Energy Dissipation and Sinter Mechanisms in a Laser Supported Generative Fabrication Process Using µm-scaled Powders

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1 18 th Plansee Seminar RM 40/1 Energy Dissipation and Sinter Mechanisms in a Laser Supported Generative Fabrication Process Using µm-scaled Powders A. Streek*, P. Regenfuss*, H. Exner* * LHM, Hochschule Mittweida, Mittweida, Germany Abstract Laser micro sintering, a high resolution version of the generative fabrication technology selective laser melting, relies on the solidification of µm-grained powder by laser radiation. It has been applied with powders from metals, preferentially tungsten, and later on molybdenum, as well as from ceramic feedstock. Several approaches have been undertaken in the past to model the mechanism of the process. Recent simulations of the interaction between laser radiation and the powder material allow for new quantitative correlations of the process performance with the applied laser regime, the dimension and consistency of the powder packing, and the powder material properties. On the basis of simulations and analytical approaches of energy dissipation in the powder layer suitable parameter windows can be defined for laser sintering with pulsed radiation. Arguments can be derived confirming the observed particular suitability of tungsten and molybdenum with regard to a stable laser micro sintering process. Keywords laser sintering, molybdenum, energy dissipation, powder metal Introduction Laser Micro Sintering Laser micro sintering is a modification of selective laser sintering, which is based on repeated cycles of coating and selective densification (sintering) of powders or pasty materials with the ends of generating, layer by layer, a three-dimensional body. In accordance with the name, the solidification of a layer is achieved by scanning a laser beam over the cross-section of the desired object. The material passes through a transitory melt phase. Since its invention by Carl Deckard & colleagues [1] selective laser sintering has been upgraded continuously to meet the requirements for the production of functional components [2]. A considerable contribution to the improvement of resolution was the modification and optimization of the already established technology in 2001 at Laserinstitut of Hochschule Mittweida. It resulted in a technology named laser micro sintering. The main features are the employment of q- switched laser pulses, focal diameters of the laser beam around 25 µm and higher and the use of

2 18 th Plansee Seminar RM 40/2 powder with particle sizes in the µm-range. The performance is a resolution that equals the focal diameter. Laser Micro Sintering and Energy Dissipation In order to narrow down the variance of parameters to the range that is suitable for a successful conduct of the process, the energy conversion of the laser beam penetrating into a powder layer will be analyzed regarding the spatial distribution of the absorption and the dynamics of the heating of the particles to the required temperature (Fig. 1). Figure 1: (a) Schematic of the three formal steps of a laser beam dissipation in a powder layer. (b) Primary dissipation denotes the spatial distribution of the power absorption (c) Secondary dissipation is the conversion into heat and the distribution throughout each individual irradiated particle. (d) Tertiary energy dissipation comprises inter-particular heat conduction through the powder layer and any type of material dynamics and migration. For these ends the conversion of the laser radiation energy absorbed by the powder packing is considered a multi-mechanistic process composed of primary, secondary, and tertiary dissipation as well as the generation of plasma with the concomitant optical and thermodynamic effects (Fig. 1b,c,d). Laser micro sintering implies irradiation with pulses on a 100 ns time-scale. Although during this irradiation period, secondary will overlap to a limited degree primary dissipation, the two mechanisms will be regarded separately for the following mechanistic consideration. Tertiary dissipation will not play a role in the calculations and simulations as the range of sinter parameters will be limited to regimes by which melting of the particles will occur, and boiling will not be possible yet. Thus, material dynamics and long range heat conduction through the powder will not be respected. During the first phase, the primary dissipation, high intensity radiation directed toward powder layer is scattered, simultaneously resulting in a three dimensional distribution of absorbed energy per pulse [3]. This dissipation corresponds to a continuous decrease of radiation intensity with increasing depth of the respective powder packing horizon. By integration of the change of intensity over the depth and over the time a pattern of primary energy dissipation in the powder packing can be derived. Influential factors are the optical density of the powder and the material specific degrees of absorption [4]. As mentioned above, especially in the case of long pulse widths, the secondary dissipation phase overlaps partially with the primary one. In this second step the energy dissipates from the outer shell throughout the entire particle. The progression of it depends on thermodynamic material properties. Next to the coefficient of heat conductivity and the heat capacity, also the particle size determines the rate of heat equilibration in a particle and the final temperature of it [5]. Depending on the reach of the intensity, determined by the primary dissipation, respectively the overall depth of the powder layer, secondary

