Modeling and Simulation of A Laer Depoition Proce rank Liou*, Zhiqiang an*, Heng Pan*, Kevin Slattery**, Mary Kinella+, Joeph Newkirk*, and Hin-Nan Chou** *Univerity of Miouri Rolla, Rolla, MO, 65409 ** The Boeing Company + ARL/MLLMP Reviewed, accepted September 4, 2007 Abtract A laer depoition proce involve the upply of metallic powder into a laer-heated pot where the powder i melted and form a melt puddle which quickly olidifie into a bead. In order to deign an effective ytem, the laer beam, the powder beam, and their interaction need to be fully undertood. In thi paper, the laer-material interaction within the melt pool i reported uing a multi-cale model: a macrocopic model to model ma, heat, and momentum tranfer. Experiment were alo conducted to validate the imulation model. Introduction The direct laer depoition (DLD) proce i an extenion of the laer cladding proce for rapid prototyping of fully dene metal component. It offer the ability to make a metal component directly from CAD drawing. It involve the upply of metallic powder into a laer-heated pot where the powder i melted and form a melt puddle which quickly olidifie into a bead a hown in igure 1. The thermal behavior of the melt pool in which powder i injected i critical for part quality. Thi paper ue imulation and experiment to invetigate the effect of the proce parameter: laer power, powder ma flow, and canning peed on the melt pool thermal behavior. During the laer depoition proce, everal defect, uch a poroity and crack, hould be paid attention to. Crack initiate corroion fracture and reduce fatigue trength of the depoited part. Crack are caued by the reidual tree created by the high thermal gradient built up during the cooling tage. Reidual tree can be reduced by a reduction of the cooling rate. Thi can be achieved by preheating the ubtrate. Moreover, the preheating caue a better aborption of the laer beam and further it i poible to melt more powder in the larger melting pool and enhance the bonding. Uually the preheating i performed in uch a manner that a very mall melting of the ubtrate material occur without powder injection. Thermal analyi of the laer depoition proce i very important for optimization of the proce. If the ubtrate urface temperature remain too low, wetted depoit material i limited. In that cae, Laer Depoition Nozzle Subtrate Powder eeder Powder delivery tube Melt pool ig 1 Laer-powder interaction at melt pool in a direct laer depoition (DLD) proce. 212
irregularly haped track with a lot of crack, poroity and a poor bonding, are produced. However, if an extremely high temperature of the ubtrate urface i reached, evere melting of the ubtrate occur. The high degree of dilution can deteriorate the clad propertie. A comprehenive numerical model ha been developed that allow the prediction of temperature ditribution and melt pool dynamic. Thi model imulate the coaxial laer depoition proce with powder injection, and conider mot of the aociated phenomena, uch a melting, olidification, evaporation, evolution of the free urface, and powder injection. Input parameter for thi model are laer machining parameter and propertie of the laer beam, a well a material propertie and laer beam aborption. To get more accurate prediction, a finer grid need to be ued. Thi, together with the iterative nature of the numerical algorithm, caue the model computationally not to be very efficient. In thi paper an analytical model i applied to the preheating proce (without powder injection) to increae the computational efficiency, while the actual depoition proce with powder injection till ue the numerical model. The output, and the temperature ditribution of the ubtrate, are ued a the initial condition of the numerical model. In thi tudy, a coaxial diode laer depoition ytem, LAMP (developed at UMR), i conidered for imulation and experiment. The blown powder method i ued to deliver powder. A the primary laer in the LAMP ytem, the diode laer