Ind. Eng. Chem. Res. 1 9 9 5 , 3 4 , 1641-1651
1641
MATERIALS AND INTERFACES Selective Laser Sintering of Polymer-Coated Silicon Carbide Powders J. Christian Nelson$ Neal K. Vail? Joel W. Barlow,*,?Joseph J. Beaman: David L. Bourell: and Harris L. Marcuss Department of Chemical Engineering and Department of Mechanical Engineering and Center of Materials Science and Engineering, The University of Texas at Austin, Austin, Texas 78712
Selective Laser Sintering (SLS) produces three-dimensional objects directly from a computeraided design (CAD) solid model, without part-specific tooling, by repeatedly depositing thin layers of fusible powder and selectively sintering each layer to the next with a rastered, modulated, CO, laser beam. This technology, originally intended to produce parts and patterns from powdered waxes and thermoplastics, can be extended through use of thermoplastic-coated inorganic powder to producing “green” shapes which contain metal or ceramic powder bound together with the thermoplastic. These shapes can be subsequently processed into metal, ceramic, or composite metayceramic parts by various methods. Generally, the strength of the green shape critically depends on the layer to layer fusion that is achieved. A model of the SLS process is presented that correctly estimates the sintering depths in poly(methy1methacrylate) (PMMA) and coated silicon carbide (Sic)powders that result from operating parameters including laser power, beam scanning speed, beam diameter, scan spacing, and temperature. Green part densities and strengths are found t o correlate with a combination of parameters, termed the energy density, that arise naturally from consideration of the energy input to the powder bed.
Introduction The Selective Laser Sintering (SLS) process, commercially produced by DTM Corporation, Austin, TX, produces a solid object from a three-dimensional CAD model by the selective sintering of successive layers of fine powder. The process, shown schematically in Figure 1,spreads a 75-250 pm layer of fusible powder on the top surface of the part container. The surface is then raster-scanned at a linear scan rate between 2 and 100 c d s with a modulated, 1-50 W, 0.5 mm diameter, CO:! laser beam. Where the part cross section in the computer file is solid, the laser is on, and the powder under the beam is fused to itself and to the preceding layer . Where the part cross section is open, the laser is off, and the powder is not fused and remains loose to be removed and recycled after the part is completely formed. The SLS process is designed to fabricate parts from thermoplastic powders such as nylon, polycarbonate, wax, and acrylonitrile/butadiene/styrene.The process can also be used to create green shapes from thermoplastic-coatedmetal and ceramic powders (Bourell et aZ., 1992, Barlow, 1992). Several systems, including glass, alumina, silicdzircon mixtures (Vail and Barlow, 1991), and copper (Badrinarayan and Barlow, 1991) have been demonstrated to form useful polymer-bound preforms. These green shapes can be processed in subsequent steps to produce metal and ceramic parts. In this paper, we present studies of polymer-bound silicon carbide materials (Vail and Barlow, 1993);
* Correspondence should be addressed to this author. t Department of Chemical Engineering.
*
Department of Mechanical Engineering and Center of Materials Science and Engineering.
Figure 1. Schematic of the Selective Laser Sintering process. (A) Scanning mirrors. (B)Laser beam. (C)Radiant heater. (D) Infrared thermometer. (E) Powder spreading roller. (F) Powder feed cylinder. (G)Part construction cylinder.
however we believe that the various issues related to model development are common to all composite powders. Recently, we presented a model of the SLS process for predicting the layer to layer fusion of polycarbonate powder (Nelson et aZ., 1993). This one-dimensional model of the SLS thermal process was able to predict, to within 20% accuracy, the effects of the primary process variables; scan speed, scan overlap, vector length, and laser power, on fusion depths of wellcharacterized polycarbonate (PC) powder. Nelson discusses these effects in some detail. It suffices to note here that the SLS machine is normally operated with a certain amount of scan overlap; that is, the distance between adjacent vector scans is somewhat less than
0888-5885/95/2634-1641$09.00/0 0 1995 American Chemical Society
1642 Ind. Eng. Chem. Res., Vol. 34, No. 5,1995
E,
Beam Intensity, I , 1.o
Reads input data
0.8
0.6 0.4
0.2 0.0
Material Properties K thermal conductivity C, specific heat p bulk density
Boundary Conditions Q laser flux h heat transfer coefficient
J Numerical Solution Solve the conductiondiffusion equation using FDorFEM, ,
Figure 2. Nomenclature used in thermal flux calculations.
