Theoretical Analysis of the Coincident Wire-Powder Laser Deposition Process

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1 Andrew J. Pinkerton Waheed Ul Haq Syed Lin Li Laser Processing Research Centre, School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Sackville Street Building, P.O. Box 88, Manchester M60 1QD, UK Theoretical Analysis of the Coincident Wire-Powder Laser Deposition Process The process of coincident wire and powder deposition by laser has recently emerged in research work as a layered manufacturing method with a higher deposition rate than the established laser direct metal deposition technique and as a means of creating functionally graded metallic surface layers in a single pass. This work analytically models the process by accounting for the incoming wire and powder as virtual negative heat sources. The major assumptions of the model are confirmed experimentally and the predicted temperature profiles compared with values measured using contact and pyrometric methods. Model accuracy outside the molten zone is excellent, but this solution does not account for latent heat and intrapool circulation effects so it gives only moderate precision when extrapolated to within the melt pool. Increasing the mass feed rate to the melt pool reduces its depth and the temperature surrounding it these effects can be quantified in three dimensions by the model. DOI: / Keywords: laser deposition, powder, wire, model, melt pool 1 Introduction This paper considers the process of coincident wire and powder deposition by laser WPDL. A moving diode laser beam is used to create a melt pool on a steel surface and wire is fed into it and simultaneously powder blown into it on an inert gas stream. Details of the process were first published in by Syed et al. in who showed it to give deposition rates approximately 87% higher than those of either the powder or wire fed process alone 1. It has since been shown to facilitate some novel material processing applications. Wang et al. 4 used WPDL to produce compositionally graded Ti alloys with a CO 2 laser and Syed et al. 5 demonstrated use of the technique to produce a graded steel nickel copper structure in a single step for application to die and mold linings. These studies have been experimental in nature. WPDL can be considered as a combination of two more developed laser processes, laser direct metal deposition LDMD and laser wire cladding LWC. In LDMD a laser Nd:YAG, CO 2, diode, or fibre is used to create a moving melt pool on the surface of the build surface substrate and powder is carried into it on an inert gas stream. As the melt pool moves on, the enlarged pool solidifies, leaving a raised track on the surface of the original substrate. Complex three-dimensional parts may be created by deposition of multiple tracks, adopting previous tracks as the substrate. A large number of exogenous process and environmental variables have been shown to affect LDMD track dimensions and final part characteristics. Literature shows that for LDMD to be successful the specific energy beam power at the melt pool/ traverse speed beam diameter must be within a defined range; too high a value results in excessive dilution and a melt pool size that limits resolution; too low a value results in poor intertrack bonding and porosity 6. A wide range of models exist to describe the process and components of it. Steen et al. 7 used a mass-energy balance method and similar methods were later used to distinguish between mass and energy limited operating regions in LDMD 8 and to quantify the heat flows within the Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received June 23, 2006; final manuscript received April 9, Review conducted by Bin Wei. process 9,10. Calculation of the quasi-stationary temperature fields around a moving laser source have been the basis of alternative approaches 11,12 this method allows approximation of the pool limits from the melt isotherms. Finite volume 13 and finite difference 14 methods have also been widely used. Advances in computing power mean that they now allow transient conditions, melt pool flow, and other factors affecting the melt pool free surface such as recoil pressure to be accounted for 13. A 1976 patent 15 teaches the use of direct wire feed under a scanning laser to give laser wire cladding. Studies comparing the method to LDMD 16,17 have highlighted the higher material efficiency achievable theoretically up to 100%, although energy efficiency is less and overall deposition rate was not found to increase markedly 16,18. Previous studies of the wire feed process indicate that many of the relationships between process parameters, such as laser power and traverse speed, and final track properties are the same as for the powder-feed process 17. The main disadvantage is the high sensitivity of the LWC process to the orientation of the wire and its alignment to the melt pool. Pool agitation, track