Numerical simulation and prediction of dilution during laser deposition

Transcription

1 Numerica simuation and prediction of diution during aser deposition Zhiqiang Fan 1, Anand Jambunathan 2, Todd E. Sparks 1, Jianzhong Ruan 1, Yu Yang 1, Yaxin Bao 1 and Frank Liou 1 1 Department of Mechanica and Aerospace Engineering, University Of Missouri Roa 2 Department of Metaurgica Engineering, University Of Missouri Roa 1870 Miner Circe, Roa, MO , iou@umr.edu ABSTRACT The aser additive manufacturing technique of aser deposition aows quick fabrication of fuy-dense metaic components directy from Computer Aided Design (CAD) soid modes. The appications of aser deposition incude rapid prototyping, rapid tooing and part refurbishment. The deveopment of an accurate predictive mode for aser deposition is extremey compicated due to the mutitude of process parameters and materias properties invoved. In this work, a heat transfer and fuid fow mode is deveoped. The mode is used to predict diution under varying process parameters for deposits of Ti-6A-4V. Experimenta vaidation of the predicted diution is presented. The aser used is a direct diode aser. 1. INTRODUCTION Laser deposition is an extension of the aser cadding process for rapid prototyping of fuy dense meta components. This aser additive manufacturing technique aows quick fabrication of fuy-dense metaic components directy from Computer Aided Design (CAD) soid modes. The appications of aser deposition incude rapid prototyping, rapid tooing and part refurbishment. A primary objective of the aser deposition process is to achieve porosity free added ayers with good bonding to the substrate and with ow diution of the added ayer in the substrate. Thus, diution is among the major concerns for the aser deposition process. Diution is an important parameter for the aser deposition process because it indexes the bonding between the added ayer and the substrate, and the utiization efficiency for the aser power. High diution indicates that too much aser power has been used to re-met the substrate and overheating may occur whie no diution at a eads to poor bonding to the substrate and even ack of fusion. Many investigations have been done on substrate diution during the past years It is considered that the contro of aser deposition for a given eve of diution which is sufficient to estabish metaurgica bonding but which minimizes diution woud be desirabe. However, such contro is difficut because diution highy depends on the metaurgica properties of the materias appied and the varying process parameters. The authors have deveoped a sef-consistent heat transfer and fuid fow mode to predict diution under different process parameters during aser deposition. In this study, A coaxia diode aser deposition system, LAMP (deveoped at UMR), is considered for simuations and experiments. The bown powder method is used to deiver power. As the primary aser in the 532

2 LAMP system, diode aser is beieved to have a number of process advantages as opposed to the CO 2 or Nd:YAG aser, incuding the better materia couping efficiency (aser absorption) and better beam profie for aser deposition. The beam profie of a diode aser is generay uniform due to the nature of the beam formation process. This profie is beneficia for many appications where uniform heating of a surface is required, as in aser surface hardening, aser aoying and aser cadding 13. Materia of both powder and substrates is Ti-6A-4V aoy, which is widey used in the aerospace industry and especiay suitabe for aser processing, since Ti-6A-4V is sti cassified as one of the extremey difficut-to-machine materias using conventiona machining MATHEMATICAL MODEL 2.1 Governing Equations Momentum and energy conservation Fig.1-Schematic of the aser deposition system Figure 1 shows a schematic diagram of the aser deposition system. In the aser deposition process, meting and soidification cause the phase transformation at the soid/iquid interface. A mushy zone containing soid and iquid is formed. To track the soid/iquid interface evoution, in this study the continuum mode deveoped by Bennon and Incropera 15, 16 is adopted, which is an extension of the cassica mixture theory. The momentum equations are written for the mixture veocities, reying on the vaue of the permeabiity in each contro voume to determine whether fow through porous mush is important in that contro voume. For the system of interest, a Newtonian, incompressibe, aminar fow is assumed in the met poo. The conservation equations for mass, momentum and energy are summarized as foows: Continuity ( V ) 0 (1) t Momentum p ( u) ( Vu) ( u) ( uu ) S t x K s x (2) Energy p ( v) ( Vv) ( v) ( vv ) gs t y K s y (3) 533