-0
a
4
0.75
Bed Density k' sintering rate e void fraction
0
0.01
0.02
0.03
0.04
0.05
0.06
time, sec
Figure 3. Calculated thermal fluxes at a point on the surface for beam diameter greater than scan spacing.
the beam diameter (see Figure 2). The laser beam intensity is not constant but is distributed in a Gaussian manner about the center. Consequently, a point on the surface of the powder is likely to see several pulses of laser energy with varying intensities, spaced in time according t o the ratio of scan length and beam speed (Figure 3). The number, time duration, intensities, and time between pulses strongly influence the depth of the thermal front and the resulting strength of the part. In addition to absorptivity to COn radiation, the important material properties for this thermal sintering process were found to be specific heat, density, thermal conductivity, and sintering rates. These properties are somewhat interrelated. For example, thermal conductivity is a function of bed density which is, in turn, a function of the degree of sintering that has occurred. Independent measurements of the effects of temperature on powder sintering rates and on thermal conductivity were made to help sort out the relationships. By combining an understanding of laser energy input, thermal characteristics, and material sintering kinetics, a numerical model for predicting the penetration of sintering fronts into the powder bed was developed. As suggested by the schematic in Figure 4,this model uses the method of finite differences to solve the onedimensional, unsteady state energy balance,
where
Figure 4. Flow chart of the combined calculation of heat transfer and sintering.
-K-
aT = a& az
- h(T
- T,)
aT -K - = -h( T - T,) az
z = 0, t 5
t
z = 0, t > t
and e is the bed density, Cp the specific heat, T(z,t)the bed temperature, K the thermal conductivity, z the distance into the bed from the exposed surface, aR the absorptivity to laser radiation, ( I ) the average intensity under the laser beam, z the pulse duration (as noted above, actually several pulses are used), h a combined radiation and convection heat transfer coefficient t o describe the rate of cooling from the powder bed surface to the environment at temperature, T,, and t the time from first exposure to the laser beam; G = 0 for the sintering of noncrystalline materials such as PC or PMMA. With polycarbonate powder, we were able to experimentally observe the thermally fused layers in a multilayer part by cutting a thin section through the part, perpendicular to the build plane. This section could be viewed in the usual light transmission mode with a lowpowered microscope. The fused portion of each layer
Ind. Eng. Chem. Res., Vol. 34,No. 5,1995 1643
0
10
20
30
40
50
60
70
80
Linear Diameter, (pm) Figure 5. Quadmodal particle size distribution.
easily transmitted light and appeared to be transparent. The less-fused portions of the layer were porous, scattered light, and appeared dark in the microscope. These observations were found to agree with our model calculations for one-dimensional sintering to within 20% relative error. This agreement suggests that our thermal model is generally correct and applicable, except for obvious changes to account for different material properties, to the present study of the composite powder of PMMA and Sic.
Materials and Procedures Materials. A Sic powder, termed Quadmodal, was supplied by Lanxide Corporation, Newark, DE, as part of a joint research agreement with the University of Texas. As shown in Figure 5, this powder ranges in particle size from 2 to 60 pm with noticeable peaks in frequency near 7 and 12pm, as measured with a Coulter Multisizer. The powder has a tapped density of 62%. PMMA polymer binder was produced as an emulsion, described elsewhere (Vail et al., 1994). This polymer was formulated to have a melt flow index (ASTM D1238) of 30 g/10 min, as measured with a Kayness Galaxy I capillary rheometer at 200 "C and 75 psi. The polymer had an actual melt flow index of 32.2 g/10 min at these conditions. Its glass transition temperature, Tg,was determined to be 105 "C using differential scanning calorimetry. Encapsulation. Polymer-encapsulated silicon carbide powder was prepared by spray drying a 50%solids slurry of the polymer latex emulsion and silicon carbide powder in an Anhydro Laboratory Spray Drier No. 1, equipped with a 2.5-in. diameter, four-nozzle centrifugal atomizer wheel. Typical operating conditions (Vail and Barlow, 1991) were 30 000 rpm wheel speed, 275 "C inlet air temperature, 115 "C exit air temperature, and 100 mumin slurry flow rate. The resulting agglomerated powder has a mean particle size less than 50 pm and a polymer composition of 30 vol % (13.8%); see Figure 6. The encapsulated powder was mixed with uncoated silicon carbide powder to reduce the polymer content to 20 vol % (8.5%). The resulting powder has a
Figure 6. Quadmodal powder that has been coated with PMMA emulsion in the Anhydro Spray Drier.