i ued. Material of both powder and ubtrate i Ti-6Al-4V, which i widely ued in the aeropace indutry. Melt Pool Governing Equation igure 2 how a chematic diagram of the calculation domain, including the ubtrate, melt pool, remelted zone, depoited layer and part of the ga region. In the laer depoition proce, melting and olidification caue the phae tranformation at the olid/liquid interface. A muhy zone containing olid and liquid i formed. In thi tudy the continuum model [Bennon87a, Bennon87b] i adopted to derive the governing equation. Depoited layer Remelted zone Shielding ga melt pool Subtrate Laer beam Powder ig. 2. Schematic of the calculation domain. The aumption for the ytem of governing equation include: (1) the fluid flow in the melt pool i a Newtonian, incompreible, laminar flow; (2) the olid and liquid phae in the muhy zone are in local thermal equilibrium; (3) the olid phae i rigid; and (4) iotropic permeability exit. or the ytem of interet, the conervation equation for ma, momentum and energy are ummarized a follow: 213
Continuity ρ v + ( ρv ) = 0 t (1) Momentum Energy v v v ρ v μl ρ v v v ( ρ V ) + ( ρvv ) = ( μl V ) p ( V V ) + ρg + S (2) t ρ K ρ l l ( ρh) v v v + ( ρvh) = ( k T) ( ρ( hl h)( V V) t (3) In equation (1)-(3), the continuum denity, pecific heat, thermal conductivity, vector velocity, and enthalpy are defined a follow: ρ ρ ρ = g + gl l c fc fc l l v v v V = f V + f V l l = + k = gk + glkl The liquid fraction temperature relationhip i given by: h= fh + flh (4) l 0 if T < T T T gl = if T T Tl Tl T 1 if T > Tl (5) The other volume and ma fraction can be obtained by: f l g ρ ρ l l = f g ρ = g + gl = 1 f = 1 fl (6) ρ The phae enthalpy for the olid and the liquid can be expreed a: h = T 0 c ( T) dt T h= c( TdT ) + ctdt ( ) + L l 0 T l m T (7) where L m i the latent heat of melting. Permeability, K, i aumed to vary with liquid volume fraction according to the Carman - Kozeny equation [Carman37] derived from Darcy law: 214
3 K gl = C (1 g ) l 2 (8) where the parameter C i a contant depending on the morphology and ize of the dendrite in the muhy zone. The S i a ource term that i defined below. Solid/liquid interface The olid/liquid interface i implicitly tracked by the continuum model [Bennon87a, Bennon87a]. In the olid phae region and liquid phae region, the third term on the right-hand v v ide of Eq. (2) vanihe. Thi i becaue in the olid phae region V = V = 0 and in liquid phae region K ince g l = 1. So thi term i only valid in the muhy zone. ree urface The liquid/vapor interface, or the free urface of the melt pool, i very complex due to urface tenion, thermocapillary force, and impaction of the powder injection. In thi tudy, the Volume- Of-luid (VO) method [Hirt81] i employed to track the evolution of the moving free urface of the melt pool. The melt pool configuration i defined in term of a volume of fluid function, (x,y,t), which repreent the volume of fluid per unit volume and atifie the conervation equation: t + ( V ) = 0 (9) Source term The ource term, S, in the momentum equation i contributed by the interface force acting on the free urface, uch a urface tenion, etc. In thi tudy, the continuum urface force (CS) model [Brackbill92] i ued to reformulate the urface force. In it tandard form, urface tenion i formulated a [Brackbill92]: r ( x v ) = nˆ γκ + Sγ r where ( x v ) i the net urface force at a point x v on a interface S. ˆn i a unit normal to S at the point x v, which i given by: n r nˆ = r (11) n where n v i the urface normal vector and can be computed from the gradient of the VO function: v n = (12) i the gradient along a direction tangential to the interface, which i defined a: S (10) 215
