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    Journal of Materials Processing Technology 212 (2012) 113119

    Contents lists available at SciVerse ScienceDirect

    Journal ofMaterials Processing Technology

    journal homepage: www.elsevier .com/ locate / jmatprotec

    Surface finish in laser solid freeform fabrication ofan AISI 303Lstainless steel

    thin wall

    Masoud Alimardani, Vahid Fallah, Mehrdad Iravani-Tabrizipour, Amir Khajepour

    Department of Mechanical andMechatronics Engineering, University of Waterloo,Waterloo, Ontario, Canada N2L 3G1

    a r t i c l e i n f o

    Article history:

    Received 15 March 2011

    Received in revised form 4 August 2011Accepted 13 August 2011

    Available online 19 August 2011

    Keywords:

    Laser solid freeform fabrication

    Temperature and thermal stress fields

    Surface finish

    Microstructure

    Numerical analysis

    a b s t r a c t

    Laser solid freeform fabrication is a flexible manufacturing technique that can be used to produce a near

    net shape component by consolidation of successive deposited layers of additive materials. This study

    investigates the effects of the main process parameters, the laser power and scanning speed, on the

    surface finish of AISI 303L thin walls through reducing the thickness of the deposited layers. To study

    the effects ofthe variations ofthe operating parameters, the process is simulated. The numerical results

    showed that by increasing the scanning speed the laser power must be adjusted in order to maintain

    the melt pool maximum temperature within a pre-defined value. In this way, the surface finish of the

    fabricated walls considerably improves due to the decreased thickness ofeach individual layer without

    significantly disturbing the melt pool and the main physical characteristics of the build-ups. This was

    also verified through experimentally fabrication ofthe walls and their microstructural examination.

    2011 Elsevier B.V. All rights reserved.

    1. Introduction

    Laser solid freeform fabrication (LSFF), among different rapidmanufacturing techniques, has demonstrated many advantageous

    features such as a small heat affected zone (HAZ), minimal dilu-

    tion, and integration of CAD tools with the production process. In

    LSFF, a near-net-shape 3D object can be fabricated directly from

    its CAD model by successive layer-by-layer deposition of metallic

    material as shown by Santos et al. (2006) and Paul et al. (2006).

    Considering these characteristics, LSFF has also been recognized

    as a potential fabrication method for functionality graded parts

    and repair of heavy duty high-value components such as turbine

    blades described by Rinaldi and Antonelli (2005). However, accord-

    ing to Chen and Huang (2004), this interdisciplinary technique is

    governed by several process parameters and physical phenomena

    occurring in various states of the process, such as melting, solid-

    ification and solid-state transformations. The resultant complex

    processing pattern imposes manufacturing limitations caused by

    the intense variations in the mechanical and metallurgical prop-

    erties, delamination, and crack formations across the structure of

    the fabricated parts. Klingbeil et al. (2002), Lee et al. (2006), and

    Alimardani et al. (2010a,b) discussed some of these limitations

    caused by residual and thermal stresses. Particularly, variation in

    Corresponding author at: Department of Mechanical and Mechatronics Engi-

    neering, University of Waterloo, 200 University Avenue W., Waterloo, Ontario,

    Canada N2L 3G1. Tel.: +1 519 888 4567x33646; fax: +1 519 8886197.

    E-mail address: [email protected](M. Alimardani).

    the local microstructure formed across a four-layer thin wall from

    the substrate interface to the top of the wall was investigated by

    Alimardaniet al. (2010b) using a numericalexperimental analysis.In this study, the four-layer wall was fabricated with a constant set

    of process parameters throughout the build-up process.

    The surface finish of the layered structures is largely affected by

    the operating parameters and contributing physical phenomena.