perturbations, ripples or serrations, and laser reflections from the wire are potential problems. It is clear from previous work that the LDMD, LWC, and WPDL processes are all required to operate within process envelopes determined by multiple exogenous process variables in order to produce good quality final parts. This work aims to establish and verify an easily applied analytical model to enable the effect of a laser heat flux and mass fluxes to be considered together in order to determine the temperature fields produced by the WPDL process. This advances understanding of the WPDL process and allows the maximum mass feed rates for a given set of process conditions to be set and also provides a modeling method applicable to the other metal deposition processes. 2 Analytical Process Model 2.1 Model Formulation and Assumptions. The model is formulated in terms of energy and mass flow into and out of the deposition melt pool, which is assumed to be in a quasi-stationary state. The process is shown schematically in Fig. 1. The initial assumptions made in formulating the model and their justifications are as follows: 1. The laser beam has a pseudo-rectangular profile and its in- Journal of Manufacturing Science and Engineering DECEMBER 2007, Vol. 129 / 1019 Copyright 2007 by ASME

2 it and hence require energy to increase their enthalpy to that of the melt pool. This occurs in a short period of time so that the enthalpy can be considered to be taken from a local area of the pool; and 7. The substrate is modeled as a semi-infinite domain x, y,z 0. The substrate block used is large relative to the track; additionally, during the experiment it is placed flat on another conductive metal surface. The term the substrate is from this point forward used to mean the portion of this domain outside the melt pool where material is in the solid phase. Fig. 1 Coincident wire and powder deposition by laser schematic : a side view x-z plane ; b plan view tensity, I x,y, can initially be described by Eq. 1 19, where r is the radius of the component Gaussian beams. It is an approximately parallel beam. This is a reasonable simplification given a long focal length of the objective lens I x,y = Q 4d L d w Erf 2x d L 2 3/2 r Erf 2x + d L 2 3/2 r Erf 2y d w 2 3/2 r Erf 2y + d w 2 3/2 r 1 2. Interaction between the laser and either powder or wire entering the pool is insignificant, meaning attenuation of the laser power, redistribution of the laser power, and heating of the powder and wire can be discounted. This assumption will be tested at the verification stage of this paper; 3. Absorption of the beam on the solid material and on the surface of the melt pool is a constant value. Absorption does not vary with incidence angle for diode laser radiation 20 and it is also only slightly affected by temperature above 400 C 21. Work 20,22 has shown that process parameters such as traverse speed affect absorption by the solid material during transformation hardening, attributed to the formation of oxide films at higher temperatures 23, but this effect is likely to be less significant in WPDL because most of the beam is incident on the molten pool; 4. The powder has a Gaussian concentration distribution about the nozzle axis. It is fully coupled with the conveyance gas and its trajectory is unaffected by gravity. This is reasonable given its short traverse distance and high initial speed. The assumption of distribution will also be tested at the verification stage. The gas from the nozzle is assumed to remain within the stream, meaning speed drops as it expands. This is in accordance with previous measurements on nozzles of this types under similar conditions 24 ; 5. All materials, powder, wire, substrate, and previous tracks, are initially at ambient temperature; 6. Wire and powder that strike the melt pool are assimilated to Based on assumption 6, the incoming wire and powder are treated in the analysis of the energy balance as negative heat fluxes. They are effectively taking heat from the melt pool surface at the point that they enter it. As shown in Fig. 1, the intersection of the center of the laser beam and the substrate surface is designated as the origin. The axes of the powder nozzle and wire feeder intersect the substrate at the rear edge of the laser beam at point d L /2,0,0. According to classic moving distributed heat source theory 25 this is the hottest position on the surface and thus can be taken as approximating the center of the melt pool. Neglecting mass addition effects and phase change, the quasi-stationary temperature increases in the substrate as a result of the laser beam alone, and T L, is given by the sum of that due to the individual Gaussian sources comprising the beam superposition. Hence, after Pinkerton and Li 26,27 d Q L /2 r d w /2 r exp H T L x,y,z = 2 3 1/2 kd L d w 1+ r d 2 L /2 +r where d dy * dx * H = 2 X + V 2 + Y X = x x * /r Y = y y * /r Z = z/r V = rv/ d w /2 +r 0 + Z2 