3 ( h) ( Vh) ( kt) ( ( h h)( VVs) t (4) In equations (1)-(4), the continuum density, specific heat, therma conductivity, vector veocity, and enthapy are defined as foows: gs s g c fscs fc V fv fv s s k gsks gk h fshs fh (5) The voume fractions of iquid can be obtained from Swaminathan and Voer s genera enthapy method 17, athough other reationships are possibe 18. Swaminathan and Voer summarized four possibe enthapy-temperature curves with different iquid fraction temperature reationships. In this work, both the deposit and the substrate materias are Ti-6A-4V, for which Curve B is more appropriate where there is a inear evoution of the atent heat over the soidification range T T s. The iquid fraction temperature reationship for this type of enthapy-temperature curve is given by: 0 if T Ts T Ts g if Ts T T (6) T Ts 1 if T T The other voume and mass fractions are can be obtained by: f g s s fs g gs g 1 fs 1 f (7) The phase enthapy for the soid and the iquid can be expressed as: T Ts T hs c ( ) 0 s T dt h c( ) ( ) 0 s TdT ctdt T Lm where L m is the atent heat of meting. (8) The assumption of a mutiphase region permeabiity requires consideration of growth morphoogy specific to the aoy under consideration. The present study foows the approach suggested by Bennon and Incropera 15, 16, permeabiity, K, is assumed to vary with iquid voume fraction according to the Kozeny-Carman equation19 derived from Darcy s aw: 3 g K K0 (9) 2 (1 g ) where K 0 is a constant depending on the morphoogy and size of the dendrites in the mushy zone. The S x and S y in the momentum equations are source terms contributed by the interfacia forces such as thermocapiary force and surface tension. s 534

4 2.1.2 Tracking of the Free Surface The iquid/vapor interface, or the free surface of the met poo, is very compex due to surface tension, thermocapiary force, and impaction of the powder injection. In this study, the Voume-Of-Fuid (VOF) method is empoyed to track the evoution of the moving free surface of the met poo. The met poo configuration is defined in terms of a voume of fuid function, F(x,y,t), which represents the voume of fuid per unit voume and satisfies the conservation equation: F ( V ) F 0 (10) t 2.2 Boundary Conditions Top Liquid-Vapor Free Surface (1) Momentum baance A free surface ce is subject to the foowing norma and tangentia boundary condition: Tangentia stress baance: us vn T ( ) (11) n s T s Norma stress baance: p pv (12) where u s and v s are the tangentia and norma veocity component at the free surface. p v is the vapor pressure in the gas region. and represent surface tension coefficient and curvature, respectivey. is given in 18: 1 n ( n) ( ) n ( n) n n where n is a norma vector of oca free surface, which is a gradient of VOF function: n F (13) (14) (2) Energy baance Energy baance at the free surface satisfies the foowing equation: T ( Paser Patten) 4 4 k h ( ) ( ) 2 c T T T T m el (15) v n R where terms on the right-hand side are aser irradiation, convective heat oss, radiation heat oss and evaporation heat oss, respectivey. P aser is the power of aser beam, P atten is the power 535

5 attenuated by the powder coud, R is the aser beam radius, is the aser absorption coefficient, which is measured by Sparks et a. 20. The aser energy distribution is assumed to be uniform, which is cose to the actua conditions. P atten is cacuated according to Frenk et a s mode 21 with minor modification: P atten 3Qextm Paser 1exp r D v p jet p where m denotes the powder mass fow rate, is the stand-off distance from the nozze exit to the substrate, is powder density, r p is the radius of the powder partice, D jet is the diameter of the powder jet, v p is the powder injection veocity, and Q ext is the extinction coefficient. It is assumed that the extinction cross section is cose to the actua geometrica cross section, and Q ext takes a vaue of unity. (16) In the evaporation term, m e is the evaporation mass fux and L v is the atent heat of evaporation. According to Choi et a. s overa evaporation mode 22, m e is of the form: og m e A ogT T (17) where A is a constant dependent on the materia. (3) Mass Baance Powder partices that inject onto the top surface can be cassified into three categories. (1) Those powder partices that have not been meted during their passage and hit the soid part of the substrate wi defect and ose. (2) Those powder partices that have been meted before they arrive on the substrate and impact the soid part of the substrate wi stick to the surface of the substrate. (3) Those powder partices that fa into the met poo incuding meted and unmeted wi merge and mix with the moten iquid in the met poo 23. In this study, the powder partices beonging to the ast two cases wi be utiized. The mass ratio of utiized powder to tota powder is reated to many factors, incuding met poo dimensions and geometry, temperatures of the met poo surface and the soid part of the substrate near the met poo, the stand off distance between the substrate top surface and the end of the nozze, and powder concentration distribution. Since the former two factors can be simuated in the present work, and the third factor is known for a specific experiment, the ast factor needs to be modeed or measured by experiments. In this study, Pinkerton and Li s mode 24 is appied. In their mode, two distinct functions are appied to describe the powder concentration distribution aong the centra axis before and after the merge point, respectivey. This mode is for coaxia deposition nozze. 536