    In LSFF, since the width of each track is limited by the laser beam

    diameter, multiple clad beads must be successively overlapped in

    order to improve the surface finish. Similarly, the multiple layered

    depositions create a stepped lateral surface and specifically in fully

    vertical deposition, like a flat wall, the curvature of each track pro-

    duce a rough lateral surface. It is shown by Kulkarni and Dutta

    (1996), and Majhi et al. (1999) that the resultant surface finish can

    be improved by reduction in the thickness of each individual layer

    or by optimization of the overlapping length in vertical or horizon-

    tal layered structures, respectively. This however may affect the

    final desired properties of the fabricated structures. Intense ther-

    mal stresses are induced across the layered structure by the high

    heating and cooling rates induced during the localized deposition

    process. Such a specific thermal condition, as shown in detail by

    Nickel et al. (2001) and Alimardani et al. (2007a, 2010a), imposes

    a high risk of crack formation during the process, while also intro-

    ducing variations in the mechanical and metallurgical properties

    across the depositedmaterial. To achieve a uniform cladsection and

    consequentlya smoother surface profile in LSFF, it is obvious that a

    consistentmelt poolmust be maintained during the deposition pro-

    cess. Hence, the process parameters need to be adjusted during the

    layered verticalor horizontallyoverlappedLSFFin order tokeep the

    0924-0136/$ see front matter 2011 Elsevier B.V. All rights reserved.

    doi:10.1016/j.jmatprotec.2011.08.012

    http://localhost/var/www/apps/conversion/tmp/scratch_7/dx.doi.org/10.1016/j.jmatprotec.2011.08.012http://localhost/var/www/apps/conversion/tmp/scratch_7/dx.doi.org/10.1016/j.jmatprotec.2011.08.012http://www.sciencedirect.com/science/journal/09240136http://www.elsevier.com/locate/jmatprotecmailto:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_7/dx.doi.org/10.1016/j.jmatprotec.2011.08.012http://localhost/var/www/apps/conversion/tmp/scratch_7/dx.doi.org/10.1016/j.jmatprotec.2011.08.012mailto:[email protected]://www.elsevier.com/locate/jmatprotechttp://www.sciencedirect.com/science/journal/09240136http://localhost/var/www/apps/conversion/tmp/scratch_7/dx.doi.org/10.1016/j.jmatprotec.2011.08.012
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    114 M. Alimardani et al./ Journal of Materials Processing Technology212 (2012) 113119

    temperature distributions throughout the process within a definite

    range. The in-processalteration of parameters, however, mayintro-

    duce a non-uniform distribution of metallurgical and mechanical

    properties across the layered structure.

    So far, several research groups have studied different aspects

    of the LSFF process such as interaction between laser beam and

    powder stream investigated by Huang et al. (2006). Specifically on

    the geometrical aspects and surface finish in laser material deposi-

    tion, LiandMa (1996) have proposed a realistic butsimple analysis

    of the overlapping process. Singh et al. (2005) have experimen-

    tally addressed the technical issues for material deposition at the

    turning points on a deposition path. To minimize the stair-step

    errors in layered manufacturing, Majhi et al. (1999) and Kulkarni

    and Dutta (1996) have proposed optimum slicing algorithms.

    Pinkerton and Li (2003a,b) experimentally studied the effects of

    the laser pulse width and pulse frequency on the microstruc-

    ture and surface finish of multiple-layer deposition of 316L steel.

    Some research groups, such as Han et al. (2004),Jendrzejewski and

    Sliwinski (2007), and He and Mazumder (2007) have also taken

    the approach of using experimentally calibrated numerical models

    to investigate the effects of the process parameters on the process

    outcomes along with the experimental analyses. Considering the

    aforementioned investigation performed in overlapping process in

    hardfacing application of the laser material deposition technique,

    this work represents a comprehensive study on the design of the

    process parameters in LSFF in order to optimize the surface finish

    and geometrical accuracy as well as the physical and metallurgical

    properties of the deposited layers. In this regard, along with the

    fabrication of AISI 303L thin walls, a coupled 3D time-dependent

    numerical model is used to monitor the effect of the processing

    parameters on the geometry, temperature distributions and stress

    fields within the depositedlayers. Throughoutthe study, the exper-

    imental observationsare used to verifyand interpretthe numerical

    analyses.

    2. Experimental setup and procedure

    A fiber laser (IPG)with themaximumpower of 1100 W wasused

    with the beam diameter set to 1.4mm at the deposition zone. A

    five-axis CNC table (Fadal) was employed as the positioning device

    underneath the stationary laser head. Gas atomized 303L stainless

    steel (Fe:70; Cr:17;Ni:13wt%) powders of particle size 50150m

    were used as theadditive material.A powderfeeder(Sulzer Metco:

    9MP-CL) was used to inject the powder particles into the process

    zone through a front-feeding lateral nozzle attached to the laser

    head.Argongas with a flowrateof 1.38 l/min wasusedas thecarrier

    gas which also shields the melt pool during the process. The main

    operating parameters are listed in Table 1.