2 2 = 2 t/r The heat flux in the substrate, Q w, due to the wire is given by Q w = T m T 0 cv w 4 This acts over an area of r 2 w the cross-sectional area of the wire but because of the small diameter of the wire used with this process it can be approximated as acting at a single point. The contribution of the wire to the quasi-stationary temperature increase in the substrate, T w, is then given by 25 where T w x,y,z = T m T 0 r 2 w v w e v x+d L /2+R /2 4 R R = x + dl /2 2 + y 2 + z 2 It should be noted in the above calculations that reference is to the substrate outside the melt pool, where the initial latent heat of melting of the wire when it enters the melt pool will have been balanced by the latent heat of solidification in the lower part of the pool. While these do not occur at exactly the same point, the shallow depth of a typical deposition melt pool allows the distance to be taken as insignificant and the virtual fluxes due to the phase / Vol. 129, DECEMBER 2007 Transactions of the ASME

3 changes to be taken to cancel out. In order to define the powder system a local coordinate system x,y,z coaxial with the powder nozzle is defined in a manner similar to Diniz Neto and Vilar 28 see Fig. 1. The origins of the two systems both lie on the substrate surface but are offset by a distance of d L /2 so conversion from one coordinate system to the other is achieved via Eq. 6 y = y x = x sin + z cos d L /2 z = x cos + z sin x = x sin z cos + d L sin /2 z = x cos + z sin + d L cos /2 6 The diameter, d p, of the powder stream at any position above the substrate z 0, expressed in terms of the divergence half angle,, nozzle standoff distance, l p, and nozzle diameter, d po, is given by d p =2 z + l p tan + d po 7 The mass fraction in the powder stream, p x,y,z, is given by p x,y,z = m p Exp 4 x 2 + y 2 2 Q g d p 8 Making the substitutions and using the global coordinate system to facilitate the calculation of laser-powder interaction this can also be expressed as p x,y,z = m p Q g Exp 2 4 x sin z cos + d L sin /2 /2 2 + y 2 2 x cos + z sin + d L cos /2 + l p tan + d po 9 As powder is coupled with the conveyance gas and the gas remains within the stream assumption 4, the equation of continuity can be applied. The velocity of powder particles, v p, at any position in the stream is then given by v p = 4Q g 2 10 d p equivalent to 4Q g v p = 2 x cos + z sin + d L cos /2 + l p tan + d po 2 11 The virtual heat flux density, Q, p at a position on the substrate x *,y *,0 due to powder being assimilated into the surface can then be given by Q x * p,y * = T m T 0 p x *,y * cv p 12 The effect of this heat flux on the temperature at any point x,y,z in the substrate is 25 T p * x,y,z = Q x* p,y * x * y * e v x x* +R / kr where R = x x * 2 + y y * 2 + z 2 valid for z 0. As for the wire, the latent heats of melting and solidification have been assumed to cancel each other out. Integrating over the area of assimilation will allow the contribution of the powder to the quasi-stationary temperature increase in the substrate, T p, to be determined. This is the area of the melt pool, but as the exact extent of this is not known it can be approximated to an area equal to that of the laser beam. Hence, as the melt pool is centered at point d L /2,0,0 0 d w /2 Qp x *,y * T p x,y,z 4 kr = d L d e v x x * +R /2 dx * dy * w /2 14 Having calculated the effects of the laser wire and powder individually, by the principle of superposition, the three-dimensional temperature distribution in the substrate z 0, T, is given by T = T 0 + T L + T w + T p 15 It is possible after first determining the surface temperature profile in this way to establish the extent of the melt pool from the region on the surface z=0 above the liquidus temperature, recalculate the virtual flux due to powder assimilation over this area, and continue in this iterative manner until a consistent melt pool size is reached. However at specific energies within the normal operating envelope of the system the initial laser spot size usually serves as a good enough approximation, especially given the Gaussian concentration distribution of the powder stream. 3 Verification 3.1 Attenuation. It was initially assumed that attenuation is insignificant. This was tested by running the experiment as shown in Fig. 1 with 316L stainless steel powder and wire feeds in place but with the substrate replaced with a sacrificial diode lens cover for effectively 100% transmissivity to 808 nm and 940 nm radiation and a Synrad Power Wizard power meter mounted vertically directly below the cover. The amount of power transmitted through the cover in the substrate position was measured at a base laser power of 78 W, which is below that required to produce any phase change in the powder. Powder flow rates were varied between 0 g/s and 0.75 g/s. The results are shown in normalized form in Fig. 2. It can be seen that, as expected, attenuation does increase with powder delivery