Numerical simulation in the absorption behavior of Ti6Al4V powder materials to laser energy during SLM

Journal of Materials Processing Tech. 268 (2019) 25–36

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Journal of Materials Processing Tech. journal homepage: www.elsevier.com/locate/jmatprotec

Numerical simulation in the absorption behavior of Ti6Al4V powder materials to laser energy during SLM

T

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Dongyun Zhanga,b, , Weidong Wanga,b, Yanwu Guoa,b, Songtao Hua,b, Dongdong Donga,b, Reinhart Poprawec, Johannes Henrich Schleifenbaumc,d, Stephan Zieglerd a

Institute for Laser Engineering, Beijing University of Technology, Pingleyuan No. 100, Chaoyang Dist., Beijing, 100124, China Beijing Engineering Reserch Center of 3D Printing for Digital Medical Health, Beijing, China c Fraunhofer Institute for Laser Technology ILT, Aachen, Germany d RWTH Aachen University – Digital Additive Production (DAP), Aachen, Germany b

A R T I C LE I N FO

A B S T R A C T

Associate Editor: A. Clare

In the paper, the effects of porosities and average particle sizes of powder layer on light absorption during SLM process were investigated, in which closed-packing models based on Horsfieled’s filling method were established and light absorption was simulated using ray tracing based on laser-material interaction mechanism. Corresponding to closed-packing models, the powder materials were prepared for absorption measurement using integrating sphere. The experimental results of light absorption verify the feasibility of the establishment of closed-packing models, the accuracy in calculation in the light absorption. The results show the absorption of powder layer of Ti6Al4V alloy is higher than 70%. The decrease of porosity of powder layer benefits to improve the absorption, while the absorption tends to decrease if porosity decreases to a certain value due to the reflection. The decrease of average particle size of powder particles benefits also to improve the absorption. If the light irradiates at positions with different particle arrangements, the absorption behavior changes with irradiation condition whether there occurs the multi-reflection. The above research provides theoretical basis for preparation of new powder materials, their parameter developing for SLM technology and even the properties regulation of SLM fabricated component.

Keywords: Numerical simulation Selective laser melting (SLM) Absorption behavior Ti6Al4V Powder material Closed-packing model

1. Introduction Ti6Al4V, an α + β two-phase titanium alloy, which has advantages of low density, higher specific strength, better corrosion resistance, and better mechanical properties at high temperature, is extensively used in aerospace, shipbuilding, petroleum, chemical, and medical industries (Yin et al., 2018). The application of titanium alloys can significantly reduce the weight of structures and improve its safety, and has already become one of the indispensable structural materials for modern aircraft and engines, the demand for titanium alloys in aviation industry has increased rapidly since the 21 st century (Günther et al., 2018). However, its characteristics of lower thermal conductivity, higher hardness, and larger elastic deformation have made conventional material processing methods unable to meet the requirements for design and integrated manufacturing (Mazur et al., 2016), which has led to the emergence of manufacturing technology for components with complicated geometry and excellent mechanical properties. Selective Laser Melting (SLM) technology is a computer-aided

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design (CAD) and manufacturing process based on the principle of discrete and integration, in which a high power laser is used to scan over the powder bed, directly melts metallic powder and deposits solidified tracks (Calignano, 2014). Through overlap from points to lines and planes, a complete 3D solid model or component is produced without any mold, and the complexity of its geometry is not limited (Xiong et al., 2017). It is one of the most potential manufacturing technologies of metallic component, and provides the possibility to manufacture components for aerospace, medical, mold and other industrial applications (Ahmadi et al., 2016). A lot of researches on SLM technology were intensively conducted to improve the quality of SLMprocessed components such as mechanical properties, surface roughness, and 3D accuracy (Xu et al., 2015). However, few investigations on the absorption behavior of powder material on the powder bed to laser energy are carried on. It is difficult to deeply understand such a complex physical, chemical, and metallurgical process in the laser-material interaction zone because of the ultra-fast heating and cooling rates, the tiny molten pool with the dimension of 100–300 μm, the ultra-short

Corresponding author at: Institute for Laser Engineering, Beijing University of Technology, Pingleyuan No. 100, Chaoyang Dist., Beijing, 100124, China. E-mail address: [email protected] (D. Zhang).

https://doi.org/10.1016/j.jmatprotec.2019.01.002 Received 23 July 2018; Received in revised form 30 November 2018; Accepted 2 January 2019 Available online 03 January 2019 0924-0136/ © 2019 Elsevier B.V. All rights reserved.

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laser absorption and irradiance distribution on the surface of powder particles and the influence of particle size distribution on the molten pool of single track. The results showed the energy absorbed on the powder bed is significantly greater than that on the dense flat material, and the irradiance distribution gradually decreases from the center to the edge of the interaction region, it was also found that the powder particle size had a significant effect on the absorption and the irradiance distribution of the powder particles. However, few investigations on the comparison among packing models of powder particles with different porosities were conducted. The porosity is normally much higher in the stochastic packing model of powder particles generated from Software, which is significantly different from that in the actual powder layer generated from recoater during SLM process. In the present investigation, the laser beam is precisely defined to be with a Gaussian energy distribution using ray tracing model in simulation. The closed-packing model for spherical powder particles based on Horsfield’s filling method was established, based on what the laserpowder material interaction with different porosities and average particle sizes was simulated, the absorption of powder layer prepared also based on Horsfield’s filling method to laser energy was measured with integrating sphere. The simulated absorption behavior of powder material to laser energy meets well agreement with that using absorption measurement, which provides the theoretical basis for preparation of powder materials, optimize the radiation condition to improve absorption of powder material to laser energy and benefit to control SLM process, further to regulate the properties of SLM fabricated components.