tapped density of 57%, relative to the density of a voidfree mixture of the polymer and Sic. Selective Laser Sintering. Materials were processed into 2 in. x 2 in. x 0.3 in. coupons for metal infiltration studies by Lanxide and into 1in. x 3 in. x 1/4 in. bars for three-point bending tests with a DTM Model 125 SLS Workstation, equipped with a calibrated, 25 W, CO2 laser. The laser beam diameter was determined to be 455 pm from determination of the beam intensity profile, as measured by beam profilometer. SLS processing was conducted in a nitrogen atmosphere ((2% 0 2 ) with a gas flow rate produced by a 0.04 in. H20 pressure differential. This standard operating atmosphere minimizes degradation of the polymer molecular weight by thermooxidation that could potentially occur during long exposure to air at elevated temperatures. Powder bed surface temperatures were controlled and maintained at 119 "C (assuming a powder bed surface emissivity of 0.9) by an infrared sensorPID system that controls an infrared heater; see Figure 1. The operating parameters and ranges explored were laser power (6-16 W), scan speed (50-100 in./s), beam
1644 Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995
spacing (0.002-0.005 in.), and powder layer thickness (0.0045 in.). Thermophysical Properties. The solution of eq 1 requires knowledge of the thermal properties of the bed of composite powder. Generally, bed properties are composition weighted functions of the these same properties of the solids comprising the composite powder, as well as of the gas in the bed voids. The PMMAcoated Sic agglomerates may also have voids; however we have no way to discriminate at the present time between voids within and voids between agglomerated particles in the bed. The solid density, eB,of the composite particle is calculated in the usual way from the densities of the components, via a mass balance,
e, = 4 l @ l +(1 - &)e2
(2)
where 41 is the volume fraction of PMMA polymer in the composite and 61 is the polymer density, 1.187 0.001 g/cm3, as measured by a pycnometer and analytical balance on compression-molded material. The density of the silicon carbide ez is 3.214 g/cm3(West, 1979). The density of the powder bed is measured by both tapped density and "density cup" methods. The density cup method uses the Model 125 Workstation to prepare cups with an inner diameter of 1.50 in. and a depth of 1.00 in. The bed density is then determined by weighing the known volume of powder contained in the cup. The powder bed densities in the Workstation are found to be lower, 1.30-1.42 g/cm3 (46%-50% relative density) than the tapped densities (57% relative density). This suggests that the powder-spreading mechanism in the Workstation does not provide optimum powder packing. The powder bed densities in the Workstation are also found to decrease systematically with cup position in the part cylinder, with the higher densities occurring closer to the feed cylinder where the powder wave being spread is larger. This density variation persists in the green parts made with the Model 125 Workstation; however this variation has been nearly eliminated in the more recently produced SLS Sinterstation which roller spreads powder in both directions from two feed cylinders located adjacent to the part cylinder (Lakshminarayan, 1993). The specific heat of the composite powder, Cp, is estimated from mass fraction average of the specific heats of PMMA, Cp1, and Sic, Cpz, via
*
c, = 01cp, + (1 - q)Cp,
(3)
where w1 is the mass fraction of polymer in the composite, and (4)
The specific heats of the composite particles were measured with a Perkin-Elmer differential scanning calorimeter, using standard procedures (Xue and Barlow, 1990; Sih and Barlow, 1993). The specific heats of the PMMA and Sic were taken from Tadmore and Gogos (1979), and Dean (19921, respectively. Figure 7 shows these data, the prediction of Cp by eq 3, and some measured composite specific heats. All specific heats are temperature dependent, although both predicted and observed values for the composite particles are little affected by the polymer because it is present a t only 8.5%. As discussed below, unsteady state measure-
0.60 j
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0 0.40 4
0
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I
0.00 200
300
500
400
600
700
800
TEMPERATURE, K Figure 7. Specific heats of materials at various temperatures. (A)PMMA. ( 0 )Sic. (-1 Calculated from eq 3 for 20 vol % P M W 80 vol % S i c Powder. (+) Experimental observations for 20 vol % P M W 8 0 vol % S i c powder.
I
0.00 1
o
20
40
60
ao
100 1 2 0 140 160
TEMPERATURE
("C)
Figure 8. Thermal conductivity of P M W S i C composite powder beds at various temperatures. (A)Measured by the laser heating method. ( 0 )Measured by the water bath method. (-1 Calculated from eqs 5 and 12. (- - -1 Calculated from eqs 8 and 12.