3 18 th Plansee Seminar RM 40/3 dissipation into the bulk of the underlying solid (i.e. the substrate or the already sintered body) might have to be regarded. During, or at the end of this secondary phase, powder particles and the substrate material in contact should have reached such a state of fusion that is prerequisite for the formation of a conjoint melt phase which will finally lead to the integration of new material into the sintered specimen. First, it will be shown that the optimum thickness of the powder layer is determined by the absorption degree of the powder material, the particle size, and the powder layer density. Secondly, the dependence of the optimum laser beam intensity, at a given pulse width, on material properties and particle size will be explained. Primary Dissipation and the Optimum Powder Layer Thickness D-Powder Model and Ray Tracing Figure 2: (a-d): Exemplary fractional rays of a laser beam inciding into a mono-disperse powder layer with a relative packing density of Pd = 15 % and a material specific absorption degree A Mat of 30 % with four different typical scattering traces. (a) Transmission without deflection. (b) Forward scattering. (c) Singular and back-scattered reflection on the powder surface. (d) multiply deflected and attenuated ray. (e-f) Scattering and absorption of a laser beam penetrating through a volume of monodisperse 5 µm-powder with an absorption degree A Mat = 30 %. (e) Side view (projection) of the powder cuboid and the beam as a bundle of 52,000 fractional rays. (f) Bottom view onto the powder layer and the partially scattered and transmitted beam. For the simulation of the spatial absorbance distribution in irradiated powder, layers consisting of monodisperse sphere-shaped particles were assumed, and an algorithm was developed [6] that employs the principle of ray tracing [3]. The idea is that the incident beam is split into a set of parallel rays; according to the angle under which a ray hits a particle its direction is changed. With each reflection the power of the respective ray is attenuated by the factor of the absorption degree. The material specific absorption degree (ratio of absorbed over incident power) is assumed independent of any other parameters. Each attenuation leads to the transfer of a defined amount of energy to the respective particle during a defined irradiation time (e.g. the laser-pulse width). The number of reflections and the lateral position allows for the calculation of the intensity distribution at any level of the powder layer. The model of a

4 18 th Plansee Seminar RM 40/4 stochastically positioned powder layer, with defined size distribution and relative packing density, has been generated by an extra recursive algorithm [6]. Table I: Characteristic partitions of the beam power that describe the primary dissipation within a powder layer Partition Symbol Definition Transmission degree Absorption degree of the powder layer Overall deg. of scattering T A S Partition of the beam power that penetrates the layer without interaction. Partition attenuated due to reflection from the particles. Sum of power of rays leaving the powder layer after at least one reflection. Forward scattering S for Sum of power of all rays leaving the powder layer through the layer surface averted from the beam source, after at least one reflection. Backward scattering S back Sum of power of all rays leaving the powder layer via the surface that faces the beam source, after at least one reflection. In Fig. 2 views of sample rays (Fig. 2a-d) and cross section views (Fig. 2e-f) of the complete bundle are presented. The virtual powder volume is composed of ~ 2,600 particles. For the calculation the laser beam was split into ~ 52,000 fractional rays. The results for the characteristic partitions (see Tab. 1 for definition) of the beam power are: Transmission degree T = 5.35 %, absorption degree of the specific powder layer A = 60 %, and the overall degree of scattering S = 34.5 %, S for = 9.6 %, and backward scattering S back =24.9 %. For several sets of powder parameters the characteristic partitions through primary dissipation have been calculated. In the case of the chosen material and powder layer a notable amount of the total radiation (~ 35 %) escapes from the powder layer after scattering, backward scattering with a ~ 70 % fraction of the overall scattering making up for the largest part. The overall absorption A powder = 60 % is already twice as high as the absorption A Mat = 30 % resulting from a singular reflection from a macroscopic surface of the bulk material. Despite the relatively large thickness, a noticeable, though small, partition results that transmits without deflection T = 5.35 %. Dissipation and Power Balance of the Penetrating Beam For a given set of parameters that characterize the optical properties of the layer (Table II) the balance of the characteristic partitions depends only on the powder layer thickness. Fig. 3 shows the plots of the characteristic partitions versus the powder layer thickness as well as the respective 6th degree polynomial fits, whereas the values can be likewise considered as the ratios of power over the beam power or the energy over the pulse energy.