existence time of the molten pool with the order of μ s and other factors. It is necessary to reproduce the ultra-fast laser-material process in numerical simulation. Huang et al. (Huang et al., 2004) studied the attenuation of the laser energy by the powder particles using Lambert-Beer and Mie theory and calculated temperature distribution inside the powder particle while it arrives at the substrate using thermal balance theory. The results showed the laser intensity during passing through spatial powder layer is attenuated along the Z direction layer by layer, the transmitted laser intensity at any spatial powder layer is considered as the incident one at next layer. Mcvey et al. (Mcvey et al., 2007) proposed an analytical relationship describing the amount of energy absorbed within preplaced powder during the laser deposition process can be used to study the absorption behavior due to multiple scattering inside a powder layer with a known attenuation coefficients and bulk absorption. Gusarov and Kruth (Gusarov and Kruth, 2005) investigated the conventional laser absorption and scattered radiation model, but it is not suitable for SLM process which is a metallic part manufacturing process with a lower porosity in a thinner powder layer. Tarvainen et al. (Tarvainen et al., 2013) established a radiation transmission-diffusion model to study the phenomenon of light transmission in turbid media in non-diffusion regions. The results showed the evaluation of the absorption and scattering using the radiative transmission-diffusion model is as good as the evaluation using only the radiative transmission equation when the diffusion equation is approximately ineffective. The above investigations are similar as the radiation of laser beam over the powder bed, but they cannot explain well the absorption behavior of powder bed to laser energy. However, the similar investigation methods could be possibly applied in the simulation researches on the absorption behavior of powder bed to laser energy. Wang et al. (Wang et al., 2002) used ray tracing to simulate the absorption of powder material to laser energy without considering the angular momentum and polarization-induced absorption changes of the incident light. Friedman (Friedman, 2011) compiled a program to generate the model for the stochastic distribution of powder particles on a powder bed and simulated the ray tracing based on the model generated by the program using FRED software. This program algorithm is similar with the rain-packing model proposed by Meakin and Jullien (Meakin and Jullien, 1987). The replacement of rain-packing model to the actual packing model of powder particles in the simulation in absorption behavior will cause greater deviations, because it is difficult to truly reflect the absorption of the actual packing of powder particles. Boley et al. (Boley et al., 2015) simulated in the absorption behavior of the ideal packing model with single particle size, stochastic packing models with dual particle sizes and Gaussian distributed particle sizes using ray tracing. The results showed multiple scattering plays an important role in energy absorption, implying the absorption changing of powder material to laser with the position and different packing arrangement in different packing model. Boley et al. (Boley et al., 2016) used ray tracing and direct calorimetry to study the absorption of a numbers of metallic powders, the results showed that the calculated results generally correlate well with the experimental results, and the absorption of powder can be predicted by that of flat-surface at normal incidence. Tolochko et al. (Tolochko et al., 2000) experimentally studied the effects of laser wavelength on the normal spectral absorption of metal, ceramic and polymer powders during SLS process, as well as the changes of the powder absorption over time. Klassen et al. (Klassen et al., 2014) established a model of the interaction between electron beam and material, which is used to calculate the beam energy attenuation curve as a function of material and incident electron energy on samples with arbitrary surfaces. Rubenchik et al. (Rubenchik et al., 2015) proposed a simple calorimetric scheme for direct absorption measurements, the absorption of various powder materials such as metal, ceramics, etc. with different particle size distribution and powder thickness to laser energy was measured. Yang et al. (Yang et al., 2018) established a three-dimensional powder bed model to study the

2. Materials and methods 2.1. Primary theory of closed-packing It is well known the face-centered cubic (fcc) and hexagonal closedpacking (hcp) achieve the closed-packed lattice in the metal-crystalfilling model, namely the highest average density of 76%, wherein spheres are closely packed with equal diameter. That means there are 24% interspaces even in the closed-packed lattice with equal sphere. In order to achieve a closed-packing model with a higher density, spheres with smaller diameter are used to fill the interspaces in the closedpacked lattice. The regular and easily calculated tetrahedral (a) and octahedral (b) interspaces in face-centered cubic are schematically shown in Fig. 1. Just like in face-centered cubic lattice, there are also the tetrahedral and octahedral interspaces in hexagonal closed-packing lattice. Horsfieled’s filling theory (Lu, 1998) is a closed-packing method, in which spheres with appropriate proportions and diameter is continuously filled in the interspaces of a hexagonal closed-packing model, so that a lattice with a highest average density is achieved. Let the diameter of hexagonal closed-packing model with an equal sphere to be d1, namely the cue sphere diameter. The diameter of spheres filled into its quadrilateral interspaces is d2. That spheres filled into its triangular interspaces is d3. Then the smaller spheres with diameter of d4 and d5 are filled into the other smaller interspaces. It can be known from filling process, the diameter of spheres filled into the interspaces gradually decreases. Finally some spheres with tiny diameter are filled into the residual interspaces to achieve the model with closed-packing. Table 1 shows the relevant parameters of Horsfieled’s interspace filling method. The calculation results show the ratios between the diameter of cue sphere and the spheres used to fill the octahedral, tetrahedrons, and other small interspace are: d2 = 0.414d1, d3 = 0.225d1, d4 = 0.117d1, d5 = 0.116d1. When the models are filled with the spheres of different diameters, their different porosities will be achieved. After the interspace filling, the porosity is 0.2594 for the closed-packing model with the first sphere, 0.2070 for that with the second sphere, 0.1900 for that with the third sphere, 0.1580 for that with the fourth sphere, and 0.1490 for that with the fifth sphere, 26

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Fig. 1. Schematic diagram of (a) tetrahedron and (b) octahedron interspace in the face-centered cubic structure, (c) Accumulative volume distribution curve of ideal closed-packing model based on Horsfieled’s filling method.