    Table 1

    Process parameters.

    Name Unit Value

    Laser power W 300450

    Scanning speed mm/s 1.515

    Powder feed rate g/min 2

    Radius of the powder jet mm 0.75

    Radius of the laser beam mm 0.7

    Ambient temperature K 298

    Melting temperature K 1690Density of powder Kg/m3 7850

    Several thin walls were fabricated with different process speeds

    and laser powers on 25mm20mm5 mm substrates of sand-

    blasted AISI 1030 mild steel. Each track was deposited on a

    15mm straight path as schematically shown in Fig. 1a. Fig. 1b

    also shows one of the walls deposited at the scanning speed of

    1.5mm/s. Cross-sectional specimens were cut from the deposited

    wallsfor metallography usingan optical microscopeequipped with

    a camera (Olympus: BH2-UMA). Prior to microscopy, the sam-

    ples were ground using SiC sandpapers with up to 1200 grain

    size and then polished with 1, 0.3 and 0.05m alumina slurries.

    To reveal the general microstructures, the polished samples were

    etched through immersion in an acid solution (consisting of 10mLHNO3 +20mLHCl+30mLdistilled water) for 5 min durations.

    3. Description of the LSFF numerical modelling approach

    and its verification

    Several models of the LSFFprocesshave recently beendeveloped

    in which the temperature distribution and stress fields have been

    studied throughout the fabrication process. However, due to the

    complexity of this multi-physics process, the analytical/numerical

    investigations in this area are still conducted based on various

    assumptions to simplify the process. For instance, the effect of

    the additive material is not considered in the model developed by

    Nickel et al. (2001), or in other approaches reported by Ghosh and

    Choi (2005), andJendrzejewski and Sliwinski (2007), a new groupof elements at each time step is activated in a dynamic fashion to

    build up a thin wall with a nonrealistic rectangular cross section.

    Peyre et al. (2008) also presented another modelling approach in

    which the shape of the deposited materials is defined in advance.

    For simulation of the LSFF process, a 3D numerical approach

    developed by Alimardani et al. (2007a) was used by which the

    time-dependent geometry of the deposited material as well as

    the coupled temperature and thermal stress fields across the pro-

    cess domain can be predicted for planar and non-planar surfaces.

    The coupled thermal and stress domains are numerically obtained

    assuming a decoupled interaction between the laser beam and

    Fig. 1. Deposition of thethin walls by theLSFF process: (a) schematic diagram of thedeposited track position on the substrate, (b)deposited thin wall with scanning speed

    of1.5mm/s.

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    M. Alimardani et al./ Journal of Materials Processing Technology212 (2012) 113119 115

    powder stream. For mathematical formulations of the temperature

    and stress fields, the transient temperature and thermal stress dis-

    tributions throughout the process domain can be obtained from

    the 3D heat conduction equation and the constitutive equation

    along with appropriate boundary conditions. In this approach, the

    moving laser energy distribution is considered in the boundary

    condition with a circular Gaussian TEM00 mode. The effects of

    the heat losses through convection/radiation, latent heat of fusion,

    Marangoni phenomena,power attenuation, and the external forces

    or displacements are also taken into account. In the numericalsim-

    ulations,for non-planar surfaces,the effectof theangleof incidence

    of the laser beam, and the powder catchment efficiency were cal-

    culated for each layer regarding their geometrical specifications.

    Based on the angle of incidence and powder catchment efficiency

    for each layer, the absorption factor of a flat surface was modi-

    fied for each non-planar layer separately. To simulate the process,

    COMSOL Multiphysics 3.5a (www.comsol.com) was used to solve

    the governing equations and their associated initial and boundary

    conditions. A combined code was also developed using MATLAB

    (www.mathworks.com) and its interface with COMSOL to incor-

    porate the additive material into the process domain. More details

    regarding the modelling process and its verification are provided

    by Alimardani et al. (2007a).

    To be consistent with the experimental analyses, all process

    parameters and other specifications such as substrate size were

    considered the same for the numerical analyses. In addition, the

    time span between each two successive deposition tracks (i.e.

    required to return the laser processing head to the starting point

    of the next deposition track) was also considered in the simula-

    tion procedure. To discretize the substrate, four-node tetrahedron

    elements were used. All required element quality checks of the FE

    model were also performed including a convergence test. For the

    process domainconsidered in this work, thefinal FE modelused for

    the first layer deposition has 82,025elements and 484,076 degrees

    of freedom.