5 18 th Plansee Seminar RM 40/5 Table II: Parameters that determine the optical properties of a powder layer Parameter Symbol Definition Packing density degree Pd Mass per volume of the powder layer divided by the specific density of the bulk material Particle size r P Particle radius. Material specific absorption degree A Mat Amount of power/energy absorbed per ray power/energy due to singular reflection from the surface of bulk material layer thickness z powder layer thickness or depth Figure 3: Simulated partitions of the beam power (for the symbols and definitions of partitions and powder parameters, see Tables I and II) inside mono-disperse powder layers with thicknesses up to 100 µm. Within the rows, the packing densities Pd (10 %, 25 %, and 35 %) are kept constant. For each packing density diagrams are shown for a powder with an absorption degree A Mat of 10 % and three different particle radii r p (1 µm, 1.5 µm, and 5 µm) and for three powders with a particle radius of 2.5 µm and three different material specific absorption degrees A Mat (0 %, 10 % and 20 %). With decreasing packing density, due to decreasing statistical relevance, increasing deviation of the individual simulated values from the fitted curve can be observed. Transmission was not obtained via numerical fitting but had been calculated by the developed Eq. 1, as the shadowing of a beam penetrating through a stochastic arrangement of mono-disperse spherical particles [6]. It merely depends on the packing density, the grain size, and the thickness of the powder layer. T 3 ln1 Pd z 2 2r ( z) e P (1)

6 18 th Plansee Seminar RM 40/6 A detailed discussion of the dependencies is reported in an earlier publication [6]. The upper limit of the powder layer absorbance is in good approximation represented by the cube root of the material absorption degree A Mat, independent of any other powder parameter. Eq. 2 is the mathematical term, describing a relation between absorption A and the powder parameters, that coincides best with the polynomial fit of the absorption data. 3 z ln1 Pd 3 A Mat 2 2rP A( z) 3 A Mat 1 e (2) Definition of the Optimum Powder Layer Thickness Though Eq. 2 does not account for the inflection point of A(z) that can be observed in the simulated data (Fig. 3) and that is also detectable in the literature [3], this inflection point can still be located by Eq. 2,as it almost exactly appears at the same powder layer thickness where the curves of A and T intersect. This maximum slope in the absorption indicates that with further increase of powder layer thickness the differential absorption per thickness, da/dz, will decline. This specific thickness is also the penetration depth of a laser beam where the most power per powder mass is absorbed and where the highest temperatures resulting from secondary dissipation are to be expected [6]. It is referred to as the optimum thickness z opt because an additive process is most probable, and the risk of overheating is least when the powder particles with the highest amount of absorbed energy are in contact with the underlying substrate or with the sinter body. The optimum powder depth or layer thickness z opt is calculated by use of Eq. (1) and Eq. (2): e 3 z opt ln 1 Pd 3 2 2rP 3 AMat 3 zopt ln1 Pd A Mat 2 2rP 1 e (3) Exemplary z opt as a function of packing density Pd are plotted for three particle sizes in Fig. 4. Figure 4: Optimum powder layer thicknesses z opt calculated according to Eq. 3 with the potential of generating the maximum melt volume at the interface between powder and substrate body for various material specific absorption degrees A Mat and mono-disperse particle radii r P. In Table III the optimum thicknesses (according to Eq. 3) are listed of powder layers from mono-disperse molybdenum powder with a particle radius of 2.4 µm for various packing densities (molybdenum powder with a mean particle radius of 2.4 µm, powder Mo-4.8 ; is preferentially used in laser micro sintering).

