Thermal modeling of laser sintering of two-component metal powder on top of sintered layers via multi-line scanning

Transcription

1 Appl. Phys. A 86, (2007) DOI: /s Applied Physics A Materials Science & Processing tiebing chen yuwen zhang Thermal modeling of laser sintering of two-component metal powder on top of sintered layers via multi-line scanning Department of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia, MO 65211, USA Received: 1 June 2006/Accepted: 22 September 2006 Published online: 3 November 2006 Springer-Verlag 2006 ABSTRACT Laser sintering of a two-component metal powder layer on top of sintered layers, with a moving circular Gaussian laser beam is modeled numerically. The overlap between the adjacent scanning lines, as well as the binding between the newly sintered layer and existing sintered layers underneath through melting, are also considered. The governing equation is formulated by a temperature-transforming model, with partial shrinkage induced by melting taken into account. The liquid flow of the molten low melting point metal powders driving by capillary and gravity forces is formulated by Darcy s law. The effects of the dominant processing parameters, including the moving laser beam intensity, scanning speed, and the number of the existing sintered layers underneath on the shape of the heat affected zone (HAZ) are investigated. PACS e; Ev 1 Introduction Selective laser sintering (SLS) is one of the few rapid prototyping processes that possess the capability of producing three-dimensional, structurally sound, and fully functional parts directly from polymers, ceramics and metals without the use of any intermediate binders. It is a layered manufacturing method that can create functional parts by fusing powdered materials with a directed laser (generally CO 2 or YAG) beam [1]. Before laser scanning, a thin ( µm thick) powder layer is spread on the building substrate by a roller. The laser beam then selectively sinters or melts the powders, and then bonds the powders into two-dimensional slices. After laser scanning, a fresh powder layer is spread and the scanning process is repeated until a 3-D part is fabricated. A brief review of the basic principles of SLS machine operation, and materials issues affecting direct SLS of metals, and the resultant properties and microstructures of the parts are discussed by Agarwala et al. [2]. An overview of the latest progress on selective laser sintering (SLS) works as reported in various journals and proceedings is presented by Kumar [3]. Melting and resolidification are the mechanisms to bond metal powder particles to form a layer and to bond differ- Fax: , zhangyu@missouri.edu ent layers together to form a functional part. Fundamentals of melting and solidification have been investigated extensively and detailed reviews are available in the literatures [4, 5]. The distinctive feature of laser-induced melting of the metal powders in the SLS process is that it is always accompanied by shrinkage due to the significant density change. When a single component metal powder is used in SLS process, the balling phenomenon caused by the use of inappropriate laser processing parameters leads to the formation of spheres with diameters approximately equal to the size of the laser [6]. The balling phenomenon is well documented, an extensive study of which can be found in Tolochko et al. [7]. The adjustment of SLS parameters must be rather strict in order to create conditions under which the balling phenomenon is prevented. The powder mixture that is composed of two types of powders that possess significantly different melting points is one of many ways to overcome the balling phenomenon as suggested by Bunnell [8] and Manzur et al. [9]. In the case of two-component sintering, a molten liquid that is formed by melting the lower melting point powders infiltrates into the voids between the higher melting point solid powders and binds them together. Meanwhile, the solid particles move downward, because the high melting point powder alone cannot sustain the powder bed structure. It should be noted that only the low-melting-point powder melts and resolidifies and the high melting point powders remain solid throughout the process. Pak and Plumb [10] presented a one-dimensional thermal model for melting of the two-component powder bed, in which the liquid motion driving by capillary and gravitational forces is considered, but the shrinkage was neglected. Zhang and Faghri [11] analytically solved one-dimensional melting of a semi-infinite two-component metal powder bed heated by a constant heat flux. Chen and Zhang [12] obtained the analytical solution of one-dimensional melting of the twocomponent metal powder bed with finite thickness subjected to a constant heat flux. Zhang and Faghri [13] simulated twodimensional melting and resolidification of a subcooled twocomponent metal powder bed subject to a moving Gaussian heat source; shrinkage was accounted for but the liquid flow of the low melting point metal is neglected. A two-dimensional model of multiple-layer SLS of a subcooled two-component metal powder layer with a moving Gaussian laser beam and adiabatic boundary condition at the bottom is presented by Chen and Zhang [14]. A three-dimensional finite element

