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International Journal of Machine Tools Selective laser sintering; Absorptance; Simulation 1. Introduction One current trend in production is the shortening of lead times for product development. New processes, especially those in the fi eld of layer manufacturing, support this trend.Inaddition,theyopennewpossibilitiesfor manufacturing 1. One group of such processes, selective laser sintering or SLS, has become popular for rapidly manufacturing freeform parts using a wide range of materials 2. Laser sintering of metallic materials shows great promise, but signifi cant further research and under- standing are still required for obtaining high-quality parts. This paper is built on previous studies on selective laser melting (SLM) of single tracks 3 and single layers 4 of ferrous alloy powders in the surface of a deep powder bed by a scanning laser beam. SLM is an emerged name for the direct route of SLS when the complete melting of powder occurs rather than the sintering or partial melting 5. The aim is to create a strong part that is usable without further post processing other than surface fi nishing. In the single track work 3, where M2 and H13 tool steel and 314S-HC stainless steel powders were examined, different track forms were identifi ed, depending on the laser power and scan speed that was used. Explanations for the transitions between these various forms of track were given in terms of the melt pool dimensions, temperatures and temperature gradients that existed. In the single-layer work 4 through studying the topography of melted layers from H13 tool steel, the onset of porosity was addressed. Subsequently the melted masses of single tracks and single layers were investigated at various process para- meters 3,4. Since at constant laser power and (for layers) scan spacing, delivered energy density to the bed reduces with increasing speed, the initial expectation was that for any level of laser power, melted mass would reduce as scan speed increased. However, the reverse was observed in both single-track and single-layer works. In fact, there existed scan speed ranges in which the mass of melted track or layer increased (or fl uctuated in the case of layer) with scan speed, at constant laser power and scan spacing. To study this, the amount of heat required to melt the observed mass was compared to the incident energy. An explanation was given in terms of absorptivity of the laser energy into the bed increasing with speed. But the observation for single track was not much emphasized as it was thought that the conditions, in which the increase occurred, being associated with the formation of elliptical section (non-fl at) tracks, ARTICLE IN PRESS 0890-6955/$-see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2006.09.013 ?Corresponding author. Tel.: +441133432165; fax: +441133432150. E-mail address: t.h.c.childsleeds.ac.uk (T.H.C. Childs). were not practically useful for processing. However, the simulated results of single-layer melting have shown that the variability of layer mass for the speed range is not predictable with a constant absorptivity a value. Indeed, understanding the causes of a variation becomes of central importance to fundamental studies of single-layer forma- tion. This paper expands the investigation towards M2 tool steel and 316L and 314S-HC stainless steel powders to identify these material behaviours in single-layer melting, in conditions in which dense layers have been formed, that might form the foundation for the subsequent layers. The questions that it addresses are the variation of a in the SLM process and effects of scan spacing and thermal history on the melted mass. In an alternative approach for explanation of mass variations, an idea based on the process effi ciency is developed later. 2. Modelling An existing fi nite element thermal model for laser sintering of polymers 6 has been developed to predict the mass of melted metallic material by the scanning laser beam. It is a transient heat conduction three-dimensional model in which the temperature rise caused by the travelling laser beam is calculated 7. The model takes into account the latent heat and the infl uence of both porosity and temperature on the thermal properties of the powder bed. In the temperature calculation, thermal conductivity k of the powder bed is assumed to vary with porosity as observed experimentally in 8: k ks1 ? ? 1 ak?0:78 ,(1) where ksis the solid conductivity and ak is chosen to fi t the measured initial bed conductivity to its measured initial porosity. ksand heat capacity Cpare assumed to vary linearly with temperature: ks k0 k1T; Cp C0 C1T,(2) where k0, k1, C0and C1 are material-dependent coeffi cients. The infl uence on temperature of phase change with latent heat L between the solidus and liquidus temperatures TSto TLis treated by the temperature recovery method 9. Powder bed density is then assumed to change from its initial value to that of solid material as temperature increases from TSto TL. In the previous work 3, concerned with melting the fi rst track in a powder bed, the temperature of the powder bed at the start of processing was assumed to be uniform, at a pre-determined ambient value. In modelling multi-track (i.e. layer) melting, the temperature existing in the bed at thestartofprocessingatrackisthetemperature distribution existing from processing all the previous tracks. Since the current model calculates temperatures in a limited volume surrounding the laser beam, it takes into account this issue (temperature history) approximately. The model presents lower estimates and approximate upper estimates of melted masses for the layer. The lower estimate assumes the bed to be cooled to ambient temperaturebeforeeachnewtrackisstarted.The approximate upper estimates are based