rate. However, losses at 0.3 g/s powder flow rate were only 4% of the total. All work covered in this paper was conducted at powder flows at or below 0.32 g/s flow rate so this small loss justifies assumption Powder Concentration Distribution. It was initially assumed that the powder has a Gaussian concentration distribution about the nozzle axis. This was tested by a nonintrusive method, based on the fact that the volume fraction of particles at a position in the powder stream is proportional to the intensity of light scattered by it derived from Mie theory 29. The experimental arrangement used is shown schematically in Fig. 3. The same nozzle as in the deposition experiment internal diameter 3 mm was held vertical and images of the powder stream using powder flows of between 0.11 g/ s and 0.34 g/ s and gas flows of between 2 L/ min and 5.5 L/ min were taken. A Canon EOS350D digital camera set to maximum resolution was used. Images were taken against a black background and light was provided by two MICROTEC Journal of Manufacturing Science and Engineering DECEMBER 2007, Vol. 129 / 1021

4 Fig. 3 Apparatus used to test powder flow Fig. 2 Power attenuation by the powder stream fiber optic lamps, positioned at a distance of 20 cm from the powder delivery nozzle and at angles of 60 deg to the left and right of the camera. Images were analyzed using the VISILOG software package and gray level data along selected radial measurement lines were exported in tabular form to Microsoft EXCEL spreadsheet software, where it was normalized and graphed. The results for a powder flow rate of 0.11 g/s are presented in Fig. 4. A Gaussian distribution can be seen at all positions. As expected, the radius of the stream radial distance at powder concentration max concentration/e 2 increases with the distance from the nozzle. For these parameters, the divergence half angle can be identified as 11 deg. These tests verify assumption of Gaussian powder distribution and additionally provide input data regarding powder stream divergence for later calculations. 3.3 Substrate Thermal Profiles. To verify that the model correctly predicts temperature distributions within the substrate, the experimental configuration shown in Fig. 5 was used. Power was supplied by a Laserline kw diode laser deliv- Fig. 4 Powder flow and distribution 0.11 g/s, 3 L/min 1022 / Vol. 129, DECEMBER 2007 Transactions of the ASME

5 Fig. 5 Apparatus used to test substrate temperature distribution ering a pseudo-rectangular beam consisting of approximately equal amounts of 808 nm and 940 nm radiation. The substrate surface was positioned 280 mm below an objective lens with a focal length of 300 mm, giving a spot size of 3.5 mm x 2.5 mm y. The substrate was EN43A AISI 1050 mild steel blocks of nominal size mm. The upper and lower surfaces were milled flat, grit blasted, and degreased. Two glassinsulated K-type thermocouples were fixed to the base of the block on a centerline under the intended deposition path on the upper surface. The block was then clamped to another block mounted on a manual vertical adjustment stage and then a Unimatic two-axis motorized table with AMC controller. Straight tracks of length 40 mm was deposited on the upper surface of the block using the WPDL method. 316L stainless steel powder was conveyed from a dual-hopper SIMATIC OP3 disk powder feeder using argon and 316L stainless-steel wire was fed from a modified arc wire feed unit. During deposition the thermal cycle on the base of the block was recorded using PICOLOG RECORDER software Pico Technology Ltd. and later exported to Microsoft EXCEL. The measured and modeled centerline temperatures on the bottom surface of the block 5 mm below the free surface are shown in Fig. 6 for WPDL conditions of high process mass feed 25 mm/s wire and 0.32 g/s powder and low mass feed 8.33 mm/s wire and g/s powder and for the two limiting cases of powder only 1.23 g/s and wire only g/s deposition. The full system and process parameters used for this experiment are shown in Table 1. The value of absorptivity,, used is based on separate experiments conducted at The University of Manchester in which the temperatures 5 mm beneath a moving laser melt pool with very low powder flow and no wire addition were measured and than matched to the theoretical values using the Rosenthal moving point solution such that where = 4 krt actual Q incident e v +R /2 16 R = x 2 + y 2 + z 2 valid for z 0. As can be seen, the model accurately predicts the temperatures surrounding the melt pool in the three cases where there is powder addition Figs. 6 a 6 c. In the case where only wire is added Fig. 6 d the difference between the modeled due to laser temperatures and measured values is up to 120 C and although the correction due to the wire addition brings the modeled results Fig. 6 Centerline temperatures 5 mm below the exposed surface: a powder mass flow rate g/s, wire mass feed rate g/s; b powder mass flow rate g/s, wire mass feed rate g/s; c powder mass flow rate 1.23 g/s; and d wire mass feed rate g/s Journal of Manufacturing Science and Engineering DECEMBER 2007, Vol. 129 / 1023