ˆ( ˆ S = N = n n ) (13) γ and κ repreent urface tenion coefficient and curvature, repectively. κ i given in [ Prakah89]: 1 n v v κ = ( nˆ ) = v ( v ) n ( n) n n (14) By uing the CS model, the urface force r i reformulated into a volume force r b a follow: r b r = S r n r = S (15) where i the averaged value acro the free urface. Thu, the ource term S in equation (2) i formulated a: v S = ( nγκ + Sγ ) (16) Boundary Condition The boundary condition at the free urface atify the following equation: T η( Plaer Patten) 4 4 k = h ( ) ( ) 2 c T T εσ T T m& el (17) v n π R where term on the right-hand ide are laer irradiation, convective heat lo, radiation heat lo and evaporation heat lo, repectively. P laer i the power of laer beam, P atten the power attenuated by the powder cloud, R i the laer beam radiu, η the laer aborption coefficient. P atten i calculated according to renk et al. model [renk97] with a minor modification: P atten 3Qextml & = Plaer 1 exp πρr D v p jet p (18) where m& denote the powder ma flow rate, l i the tand-off ditance from the nozzle exit to the ubtrate, ρ i powder denity, r p i the radiu of the powder particle, D jet i the diameter of the powder jet, v p i the powder injection velocity, and Q ext i the extinction coefficient. It i aumed that the extinction cro ection i cloe to the actual geometrical cro ection, and Q ext take a value of unity. In the evaporation term, m& i the evaporation ma flux and L v i the e 216
latent heat of evaporation. According to Choi et al. overall evaporation model [Choi87], m& e i of the form: 18836 log m& e = A+ 6.1210 0.5logT (19) T where A i a contant dependent on the material. The boundary condition at the bottom, left and right wall atify the following equation: T k = h ( ) c T T n (20) u = 0 v = 0 (21) Powder injection Powder particle that inject onto the top urface can be claified into three categorie. 1) Thoe powder particle that have not been melted during their paage and hit the olid part of the ubtrate will deflect and loe; 2) Thoe powder particle that have been melted before they arrive on the ubtrate and impact the olid part of the ubtrate will tick to the urface of the ubtrate; and 3) Thoe powder particle that fall into the melt pool including melted and unmelted will merge and mix with the molten liquid in the melt pool [Han04]. In thi tudy, the powder particle belonging to the lat two cae were modeled. Numerical imulation Simulation i performed baed on the capability of the experimental facilitie to compare the imulation reult with the experimental meaurement. A continuou wave diode laer with an 808 nm wavelength i conidered a the energy ource. The laer intenity ditribution i uniform. or ubtrate, Ti-6Al-V4 plate with a thickne of 0.25 inch are elected. Ti-6Al-V4 powder particle with a diameter from 40 to 140 μm are ued a depoit material. The laer aborption coefficient i meaured by Spark et al. [Spark06]. The material propertie and the main proce parameter are hown in Table 1. igure 3 how typical imulation reult for normal depoition and lack of fuion. ig. 3. Typical reult (a) Temperature for imulation field of normal depoition (b) Velocity (left) and field lack of fuion (right). 217
Experimental Study The experiment were performed on the LAMP ytem which conit of a diode laer, powder delivery unit, 5-axi CNC machine, and monitoring ubytem. The laer ytem ued in the tudy wa Nuvonyx (Nuvonyx Inc.) ISL-1000M Laer Diode Sytem which combine tate-ofthe-art micro-optic with laer diode to produce the only ingle wavelength fiber coupled direct diode laer at power level up to 1000 watt CW. The laer emit at 808 nm and operate in the continuou wave (CW) mode. The ubtrate have dimenion of 2.5 2.5 0.4 in. The Ti-6Al-4V ample were irradiated uing a laer beam with a beam pot diameter of 2.5 mm. Table 1. Material propertie for Ti-6Al-4V and main proce parameter Nonmenclature Symbol Value (unit) Melting temperature T m 1900.0K Liquidu temperature T l 1923.0K Solidu temperature T 1877.0K Evaporation temperature T v 3533.0K Solid pecific heat at contant c p 483.04 + 0.215T T 1268K preure [Kelly04] 412.7 + 0.1801T 1268 < T 1923 J / kg K Liquid pecific heat at contant preure [Mill02] Thermal conductivity [ Kelly04] c pl 831.0 