2 214 Applied Physics A Materials Science & Processing simulation for temperature evolution in the SLS process was conducted by Kolossov et al. [15], who considered the nonlinear behavior of thermal conductivity and of specific heat due to temperature changes and phase transformations. A threedimensional thermal model of SLS of a two-component metal powder layer was presented by Chen and Zhang [16], who considered the effects of the solid particle velocity induced by shrinkage and the liquid flow driven by capillary and gravitational forces. The porosity, ε, defined as volume fraction of void that can be occupied by either gas or liquid, is equal to ϕ g,s in the loose powder and it becomes ϕ l + ϕ g,l after melting. If the volume of the gas being driven out from the powder bed is equal to the volume of the liquid generated during melting, the porosity of the powder bed before and after melting will be the same, i.e., ε = ϕ g,s = ϕ s + ϕ g,l ; this is referred to as the constant porosity model [10]. If the volume fractions of high and low melting point powders before sintering satisfy ϕ s /(ϕ H +ϕ s ) = ϕ g,s,the powder bed can be fully densified (ϕ g,l = 0) under the constant porosity model [16]. At the other extreme, if there is no shrinkage, one would expect that ϕ g,l = ϕ g,s and the porosity, ε, would increases since ϕ l increases during melting. In reality, the volume fraction of gas in the HAZ may not be zero because the life span of the liquid is not long enough to allow all gas to escape from the powder bed [16]. Therefore, the rate of the shrinkage in the SLS process may be somewhere between complete shrinkage and no shrinkage. A partial shrinkage model for SLS of the two-component metal powders was developed and the effects of the volume fraction of the gas in the HAZ on the shape and size of the HAZ were investigated by the authors [17]. A three-dimensional sintering process of the two-component metal powders for a single-line scanning of a loose powder layer on top of the existing sintered metal layers was investigated by Chen and Zhang [18]. In this paper, a three-dimensional multi-line laser scanning sintering process of a two-component metal powder layer on the top of multiple existing sintered layers will be investigated. To obtain sound metallic bonding between sintered layers, the overlaps between vertically deposited layers as well as lines at horizontal neighbors are considered. The effects of the volume fraction of the gas in the HAZ, laser scanning velocity and the number of the existing sintered layers on the shape of the HAZ will be discussed. 2 Physical model During the SLS process, the position of the laser beam will be reset and will begin to start another scan along the x-direction. The scan spacing determines the overlap between the adjacent lines. Values of scan spacing are small, typically 0.5, 0.25 or of the laser beam diameter [19]. The value of overlap between lines is assumed to be 0.5 in this paper in order to get optimum bonding which aids densification. After the completion of the sintering process on the x y plane, the sintered layer is lowered and a fresh layer of powders is spread into the build zone in order to repeat the process. Bonding also occurs between layers as the new layer is sintered, i.e., the overlap between newly sintered layers and existing sintered layers below is considered. The sintering depth will pierce into the previously sintered layers below so that the newly sintered layer can be bound to the existing layer to form an integrated resolidified region. The overlap between layers is defined as the ratio of the width of the liquid pool at the bottom surface of the fresh layer and that of the liquid pool at the top surface; it is taken as 50% in this study. The physical model of the multi-line scanning problem is shown in Fig. 1. It is assumed that the laser beam diameter is much smaller than the horizontal sizes of the workpiece to be built. The first layer sits on top of the existing sintered layers. The half of the first layer (y < 0) is sintered while another half (y > 0) is still loose powder. Laser sintering takes place at the center of the laser beam that coincides with the origin of the coordinate system. Therefore, the top surface of the physical domain before the sintering process is not a flat surface. The configuration of a previously scanned line of a neighbour needs to be considered. The shape of the previously sintered region can be estimated by the regression of the HAZ shape in a single scan line model with the same porosity and number of existed sintered layers below. Therefore, the physical domain will have different shapes on the top surface for different rates of shrinkage. The initial top surface profiles of the physical domain are regressed approximately, from the simulation results in [18] for all cases. In this paper, the different shrinkage rate due to the different volume fraction of gas in the liquid phase, ϕ g,l, will be considered in the physical problem. The energy equation, formulated by a temperature transforming model [20], is (ϕ l V l C L T) U b X [(ϕ H + ϕ s C L ) T] + W s Z [(ϕ H + ϕ s C L ) T] { = (K T) τ [(ϕ l + ϕ s )S L ]+ (ϕ l V l S L ) } + W s Z (ϕ ss L ) U b X [(ϕ l + ϕ s )S L ] (1) which can be derived by substituting dimensionless enthalpy H = (ϕ l + ϕ s )(C L T + S L ) + ϕ H T into the energy equation in the enthalpy form. In the resolidified region other than the liquid pool and the loose powders, the volume fraction of the resolidified low melting point component is still represented by ϕ l, which differs from ϕ s that represents the volume fraction of the low melting point component before melting occurs. In another words, ϕ l is used to represent the volume fraction of the liquid in the liquid pool or volume fraction of the resolidified low melting point component in the resolidified region. The dimensionless shrinkage velocity, W s, the heat capacity of low melting point component, C L, source term, S L, and thermal conductivity, K, in (1) in the loose powder layer are different from those in existing or resolidified sintered regions. In the loose powder layer, { ( ) ϕsi ηst W s = 1 ε τ U b η st Z η X st (2) 0 Z >η st C LH ( ) T < T C L = C LH Sc T T < T < T (3) T > T C LH