6 Table 1 Experimental and system parameters used for model verification tests Property Value for verification a 1,2 Laser power W 1500 Diode laser beam length x axis m Diode laser beam width y axis m Component beam radius m Absorptivity 0.35 Thermal conductivity Wm 1 K 1 b 21.5 Specific heat capacity Jkg 1 K 1 b 500 Density kg m Thermal conductivity Wm 1 K Thermal diffusivity m 2 s 1 b Ambient temperature K 287 Deposition material melting temperature K 1713 Beam traverse speed ms Wire radius m Angle of wire feeder to substrate, deg 45 Angle of powdernozzle to substrate, deg 45 Powder stream divergence half angle deg 11 Nozzle standoff distance m Nozzle diameter m Powder mass flow rate gs Wire mass feed rate gs Conveyance gas flow rate m 3 s a Values based on 316L stainless steel. b Value taken at 500 C closer to the actual values, the model still overestimates the temperatures that occurred. The reasons for this are considered in Sec. 4. Figure 7 compares the modeled effects of the mass addition on the temperature of the lower block surface for the cases with simultaneous wire and powder addition in the same experiment. The powder and wire both serve to reduce the temperature but, as expected, the temperature reduction is greater at higher mass flow rates. At the parameters tested, the effect of the deposited wire was more significant than that of the powder in reducing temperatures 5 mm below the surface. 3.4 Upper Surface Thermal Profiles. Images of the melt pool during deposition of the central part of deposition tracks were taken using an Agema ThermaCAM 550 thermal camera positioned at approximately 60 deg to the substrate. The camera monitored radiation levels in the m wavelength band and temperatures up to 2000 C. On the basis of previous work, emissivity was set on a selective area basis at 0.5 for solid material and 0.15 for molten material; the strong reflectivity in deposition melt pools is a problem that has also been recognized by other researchers 30 as it tends to obscure detail within the pool. Thermal images were exported to a microcomputer where they were analyzed using the proprietary IRWIN RESEARCH software package and Microsoft EXCEL. Figure 8 shows a thermal image of the upper surface of the melt pool for the conditions of low process mass feed 8.33 mm/s wire, equivalent to g/s, and g/s powder. Other system and process parameters were as in Table 1. The position of the laser beam and the boundaries of the melt pool can be clearly distinguished. A temperature profile was taken along the x axis, as shown, and is compared with the modeled results for this set of parameters in Fig. 9. Both the modeled and measured temperature profiles in Fig. 9 show a distinctive sharp initial rise in temperature. The measured value lags slightly behind the modeled value, attributable to the thermal arrest at the melting point due to the latent heat required. The limit of the thermal monitoring equipment is quickly reached, but from the rate of increase it is highly likely that peak temperatures in excess of the recorded values of 2000 C were reached. This is similar to the LDMD process where Fig. 7 The effect of mass addition on temperature 5 mm below the exposed surface modeled Fig. 8 A thermal image of the upper surface of the melt pool 8.33 mm/ s wire, equivalent to g/ s, and g/ s powder mass feed rates 1024 / Vol. 129, DECEMBER 2007 Transactions of the ASME

7 Fig. 9 Measured and modeled centerline temperatures on the exposed surface strong superheat under the laser beam has also been noted 30. The extent of this superheat region appears to be shorter than the length of the laser beam, possibly due to the cooling effect of the incoming wire towards the rear of the beam. The model captures the general form of an initial high-temperature region followed by a sharp drop and then a secondary lower temperature region. The temperatures are generally much more even and less subject to variation within the melt pool than modeled. According to Fig. 9, the temperature drops to an approximately constant value of 1500 C for the area of the melt pool to the rear of and behind the laser beam. This indicates only slight superheat in the majority of the melt pool. Taking values over the melting point of the deposition material gives modeled and measured melt pool lengths of 3.9 mm and 4.3 mm, respectively. At the rear of the melt pool the measured thermal gradient becomes steeper. The measured temperatures are initially approximately 200 C higher than the modeled one but this difference rapidly decreases as the distance behind the melt pool increases and the temperatures converge approximately 8 mm behind the origin. In general, real time thermal images indicated that although the assumption of