spheres, the diameter of bigger (cue) sphere is 35 μm, that of smaller one is 35 × 0.414 = 14.49 μm. For closed-packing models with three spheres, the diameter of bigger (cue) sphere is 35 μm, that of medium one is 35 × 0.414 = 14.49 μm, and the smallest one is 35 × 0.225 = 7.875 μm. The detailed information about the above three models is listed in Table 2, and the established three models and their top views will be shown in Section 3. For study the effect of average particle sizes of powder layer on the light absorption, three kinds of closed-packing models with different average sphere sizes are established in the simulation. The porosity of all three kinds of models is 0.1900. For the first packing model, the diameter of bigger sphere is 45 μm, that of medium one is 45 × 0.414 = 18.63 μm, and the smallest one is 45 × 0.225 = 10.125 μm, respectively. For second packing model, the diameter of bigger sphere is 35 μm, that of medium one is 35 × 0.414 = 14.49 μm, and the smallest one is 35 × 0.225 = 7.875 μm. For third packing model, the diameter of bigger sphere is 25 μm, that of medium one is 25 × 0.414 = 10.35 μm, and the smallest one is 25 × 0.225 = 5.625 μm. The detailed information about the above three models is listed in Table 2.

Table 1 Relevant parameters of Horsfieled’s interspace filling through calculation. Filling status

Diameter of filled sphere

Relative number of spheres

Porosity (%)

First sphere Second sphere Third sphere Fourth sphere Fifth sphere Other filling materials

d1 0.414d1 0.225d1 0.117d1 0.116d1 Tiny sphere

1 1 2 8 8 A large of number

25.94 20.70 19.00 15.80 14.90 3.90

respectively. The number ratio of five spheres filled into the hexagonal closed-packing model is 1: 1: 2: 8: 8. The diameter ratio of spheres is 1: 0.414: 0.225: 0.117: 0.116. The relevant parameters based on Horsfieled’s interspace filling are listed in Table 1. Based on Horsfieled’s interspace filling, a filling method for closedpacking model of powder material was proposed. Five continuously distributed powder particle sizes are used as cue spheres of five models for powder material, respectively, in which they are filled using the above method. In order to calculate the total number of powder particles with each diameter and their volume, a program was compiled using Matlab software, and an accumulative volume distribution curve with continuously distributed particle size is obtained (Fig. 1(c)). It can be seen from Fig. 1(c) that the cumulative volume fraction increases gradually with the increase of particle sizes. Particles with larger sizes account for a higher volume fractions based on Horsfieled’s filling methods. The model established based on Horsfieled’s filling method is an ideal closed-packing model with size continuously distributed particles. The actual powder layer with higher average density can reduce volume shrinkage during model or component SLM building process, which benefits to improve the 3D accuracy and reduce shrinkage stress. Based on the above closed-packing model, the absorption behavior of powder layer to laser beam, namely the effect of porosity and arrangement of average particle size of powder layer on the absorption will be investigated.

2.3. Ti6Al4V powder material prepared for experiments The original powder material used in the investigations is domestic gas atomized Ti6Al4V alloy. Its nominal chemical composition is Ti6.08Al4.04V0.037Fe0.05C, and its morphology of powder particles and accumulative volume distribution curve are shown in Fig. 2. The majority of powder particles are spherical, with some tiny satellites. Its particle size is Gaussian distribution from 1 to 160 μm. The D(10) is 27.298 μm, D(50) 64.564 μm and D(90) 118.947 μm, respectively. The proportion of powder particle with a size near D50 is the largest, while those with larger and smaller particle sizes of powder material with Gaussian particle size distribution are relatively small. And its cumulative volume distribution curve is significantly different from that of ideal closed-packing model based on Horsfieled’s filling method, in which powder particles with larger particle size occupy a higher Table 2 Comparison of particle sizes between closed-packing models in numerical simulation and prepared powder materials for experiments based on Horsfield’s filling method.

2.2. Closed-packing models in simulation In order to study the effect of porosities of powder layer on the light absorption, three kinds of closed-packing models with equal sphere, dual spheres, and three spheres are established in the simulation with porosities of 0.2594, 0.2070 and 0.1900, respectively. Normally the layer thickness is about 30 μm during SLM fabrication process, D50 of powder material should be chosen in the range of 34–37 μm. Thus, the diameter of cue spheres in the closed-packing model should be about 35 μm. For closed-packing models with equal sphere, the diameter of cue sphere is about 35 μm. For closed-packing models with dual

Porosities

Particle sizes in models (μm)

Particle sizes of prepared powder materials (μm)

0.2594 0.2070 0.1900

35 35 and 14.49 35, 14.49, and 45, 18.63, and 35, 14.49, and 25, 10.35, and

30–40 30–40 and 10–20 30-40, 10–20 and 0–10 35–45 25–35 15–25

0.1900

27

7.875 10.125 7.875 5.625

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Fig. 2. Morphology of (a) powder particles and (b) accumulative volume distribution curve for gas atomized Ti6Al4V alloy.

average particle sizes of powder layer on the absorption. Corresponding to the established models, three powder materials with different powder particles blending and three powder materials with different particle sizes distribution are prepared. The theoretical basis for the establishment of closed-packing models and preparation of powder materials is based on Horsfield’s filling method. The comparative investigations on light absorption between simulation and measurement are conducted to verify the feasibility of establishment of closedpacking models and the further accuracy in simulation in its light absorption. However, the powder material we used during SLM building process is gas atomized powder Ti6Al4V alloy with Gaussian distributed particle sizes, in which the powder layer generated by the recoater is a stochastic stacking of powder particles with above mentioned powder material. Through comparison between accumulative volume distribution curve for ideal closed-packing based on Horsfieled’s filling method in Fig. 1(c) and gas atomized Ti6Al4V alloy in Fig. 2(b), the particle size in the ideal closed-packing model is normally larger and the most of particle sizes of prepared powder material is near D50. The difference in powder particle size between numerical simulation using closed-packing models and experimental investigation using prepared powder materials causes the difference in absorption behavior of powder layer to light, what should be investigated and discussed in the following.

