeling, the layer can be only deposited if only a melt pool area on the substrate is developed for any given time. The average errors between the two results for Conditions 2–4 are listed in Table 3. The same justification can be mentioned for the case when the laser pulse frequency is changed as seen in Fig. 11. For this case, Condition 5 does not provide a good quality clad whereas Condition 6 provides a relatively good quality clads. For Conditions 7 and 8 the quality of clads are perfect. The average errors

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between the experimental and numerical results for Conditions 7 and 8 are also listed in Table 3. To further investigate clad/substrate geometrical profile and comparison between the numerical and experimental results, sections through the clad/substrate couples were made for selected samples. These sections were then mounted and polished to unveil their profiles. Figs. 12a and b depict the clad/substrate macrostructure for Condition 4 with E ¼ 4 J; W ¼ 3:0 ms; F ¼ 100 Hz and U ¼ 1 mm=s and Condition 8 with

Fig. 12. Comparison between numerical and experimental clad’s profile for (a) Condition 4, (b) Condition 8.

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a E ¼ 3:5 J; W ¼ 3:0 ms; F ¼ 100 Hz and U ¼ 1 mm=s; respectively. The clad deposit is clearly visible and the clad has a good profile. The comparison between the numerical and experimental profiles shows that the model has predicted the clad profile very well. Referring again to Figs. 10–12 and Table 3, it can be concluded that the numerical model can predict the geometry of the produced clads accurately for those conditions that a good quality clad is expected to occur. Also, the clad height increases with either laser pulse energy or laser pulse frequency increase. There are several reasons for the error between the model and experimental results which are under investigation. Some of the main reasons are the instability of the powder feeder, the thermocapilary effect in the process, losses in energy due to the fiber optic and processing head, error in the coefficients used for calculating power attenuation and overall absorption factor, and error in the material properties.

6. Conclusion A new 3-D transient finite element modeling technique was developed to predict the laser cladding process by powder injection. A solution strategy was developed to incorporate the change in the geometry of the substrate. The model then used in predicting the dependency of clad geometry on the laser pulse shaping. An experimental analysis was developed to use in comparing the numerical and experimental results. The results were promising and showed that the model is capable of predicting the laser cladding process accurately for the cases that a high clad quality was expected from the experimental analysis.

Acknowledgements The authors would like to acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC).

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