3 CHEN et al. Thermal modeling of laser sintering of two-component metal powder on top of sintered layers 215 FIGURE 1 Physical model 0 T < T C LH S L = 2 Sc T < T < T (4) C LH Sc T > T K eff T < T K = K eff + K l K eff (T + T ) T < T < T 2 T (5) K l T > T or in the HAZ K l = (ϕ l + ϕ s ) K L + ϕ H, (6) where K eff and K l are the dimensionless thermal conductivity of the loose powders and liquid pool, respectively [13]. In the resolidified region, W s = 0 (7) C L = C LH (8) S L = C L Sc (9) K = K l. (10) The dimensionless velocities of the liquid phase, V l, can be obtained by Darcy s law [16] V l ( U b i + W s k) = where Ma = γ 0 m d p α H µ, ε Ma ψ 3 e 180(1 ε)2 ψ P c + ε2 Ma Bo ψ 3 e 180(1 ε) 2 ψ k Bo = ϱ lgrd p γ 0 m (11). (12) The dimensionless capillary pressure,p c, in (11) can be calculate by [21], P c = 1.417(1 ψ e ) 2.12(1 ψ e ) (1 ψ e ) 3 (13) AISI 1018 BNi-2 ϱ H 7892 kg/m 3 ϱ L 8257 kg/m 3 k H 48.3W/m K k L W/m K c ph 451.8J/kg K c pl 462.6J/kg K α H m 2 /s T m 1271 K h sl J/kg µ kg/s m γ N/m TABLE 1 Summary of the thermal properties of AISI 1018 and BNi-2

4 216 Applied Physics A Materials Science & Processing FIGURE 2 Three-dimensional shape of the HAZ ( s = 0.25, U = 0.1, N = 1) B i N R Bo Sc 1.38 C L 1.07 T 1.0 K g ϕ gs 0.42 K L 0.2 ϕ g,l 0.0, 0.2, 0.42 Ma ψ ir 0.08 N t T N 1 TABLE 2 Sintering parameters applied in the numerical simulation where the normalized saturation, ψ e, in (13) is obtained by { ψ ψir ψ e = 1 ψ ir ψ>ψ ir, (14) 0 ψ ψ ir and ψ ir is the irreducible saturation, below which liquids do not flow. The volume fraction of the liquid phase of the low melting point powders, ϕ l, can the obtained from dimensionless continuity equation of the liquid in the moving coordinate system ϕ l τ U ϕ l b X + (ϕ lv l ) = Φ L. (15) The continuity equations for the solid phase of the low melting point powder and high melting point powder, by assuming shrinkage occurs in the z- direction only, are ϕ s τ U ϕ s b X + (ϕ sw s ) = Φ L (16) Z ϕ H τ U ϕ H b X + (ϕ Hw s ) = 0 (17) Z and the following relationship is valid in all regions ε + ϕ s + ϕ H = 1. (18) The volume production rate, Φ L, can be obtained by combining (12) (14), i.e., Φ L = (1 ε) τ (1 ε) + U b X Z [(1 ε) W s] (19) where the porosity, ε, is not constant during the sintering process under the partial shrinkage model since the porosity, ε,is FIGURE 3 The temperature distribution at the surface of the powder layer ( s = 0.25, U = 0.1, ϕ g,l = 0.0, N = 1) defined as the volume fraction of a void that can be occupied by either a gas or liquid. The value of the porosity depends on the volume fraction of the gas in the loose powders or the HAZ. The location of the liquid surface is related to the sintered depth by η 0 (X, Y) = 1 ε l ϕ H,i 1 ε l η st (X, Y) η st < s 1 ε l ϕ H,i 1 ε l s η st s. (20) The heat loss at the surface of the powder layer due to the radiation and convection was investigated by Zhang and Faghri [13], who concluded that its effect on the SLS process is not negligible. The boundary conditions with the consideration of the heat loss at the top of the powder layer is K T Z = N i exp( X 2 Y 2 ) N R [(T + N t ) 4 (T + N t ) 4 ] Bi(T T ) Z = η 0 (X) (21)