7 18 th Plansee Seminar RM 40/7 Table III: Optimum layer thicknesses for mono-disperse molybdenum powder (r P = 2.4 µm; A Mat = 30 %) Packing density z opt [µm] Secondary Dissipation and the Definition of an Optimum Intensity Figure 5: Simulated 3d-distribution of heated powder particles immediately after irradiation with a laser pulse. The units are relative to the highest obtained temperature, phase transitions are not regarded. (a) Mono-disperse size distribution. (b-c) Two different poly-disperse distributions. Only the particles are displayed that show a relative temperature > 5 % of the highest resulting temperature. The first and rapid step of secondary dissipation is the conversion of electronic energy into heat, if the frequency of the radiation lies in the NIR/Vis region. Simultaneously heat flow sets on, toward equilibration of the heat throughout the particle. If energy and intensity of the considered laser pulse are restricted to an extent that phase transition is avoided, the temperature distribution over the particles is similar to the calculated results in Fig. 5. It is, however, crucial for the laser sinter process, that the better part of the powder is converted into melt phase by thermal equilibration of the individual particles. Due to the finite thermal conductivity during or at the end of the applied laser pulse, over-heating can occur with the effects of boiling and concomitant loss of melt that will not be available to the sinter process any more. Consequently boiling should possibly be avoided. Therefore, the search for a suitable sinter regime is always a search for the conditions under which the highest portion of the processed material is fused at the lowest extent of boiling. The intensities indicated in the following sections shall be understood as absorbed intensities, the absolute values of the partitions that are absorbed by a singular reflection. To obtain the corresponding intensity of the incident radiation the indicated values have to be divided by the material specific absorption degree A Mat. Calculation of Intensity Limits Analogue to One Dimensional Heat Conduction in an Infinite Rod Irradiation of a solid with a laser beam is equivalent to an energy flow through the surface. It is carried on as heat flow into the depth of the solid. Under the presumptions, that the irradiated body has a prismatic shape, the irradiation of the surface is homogenous, heat transfer into the environment can be neglected, and the depth of the body is large compared to the thermal penetration depth, the ideal one-

8 18 th Plansee Seminar RM 40/8 dimensional solution of Fourier s heat equation for an infinite rod is applicable. The rate of temperature increase on the solid surface during irradiation depends on the intensity, the thermal conductivity and the heat capacity of the solid. The surface temperatures achieved at the end of the irradiating pulse, in relation to the phase transition temperatures of the processed solid materials, serve to classify the material specific intensity windows for laser sintering with the respective pulse width. Three characteristic intensities are defined according to the following criteria: The intensity I min by which the surface temperature reaches the fusion temperature is considered the required minimum. With the optimum intensity I opt, the surface reaches the boiling temperature, which means that the maximal depth of melt without ablation can be obtained. A good approximation for the upper limit is an absorbed intensity I max that exceeds I opt by the amount that supplies enough additional energy for the comprehensive ablation of the melt quantity generated under I opt. Figure 6: Intensity for laser sintering of various metals with a 180 ns pulse, according to the approach of one-dimensional heat conduction within an infinite rod. The vertical marks within each bar denote the optimum intensity for the respective material. Fig. 6 shows the intensity windows for laser sintering with a pulse width of H = 180 ns, using the infinite rod as a particle model. The broader the process window, the more stable is the conduct of the process. The apparent outstanding suitability of aluminum and copper due to their wide intensity ranges are modified by the high reactivity of the heated materials toward environmental atmosphere. Furthermore, as both, aluminum and copper, have lower material absorption degrees A Mat (Table IV) it can be deducted from Fig. 4 that they require thicker powder layers at the same relative packing density. Thicker powder layers in turn deteriorate the resolution of the process. Table IV: Absorption degree A Mat of metals for 1064 nm radiation (ideal values according to the Fresnel equation) Metal Mo W Cu Al Fe Ti A Mat Calculation of Intensity Limits Analogue to One Dimensional Heat Conduction in a Finite Rod Calculation of the surface temperature by the model of the infinite rod is only admissible if particles are concerned that are considerably larger in diameter than the thermal penetration depth. For small particles, however, the solutions for heat conduction in a finite rod have to be applied. The rate of temperature increase on the irradiated surface is higher for a rod with limited depth. Additionally, the interface between the liquid phase and the solid inside an infinite rod starts to withdraw immediately once the irradiation of the surface stops, temperature equilibration approaches the value of the nonirradiated body. In a finite rod, however, secondary dissipation after termination of the laser pulse can also lead to post-irradiative expansion of the melt phase throughout the entire volume of the body.