J/kg K k 1.2595 + 0.0157T T 1268K 3.5127 + 0.0127T 1268 < T 1923 W / m K -12.752 + 0.024T T > 1923 Solid denity [Mill0] ρ 4420 0.154 (T 298 K) Liquid denity [Mill0] ρ l 3920 0.68 (T 1923 K) Latent heat of fuion [Mill0] L m 2.86 10 5 J/kg Latent heat of evaporation L v 9.83 10 6 J/kg Dynamic vicoity μ 3.25 10-3 N/m (1923K) 3.03 10-3 (1973K) 2.66 10-3 (2073K) 2.36 10-3 (2173K) Radiation emiivity [Lip 05] ε 0.1536 + 1.8377 10-4 (T - 300.0 K) Laer aborption coefficient [ Spark04] Powder particle diameter D p 40-140 μm Shielding ga preure P g 5 pi Ambient temperature T 300K Convective coefficient h c 10 W/m 2 K η 0.4 In order to validate the model prediction, ingle path depoition experiment are conducted. The comparion between model prediction and experimental reult are conducted in term of melt pool peak temperature. The melt pool peak temperature i calibrated through the dualwavelength non-contact temperature enor, which can effectively decreae the diturbance from the powder and other dut. Comparion and dicuion ig. 4 and ig. 5 how the comparion between experimental meaurement and model prediction. ig. 4 how the effect of laer power on melt pool peak temperature. It can be een that an increae in the laer power will increae the melt pool temperature. Thi i eay to 218
undertand. A the laer power increae, more power i available for melting the ubtrate. ig. 5 how the effect of laer canning peed on the melt pool peak temperature. An increae in the laer canning peed will decreae the melt pool peak temperature. Thi i becaue, a canning peed decreae, the laer material interaction time i extended. rom ig. 4-5, one can ee that the general trend between experimental meaurement and model prediction i conitent. At a different power intenity level, there i a different error from 10 K (about 0.5%) to 121K (about 5%). It can be een that at a higher power intenity level, there i a bigger error between meaurement and prediction. Thi i becaue the numerical model i two-dimenional. It doe not conider the heat and ma tranfer in the third direction. At a higher power intenity level, heat and ma tranfer in the third dimenion are more ignificant. The error between experimental meaurement and model prediction are analyzed to mainly come from the following apect: (1) The two-dimenional nature of the numerical model; (2) The thermo-phyical propertie taken for the analytical model; (3) The uncertaintie of the material propertie and the appropriatene of the ub-model for the numerical model; (4) Boundary condition. Adiabatic boundary condition are aumed in the analytical model and the numerical model for the bottom urface and ide urface. Meaurement alo have been taken to achieve uch boundary condition in experiment. But it i hard to get abolute adiabatic boundary condition. 2600 Melt Pool Peak Temperature, K 2500 2400 2300 2200 2100 2000 Experimental reult Model prediction 1900 400 500 600 700 800 900 Laer Power, W ig. 4 Comparion between experimental meaurement and model prediction at a contant powder ma flow rate of 5g/min and a contant laer canning peed of 20 inch/min. (or actual depoition) 219
Melt Pool Peak Temperature, K 2500 2450 2400 2350 2300 2250 2200 2150 2100 Experimental reult Model prediction 2050 0 10 20 30 40 Laer Scanning Speed, inch/min. ig. 5 Comparion between experimental meaurement and model prediction at a contant powder ma flow rate of 5g/min and a contant laer power of 700 W. (or actual depoition) The imulation model wa alo ued to predict the lack of fuion to depoit Ti64. Twenty-eight Ti64 ample were built to validate the imulation model. The idea wa to ue the imulation model to predict the lack of fuion, and the correponding laer power i ued a nominal power. The depoition are then baed on Nominal, Nominal +- 10%, Nominal +- 20%, and Nominal +- 30%. The nominal i about 600 W for the direct diode laer. The nominal power i then et at 600W with a travel peed (canning peed) at 10ipm and powder flow rate ~ 5g/min. The experiment wa performed at -30% (420W), -20% (480W), -10% (540W), nominal (600W), 10%(660W), 20%(720W), 30% (780W). If the predicted model for lack of fuion i accurate, about 50% of the part will be oberved a lack of fuion. Seven ample of thick wall are hown in igure 6. It can be oberved that mot ample with lower power than the nominal howed obviou poroitie on the ample urface. (a) Sample produced at -30% laer power (b) Sample produced at -20% laer power 220