volume fraction. In order to compare the simulated and measured light absorption of powder layers with different porosities and average particle sizes, different powder materials were prepared through sieving, blending and other process from the original powder material. In view of the powder requirement of actual SLM fabrication process, powder materials with different particle sizes and number of different particle sizes are prepared according to Horsfield’s filling method (in Table 1). For the effect of porosity of powder layer on light absorption, three kinds of powder materials were prepared for absorption measurement, which correspond to the three models with porosities of 0.2594, 0.2070 and 0.1900 described in Section 2.2. The particle sizes of powder material with a porosity of 0.2594 distribute in the range of 30–40 μm, which corresponds to the closed-packing model with equal sphere of 35 μm. The blending of powder materials with particle size in the range of 30–40 μm and 10–20 μm is prepared, which corresponds to the model with double particle sizes of 35 μm and 14.49 μm. The blended powder materials with particle size in the range of 30–40 μm, 10–20 μm and 0–10 μm corresponds to the model with three particle sizes of 35 μm, 14.49 μm and 7.875 μm. The number ratio of largest, medium, and smaller powder particles is 1:1:2, and the diameter ratio of powder particles is 1:0.414:0.225. The calculated mass ratio is 1: 0.71: 0.023. The detailed information about the above three powder materials prepared is listed in Table 2. Three kinds of powder materials with different average particle distributions in the range of 15–25 μm, 25–35 μm, and 35–45 μm were prepared, respectively. They are used to investigate the effect of average sphere sizes of powder layer on their absorption to light. These three kinds of powder materials with different average particle distributions correspond to the models with different largest sphere sizes of 25 μm, 35 μm and 45 μm described in Section 2.2, respectively. The detailed information about the above three powder materials prepared is listed in Table 2. As descripted above, three closed-packing models with different porosities and three closed-packing models with different largest sphere sizes are established, in order to investigate the effect of porosities and

2.4. Physical model of laser-powder interaction and the heat source The laser-powder interaction during SLM process is shown in Fig. 3. The absorption behavior of powder material to laser energy is only affected by powder particle arrangement and their sizes on the powder bed if we neglect the influence of technology parameters such as spot size, laser power, scanning speed, layer thickness, and overlap as well. Because SLM processing for Ti6Al4V alloy is developed in our research team, its technology parameters are fixed with excellent mechanical properties. Although the theoretical closed-packing models for powder particles described above is different from the stochastic stacking of

Fig. 3. Interaction between laser energy and powder layer during SLM process. 28

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Fig. 4. (a) Gaussian distribution of laser energy, (b) Schematic diagram of mesh generation of the geometric model.

light in the interaction zone and are set to be randomly and uniformly distributed between 0 and π (Dingle et al., 2013). During the interaction between laser and powder material, the absorption of laser energy at an incident angle and the first scattering by the metal particles is determined by the absorbance defined by the Fresnel equation (Born and Wolf, 2013):

powder particles on the powder bed during the actual SLM process, the general rule of interaction between laser beam and powder layer can be explored to precisely regulate temperature field of the molten pool during SLM process. It is the theoretical basis to improve surface roughness, 3D accuracy of SLM-processed components, and further regulating their microstructure and mechanical properties. Boley et al. (Boley et al., 2015) pointed out when the laser energy irradiates on the powder bed during SLM process, part of the energy is absorbed through multiple scattering occurring in the powder layer, thereby improving the absorption; part of the energy is absorbed by the substrate, and the remaining energy is scattered to the surroundings. In detail, the absorption of powder layer to laser energy varies with the different positions even in a powder-packing model, the absorption of powder layer is not homogeneous. The absorption of powder layer to laser beam on a Gaussian or bimodal distributed powder bed is quite different. In order to establish a model of interaction between laser energy and powder layer, the following assumptions are made,

• •

index of 1.003 before arrival at powder layer in the forming chamber; The state in which the laser beam arriving at powder layer is set to be diffusely scattering with an absorption, and the surroundings is set to be a frozen state; No phenomena such as the melting and temperature change of powder layer are taken into account in the simulation; The shape of powder particles in simulation is spherical.

(1)

kn2) cos (∅)

(2)

kt 2 = (k c ∙k c −

kn = |k c| × cos (θ)

αp (θ ) = 1 − |n2 cos θ − (n2 − sin2θ)1/2 / n2 cos θ + (n2 − sin2θ)1/2|2

(5)

I0 (x , y ) = P0/(π × R2) × exp [−(x 2 + y 2 )/ R2]

(6)

Where I0 (x, y) refers to the initial laser intensity at the entrance, P0 represents the initial laser power of 280 W, R refers to the radius of laser beam of 50 μm. The laser intensity with Gaussian distribution of 7.13 × 1010 W/m2 can be calculated according to above parameters, and is shown in Fig. 4(a). Based on the basis theory of the interaction between laser and powder material and above assumptions in the simulation, the powder particles are homogeneously spread on the substrate. A parallelepiped is defined to be the working space, namely the forming chamber consisting of 6 side walls. Its top surface is the entrance of laser beam, the bottom one is the substrate covered with powder particles, namely the powder bed. Fig. 4(b) shows the geometric model and its mesh generation defined by refinement. The red arrow on the model indicates the moving direction of the laser beam.