    4. Results and discussion

    The surface finish of a layered structure can be improved by

    reducing the thicknesses of the deposited layers. This can be done

    most efficiently by only increasing thescanning speed.Technically,

    unlike other process parameters such as the powder feed rate, the

    laser scanning speed can be easilyadjustedduring the process. Any

    sudden change in the powder feed rate in the course of the process

    will require a period of time to achieve a steady flow rate. Further-

    more, according to Fallah et al. (2010), it was shown in the past

    studies that changing only the laser scanning speed does not affect

    the mass-energy balance in the system. On the other hand, chang-

    ing other parameters such as powder feed rate disturbs the balance

    between the injected mass of the powder and the laser energy

    entering the system, thus affecting the final metallurgical quali-

    ties of the clad sections. Toyserkani et al. (2003) showed that theheighthof a depositedlayercan be calculated using thefollowing

    mass conservation equation.

    h =mt

    Ameltjet

    p(1)

    where m kg/s) is the powder feed rate, Ameltjet

    (m2) is the intersec-

    tion of the melt pool and the powder stream area on the substrate,

    t (s) is the time step, and p (kg/m3) is the density of the pow-

    der. By decreasing the powder feed rate, the deposition thickness

    h at each time step reduces, and so does the total height of the

    deposited track. However, by increasing the scanning speed, the

    absorbed energy by the substrate decreases and this may affect the

    melt pool conditions.

    Fig.2. Maximumtemperatures (K)along withthe deposition track forthe firstlayer

    with different scanning speeds.

    4.1. Effect of scanning speed on temperature distribution

    Itwas shown by Fallahet al.(2010) and Alimardani et al. (2007b)

    that a proper deposition can be achieved with the laser power of

    300Wandscanningspeedof1.5mm/s (andthe parameters listed in

    Table 1) using an energy-based optimization procedure. To investi-gate theeffect of scanning speed on thedeposited layer,the process

    is simulated for the laser power of 300 W with the process speed of

    1.5, 6, 10.5, and 15mm/s with the other specification explained in

    the preceding sections (Table 1 and Fig. 1a). Fig. 2 shows the maxi-

    mum temperatures along with the deposition track with different

    process speedsduring thedeposition of the first layer of a thin wall.

    In this figure,the position of thelaserbeam andthe maximum tem-

    perature along thex axis can be found at a given scanning speed

    and a simulation time (shown at the topof the figure). Forinstance,

    for Point M at the simulation time t= 2s and the scanning speed of

    1.5mm/s, thelaserbeamis atx= 8 mmon the substrate (orx= 3 m m

    on the deposition track relative to the coordinate system shown in

    Fig. 1a).

    As seen in Fig. 2, the maximum temperature throughout thefabrication process decreases by increasing the scanning speed.

    Considering the melting temperature of the substrate and additive

    material (i.e., 1690K, referring to Table 1), a proper melt pool

    cannot be formed for the processes with the scanning speed of

    6, 10.5 and 15mm/s. For the process with the scanning speed of

    1.5 mm/s, as shown in Fig. 2, the maximum melt pool temperature

    increases with a steadyslope which results in larger powder catch-

    ment efficiency and a non-uniform clad throughout the track. For

    this case, the geometrical prediction and its experimental counter-

    part are shown in Fig. 3. Regarding the temperature profiles shown

    in Fig. 2, more uniform tracks are expected for the processes with

    higherscanning speeds. However, at higherscanning speed, it takes

    longer for the substrate temperatures to reach their steady-state

    conditions at the beginning of the process. Fig. 4 shows the aver-age maximum thermal stresses during the process at 1 mm under

    the top surface of the substrate. As it was expected, the thermal

    stresses decrease by increasing the process speed.

    4.2. Process optimization

    To find the effect of scanning speed on the melt pool, the LSFF

    process was simulated with different scanning speeds (i.e. 1.5, 6,

    10.5 and 15mm/s) and laser powers (i.e. 300, 350, 400 and 450 W).