5 CHEN et al. Thermal modeling of laser sintering of two-component metal powder on top of sintered layers 217 FIGURE 4 Effects of laser intensity and scanning velocity on the sintering process (ϕ g,l = 0.0, N = 1) FIGURE 5 Effects of laser intensity and scanning velocity on the sintering process (ϕ g,l = 0.2, N = 1) T Z = 0, Z = s + N l (22) T = 0, X (23) X T = 0, Y. (24) Y 3 Numerical solutions The optimum combinations of dimensionless laser beam intensity and scanning velocity are sought to obtain the expected sintering depth and the overlaps between the newly sintered layers and the existing sintered layers. The energy equation is solved by the false transient method in the moving coordinate system. The converged steady-state solution is obtained when the temperature distribution does not change with the false time. For any given laser scanning velocity, computation is performed with different laser intensities beginning with a lower intensity, at which the desired sintering depth is not reached. The laser intensity will then be gradually increased until the required sintering depth and 50% overlap between the HAZ and existing sintered layers underneath are obtained. The false transient time step in the paper is 0.12 and the grids number are (X Y Z). The grids in the X- and Y-directions are non-uniform but uniform in the Z-direction. A block-off technique [22] is used to transfer the irregular physical domain into the regular computational domain in order to simplify the numerical calculation. The irregular shape of the physical domain is caused by the possible movement of the top liquid surface due to the shrinkage and possible irregular initial shape of the physical domain by considering multiple laser scan lines. The thermal conductivity in the empty space created by the shrinkage is zero. Iterations are needed due to the coupled procedures to obtain solutions of velocities of the liquid phase of the low melting point powder and ϕ l. 4 Results and discussions Effects of the volume fraction of the gas in the heat affected zone (HAZ) on the shape of the HAZ are investigated. The combined optimal scanning velocities and the intensities of the laser beam that can yield the required sintering depth and overlaps are obtained. The powder mixture with nickel braze (BNi-2) as the low melting point powder and AISI 1018 Steel as high melting point powder are considered. The di-

6 218 Applied Physics A Materials Science & Processing FIGURE 6 Effects of laser intensity and scanning velocity on the sintering process (ϕ g,l = 0.42, N = 1) FIGURE 7 Effects of laser intensity and scanning velocity on the sintering process (ϕ g,l = 0.0, N = 3) mensional properties of AISI 1018 and BNi-2 are summarized in Table 1. The average diameters of nickel braze and AISI 1018 steel are 45µm and 68µm, respectively. The dimension less parameters that are used in the numerical simulation are shown in Table 2. The 3-D shapes of the HAZ with different volume fractions of the gas in the HAZ, ϕ g,l, with one existing sintered layer underneath are shown in Fig. 2. The shrinkage is smaller when the volume fraction of gas in the liquid pool increases and there is no shrinkage when ϕ g,l is up to ϕ g,s. The optimal laser beam intensity increases with increasing ϕ g,l in order to obtain the same sintering depth and overlap because a higher ϕ g,l causes the smaller shrinkage and thicker existing sintered layers underneath. Part of the initially overlapped region, which was the resolidified region after previous scanning, re-melts again. Therefore, the neighbored scan lines can have a solid bond after the liquid metal is resolidified again when the laser beam moves away. In addition, the higher magnitude of the laser power is needed since the thermal conductivity of the existing sintered layers is much higher than that of the loose powder layer. The HAZ becomes more porous with increasing volume fraction of the gas in the HAZ, which in turn will cause the weak density of the sintered part. Figure 3 shows the surface temperature distribution of the powder layer at the quasi-steady-state during the sintering process. The surface temperature of the overlap region is higher than that of the loose powders. Figures 4 6 show the longitudinal and transverse sectional plots of HAZ with the optimal combination of scanning velocity and laser beam intensity when ϕ g,l increases from 0 to 0.42 (N = 1). The complete shrinkage occurs when ϕ g,l = 0.0 while the HAZ has no shrinkage when ϕ g,l = The partial shrinkage happens as 0.0 ϕ g,l The optimal laser beam intensity increases with increasing ϕ g,l because the thickness of the existing sintered layers underneath is higher with higher ϕ g,l. The shapes of HAZ are similar when the laser scanning speed increases with respect to the specific ϕ g,l but the volume of the liquid pool and resolidified region become smaller with increasing laser scanning speed. The overlapped region at the bottom of the HAZ of the newly sintered powder layer can be seen and it has reached the bottom of the physical domain. The transverse sections of the HAZ are not symmetric along the Y-direction because of the different thermal properties of sintered and unsintered regions. The optimal combinations of dimensionless scanning velocities and laser beam intensities when ϕ g,l increases from 0.0to0.42forN = 3 are shown in Figs The laser beam