9 18 th Plansee Seminar RM 40/9 The following example (Fig. 7) refers to a laser pulse width of 180 ns. The determination of the intensity window that allows for satisfactory sintering performance is approached from two sides. Firstly, the extent of absorbed energy has to provide for comprehensive fusion, but it should not reach the amount that suffices for the boiling of the entire particle. Secondly, the irradiated surface has to reach the temperature of fusion and remain below the boiling temperature. The first of these prerequisites is a matter of energy balancing. The results are presented as the straight lines in Fig. 7 denoted min(q), opt(q), and max(q). min(q) contains the intensities by which, disregarding possible over-heating, the cross section of the respective particle absorbs during the pulse width of 180 ns the energy that would be just sufficient to convert the entire particle into liquid phase. By the intensities in the curve opt(q) the amount of energy that equals the heat required to raise the particle temperature to the boiling point plus the enthalpy of fusion is absorbed. This is the energy that could convert the entire particle mass into melt phase at boiling temperature and thus the highest intrinsic energy that the particle can bear without boiling. The intensities max(q) deliver the minimum energy that is needed to raise the temperature to the boiling point, plus the energy for comprehensive evaporation of the particle. Figure 7: Characteristic (absorbed) intensities for the fusion of molybdenum particles with a 180 ns laser pulse vs. particle radius. The straight lines contain the intensities that yield per pulse the net amount of energies per particle cross section, that would be sufficient to fuse the particle (min(q)), to fuse and heat the particle to boiling temperature (opt(q)), and to heat the particle to boiling temperature and evaporate the entire mass (max(q)) in an imaginary, slow heating process. The bent curves consist of the intensities that lead to the fusion temperature on the irradiated particle surface (min()), the boiling temperature on the irradiated particle surface (opt()), and to comprehensive boiling of the fused portion of the particle when the irradiated surface has reached the boiling temperature (max()), as a consequence of energy absorption from the described laser pulse. The second prerequisite is determined by heat conduction. It is taken account of in Fig. 7 by the solution of Fourier s equation for one-dimensional heat conduction within finite rods. As a first approximation the heat conduction in spheric particles has been equated with the one in cylindrical rods of the same crosssection and volume; on the abscissa, the radii of the spheric particles are indicated. The three intensity curves in Fig. 7, max(),opt(), and min(), represent the following thermal conditions at the end of the pulse. The curve min() consists of the intensities by which the particle surfaces have reached the fusion temperature at the end of the pulse. Any further energy would lead to the onset of melting in the surface zone. It is considered the minimum energy where partial fusion of particles might be observed. opt() are the intensities by which the irradiated surface acquires boiling temperature. With these intensities, the maximum energy can be absorbed by the respective particles without any ablative loss. With intensities of curve max() not only the irradiated surface reaches boiling temperature, but

10 18 th Plansee Seminar RM 40/10 additional energy has also been absorbed that is equivalent to the evaporation enthalpy for the already fused portion of the particle mass. This would imply ablation of the entire liquid phase and preclude any inter-particular fusion. The values in Fig. 7 have been calculated for the material properties of molybdenum, which are c p = 250 Jkg -1 K -1, ρ = 10.3 gcm 3, = 139 Wm -1 K -1. The shaded section between the curves min(q) and opt() denotes the range of particles that can be comprehensively converted into liquid phase without ablation by a 180 ns laser pulse and the respective intensities. The largest molybdenum particle (max(r p-melt ) in Fig. 7) that can be comprehensively fused by a 180 ns laser pulse has a radius of around 2.1 µm. This is close to the mean molybdenum particle radius (2.4 µm) of the preferentially used metal powder in laser micro sintering. Larger particles require longer irradiation times (Fig. 8). The corresponding intensity of Wcm -2 absorbed by the 2.1 nm particle requires an intensity = Wcm -2, which is close to the preferred intensity that is applied in laser micro sintering of the commercial powder Mo-4.8. Figure 8: Intensity/particle-size windows for comprehensive melting of molybdenum particles with laser pulses of various pulse widths, deducted analogue to the values in Fig. 7. Fig. 9 shows the results, obtained by numerical simulation, for the stage of heat distribution at the end of a 180 ns laserpulse. The calculated case 1 through 4 represent the likewise numbered green circular dots on Fig. 7. From the characteristic intensities (Fig. 7) the following should be anticipated (Table V): Table V: Anticipation of the temperature and phases of the denoted Intensity/particle-size couples in Fig. 7 according to the characteristic intensities. Couple No Phases vapor vapor and liquid (solid?) liquid solid liquid Temperatures > 4900 K 4900 K (vapor) K 4900 K (liquid) The simulated results (in Fig. 9) agree with the phase transition behavior of the denoted four particles at the indicated intensities in Fig. 7. The subsistence of a solid phase in the case of particle 2 cannot be deducted from Fig. 7 but results also from the calculation, leading to the characteristic intensities, and is corroborated by the numerical simulation.