a quasi-stationary state was highly desirable for this modeling it must be regarded as an approximation rather than a true depiction of the process. The WPDL melt pool tended to show small, apparently random, variations in shape and temperature distribution with time. 4 Discussion and Application Comparison of modeled and measured temperatures during the deposition of 316L stainless steel verified that the model is accurate for different levels of mass feed rate in WPDL, including the limiting case of powder only deposition. The overestimation of temperatures seen when using wire alone can probably be attributed to a change in the surface absorptivity when there was no powder addition. The absorptivity value used in the model was determined from experiments using powder addition and it is known that this can have a disturbing effect on the upper melt pool surface which can enhance absorptivity. Use of wire only would therefore reduce the actual surface absorptivity below this value leading to the lower than modeled temperatures seen. The model could be corrected by using a more accurate absorptivity value. It should also be noted that because absorptivity on the surface of a deposition melt pool is governed by other multiple factors, some of which are mentioned in assumption 3 in Sec. 2.1, all such values should be considered to have some margin of error. Application of the model showed that the wire had a higher contribution to the temperature drop surrounding the melt pool than the powder Fig. 6, despite the wire mass feed rate being less than half that of the powder s. This can probably be attributed to the 100% deposition efficiency of this delivery method, although it may also have been artificially enhanced near or slightly behind the origin by the modeling method of taking the wire s thermal contribution as a point source. Thermal images also indicated only slight superheat in the melt pool outside the extent of the beam. In comparison, Griffith et al. 31 recorded a superheat of greater than 250 C in the melt pool during LDMD of 316 steel using a Laser Engineered Net Shaping LENS system at powers of below 500 W. This indicates that WPDL has the potential to add additional material while producing less of a thermally affected zone. The simultaneous addition of the wire and powder could moderate the temperature both on and below the surface to a greater extent than the powder alone could, thereby reducing the stresses subsequently induced during cooling by thermal contraction. This would reduce substrate distortion and the risk of cracking. Deposition rates would, however, have to be quite high for this effect to be significant within a part. The measured temperature profile was extremely flat within the melt pool. Naturally, this can be attributed to circulatory motion tending to normalize temperatures over the extent of the melt pool 32. The melt pool lengths indicated were on the order of 3 5 mm, which for a material with a Prandt number of approximately 0.15, would give a melt pool in which neither convective nor conductive heat transfer completely dominate 33. As the model accounts only for the conductive element, this is one reason why it is applicable only to regions outside the melt pool; latent heat effects are another. 316L stainless steel is a low sulphur stainless steel 30 ppm and as such is known to have a negative coefficient of surface tension 34. This leads to outward Marangoni flow at the surface of a laser melt pool, which tends to broaden and lengthen the pool and can in some cases give a pool bottom that is convex towards the melt 33,35. This explains the greater measured than modeled pool length in this case. The substrate surface would then cool from the limit of the melt pool, which would be at a higher temperature than it would have been without the intrapool circulation, explaining the initially higher measured than modeled temperatures behind the melt pool in Fig. 9. Despite this, the accuracy of the model beyond the limits of the melt pool is still good. Previous work by Picasso and Hoadley 36, concentrating on modeling of flow in the melt pool by a combination of enthalpy, stepwise Navier-Stokes, and interface calculations, showed the importance of thermocapilliary and powder injection forces in determining melt pool shape and extent. These may also have changed the shape of the melt pool from that predicted by this model and introduced some discrepancies between measured and modeled results. Nevertheless, the current model is considerably easier to apply than that of Picasso and Hoadley, yet still manages to capture the shape of the melt pool. It can also predict temperatures around it more realistically than analytical models based purely on single moving point or area heat fluxes e.g., Refs. 37,8 and does not require the finite element methods of, e.g., Kim and Peng 38. The strength of this model is its simplicity: it allows heat and mass