    The average maximum temperature throughout the deposition

    process of the first layer is shown in Fig. 5. The non-shaded part

    of this figure identifies the region within which a proper melt pool

    can be formed (considering the melting temperatures of the sub-

    strate and powder particles). To maintain the melt pool average

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    116 M. Alimardani et al./ Journal of Materials Processing Technology212 (2012) 113119

    Fig. 3. Material deposition for the first layer of a thin wall: (a) geometrical predic-

    tions of the additive material, (b) geometrical comparison between experimental

    and simulation results.

    Fig. 4. Average maximum thermal stresses (Von Mises) along thex axis at 1 mm

    under thetop surface of thesubstrate fordifferent process scanning speeds.

    temperature close to that of the sample made at 1.5mm/s scan-

    ning speed and 300 W laser power (as the reference case), the laser

    power should be increased to 350, a value within 350400, or

    400 W at the scanning speeds of 6, 10.5 or 15mm/s, respectively.

    Simulation results shows that by increasing the laser power the

    thermal stresses alsoincrease.For instance,at the scanning speedof

    10.5mm/s,by changing thelaserpowerfrom300to 350and400 W,

    the thermal stresses increase by 19 and 36%,respectively. However,

    as seen in Fig. 4, the thermal stresses decrease with increasing the

    scanning speed (27% reduction for process with 10.5mm/s scan-

    ning speed compared to the one with 1.5mm/s speed). Therefore,

    the thermal stresses for the process with the scanning speed of

    10.5mm/s and laser power of 350 W still show 13% reduction com-

    pared to that of the deposition with the laser power of 300W and

    Fig.5. Averagemaximum temperaturesof thefirstlayerfor differentprocessspeeds

    and laser powers.

    Fig. 6. Average maximum temperatures of the second layer for different process

    speeds and laser powers.

    Table 2

    Optimum process parameters.

    Name Unit Value

    Powder feed rate g/min 2

    Radius of the powder jet mm 0.75

    Radius of the laser beam mm 0.7

    Scanning speed: 6 mm/s

    Laser power first layer W 350

    Laser power second and upper layers W 315

    Scanning speed: 10.5mm/sLaser power first layer W 370

    Laser power second and upper layers W 325

    Scanning speed: 15mm/s

    Laser power first layer W 400

    Laser power second and upper layers W 350

    scanning speed of 1.5 mm/s. For the same case (scanning speed of

    10.5mm/s) but with the laser power of 400 W, the thermal stresses

    are almost the same and even lower than those with the scan-

    ning speed of 1.5mm/s and laser power of 300W. Consequently,

    the deposition process with the scanning speed of 10.5mm/s and

    laser power of 400 W produces almost the same temporal ther-

    mal stresses as that of with the scanning speed of 1.5mm/s and

    the laser power of 300W. In addition, a more properly developedmelt pool is also formed for the process with the scanning speed

    of 10.5mm/s and laser power of 400W (as can be inferred from

    Fig. 5). Although the maximum temperatures increase during the

    depositionof the upperlayers,due to geometrical changes, the tem-

    perature gradients across the layered structure and consequently

    the average maximum thermal stresses decrease. In this regard,

    more discussion is provided by Alimardani et al. (2007a). In order

    to determine the optimum laser power for the deposition of the

    upper layers, the LSFF process wassimulated for different scanning

    speeds. Figs. 6 and 7 show the average maximum temperatures

    throughout the deposition of the second layer, and their corre-

    sponding temporal thermal stresses imposed on the interface of

    the first layer and substrate for different scanning speeds and laser

    Fig.7. Averagemaximum thermalstresses (VonMises)of thesecondlayer imposed

    on theinterface of thefirst layer and substrate fordifferent process speeds.

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    M. Alimardani et al./ Journal of Materials Processing Technology212 (2012) 113119 117

    Fig. 8. The optical micrographs of the deposited stainless steel walls with different process speeds: (a) longitudinal views, (b) cross-sectional views.

    Fig. 9. Theopticalimages showing thegeneralmicrostructure of thecross-sectional views from thestainless steel wallsdeposited at:(a) 1.5, (b)6, (c)10.5, and(c) 15mm/s.