6 2.2.2 Bottom and side wa surfaces The boundary conditions at the bottom, eft and right wa satisfy the foowing equations: T k hc ( T T ) n u 0 v 0 (19) Note that the radiation heat oss at these surfaces is negected due to the fact that the temperature differences at these surfaces are not arge. (18) Heating of powder partices Powder partices are heated by the aser beam during their fight, and accumuated energy is finay transmitted to the substrate. In this study, a mode proposed by Jouvard et a., [25] which is in good agreement with the experiment, is taken in the cacuation of the powder temperature. 2.3 Numerica Soution The SOLA-VOF agorithm 26 is used to sove the continuity and momentum equation (2)-(4). At each time step, the discretized momentum equations cacuate new veocities in terms of an estimated pressure fied. Then the pressure fied is iterativey adjusted and veocity changes induced by each pressure correction are added to the previous veocities. This iterative process is repeated unti the continuity equation is satisfied under an imposed toerance by the newy computed veocities 27. The energy equation (4) is soved by an impicit method. Staggered grids are empoyed where the temperatures and pressures are ocated at the ce center and the veocities at the was. Uniform grid points were utiized with the mesh size of 10m, which was proved to achieve grid independence. The time step is taken at the eve of 10-6 s initiay and adapted subsequenty according to the convergence and stabiity requirements of SOLA-VOF. 3. Simuation Resuts The parameters for the simuation are chosen based on the capabiity of our experimenta faciities to compare the simuation resuts with the experimenta measurements. A continuous wave diode aser with an 808 nm waveength is considered as the energy source. The aser intensity distribution is uniform. Three aser powers of 490,700, and 910W, three trave speed of 15, 20, and 25ipm, and three powder mass fow rate of 4, 6, 8g/min are considered. For substrates, Ti-6A-V4 pates with a thickness of 0.25 inch are seected. Ti-6A-V4 powder partices with a diameter from 40 to 140 m are considered as deposit materia. The aser absorption coefficient is measured by Sparks et a. 20. Powder injection speed of m/s 537

7 is obtained using Pan s stochastic non-spherica partice coision mode 28. Fig. 1 shows the simuation resuts at t = 250 ms for one case in which aser power is 700W, trave speed is 20ipm, and powder mass fow rate is 8g/min. As expected, the met poo depth in this case is sma, that is, the met poo is fat since the aser power distribution is uniform instead of Gaussian. (a) Temperature fied (b) Veocity fied (c) Voume of Fuid Figure 1 Simuation resuts at t = 130 ms for the case: aser power: 910W, trave speed: 20ipm, powder mass fow rate: 4.68g/min. It is convenient to compute diution using the function of Voume of Fuid (VOF), which hep visuaize the met poo ceary. A ce with a VOF vaue greater or equa to 0.5 is counted as a iquid ce. Diution d is defined as the ratio of moten buk materia of cross section A b to the tota moten cross section A c + A b 32: d Ab A A b c (20) Fig.2 shows how the met poo evoves. Fig. 2 (a)-(c) shows the process in which a compete met poo forms. Fig. 2 (d)-(f) shows that the met poo is entering a steady state in terms of shape and dimensions. The diution cacuation is based on the average vaue of the transient data in a steady state of the met poo. The simuation resuts of diution for different cases are presented in the next section. 4. Experimenta resuts and mode vaidation 4.1 Experimenta Setup The experiments were performed on the LAMP system shown in Fig. 3. The system consists of a diode aser, powder deivery unit, 5-axis CNC machine, and monitoring subsystem. The aser system used in the study was Nuvonyx (Nuvonyx Inc.) ISL-1000M Laser Diode System which combines state-of-the-art micro-optics with aser diodes to produce the ony singe waveength fiber couped direct diode aser at power eves up to 1000 watts CW. The aser emits at 808 nm and operates in the continuous wave (CW) mode. To protect oxidization of Ti-6A-V4, the system is covered in an environmenta chamber to suppy argon gas for titanium deposition. The aser spot diameter is 2.5 mm. For the other aspects of the system architecture, refer to Liou et a. [33] and Boddu et a.[34]. 538