ments of thermal conductivity require specific heat information. For this reason, the experimental data for the composite particles was taken over a limited temperature range. Over that range, eq 3 and experiment agree within 15%relative error. Although the deviation may be more systematic than random, eq 3 appears to estimate the specific heat of the composite powder quite well. The thermal conductivity of the bed of composite powder was measured by Sih (Xue)using two different transient methods: the water bath method in which a thermally equilibrated tube of powder is placed in a water bath at a different temperature and the transient temperature at the tube center is measured and analyzed (Xue and Barlow, 1990); and the laser heating method (Sih and Barlow, 1993)in which the top surface of the powder is exposed to a laser beam and the transient temperature at a point below the powder surface is followed.. In both measurement techniques, the temperature difference used in the measurement is kept small, usually AT I 10 "C, to permit the assumption of temperature-independent thermal properties to be made during analysis. The bed temperature is then brought to a new equilibrium temperature and the experiment repeated. Figure 8 shows measurements of the thermal conductivity of the powder bed by both methods for a 20 vol % PMMA coating on Sic at an initial relative bed density of 47% at 30 "C. Over the temperature range where they can be compared (2'
Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 1646
100 "0,the disagreement between the two experimental techniques is only 2% relative error. The thermal conductivity of the powder bed (Figure 8) increases with increasing temperature because the conductivities of air, Kg(McAdams, 19541, and of solid PMMA, K1 (Eirmann and Hellwege, 19621, increase with increasing temperature while that of solid Sic, K2 (West, 1979), is largely unchanged. The values of these conductivities range by 4 orders of magnitude from about 400 W/(m*K)for solid Sic to typically 0.2 W/(m*K) for PMMA and 0.03 W/(m*K)for air, and prediction of the thermal conductivities of powder beds that contain these widely different materials is a challenge. We use the Yagi-Kunii (1957) model for the conductivity in packed beds, K, given by
where E is the void fraction of the bed,
1 and p x 1 for beds of spherical or cylindrical particles, Kg is the thermal conductivity of gas in the bed, KSis the thermal conductivity of the solid particulate, Dp is the average particle diameter, es and e are the solid and bed densities, and h, and h,, are radiation heat transfer coeEcients for void to void and solid to solid, respectively. These transfer coefficients are relatively unimportant at temperatures less than 100 "C, and eq 5 reduces to y
(7) The parameter, q,in eq 7 is defined as the ratio of the effective fluid film thickness to the mean diameter of the powder. From experimental measurements in air, Yagi and Kunii show a correlation that corresponds to
9 =0.193~~,*~~
(8)
We estimate the thermal conductivity, Ks, for a solid composite particle, assuming it to have an inorganic core material, 2, polymeric coating material, 1, coating thickness, t , and overall radius, R , by
(9) where,
B = 2k)K1
+ 2 ( 1 - j)K2
(10)
Equations 9 and 10 were recently derived by Badrinarayan and Barlow (19901, following and correcting Swift (1966). They showed that when combined with the Yagi-Kunii (1957) model for thermal conductivity in packed beds, eqs 9 and 10 predicted the observed experimental values for the bed conductivity of polymercoated lead shot to within 10% relative error. The spray-dried composite particles (Figure 6) clearly have more complex morphologies than can be described by a polymer-coated sphere; however we attempt t o estimate
KS by making this assumption. For a polymer volume
fraction in the composite particle, 41,the corresponding "thickness" of polymer coating in our idealized, coated sphere is given by t/R = 1 - ( 1 - 41)1'3
(11)
To provide some perspective, K1 for PMMA is 0.195 W/(mK) at 300 K, and K2 for Sic is 456 W/(m-K). The corresponding calculated thermal conductivity of the composite particle containing 20 vol % polymer is KS= 2.7 W/(mK) from eqs 9-11. The Maxwell-Eucken model (Eucken, 1940) predicts Ks = 2.8 W/(m*K)for the conductivity of the composite particle, and the Orr model (Orr, 1966), another method for estimating the thermal conductivity of dispersions of spheres, estimates the Ks = 2.5 W/(mK). Clearly, these models all give about the same estimate for the composite particle thermal conductivity. Figure 8 compares the estimated bed conductivity, calculated from eqs 5-11 with experimental values for powder beds of 20 vol % PMMA-coated Sic particles. Agreement between prediction and experiment are fair. At temperatures below 380 K, the increase in K is the result of increases in the thermal conductivities of all bed ingredients with increasing temperature. Above 380 K, the PMMA rapidly softens and flows, causing the bed density to increase. From 370 to 420 K, the bed void fraction, as measured by Xue, decreases from 0.53 to 0.41. This change in E is largely responsible for nearly tripling the bed conductivity over the 50 K range. When these experimental void fractions are used in the Yagi-Kunii model, the calculated results are seen (Figure 8) to underpredict the observed changes in K. This may indicate that the Yagi-Kunii model is insufficiently sensitive to changes in porosity (Xue, 1991). Sintering Rates. In our previous work with polycarbonate (PC) powder (Nelson et al., 19931, we established the importance to the successful modeling of the system of obtaining an empirical expression for the powder sintering rate as a function of temperature. With PC powder beds, substantial fusion of the powder t o form a void-free, completely consolidated, layer occurred during sintering. This consolidation greatly increased the thermal conductivity of the sintering layer. Modeling of sintering in this system required simultaneous solutions to equations for the rate of collapse of porosity by sintering and for changes in local thermal conductivity caused by the sintering. In that work, isothermal oven sintering rate data were obtained by heating 0.6 cm layers of the PC powder t o temperatures 10-15 "C above Tg. At these temperatures sintering rates are much slower (90-120 min to complete) than heat transfer rates (10 min to complete), thus ensuring isothermal conditions. Sintering was followed by a low normal stress surface probe whose position was monitored by a linear variable differential transformer (LVDT). Change in height information was collected and converted to a simple first order rate expression, - dddt = k'(6 - E,)
(12)
where E, is the plateau porosity at sintering temperature, T. The rate constant, K', was found to follow an hrhenius form,
k' = A eXp(-EA/RT)
(13)
The activation energy, EA= 41.7 kcallmol, was found
1646 Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995
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in (X io3) (KI) Figure 9. Effect of temperature on the sintering rate constant for (A)pure PMMA and (0)20 vol % PMMA-coated Sic.