7 CHEN et al. Thermal modeling of laser sintering of two-component metal powder on top of sintered layers 219 FIGURE 9 Effects of laser intensity and scanning velocity on the sintering process (ϕ g,l = 0.42, N = 3)s FIGURE 8 Effects of laser intensity and scanning velocity on the sintering process (ϕ g,l = 0.2, N = 3) intensity increases significantly with increasing numbers of existing sintered layers underneath with respect to the specific laser scanning velocity. In reality, it is a way to obtain both highly densified sintered parts and a lower laser beam intensity at the same time by decreasing ϕ g,l and then decreasing the thickness of the pre-deposited sintered layers below. Accurate density and geometry of the fabricated part are significantly affected by the metallic bonding between layers and the shrinkage. Therefore, the appropriate combination of processing parameters to obtain the desired overlaps and investigation of the HAZ formation affected by different shrinkage become necessary. 5 Conclusions The three-dimensional sintering process of a twocomponent metal powder layer on top of existing sintered layers with multiple-line scanning was investigated. The asymmetric geometry in the y-direction due to the overlapped region of neighbored lines was considered. The effects of different volume fractions of the gas in the HAZ that causes different shrinkages on the sintering process were investigated. The optimal combined dimensionless laser beam intensities and scan velocities were obtained. The results demonstrate that the shape of the HAZ is significantly affected by the fraction of the gas in the HAZ and by processing parameters such as the laser beam intensity and the scanning velocity. ACKNOWLEDGEMENTS Support for this work by the Office of Naval Research (ONR) under grant number N is gratefully acknowledged. REFERENCES 1 J. Conley, H. Marcus, J. Manuf. Sci. Eng. 119, 811 (1997) 2 M. Agarwala, D. Bourell, J. Beaman, H. Marcus, J. Barlow, J. Rapid. Prototyp. 1, 26 (1995) 3 S.Kumar, JOM55, 43 (2003) 4 R. Viskanta, Phase Change Heat Transfer in: Solar Heat Storage: Latent Heat Materials, ed. by G.A. Lane, (CRC Press, Boca Raton, FL, 1983) 5 L.C. Yao, J. Prusa, Adv. Heat Transf. 25, 1 (1989) 6 D.L. Bourell, H.L. Marcus, J.W. Barlow, J.J. Beaman, Int. J. Powder Metall. 28, 369 (1992) 7 N.K. Tolochko, S.E. Mozzharov, I.A. Yadroitsev, T. Laoui, L. Froyen, V.I. Titov, M.B. Ignatiev, J. Rapid Prototyp. 10, 78 (2004) 8 D.E. Bunnell, Fundamentals of Selective Laser Sintering of Metals, Ph.D. Thesis, University of Texas at Austin (1995) 9 T. Manzur, T. DeMaria, W. Chen, C. Roychoudhuri, Potential Role of High Powder Laser Diode in Manufac., SPIE Photonics West Conf., San Jose, CA (1996) 10 J. Pak, O.A. Plumb, J. Heat Transf. 119, 553 (1997) 11 Y. Zhang, A. Faghri, Int. J. Heat Mass Transf. 42, 775 (1999)

8 220 Applied Physics A Materials Science & Processing 12 T. Chen, Y. Zhang, Appl. Therm. Eng. 26, 751 (2006) 13 Y. Zhang, A. Faghri, ASME J. Heat Transf. 120, 883 (1998) 14 T. Chen, Y. Zhang, Numer. Heat Transf. A 46, 633 (2004) 15 S. Kolossov, E. Boillat, R. Glardon, P. Fisher, M. Locher, Int. J. Mach. Tools Manuf. 44, 117 (2004) 16 T. Chen, Y. Zhang, J. Manuf. Sci. Eng. 128, 299 (2006) 17 T. Chen, Y. Zhang, Int. J. Heat Mass Transf. 49, 1489 (2006) 18 T. Chen, Y. Zhang, Three-Dimensional Modeling of Laser Sintering of a Two-Component Metal Powder Layer on Top of Sintered Layers, Proc. ASME Summer Heat Transfer Conf., San Francisco, CA, July 17 22, C. Hauser, T.H.C. Childs, K.W. Dalgarno, Proc. Solid Freeform Fabrication Symp. 1999, pp Y. Cao, A. Faghri, J. Heat Transf. 112, 812 (1990) 21 M. Kaviany, Principles of Heat Transfer in Porous Media (Springer, New York, 1995) 22 S.V. Patankar, Numerical Heat Transfer and Fluid Flow (McGraw-Hill, New York, 1980)