8 Ti-6A1-4V powder (Accumet Materias Co.) has diameters between 40 m and 140 m. The substrates have dimensions of in. (a) t = 50 ms (b) t = 60 ms (c) t = 70 ms (d) t = 110 ms (e) t = 120 ms (f) t = 130 ms Figure 2 Evoution of met poo for the case: aser power: 910W, trave speed: 20ipm, and powder mass fow rate: 4.68g/min Figure 3-Schematic of experimenta setup 539

9 4.2Experimenta Procedure The Ti-6A-4V sampes were irradiated using a aser beam with a beam spot diameter of 2.5 mm and aser powers (measured using a power meter) of W. The aser deposited sampes were cut using a Wire-EDM machine. A SEM (Scanning Eectron Microscope) ine trace was used on each of the sampes to determine the diution of the cad ayer. The deposited Ti-6A-4V is of Widmansttaten structure. The substrate has a roed equi-axed apha+ beta structure. Even though these two structures are consideraby different and are easiy distinguishabe, the HAZ is arge and has a martensitic structure that can be associated with it. Hence sma quantity of too stee in the order of 5% was mixed with Ti-6A-4V. The sma quantity makes sure that it does not drasticay change the deposit features of a 100 % Ti-6A-4V deposit. At the same time, the presence of Cr in too stee makes it easiy identifiabe by means of EDS scans using SEM. Knowing the exact ocation of Cr in the substrate woud provide the depth of the met poo in the substrate to measure diution. 4.3 Resuts A diution anaysis using SEM is shown in Fig.4. The upper part is the deposit. The ower part is the re-met area, ony part of it is shown in the images. In order to understand the effects of aser power, trave speed and powder mass fow rate on diution, and to vaidate the numerica simuation, both simuation resuts and experimenta resuts are shown in Fig Laser Power (W) Tabe 2 Measured and simuated diution on Ti-6A-4V Trave Speed (in./min) Powder Mass Fow Diution Depth (m) Diution (%) Rate (g/min) Measured Simuated Measured Simuated

10 (a) Beginning of deposit (b) Midde of deposit (c) End of deposit Figure 4-SEM pictures of diution anaysis. (Laser power: 910W, trave speed: 20ipm, powder mass fow rate: 6.7g/min) 5. Discussion Diution depth depends on the energy absorbed by the substrate, given the specific materia, the geometry of the substrate, aser beam spot size, and the beam profie. Laser power and aser trave speed determine the tota energy density potentiay absorbed by the substrate. Powder mass fow rate affects the energy actuay absorbed by the substrate by the mechanism of power attenuation due to the powder coud. Laser power, trave speed and powder mass fow rate are the three main process parameters to determine the diution depth. Diution, defined as the ratio of the cross section of the moten substrate materia to the tota moten cross section, depends on both the diution depth and the cross section area of the cad. The cross section area of the cad is determined by the cad height and the rippe of cad surface, which are out of this paper s scope. Diution Depth (micron) Measured 140 Simuated Laser Power (W) Diution (%) Measured Simuated Laser Power (W) (a) Diution depth (b) Diution Figure 5-Diution depth and diution as a function of aser power for trave speed of 20 ipm and powder mass fow rate of 4.68g/min for aser deposited Ti-6A-4V 541