to be similar in magnitude to that for viscous flow of the PC polymer, a result that seems reasonable for viscous sintering (Frenkel, 1945; Ristic, 1987; Scherer, 19771, where the rate constant, k', is considered to be proportional to the surface tension to viscosity ratio, y/p, and a function of particle geometry, the details of which vary with assumptions. Typical measured values for k' vary from 0.00025 to 0.0012 s-l in the temperature range from 20 to 40 "C above Tg. Oven sintering tests on Sic composite powders with 20 vol % PMMA were performed in the same apparatus that was used in the previous study of PC powders. Sintering rates were determined at isothermal temperatures between 100 and 150 "C. In contrast t o the PC powder which showed up to 40% reduction in normalized bed height, the composite powder showed only 3-5% reduction in normalized bed height after 20 min at 150 "C (45 "C above Tg).Since only the polymer is likely to consolidate by sintering, one could argue that the smaller reduction in bed height is reasonable. A powder bed with 50% relative density typically has 50 vol % pores, 40 vol % Sic, and 10 vol % polymer. If the polymer "phase" has the same porosity as the ceramic "phase", one would expect an overall reduction in volume of only 5 % caused by consolidation of the polymer phase. As discussed earlier (Nelson et al., 19931, the change in bed height in our oven sintering test appears to be directly proportional to the change in bed volume for PC powder. These results for composite powders also appear to be consistent with that earlier observation. Figure 9 shows the effect of temperature on initial sintering rates of pure PMMA and of the 20 vol % PMMA composite with Sic, evaluated using E , = 0, from initial slopes of normalized bed height time plots. The ratio of sintering rates of PMMA to the sintering rates of the P M W S i C composite vary from 25 to 7 over the temperature range, bracketing the ratio of 10, expected from the argument above. At temperatures below 127 "C, the activation energy for the composite powder is about twice the value, EA = 9.2 kcavmol, measured for the same PMMA powder as that comprising the composite. The reason for this behavior is not clear; however we note that the activation energy for the composite powder does appear to approach that for pure PMMA at temperatures greater than 127 "C. Interestingly, the sintering rates for the pure PMMA, 0.00025 s-l at 20 "C above Tg, are similar in magnitude t o those for pure PC a t a similar temperature above its Tg.Since both materials have similar melt flows, 30 g/10 min at 200 "C (100 "C above Tg) for PMMA versus
1.5 time,
2
2.5
3
8
Figure 10. Calculated temperature profiles for (-1 PC and for (- - -) 20 vol O/o PMMA-coated Sic, both scanned with identical parameters; (0)at surface, (0)0.1 mm below surface, (A) 0.25 mm below surface.
35 g/10 min at 300 "C (135 "C above Tg)for PC, this similarity in rates of sintering may point out, again, the importance of melt viscosity in determining rates of sintering.
Results and Discussion The oven sintering test results suggest that only small changes in density are likely to result during SLS processing of composite powders due to the small volume fraction of sinterable polymer employed. Both model calculations and photographic evidence from fracture surfaces, discussed below, are consistent with this suggestion. Typical calculated temperature profiles that compare PC powder bed response with that of the P M W S i C composite powder are shown in Figure 10. The surface temperatures clearly show the characteristic thermal spikes that result from the laser pulses associated with beam overlap (Figure 2). When processed with identical operating parameters, the calculated profiles for PC show higher temperatures for longer times than are seen for the composite powder. This is believed to be a consequence of the lower heat capacity per unit volume of bed, QCp,of the PC system. This feature, combined with a higher activation energy and higher rates for PC sintering kinetics at laser processing temperatures, leads to more sintering of the PC powder with greater porosity reduction than can occur with the P M W S i C composite. The higher sintering rates and consolidation of the PC powder also lead to improved conduction of heat into the PC powder bed, relative t o that in the bed of composite powder. The net result of these differences is that more energy must be put into the bed of composite powder to achieve interlayer fusion and part strengths that are comparable to those of PC. In his modeling work with PC powders, (Nelsonet al., 1993) has shown that combinations of three operating parameters-laser power, P, laser scan speed, SCSP, and laser beam spacing, BS- can be used to estimate the energy density through the expression energy density
P 2w 2w =nu2 BS SCSP -
P
BS x SCSP
(14)
where o is the effective beam radius. The first term in
Ind. Eng. Chem. Res., Vol. 34,No. 5, 1995 1647 Table 1. Effect of Laser Operating Parameterson Part Properties
100’
0
I
I
I
I
0.2
0.4
0.6
0.8
1
1
time, s Figure 11. Calculated temperature profiles in SiC/PMMA powder beds that are scanned at different laser powers holding the energy density constant. (- - -1 Lower power. (-) Higher power. For each set, highest temperature is a t surface, lowest at 0.25 mm below surface, and intermediate at 0.10 mm below surface.