on calculating melted masses of raster-scanned tracks each 3mm (fi ve laser beam diameters) long, allowed to cool down to the point that all molten material has resolidifi ed before the next track is started. The initial temperature distribution for melting the next track is taken to be that existing at the instant that the previous track has just resolidifi ed. This is felt to give an overestimate to the initial temperature distribution around the region of the next track. In this sense, the calculated melted mass of the next track is likely to be approximately an upper estimate. Thermal conductivity k and absorptivity a of a powder bed are inputs to the thermal model. A calorimetric approach based on theory in 10 was used in 1 to determine these values. It was shown that these obtained data validated the simulation in a low scan speed region 11. An alternative approach to predict the absorptivity, based on heat balance, is used here. Assuming that no evaporation occurs on the surface of the powder bed the overall energy balance equation is expressed as Qabs Qmelt Qloss,(3) where Qabsand Qmeltare the absorbed energy and required energy to melt a layer mass m per unit area, respectively, and Qlossis the rest of energy which disappears through the powder bed. The heat absorbed per unit area scanned at speed U by a laser of power P is aP=Us, where s is scan spacing. Qmelt is defi ned as mCPaveTm? T0 L, where CPave is the average specifi c heat from ambient bed temperature T0to the metals melting temperature Tm and L is the latent heat of fusion. Energy is lost from the melting zone by conduction, convection and radiation. However, the major source of heat loss through the powder bed is the conduction mode and contributions of convec- tion and radiation are so small as to be neglected without any loss of accuracy. By the assumption of negligible heat losses through the powder bed in the heat balance Eq. (3), the minimum estimate of absorptivity aminof laser energy into the powder bed can be expressed as amin m Us=P ? CPaveTm? T0 L ?. (4) Although, Eq. (4) gives only a minimum estimate of a in a heat balance sense, it expresses dependency of absorptivity on the process parameters. This issue is discussed later. Consideration of a values and their reliability is of major importance in this paper. 3. Experimentation Single layers have been produced, by a scanning CO2 laser beam, in the surface of beds made from gas-atomized powders of composition and size fraction listed in Table 1. All powders were obtained from Osprey Metals Ltd, UK and, were spread and levelled in a fl at tray of area ARTICLE IN PRESS M. Badrossamay, T.H.C. Childs / International Journal of Machine Tools (a)(c) cases are explained in text. 0100 (a) 314S-HC, P=80 W 314S-HC, P= 110W M2, P= 110 W M2, P= 140 W s= 0.3 mm (50%) M2 0100125 0.0 0.2 0.4 0.6 0.8 s= 0.06 mm s= 0.18 mm s= 0.30 mm s= 0.48 mm s= 0.60 mm Scan speed (mm/s) Absorptivity min. 0.6 0.3 0.0 Scan speed (mm/s) 255075255075150 314S-HC Absorptivity min. (b) Fig. 4. Estimates of aminvs. scan speed, (a) for M2 and 314S at powers 80, 110 and 140W and s 0.3mm, (b) for 316L at 110W and various scan spacings. M. Badrossamay, T.H.C. Childs / International Journal of Machine Tools & Manufacture 47 (2007) 779784783 The Rosenthal model for moving line sources is a well- established solution for simulation of either single pass welding in thin materials or a fully penetrating keyhole weld, as well as laser beam cutting process. The model assumes that the energy is absorbed uniformly along a line in the depth direction. As the penetration of a laser beam in the powder bed is much longer than in bulk materials, this model could be applied for SLM as well. Swifthook and Gick 17 presented an analytic solution to the model depending on the scanning speed. From their solution it can be derived that at high speeds (typically 450mm/s) around 52% of the delivered energy is lost through conduction 18, while, for low speeds (typically o5mm/s) the loss could be around 95%. On the other hand, Schulz etal.19gaveacorrelatedanalyticalsolutionof conduction loss taking into account the cylindrical heat sourceinlasercuttingprocessasPcon 2rCPDT urt Pe=2 ?0:7 where Pconis the conduction loss, r the material density, Cpthe heat capacity, DT the relative elevated temperature, u the cutting speed, r the radius of beam, t the material thickness, and Peis the Peclet number, which equals ru/k (k is the thermal diffusivity). It can be seen that with increasing Peclet number, cutting speed and heat loss decrease. Finally, as discussed so far, it seems the neglecting heat loss assumption cannot be applied in all ranges of process parameters. In fact, in low speed processing heat losses play an important role in the process and can not be neglected. The layer mass variations might be addressed by this route. However, more work is needed to confi rm this issue in a quantitative way. 5. Conclusion Experimental studies on melting single layers of M2 high speed steel and 316L and 314S-HC stainless steels in the surface of powder beds, by a raster-scanning laser beam have confi rmed that variations of layer mass with scan speed are not consistent with what is expected from the delivered energy to the powder bed. Two explanations are suggested. The fi rst one, which was supported by the simulation as well, suggests that absorptivity may increase with increasing scan speed. In the second one the heat loss decreasing with scan speed is proposed. In addition, effects of scan spacing on the layer mass and absorptivity was studied. Experimental and simulation results also showed that the thermal history of processing is infl uential in determining the amount of melt under a laser beam irradiation. References 1 G.N. Levy, R. Schindel, J.P. 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