The simulation in the laser-powder interaction using ray tracing can be effective only when the particle size is much larger than the wavelength of the laser. In general, the average particle size used in SLM process is 35 μm, and the wavelength of fiber laser used is 1.06 μm, ray tracing can be used to simulate the laser-powder interaction in the SLM process. According to the law of light reflection, the tangent and normal components of the scattered light at the particle scattering point can be obtained according to Eqs. (1)–(3):

kt1 = (k c ∙k c − kn2) sin (∅)

(4)

Where αs and αp refer to the absorption of metallic particles to S-polarized and P-polarized light, respectively, and n represents the relative refractive index of the powder material. Its refraction is 3.5–4.02i at the wavelength of 1.06 μm corresponding to the YAG laser (Meakin and Jullien, 1987). The module of ray tracing in COMSOL Multiphysics Software is used to establish a laser source with Gaussian distribution to investigate the interaction between laser beam and powder particles. Therefore, the laser beam with a Gaussian distribution defined at the entrance is a geometric model as shown in Fig. 4(a), which is set to be an unpolarized laser, and is divided into 50,000 rays to simulate the effect of numerous photons in the actual laser beam. The definition of the Gaussian beam is determined by Eq. (6):

• The laser energy is in Gaussian distribution, and laser beam is in cylindrical shape without convergence and divergence; • The laser beam passes through the argon medium with a refractive •

αs (θ) = 1 − |cos θ − (n2 − sin2θ)1/2 /cos θ + (n2 − sin2θ)1/2|2

2.5. Ray tracing and energy loss When the laser beam irradiates on the powder bed, it will be absorbed, reflected or frozen (namely disappeared or absorbed) around during SLM process. This involves the interaction of the laser beam with the medium, the powder layer, and the surrounding six sidewalls in the forming chamber. These factors should be taken into account in the boundary condition setting process before the simulation. When the laser beam irradiates on the surface of the powder layer, their

(3)

Where kc refers to the ray wave vector when the ray hits on the surface of particles, t1 and t2 are the two tangential components, and n is the normal component. The actual gas atomized powder particles are spherical or quasi-spherical, and ∅ and θ are random for all scattered 29

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Fig. 5. (a) A laser beam with Gaussian distribution irradiate on the powder bed, (b) Ray trace trajectory, (c) The process of energy loss carried by light due to multiple reflection.

carried on. The reflection measurement devices used in the experiment includes a light source, an integrating sphere, a spectrometer, and two optical fibers connecting all of the above together. Then the data of reflection generated from the spectrometer are transmitted to a PC through USB2 at 480 Mbps. Fig. 6(a) shows the experimental setup for reflection measurement. A set of optical system is used to measure the reflection of powder layer to light at the full spectrum. The light source is a combined deuterium and halogen light with the wavelength in the range of 200–1100 nm and a diameter of 4.92 mm. During the experiment, the light was guided to the illumination port through an optical fiber into an integrating sphere system at an incident angle of 8°with respect to the vertical direction (shown in Fig. 6(b)). The interior of the integrating sphere is spherical, which inner surface is coated with a thin layer of material with high reflectivity. The incident light is reflected by the sample of powder material, multiple reflection occurs inside the integrating sphere. After time-spatial integration of powder layer reflected light in the sphere, the data of reflection spectrum of powder layer is calculated by the Ava software connected to the spectrometer. In order to avoid the influence of air, dust and other factors on the measurement accuracy, a standard reflector with high reflectivity is tested as a reference before the experiment. The absorption spectrum is finally obtained by dividing the number of photons in the experimental sample by the number of reference photons. In order to reduce the error caused by the operation or other factors, three measurements are made for each material, and finally the average value is obtained by calculation. The container with a circular indentation for powder layer preparation was designed, and fabricated by our research team using SLM for Ti6Al4V alloy, its geometry and morphology of bottom surface are shown in Fig. 6(c–d). The depth of the indentation of the special container is about 50 μm, which is larger than the actual layer thickness during SLM process due to the difficulty in the preparation of thinner powder layer. The self-designed and fabricated powder container not only benefits to prepare the powder layer, but also provides the same absorption condition during component fabrication process using SLM.

interaction is set to be diffuse scattering, and since the incident laser beam has both S and P-polarized light, the surface absorption coefficient of powder particles is set by the Eq. (7) (Born and Wolf, 2013): 1

1

2

α = 1 − 0.5 × ( ⎡n2 cos θ − (n2 − sin2θ) 2⎤/[n2 cos θ + (n2 − sin2θ) 2] ⎣ ⎦ 1

1

+ ⎡cos θ − (n2 − sin2θ) 2⎤/[cos θ + (n2 − sin2θ ) 2] ⎣ ⎦

2

(7)

As mentioned above, the refractive index of Ti6Al4V alloy under irradiation of a laser beam with a wavelength of 1.06 μm is 3.5–4.02i. The medium around the powder particles is air, and its refractive index is set to be 1. For a geometric model, the boundary conditions of laser beam interacting with the surrounding six sidewalls are set to be frozen, that is, once the laser beam reaches any of the six walls, the laser transportation will be stopped. The information on the powder material was selected from the Ti6Al4V (UNS R56400) in COMSOL Multiphysics Software library. After the boundary conditions setting, the simulation using ray tracing is started. In the model a laser beam with Gaussian distribution vertically irradiates on the powder bed, as shown in Fig. 5(a). The laser energy could be absorbed by powder particles or the substrate, the rest could be also reflected onto the sidewalls or top wall in the forming chamber, and frozen there, Fig. 5(b) gives out the trajectory of ray tracing described above. When an incident laser beam irradiates on the surface of spherical powder particle, it forms an angle with the normal vector at the point of incidence, that is, the angle of incidence. The incident laser energy becomes weaken after reflection at the point of incidence. It follows the law of energy loss defined by Eqs. (4) and (5), indicating by the light color change. When the reflected laser irradiates on the surface of powder particles for the second time, it will be reflected again and its energy continues to be lost. Fig. 5(c) depicts the color changes of the light after multiple reflection on the surface of powder particles. Its color changes from red to brown, finally to green, which indicates the gradual loss of energy. 2.6. Measurement of absorption In order to verify the simulation in absorption behavior of powder layer with different porosities and average powder particle sizes, the experiment for absorption measurement of different powder material is 30

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Fig. 6. (a) The experimental setup for reflection measurement, (b) The structural diagram of integrating sphere, (c) Special sample container with a circular indentation for powder layer preparing with the depth of 50 μm, (d) Magnification of bottom surface morphology of the circular indentation fabricated with SLM.