2.0
-
1.6 1.4 -
1.8
1.2 1 .o
-
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
ENERGY DENSITY, cal/cm2 Figure 12. Calculated changes in void fraction of P M W S i C composite powder beds as a function of energy density.
eq 14 is simply the power density sorpted at the surface, aR(I) - h(T-T.), noted in the boundary condition of eq 1. The second term approximates the time that a circle with radius cu is under the laser beam during one “pulse” of thermal energy. The third term estimates the number of pulses received by a point on the surface (see Figure 3). Equation 14 is identical in form, though derived on a different basis, to the exposure, E,, derived in Jacobs (1992)to explain the effect of drawing speed on cure of photopolymerizable materials in the StereoLithography process. Figure 11 compares some computed temperature profiles for two runs that are scanned at different laser power but the same energy density. There appear to be significant differences between the surface temperatures achieved in the two runs; however, these temperature differences are reduced to only 10 “C at a depth of just 0.01cm below the surface. At 0.0254cm below the surface, the thermal profiles are nearly identical. To the extent that our model, calculated by the schematic, Figure 4, with eqs 1, 3, and 6-13, accurately portrays the physics of combined heat transfer and sintering, we expect densification by sintering of the polymer to be the nearly the same in both cases. We also expect from calculations of density change for different energy density values between 0.5 and 2.5 cal/ cm2 (Figure 12) that less than 2.5% density change should occur.
energy density, caVcm2 0.41 0.46 0.74 0.79 0.79 1.32 1.35 1.74 1.74 1.74 2.27 2.28
laser power,
W
scan spacing, in.
7 8 8 8 8 8 12 13 12 12 14 12
5 5 4 3 5 5 3 3 4 3 3 3
scan speed, in./s 125 125 100 125 75 75 110 92 64 85 76 65
density, gIcm3 1.35 1.37 1.37 1.38 1.40 1.40 1.37 1.33 1.35 1.32 1.35 1.34
green strength, psi 9.1 12.1 76.1 73.4 72.4 183.2 170.3 186.0 186.4 192.9 205.2 205.8
Table 1 shows experimental results of the influences of operating parameters on the resulting green, PMMN Sic, test bar densities and strengths for conditions where the parameters are varied but the energy density is held nearly constant. These data clearly show that green strength and density both increase with increasing energy density, and that nearly identical densities and strengths are achieved when the energy density values are the same, even though the individual parameters that comprise the energy density may vary widely. Figure 13 shows the influence of energy density on the green strength of test bars. A transition in green strength occurs at about 1.2 cal/cm2. Above this value the rate of strength increase is reduced to roughly 20% of the rate below 1.2 cal/cm2. Figures 14 and 15 show SEM photomicrographs of the fracture surfaces of these bars at energy density values below and above 1.2 cal/ cm2,respectively. At low values, the layered structure of the part is quite noticeable. This layered structure tends to disappear in parts which are prepared at higher energy densities, and one might imagine that the increase in observed strength with increasing energy density may be a consequence of improving the bonding between layers through increased sintering to achieve a more homogeneous product. Certainly, the part density does increase from 48 to 51% relative density over the range in energy density from 0.5 to 1.6 cal/ cm2, as shown in Figure 16. The reason for the knee in the strength curve (Figure 13)is not exactly clear. A simple explanation is that strength follows density (Knudsen, 1959;Rice, 1977), density is a nonlinear function of energy density, therefore so is the strength. This could be, however our calculations indicate a very linear dependence of part density on the energy density used to make it. Further investigation (Figure 17)of the reasons for an experimentally nonlinear relationship between part density and energy density suggests that the nonlinearity could be the result of degradation and vaporization of the PMMA binder. A steady decline in polymer content of SLS-processed test bars, as determined by gravimetric measurements in which the bars are fired at 600 “C for 2 h to remove the polymer, suggests that the rate of densification decreases with increasing energy density because binder is being lost and gas formed. We are presently considering the addition of a term to eq 14 to estimate the “thermal efficiency” of the heating process,
IED = energy density
x fl2culL)
(15)
That is, for a fixed scanning speed, the fraction of time
1648 Ind. Eng. Chem. Res., Vol. 34, No. 5 , 1995 250
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ENERGY DENSITY, cal/cm2 Figure 13. Influence of energy density on green strength of test bars in three-point bending.