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    118 M. Alimardani et al./ Journal of Materials Processing Technology212 (2012) 113119

    Fig. 10. (a) Temporal temperature profiles on the surface of the substrate at point

    (12.5, 0) mm of the first layer deposition for different scanning speeds, and (b) the

    correspondingcooling rates.

    powers, respectively. As can be seen in Fig. 6, compared to the pro-

    cess with the scanning speed of 1.5mm/s and the laser power of

    300 W, to achieve the same average maximum temperatures with

    the scanning speeds of 6, 10.5, and 15mm/s laser powers of315,

    325and350 W arerequired,respectively.It shouldbe notedthatsince themaximum temperaturesincreasefor thedeposition of the

    upper layers, therefore, the results for the laser power of 450W are

    not shown for the second layer, Figs. 6 and7, as theyare outof the

    acceptable range.

    4.3. Experimental and microstructural observations

    In order to experimentally investigate the effect of parameters

    on the surface finish, several thin walls (with the sectional geome-

    tries illustrated in Fig. 1a) were deposited using the optimized sets

    of operating parameters. Table 2 lists the optimum process param-

    eters used to deposit the thin walls with scanning speed of 6, 10.5

    and15 mm/s.These parameters canbe used to optimize thesurface

    finish of the wall deposited with scanning speed of 1.5mm/s. Forthe wall with scanning speed of 1.5 mm/s (i.e., reference case), the

    process parameters are listed in Table 1. As can be seen in Fig. 8a,

    the smoothness and uniformity of the walls lateral surfaces were

    substantially enhanced by increasing the scanning speed. The opti-

    cal micrographs of the intersectional views of the wall, as shown

    in Fig. 8b, also depict the improvement of the surface finish of

    both lateral sides. This was also predicted throughout the numer-

    ical analyses since the increased scanning speed helps to reduce

    the thickness of the individual layers. In addition, no cracks and

    delamination were detected across the deposited walls.

    Fig.9 represents the general microstructureof the stainless steel

    walls deposited at different scanning speeds. A coarse dendrite

    structure can be identified within the large equiaxed grains in the

    microstructure shown in Fig. 9a. The microstructure of the sample

    (deposited ata higherscanvelocity) shownin Fig.9b reveals a much

    finer dendrite structure mostly with a directional pattern towards

    the top surface of the wall. As can beclearly seen in the microstruc-

    ture of the samples shown in Fig. 9c and d, increasing the scanning

    speed enhances the fineness of the dendrite and equiaxed grains

    structures. This is believed to be the result of the increased cool-

    ing rates at higher scanning speeds. Fig. 10a shows the numerical

    results of the temporal temperature of a point on the surface of the

    substrate (at (12.5, 0) mm relative to the coordinate system shown

    in Fig.1a) duringthe deposition of thefirst layer.These results were

    obtained from numerical simulations of the process using the opti-

    mumoperating parameters as listedin Tables 1 and 2. Cooling rates

    profiles illustrated in Fig. 10b shows a significant increase by the

    scanning speed.

    Therefore, by increasing the scanning speed and adjusting the

    number of layers for a pre-defined height, more uniform sur-

    face profiles and finer dendrite structures can be obtained in the

    deposited walls. With the knowledge obtained from the numerical

    results along with the experimental investigation, it is possible to

    determinea setof optimum process parameters inorderto enhance

    the surface finish of the LSFF product.

    5. Conclusions

    The effects of the main process parameters on the surface finish

    of the thin walls of AISI 303L steel fabricated using the LSFF process

    were both experimentally and numerically studied. An experimen-

    tally verified 3D coupled time-dependent numerical model was

    used to simulate the temperature distributions and thermal stress

    fields induced throughout the deposition process using different

    sets of process parameters. Considering the microstructural obser-

    vations and numerical results for the temperature and thermal

    stress fields across the deposited layers, the following conclusions

    can be made:

    - By increasing the scanning speed and simultaneously adjusting

    the laser power in order to maintain a consistent melt pool (i.e.

    through controlling the average maximum temperature through-outthe deposition process),the surface finish of thethin walls can

    be significantly improved.

    - The microstructural observations revealed that increasing the

    scanning speed enhances the fineness of the dendrite and

    equiaxed grains structures across thedeposited walls.This wasin

    a good agreement with the simulation results which show sub-

    stantially increased cooling rates by the increase of the scanning

    speed.

    Acknowledgements

    The authors would like to acknowledge the financial support of

    the Ontario Centres of Excellence (OCE) and the Natural Sciences

    and Engineering Research Council of Canada (NSERC).

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