3. Results and discussion

model, the surface is namely the distance of laser beam with a diameter travels across during each calculation distance. The ratio between the light intensity in the interaction zone and the surface of laser beam travel across, its unit is W/m4, is define as the density distribution of light intensity in the interaction zone. The density distribution of light intensity in the interaction zone between laser and closed-packing models with equal sphere, dual spheres and three spheres is showed in Fig. 8(a–c), respectively. The density distribution of light intensity at the same position in the interaction zone between laser and closedpacking models with equal sphere, dual spheres and three spheres is showed in Fig. 8(d–f), respectively. It can be seen from Fig. 8(a–c), the maximum density distribution of light intensity in the interaction zone between light and closed-packing models with equal sphere, dual spheres and three spheres is 1 × 1022 W/m4, 1.31 × 1022 W/m4, 2.66 × 1022 W/m4, respectively, which continuously distributes on the top surface of closed packed spheres. The density distribution of light intensity increases with the decreasing porosity. The smaller the porosity of closed-packing model is, the more chance the light interacts with the spheres, the more density of light intensity accumulated on the surface of the closed-packing model is. If the interspaces among large spheres are filled with smaller spheres, the incident light is absorbed by multiple reflection or reflected by the large sphere. The multi-reflected light will be transmitted to the substrate or run out of the interspaces onto the surrounding walls in the forming chamber. Furthermore, it can be seen that the density distribution of light intensity in the interaction zone with equal sphere, dual spheres and three spheres is 1 × 1022 W/m4, 1.05 × 1022 W/m4, 2.56 × 1022 W/m4 in Fig. 8(d–f), respectively. It distributes mostly on the large sphere in the middle position, and secondly on the large spheres in the under left corner for these three models. It is worth mentioning light intensity accumulated on the medium and small spheres for models with dual

3.1. Simulation in the absorption behavior of powder layer The laser parameters are selected as non-variables in the simulation. The variables are the parameters related to powder particle packing model, such as porosity and average particle size of powder layer. The numerical solution focuses on the change of laser intensity distribution on the surface of powder layer, namely the effect of porosity of powder layer and average powder particle size on the laser absorption. 3.1.1. Effect of porosity of powder layer on absorption In Section 2.2, three kinds of closed-packing models with equal sphere, dual spheres, and three spheres were established for investigation on the effect of porosity of powder layer on absorption, in which their porosities are 0.2594, 0.2070 and 0.1900, respectively. Fig. 7 shows the closed-packing models with equal sphere (a), dual spheres (b), and three spheres (c) and their top views. From top views, there are same arrangements of largest spheres, the difference lies in the filling method in the interspaces, which causes the different porosities. Mesh generation has effect on the simulation accuracy and time. In order to improve the accuracy and reduce time of calculation, different meshes for the different closed-packing models in porosity and sphere sizes are generated. The meshes for closed-packing models of equal sphere and dual spheres are generated using a detailed classification criteria, while that for three spheres is generated using a refined classification criteria due to the size of the smallest sphere of 7.857 μm, the parameter of mesh generation in simulation is listed in Table 3. After mesh generation, a light intensity accumulator is applied on the surface of the closed-packing model, and the calculation distance is 5 μm. The light intensity accumulator is the integration of the density of light intensity distributed on the certain surface of closed-packing 31

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Fig. 7. Closed-packing models with (a) equal sphere, (b) dual spheres, (c) three spheres and their top views.

three spheres substrates.

spheres and three spheres is also very high. The color of the medium spheres is red, while that of the large spheres in its surrounding are yellow or brown in Fig. 8(e). The color of the smaller spheres is crimson in Fig. 8(f), while the surrounding large spheres are still green or yellow. That means multiple reflection occurs in the interspaces between large and small spheres, the smaller ones can easily reach the maximum light intensity due to the much irradiating from the reflected light. The curve of light absorption of powder layer at different positions is plotted in Fig. 9, and the absorbed light energy simulated at eight different positions of closed-packing models with equal sphere, dual spheres and three spheres is listed in Table 4, respectively. It can be seen that the light absorption of closed-packing model with equal sphere is the lowest, that for model with dual spheres is the highest, and that for model with three spheres is a medium value. A conclusion can be drawn that light absorption for all of three models is the range of 76–80%, with the decrease of porosity of closed-packing models, their light absorption obviously increases. While porosity decreases to a certain value, light absorption will no longer increase, but slightly decrease. Because porosity of closed-packing model decreases to a certain value, the laser beam will hardly pass through the spheres into interspaces, few multiple reflection occur. The majority of the first and second reflected light will be frozen on the walls in the forming chamber. Light absorption at different positions is different because of different spheres arrangement and different reflection condition. Furthermore, Table 4 gives out the detailed absorbed light energy on the top of spheres, spheres, the surroundings and substrates for all of three models in simulation, respectively. It can be seen that the absorbed light energy on the substrate for closed-packing models with equal sphere is 4 orders larger than that of dual spheres and three spheres. That shows part of irradiating light directly arrive at the substrate surface for closed-packing models with equal sphere due to relatively higher porosity, while the irradiating light arrives at the substrate surface through multiple reflection for models with dual and