fluxes to be treated in the same way to quickly evaluate the effect of mass addition on the thermal profile around the melt pool and thus the limiting effect that they have on extent. Figure 10 shows the modeled effect of increasing the mass feed rates while keeping other WPDL process parameters constant. For these simulations, system parameters such as nozzle angles are unchanged from the previous verification tests, absorbed power is 1000 W, and traverse speed is 5 mm/s. Sharp changes in temperature due to the wire and powder occur only on or near the surface, while deeper into the substrate the thermal profile is smooth even though the temperature reduction due to mass addition is evident. The profiles indicate that surface temperatures would have been sufficient for deposition with minimal dilution Journal of Manufacturing Science and Engineering DECEMBER 2007, Vol. 129 / 1025

8 sources their effects on the substrate thermal profile are then modeled using combinations of established moving heat flux solutions. Agreement with experimental results some distance below the surface is excellent. Agreement on the upper, exposed surface outside the melt pool is good but the effects of latent heat absorption or release and intrapool flow mean that the surface temperature distributions close to and within the bounds of the melt pool are not well predicted. The wire has a greater effect than the powder on the temperature of the substrate at the parameter combinations tested. This model is three dimensional and so can be used to test the effect of any of the input parameters on the final thermal cycle or temperatures at any position within the substrate and it can also be applied to the limiting cases of wire-only and powder-only deposition. The use of virtual heat sources to represent incoming mass requiring heating or phase change can be extended to other processes. Acknowledgment The authors would like to acknowledge the financial support of the UK Engineering and Physical Sciences Research Council and the National University of Sciences and Technology, Pakistan. Fig. 10 Modeled centerline temperatures showing the effect of increasing total mass feed rate: a at the upper surface; b 2.5 mm below surface; and c 5 mm below surface less than 2.5 mm melt pool depth at all calculated mass flow rates, although melt pool depth decreases with increasing mass feed rate. The model in its present form is easily applicable to the LDMD and LWC processes where lateral noncoaxial nozzles are being used. Indeed, it becomes simpler than the application demonstrated here as one of the negative heat fluxes can be removed. Future work will adapt it for coaxial powder deposition processes and consider methods for allowing for the intrapool effects. 5 Conclusions An analytical method of predicting the quasi-stationary temperature distribution in the substrate during coincident wire and powder deposition by laser has been developed. The method considers the incoming wire and powder as virtual negative heat Nomenclature x, y, z, x *, y * linear dimensions, global coordinate scale m x,y,z linear dimensions, local coordinate scale m X, Y, Z normalized linear dimensions R distance from origin to point x,y,z m Q laser power W d L diode laser beam length x axis m d w diode laser beam width y axis m r component beam radius m absorptivity k thermal conductivity Wm 1 K 1 c specific heat capacity Jkg 1 K 1 density kg m 3 k thermal conductivity Wm 1 K 1 thermal diffusity m 2 s 1 T 0 ambient temperature K T L contribution of laser to quasi-stationary temperature change K T w contribution of wire to quasi-stationary temperature change K T p contribution of powder to quasi-stationary temperature change K T m deposition material melting temperature K v beam traverse speed m s 1 V normalized beam traverse speed t time s dimensionless time r w wire radius m angles of powder nozzle to substrate deg powder stream divergence half angle deg d p powder stream diameter m l p nozzle standoff distance m d p0 nozzle diameter m m p powder mass flow rate gs 1 v p speed of powder particles in the powder stream ms 1 p powder mass fraction in the powder stream kg m 3 Q p virtual heat flux density at a position on the substrate Js 1 m 2 Q g conveyance gas flow rate m 3 s 1 Erf error function Exp exponential function 1026 / Vol. 129, DECEMBER 2007 Transactions of the ASME

9 References 1 Syed, W. U. H., Pinkerton, A. J., and Li, L., 2004, Combined Wire and Powder Feeding Laser Direct Metal Deposition for Rapid Prototyping, Proceedings 23rd International Congress on Applications of Lasers and Electrooptics (ICALEO), CD Rom, San Francisco, CA, October Syed, W. U. H., Pinkerton, A. J., and Li, L., 2004, Simultaneous Wire- and Powder-feed Direct Metal Deposition: An Investigation of the Process Characteristics and Comparison with Single-feed Methods, J. Laser Appl., submitted. 3 Syed, W. U. 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