(c) Sample produced at -10% laer power (d) Sample produced at nominal laer power (e) Sample produced at +10% laer power (f) Sample produced at +20% laer power (g) Sample produced at +30% laer power ig 6. A thick wall Ti64 part produced at variou laer power (Nominal, Nominal +- 10%, Nominal +- 20%, and Nominal +- 30%) in the UMR LAMP lab. Lack of fuion can be oberved from ome urface of the ample with lower power. Concluion The thermal behavior of melt pool i the mot critical phenomenon in laer depoition. An analytical model for thermal analyi of temperature rie due to a moving heat ource i combined into a comprehenive heat tranfer and fluid flow numerical model for the laer depoition proce. The analytical model i ued for the preheating proce before the actual 221
laer depoition with powder injection. And the numerical model i ued for the actual laer depoition proce. Thu the output of the analytical model are ued a the input of the numerical model. Experiment have been conducted to validate the model prediction. A conitent general trend i found between experimental meaurement and the model prediction. The ource of the error have alo been analyzed. Acknowledgement Thi reearch wa upported by the National Science oundation Grant Number DMI-9871185, the grant from the U.S. Air orce Reearch Laboratory contract # A8650-04-C-5704, and UMR Intelligent Sytem Center. Their upport i greatly appreciated. Reference Bennon, W.D.,.P. Incropera, A continuum model for momentum, heat and pecie tranport in binary olid-liquid phae change ytem-i. Model formulation, International Journal of Heat and Ma Tranfer 30 (1987a) 2161-2170. Bennon, W.D.,.P. Incropera, A continuum model for momentum, heat and pecie tranport in binary olid-liquid phae-change ytem--ii. Application to olidification in a rectangular cavity, International Journal of Heat and Ma Tranfer 30 (1987b) 2171-2187. Brackbill, J. U., D. B. Kothe, C. Zemach, A continuum method for modeling urface tenion, Journal of Computational Phyic 100 (1992) 335-354. Carman, P.C., luid flow through granular bed, Tran. Intitution Chem. Engr. 15 (1937) 150-166. Choi, M., R. Greif, M. Salcudean, A tudy of the heat tranfer during arc welding with application to pure metal or alloy and low or high boiling temperature material, Numerical Heat Tranfer 11 (1987) 477-491. renk, A., M. Vandyouefi, J. Wagniere, A. Zryd, W. Kurz, Analyi of the laer-cladding proce for tellite on teel, Metallurgical and Material Tranaction B (USA) 28B (1997) 501-508. Han, L.,.W. Liou, K.M. Phatk, Modeling of laer cladding with powder injection, Metallurgical and Material Tranaction B 35B (2004) 1139-1150. Hirt, C.W., B.D. Nichol, Volume of fluid (VO) method for the dynamic of free boundarie, Journal of Computational Phyic 39 (1981) 201-225. 222
Kelly, S.M., Thermal and microtructure modeling of metal depoition procee with application to Ti-6Al-4V, Ph.D. thei, Virginia Polytechnic Intitute and State Univerity, 2004. Mill, K. C., Recommended value of thermophyical propertie for elected commercial alloy, Woodhead, Cambridge, 2002. Lip, Tobia, Bent ritche, A comparion of commonly ued re-entry analyi tool, Acta Atronautica 57 (2005) 312-323. Prakah, C., V. Voller, On the numerical olution of continuum mixture model equation decribing binary olid-liquid phae change, Numerical Heat Tranfer 15B (1989) 171-89. Spark, Todd E., Zhiqiang an, Meaurement of laer aborption coefficient of everal alloy for diode laer, unpublihed report, 2006. 223