3.1.2. Effect of average particle sizes of powder layer on absorption In Section 2.2, three kinds of closed-packing models with different largest sphere of 45 μm, 35 μm and 25 μm were established, respectively, for investigation on the effect of average sphere size on absorption, in which porosities for three models are 0.1900. Fig. 10(a–c) shows the density distribution of light intensity in the interaction region between laser and closed-packing models with the largest sphere of 45 μm, 35 μm and 25 μm, respectively. The density comparison of light intensity in the interaction zone at positions with same spheres arrangement between laser and closed-packing models with the largest sphere of 45 μm, 35 μm and 25 μm is shown in Fig. 10(d–f), respectively. It can be seen from Fig. 10(a–c), the maximum density of light intensity accumulated on the sphere for models with the largest sphere of 45 μm, 35 μm and 25 μm is 1.24 × 1022 W/m4, 1.31 × 1022 W/m4, 5.24 × 1022 W/m4, respectively. With the sphere radius decreases, the greater the number of spheres a light beam can irradiate, the more homogeneous the density of light intensity distribution on the spheres and the greater that is. The density comparison of light intensity at position with same spheres arrangement is 1 × 1022 W/m4, 1.05 × 1022 W/m4, 4.09 × 1022 W/m4 for closed-packing models with the largest sphere of 45 μm (Fig. 10(d)), 35 μm (Fig. 10(e)) and 25 μm (Fig. 10(f)), respectively. Light intensity for the models with the largest sphere of 45 μm (Fig. 10(d)) distributes mostly on the sphere in the middle position. Light intensity for the models with the largest sphere of 35 μm (Fig. 10(e)) distributes mostly on the sphere in the middle position, and secondly on the large spheres in the left corner. While light intensity for the model with the largest sphere of 25 μm (Fig. 10(f)) distributes much homogeneously. The value of light intensity is also much higher than that for the models with the largest spheres of 45 μm (Fig. 10(d)) and 35 μm (Fig. 10(e)). It verifies again the smaller the sphere diameter is, the greater the number of spheres a light beam can irradiate, the more

Table 3 Parameters of mesh generation in simulation.

The Max. element size (μm) The Min. element size (μm) Maximum unit growth rate Curvature factor Narrow area resolution

Mesh for detailed classification

Mesh for refined classification

46.7 3.4 1.4 0.4 0.7

29.8 1.27 1.35 0.3 0.85

32

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Fig. 8. The density distribution of light intensity in the interaction region between laser and closed-packing models with (a) equal sphere, (b) dual spheres and (c) three spheres; The density comparison of light intensity in the interaction zone with same sphere arrangement between laser and closed-packing models with (d) equal sphere, (e) dual spheres and (f) three spheres.

homogeneous its distribution is, which was beneficial to the absorption of light intensity. Fig. 11 depicts the simulation in light absorption at eight different positions of closed-packing models with the largest sphere of 45 μm, 35 μm and 25 μm, respectively. It can be seen the average sphere diameter becomes smaller, the absorption of models to laser tends to increase, but no obvious absorption increase is observed. In particular, the absorption of closed-packing model with the largest sphere of 45 μm significantly fluctuates with different positions. Comparing the light intensity distribution at position 2 and 5 in Fig. 11, it is reasonable to consider a higher absorption can be achieved when a light beam irradiates into the interspace among the spheres. While the light irradiates on the surface of spheres with larger diameter, the majority of light is reflected.

3.2. Absorption measurement of prepared powder materials to light

Fig. 9. Simulation in light absorption of closed-packing models with equal sphere, dual spheres and three spheres.

In order to verify the effects of powder materials with different porosities and average particle sizes on their absorption to light in simulation, two sets of powder materials were prepared for the 33

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Table 4 The absorbed light energy at substrate simulated at eight positions of closed-packing models with equal sphere, dual spheres and three spheres.

Model of equal sphere Model of dual spheres Model of Three spheres

Top Spheres Surrounding Substrate Top Spheres Surrounding Substrate Top Spheres Surrounding Substrate

Position 1

Position 2

Position 3

Position 4

Position 5

Position 6

Position 7

Position 8

1.43E+13 5.24E+13 2.94E+11 1.17E+12 1.53E+13 5.92E+13 5.11E+11 3.23E+09 1.38E+13 5.06E+13 3.72E+11 1.73E+09

1.4E+13 5.31E+13 2.66E+11 1.17E+12 1.58E+13 5.88E+13 3.25E+11 2.35E+09 1.37E+13 5.1E+13 2.24E+11 4.66E+08

1.37E+13 5.38E+13 2.71E+11 1.08E+12 1.56E+13 5.93E+13 3.49E+11 3.1E+09 1.39E+13 5.08E+13 1.76E+11 3.26E+08

1.42E+13 5.26E+13 2.35E+11 1.23E+12 1.52E+13 5.98E+13 3.42E+11 1.4E+10 1.39E+13 5.05E+13 9.18E+10 2.85E+08

1.44E+13 5.23E+13 1.82E+11 1.14E+12 1.5E+13 5.99E+13 5.2E+11 3.89E+09 1.4E+13 5.07E+13 1.47E+11 8.49E+08

1.43E+13 5.27E+13 2.45E+11 1.08E+12 1.55E+13 5.91E+13 3.41E+11 1.23E+10 1.38E+13 5.09E+13 1.55E+11 2.18E+08

1.43E+13 5.23E+13 2.03E+11 1.23E+12 1.55E+13 5.95E+13 2.6E+11 1.74E+09 1.39E+13 5.03E+13 2.6E+11 1.85E+08

1.42E+13 5.25E+13 2.88E+11 1.11E+12 1.55E+13 5.93E+13 3.8E+11 2.08E+09 1.38E+13 5.06E+13 1.64E+11 8.31E+08

1, the distribution of the absorption of powder materials to light as function of wavelength can be obtained by corresponding conversion. The absorption of powder material with particle sizes in the range of 30–40 μm and porosity of 0.2594, blending powder material with

experiments of absorption measurement. Their detailed information is listed in Table 2. The reflection of powder particles to the light is measured using integrating sphere. Since the sum of the reflection and the absorption is