11 18 th Plansee Seminar RM 40/11 Figure 9: Simulation results of the highlighted intensity/particle-size couples in Fig. 7. In the data column on the right the absorbed intensities are denoted as I 0, and the maximum and minimum material temperatures as T min and T max. The temperature distributions in the in the non-volatile particle masses are shown in the left column (temperature map of the particle). The right graphic column (phase map) shows the extension of the phases. T min and T max comply well with the anticipations (Table V) on the basis of the characteristic intensities. By the simulation the mass loss through boiling during the laser pulse is represented by the size and shape of the remaining particle, explicitly visible in the case of particle 1. Furthermore the simulation includes the radiative heating of the environmental atmosphere through the heated surface of the particle.

12 18 th Plansee Seminar RM 40/12 Summary and Outlook: In order to estimate the process windows for laser micro sintering, a calculatory approach for the energy conversion of a laser beam penetrating into a powder layer has been made that splits energy dissipation up into a primary, a secondary, and a tertiary step. Especially for the short laser pulses that are applied, the primary and secondary step can be considered separately. The calculation of the first step has been carried through with an analytically derived equation for the transmission through a powder layer that consists of particles with 100 % absorption. The scattering has been simulated with a ray tracing algorithm. With the combination of both relations, the spatial distribution in the powder layer of the total absorbed energy per pulse can be determined. From this information the optimum layer thickness results. Secondary dissipation of the absorbed energy by heat transport throughout each individual particle (intra-particle dissipation) has been calculated principally by solving Fourier s equation for onedimensional heat transfer inside a finite rod. Together with fundamental thermodynamic considerations, these calculations allow for the determination of characteristic energies and intensities of the employed laser pulse. With the deduced dependencies, the crucial prerequisites for a successful laser micro sintering regime can be defined. The present calculations refer to mono-disperse powders with spheric particles and random distribution of the particles in the powder volume. Future calculations will have to draw into account agglomerates and other possible particle arrangements in powders. Furthermore, for the process performance, tertiary dissipation and material dynamics play an important role. These effects are not yet regarded in the above considerations. The respective enhanced calculations and appropriate models that are currently being derived will be object of future publications. References 1. C. Deckard, US patent 4,863,538. Filed: October 17th, 1986, published September 5th, M. Shellabear and O. Nyrhilä, Proceedings 4th LANE 2004, Sept , M. Geiger and A. Otto Eds., Meisenbach-Verlag, Erlangen, Germany, ISBN , (2004). 3. X. C.Wang and J. P.Kruth, CCP 67 [1.7], B. H. V. Topping Ed., Civil-Comp Press, Edinburgh, UK, doi: /ccp , (2000). 4. A.V.Gusarov and J. P.Kruth, Intern. J. Heat and Mass Transfer 48, (2005). 5. C. Konrad, Y. Zhang and Y. Shi, Int. J. Heat Mass Transfer 50, (2007). 6. A. Streek, P. Regenfuss and H. Exner, Proceedings LIM 2013, C. Emmelmann, M. Schmidt, M. Zäh and T. Graf Eds., Physics Procedia Elsevier B.V., Amsterdam, Netherlands, Submitted (2013).