11 Diution Depth (micron) W Measured 700W Simuated 910 W Measured 910W Simuated Diution (%) W Measured 700W Simuated 910W Measured 910W Simuated Laser Trave Speed (ipm) Laser Trave Speed (ipm) (a) Diution depth (b) Diution Figure 6-Diution depth and diution as a function of aser trave speed for powder mass fow rate of 4.68g/min for aser deposited Ti-6A-4V Diution Depth (micron) W Measured 700W Simuated 910W Measured 910W Simuated Powder Mass Fow Rate (g/min) Diution Depth (micron) W Measured 700W Simuated W Measured W Simuated Powder Mass Fow Rate (g/min) (a) Diution depth (b) Diution Figure 7-Diution depth and diution as a function of powder mass fow rate for trave speed of 20 ipm for aser deposited Ti-6A-4V From Fig. 5-6, it can be seen that an increase in the aser power wi increase the diution depth. An increase in the aser trave speed wi decrease the diution depth. It is cear that the diution depth has a inear dependence on the aser power and the aser trave speed. This is easy to understand. As the aser power increases, more power is avaiabe for meting the substrate. As trave speed decreases, the aser materia interaction time is extended. But since the powder catchment efficiency and thus the cross section area of the cad aso increase with increased aser power and decreased aser trave speed the diution can be seen not to vary proportionay with the diution depth. From Fig. 7, it can be seen that an increase in powder mass fow rate wi decrease the diution depth. But the effect of powder mass fow rate on diution depth is more significant at a ower eve of powder mass fow. It is ikey that at a ower eve of powder mass fow, the effect of powder mass fow rate on powder catchment efficiency is more significant. Aso at a higher eve of aser power, the effect of powder mass fow rate on diution depth is more significant. It is ikey that at a higher eve of aser power, on one hand more power is attenuated given a constant attenuation ratio and more power is absorbed by the powder; on the other hand, the deposited materia can decrease the temperature gradients more significanty. From Fig. 5-7, we can see that the genera trend between simuations and experiments is 542

12 consistent. The errors between the simuated and measured diution depths are anayzed to come from four aspects: (1) Resoution of the computationa mesh (that is, the mesh size) imits the accuracy of the simuation. In this study, mesh size is 10 m. But the resoution of SEM measurement is 1 m. (2) The SEM measurement of the diution depth may bring about some errors. This method described before may not be very accurate since it is to track the trend of Chromium distribution. (3) The mode is two-dimensiona but the process is three dimensiona in nature. The mode intrinsicay negects heat and mass transfer in the third dimension. One can see that the errors between the simuated and measured diution depths increase with increase aser power and decreased aser trave speed. This may be because that at a higher energy density heat and mass transfer in the third dimension is more significant. (4) The uncertainties of the materia properties and the appropriateness of the sub-modes are other possibe sources of the errors. In this study, the mode is vaidated in terms of diution depth and diution. This heat transfer and fuid fow mode can aso predict temperature fied, veocity fied, pressure fied of the met poo, cad height, and met poo geometry. The measurement of these quantities is not presented here since this paper focus on the prediction of diution. 6. Concusions A sef-consistent aser deposition mode is presented, which simuates heat transfer, fuid fow, met poo geometry during the aser deposition process. The SOLA-VOF25 method is adopted to track the evoution of the met poo free surface (iquid/vapor interface). The continuum mode 15, 16 is appied to derive the mass, momentum and energy conversation equations, which are vaid for soid and iquid. The movement of soid/iquid interfaces are aso simuated using the continuum mode15, 16. In this study, processes associated with the met poo free surface, incuding free surface evoution, convection, evaporation, surface tension, heating of powder partices, powder fow veocities, and powder concentration distribution have been modeed. The numerica mode is used to predict diode aser-induced diution in Ti-6A-4V that was in agreement with those measured by SEM. The sources of the errors between the simuated and measured diution have been anayzed. It is expected that a three dimensiona mode with finer mesh wi improve the accuracy of prediction in diution. Acknowedgments This research was supported by the Nationa Science Foundation Grant Number DMI , the grant from the U.S. Air Force Research Laboratory contract # FA C-5704, and UMR Inteigent Systems Center. Their support is greaty appreciated. 543