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ENERGY DENSITY, cal/cm2 Figure 14. SEM photomicrographs of cross sections of test bars produced using energy density = 0.6 cal/cm2.
Figure 16. Influence of energy density on green density of test bars.
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ENERGY DENSITY, cd/cm2 Figure 17. Effect of energy density on polymer content. Figure 15. SEM photomicrographs of cross sections of test bars, produced using energy density = 1.3 cal/cm2.
that the material is being heated in a given scanning cycle is approximately 2 d L , where L is the length of the scan vector. During the rest of the cycle, the surface of the material cools, primarily by radiation, and much of the sorbed energy is lost. The term is included to
conceptually explain experimentally observed phenomena such as poor laser power utilization, and reductions in layer fbsion when all operating parameters are held fured, but part size and vector length are increased. An example of the latter phenomenon is shown in Figure 18, where it can be seen that the bending strength of green test bars, made with the 20 vol % PMMA-coated Quadmodal, decrease by a factor near 2 when the scan vector length is increased from 3 to 6 in. at fured energy
Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 1649 130
n
2
.- 130
0
v)
cp
1.45
2
1.40
Y
-120 I '
g 110 1 z w E 100 -
G
z
1.35
v,
w
m
90:
z
80 ;
[ (3
1.30 r
.
1.25' 0.50
VECTOR LENGTH, in. Figure 18. Effect of vector length on green strength of bars produced at energy density = 1.75 cal/cm2.
250
-
-
-
1.00
1.50
-
-
-
2.00
2.50
ENERGY DENSITY, cal/cm* Figure 20. Influence of beam radius on density of green parts. (+) 233 pm. (A)338 pm. (0)483 pm.
200 150 100
vv
0.50
1.00
1.50
2.00
2.50
ENERGY DENSITY, cal/cm2 Figure 19. Influence of beam radius on three-point bending strengths of test bars. (+) 233 pm. (A)338 pm. (0)483 pm.
density = 1.75 cal/cm2. This result suggests that the function fl2cu/L) in eq 15 is approximately inversely proportional to vector length, L. In contrast to the samples in Figure 13, which were prepared by laser scanning alternate layers of 3 and 1 in. overlapping vectors to form a hatch pattern, the bars in Figure 18 were cut from square tiles that ranged in edge length from 3 to 6 in. Alternate layers in these tiles were laser scanned at right angles to form the same hatch pattern; however the vector lengths and the cooling times between energy input pulses at surface points in the square tiles are considerably longer than those in the 3 in. x 1 in. bars. This difference seems to explain the observations that the strengths at energy density = 1.75 cal/cm2are much higher, 175 psi versus 133 psi, in the 3 in. x 1in. bars that were laser scanned to shape than in the bars that were cut from the square tiles. The efficiency term can also conceptually account for some changes in properties of specimens with fixed geometry when the laser beam diameter is changed, all other parameters held constant, and for problems with polymer decomposition due to excessive heating when scan lengths are reduced. For example, Figures 19 and 20 show that doubling the beam radius, at fured energy density values in excess of 1.1 caVcm2, increases the bending strength of test bars by approximately 30 psi and decreases their densities by approximately 4% over the entire range of energy density values. While not a large effect in the testing parameter range examined, increasing the beam radius at fixed energy density should increase the net energy input to the material,
Figure 21. Typical green parts.
according to eq 15, thereby increasing strength and decomposing the binder in much the same qualitative way as is caused by increasing the energy density. We have yet to determine the exact functionality of the efficiency term in eq 15. Work is continuing to determine this in other composite metal/polymer and ceramic/ polymer systems and will be reported in subsequent papers. Figure 21 shows some typical green parts that were made for metal infiltration by the Lanxide Corporation (Newark, DE) PRIMEX pressureless metal infiltration process. These parts were successfully infiltrated to form composites with 45 vol % Sic,47 vol % Aluminum, and 8 vol % porosity. Typical four-point bending strengths were approximately 40 x lo3 psi, the elastic moduli were near 26 x lo6 psi, and part densities approached 3.0 g/cm3(Deckard and Claar, 1993). Typically, parts with green strengths greater than 125 psi, corresponding to energy density > 1.0 cal/cm2, were preferred because they had sufficient strength for handling and shipping and because they did not delaminate during the metal infiltration step. The present paper has been more concerned with modeling the relationships between heat transfer, sintering, and the resulting mechanical strengths of green parts; however accuracy and repeatabilty of part formation are issues often raised by potential users of all rapid prototyping processes, including SLS. One approach toward answering these questions is to do statistical analyses on measured dimensions of a large number of test parts; see Jacobs (1992). We simply note, here, the uncertainties in measured dimensions of the various rectangular test coupons that we generated in the
1650 Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 Table 2. Accuracy and Repeatability
no. of samdes