13 References 1. R.R. Unocic and J.N. DuPont, Composition Contro in the Direct Laser-Deposition Process, Metaurgica and Materias Transactions B. Vo. 34B, no. 8, pp. 439-, H. Gedda, A. Kapan, and J. Powe, Met-Soid Interactions in Laser Cadding and Laser Casting, Metaurgica and Materias Transactions B. Vo. 36B, no.10, pp.683-, T. C. Lei, J. H. Ouyang, Y. T. Pei, and Y. Zhou, Microstructure and Siding Wear Properties of Laser Cad TiN reinforced Composite Coating, Surface Engineering, vo. 12 no. 1 pp.55-60, A. F. H. Kapan and G. Groboth, Process Anaysis of Laser BeamCadding, Journa of Manufacturing Science and Engineering (Transactions of the ASME) (USA). Vo. 123, no. 4, pp Nov K. G. Watkins, Achieving the Potentia of Direct Fabrication with Lasers, Proc 3rd Internationa Conference on Laser Asssisted Net Shaping (LANE 2001) Erangen, August, 2001 pp Meisenbach- Verag Bamberg. 6. M. L. Griffith, et. a., Materias and Design, vo. 20, pp , W. Hofmeister, et. A., JOM, vo. 51, no.7, A. Vasinonta, J. Beuth, and M. Griffith, Proceedings of the Soid Freeform Fabrication Symposium, Austin, TX, pp , C. A. Brice, K. I. Schwendner, D. W. Mahaffey, E. H. Moor, and H. L. Fraser, Proceedings of the Soid Freeform Fabrication Symposium, Austin, TX, pp , J. Brooks, C. Robino, T. Headey, S. Goods, and M. Griffith, Proceedings of the Soid Freeform Fabrication Symposium, Austin, TX, pp , Bake, A.G. and Eboo, G.M., State of the Art Laser Hardfacing Using Dynamic Powder Feed Technoogy, Conference on the Laser vs. the Eectron Beam in Weding, Cutting and Surface Treatment, Reno, Nevada, pp , Kennedy, E; Byrne, G; Coins, D N, A review of the use of high power diode asers in surface hardening, Journa of Materias Processing Technoogy. Vo , pp Nov Ezugwu, E. O. and Wang, Z. M. Titanium aoys and their machinabiity-a review, J. Mater. Processing Techno., 1997, 68(3), W. Bennon and F. Incropera, Internationa Journa of Heat and Mass Transfer, vo. 30, pp , W. Bennon and F. Incropera, Internationa Journa of Heat and Mass Transfer, vo. 30, pp , C. R. Swaminathan, and V. R. Voer, A Genera Enthapy Method for Modeing Soidification Processes, Metaurgica Transactions B (USA). Vo. 23B, no. 5, pp Oct C. Prakash and V. Voer, Numerica Heat Transfer, vo.15b, pp171-89, S. Asai and I. Muchi, Trans. Iron Stee Inst. Jpn., vo. 18, pp , Todd E. Sparks and Zhiqiang Fan, measurement of aser absporption coefficient of severa aoys for diode aser, unpubished report, A. Frenk, M. Vandyoussefi, J Wagniere, A. Zryd, and W. Kurz: Meta. Mater. Trans. B, 544

14 1997, vo. 28B, pp M. Choi, R. Greif and M. Sacudean, Numerica Heat Transfer, vo. 11, pp , L. Han, F.W. Liou, and K.M. Phatk, Metaurgica and Materias Transactions B. Vo. 35B, no. 6, pp B. Dec Andrew J. Pinkerton and Lin Li, Journa of Manufacturing Science and Engineering, vo. 126, pp , February J.M. Jouvard, D.F. Grevey, F. Lemoine, and A.B. Vannes: J. Laser App., vo. 9, pp , B. D. Nichos, C.W. Hirt, R. S. Hotchkiss, SOLA-VOF: A soution agorithm for transient fuid fow with mutipe free boundaries, LA-8355, Los Aamos Nationa Laboratory. 27. Henry Hu and Stavros A Argyropouos, Mathematica modeing of soidification and meting: a review, Modeing Simua. Mater. Sci. Eng. 4, pp , Heng Pan and Frank Liou, Journa of Materias Processing Technoogy. Vo. 168, no. 2, pp Sept S.M. Key, Therma and Microstructure Modeing of Meta Deposition Processes with Appication to Ti-6A-4V, Ph.D. thesis, Virginia Poytechnic Institute and State University, K. C. Mis, Recommended vaues of thermophysica properties for seected commercia aoys, Woodhead, Cambridge, Tobias Lips and Bent Fritsche, "A COMPARISON OF COMMONLY USED RE-ENTRY ANALYSIS TOOLS", 55th Internationa Astronautica Congress Vancouver, Canada IAC-04-IAA , P.9, SCARAB mode. 32. A. F. H. Kapan and G. Groboth, Process Anaysis of Laser BeamCadding, Journa of Manufacturing Science and Engineering (Transactions of the ASME) (USA). Vo. 123, no. 4, pp Nov F. Liou, J. Choi, R. Landers, V. Janardhan, S. Baakrishnan, and S. Agarwa: Proc. 12th Annua Soid Freeform Fabrication Symp., Austin, TX, Aug. 6 8, 2001, pp M. Boddu, S. Musti, R. Landers, S. Agarwa, and F. Liou: Proc. 12 th Annua Soid Freeform Fabrication Symp., Austin, TX, Aug. 6 8, 2001, pp