X . mm Y. mm Z . mm Case 1. Test Coupons, 50.8 x 50.8 x 7.62 mm 39 50.63 f 0.25 50.65 f 0.22 7.75 f 0.16 Case 2. Three-Point Bend Bars, 76.20 x 25.40 x 6.40 mm 30 (build 1) 76.11 f 0.17 25.34 f 0.15 6.42 f 0.09 25.57 f 0.13 6.65 i 0.11 50 (build 2) 76.35 f 0.10
course of our work, Table 2. These parts were all made at 0.114 mm layer thickness, 119 "C bed temperature, and energy density between 0.5 and 2.5 cal/cm2. Parts in cases 1and 2 were made from 25 vol % PMMA-coated Sic that was mixed with uncoated Sic to drop the overall polymer content to 20 vol %. Overall, the dimensions appear to be randomly uncertain by about k0.2 mm (kO.010 in.) regardless of the batch being processed and regardless of the direction observed; that is, the dimensions in the X-Y build plane (within the layers) seem to have about the same uncertainty as that in the 2 direction, the direction perpendicular t o the layer plane. The machine seems to be repeatable, insofar as the parts made from the same material batch on different days, build 1 versus build 2, seem to be statistically equivalent; see case 2. The expected bar dimensions sent by the computer from the part dimension file to the laser control and scanning system are given in the case subheadings in Table 2. Comparison of these dimensions with those actually obtained suggests in cases 1 and 2 that very little systematic error exists; within the envelope of uncertainty in the measured dimensions, the measured dimensions coincide quite well with the expected dimensions.
Summary and Conclusions This work clearly demonstrates that the current SLS technology can produce polymer-bound, porous, ceramic shapes from composite powders that show acceptable strength and dimensional accuracy. This demonstration is just one of many, including composite powders of PMMA with alumina, copper, glass, silicdzircon, and, more recently, iron (Tobin et al., 1993; Badrinarayan, 1994) that can be prepared by SLS and subsequently processed to eliminate the PMMA binder. As shown in the present P M W S i C system (Figure 16) all shapes made from composite powders tend to be nearly as porous as their respective powder beds. This behavior contrasts sharply with the substantial consolidation observed when forming shapes from waxes, nylon, and polycarbonate powders by the SLS process (Nelson et al., 1993). The thermal calculations, Figures 10-12, suggest that this difference is largely due to the greater thermal masses of the composite powders, although some resistance to polymer sintering, suggested by the differences in activation energies observed when oven sintering pure polymer and composite powders (Figure 91,may also be involved. Very good dimensional accuracy is possible when composite powders are used (Table 21, and very little warp or curl, effects that are related t o polymer consolidation (Forderhase, 1993), is observed. The porosity of the green object can be reduced and its strength improved by increasing the polymer content of the composite powder. However, this increases the void content of the structure on subsequent removal of the polymer for metal infiltration by the Lanxide PRIMEX process, or for resin infiltration (Tobin et al., 19931, or for inorganic colloid infiltration
(Glazer et al., 1993; Vail and Barlow, 1992) and can adversely affect the final properties of the structural part. Improvement in powder bed density is needed to further reduce porosity and t o improve the final Sic loading and properties of the metal matrix composite (Deckard and Claar, 1993). The Quadmodal Sic powder distribution was designed to provide this improvement; however most of the gain in bed density associated with this distribution is lost when the powder is agglomerated and coated in the spray drier. Work is continuing on this fundamental problem. This study of P M W S i C composite powders has shown that strengths and, to some extent, densities of green parts can be increased by increasing the energy input density, characterized, in part, by the energy density. Green part strengths and densities are found to increase in a nonlinear manner with increasing energy density from 0.5 to 2.5 cal/cm2. The data suggest that an optimum energy density may exist near 2.5 call cm2 for the 3 in. test bars that were scanned longitudinally. This optimum is probably the result of binder loss through thermal degradation at the higher energy density values. The efficiency term in the IED, eq 15, serves to emphasize that the Input energy density and resulting properties are dependent on the laser scan geometry as well as on the laser power, scan rate, and scan spacing parameters that are identified in the energy density. Consequently, energy density values that are appropriate for a 3 in. vector length may be too high if the vector length is reduced to 0.5 in., or if the beam diameter is increased at fixed vector length. This dependency of Input energy density on vector length suggests that advanced control strategies in which the energy density is continually adjusted to account for geometry-based thermal losses may need to be developed. Work toward developing a more comprehensive understanding of the efficiency term is continuing.
Acknowledgment Financial support for this research by DARPNONR Grant N00014-92-5-1394 and DARPA Grant MDA 97292-5-1026, through Lanxide Corporation, is gratefully acknowledged. The authors also wish to thank Mr. Mike Durham of the DTM Austin Service Bureau for his cooperation in providing SLS Workstation time.
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IE930661N ~~
Abstract published in Advance ACS Abstracts, April 1, 1995. @