Fig. 10. The density distribution of light intensity in the interaction region between laser and closed-packing models with the largest sphere of (a) 45 μm, (b) 35 μm and (c) 25 μm; The density comparison of light intensity in the interaction zone with same spheres arrangement between laser and closed-packing models with the largest sphere of (d) 45 μm, (e) 35 μm and (f) 25 μm. 34

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45 μm, 35 μm and 25 μm in the simulation results shown in Fig. 11. Both of Fig. 12(b) and 11 show us that the smaller powder particle size is, the better the absorption of powder material to later beam is. However, absorption of powder materials to laser energy in experiments is higher than that of closed-packing models to light in simulation. Just as mention above, the particle size of accumulative volume distribution curve in the ideal closed-packing based on Horsfield’s filling method is normally larger, while the most of particle size of prepared powder material is near D50. According to our simulated absorption behavior, the light absorption of powder layer with smaller particle sizes is relatively higher than that of with larger ones.

4. Conclusion In the paper, the effects of different porosities and average particle sizes of powder layer on light absorption was investigated, in which closed-packing models with different packing parameters based on Horsfield’s filling method was established. Corresponding to it, powder materials with different porosities and powder particle sizes were prepared also for absorption measurement using integrating sphere. The experimental results of light absorption for prepared powder materials verify the feasibility of the establishment of closed-packing models, the calculation in the irradiating light intensity and light absorption through light intensity accumulator. The following conclusions can be drawn from numerical simulation:

Fig. 11. Simulation in light absorption of closed-packing models with the largest sphere of 45 μm, 35 μm and 25 μm.

particle sizse in the range of 30–40 μm and 10–20 μm and porosity of 0.2070, blending powder material with particle sizes in the range of 30–40 μm, 10–20 μm and 0–10 μm and porosity of 0.1900 is shown in Fig. 12(a). It can be seen from Fig. 12(a), with the decrease of porosity, absorption of powder materials to light energy increases when the light wavelength is in the range of 200–940 nm, while the absorption curves fluctuate significantly when the light wavelength is in the range of 940–1200 nm, even intersect with each other. The highest absorption of powder materials to laser energy is achieved when the laser interacts with blending powder material with particle size in the range of 30–40 μm and 10–20 μm and porosity of 0.2070. The above phenomena are similar as the simulation in light absorption of closed-packing models with equal sphere, dual spheres, and three spheres. Furthermore, the light absorption is measured experimentally when the light wavelength is in the range of 940–1200 nm, the simulation is carried on at the light wavelength of 1.06 μm A conclusion can be drawn from above comparatively investigations that theoretical light absorption of closed-packing models in simulation meets well agreement with the light absorption measurement of prepared powder materials in experiment. That means, the experimental results of light absorption of prepared powder materials verify the feasibility of the establishment of closed-packing models based on Horsfieled’s filling method, the calculation accuracy in the light absorption through ray tracing. Absorption curve of powder materials with particle size distribution in range of 15–25 μm, 25–35 μm, 35–45 μm to light energy as function of wavelength is shown in Fig. 12(b). These curves are analogous to the light absorption of closed-packing models with the largest sphere of

(1) The light absorption of powder layer of Ti6Al4V alloy is higher than 70% both by the simulation in light absorption and measurement using integrating sphere. (2) With the decrease of porosity, the light absorption of powder layer gradually becomes larger, and the change of absorption is not obvious. While the light absorption tends to decrease when the porosity decrease exceeds a certain value due to the large amount of reflected light. (3) With the decrease of average particle size of powder particles, their light absorption gradually becomes larger. When the light irradiates into the interspaces among the spheres in packing model, the absorption becomes large due to the multi-scattering of the light, and when the light irradiates onto the surface of the large spheres in packing model, more light is reflected and the absorption decreases.

Acknowledgement This work was supported by the National Natural Science Foundation of China (Project No. 51675012).

Fig. 12. Light absorption measurement of (a) powder layer with different porosities and (b) different average powder particle sizes. 35

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References

failure behavior of Ti-6Al-4V lattice structures manufactured by selective laser melting (SLM). Int. J. Adv. Manuf. Technol. 84, 1391–1411. Mcvey, R.W., Melnychuk, R.M., Todd, J.A., Martukanitz, R.P., 2007. Absorption of laser irradiation in a porous powder layer. J. Laser Appl. 19 (4), 214–224. Meakin, P., Jullien, R., 1987. Restructuring effects in the rain model for random deposition. J. Phys. 48, 1651–1662. Rubenchik, A., Wu, S., Mitchell, S., Golosker, I., Leblanc, M., Peterson, N., 2015. Direct measurements of temperature-dependent laser absorptivity of metal powders. Appl. Opt. 54 (24), 7230–7233. Tarvainen, T., Kolehmainen, V., Lehtikangas, O., Kaipio, J.P., Arridge, S.R., 2013. Utilising the coupled radiative transfer – diffusion model in diffuse optical tomography. Int. Soc. Opt. Photonics 8799, 236–242. Tolochko, N.K., Laoui, T., Khlopkov, Y.V., Mozzharov, S.E., Titov, V.I., Ignatiev, M.B., 2000. Absorptance of powder materials suitable for laser sintering. Rapid Prototyp. J. 6 (3), 155–161. Wang, X., Laoui, T., Bonse, J., Kruth, J.P., Lauwers, B., Froyen, L., 2002. Direct selective laser sintering of hard metal powders experimental study and simulation. Int. J. Adv. Manuf. Technol. 19, 351–357. Xiong, J., Gu, D., Chen, H., Dai, D., Shi, Q., 2017. Structural optimization of re-entrant negative Poisson’s ratio structure fabricated by selective laser melting. Mater. Des. 120, 307–316. Xu, W., Brandt, M., Sun, S., Elambasseril, J., Liu, Q., Latham, K., Xia, K., Qian, M., 2015. Additive manufacturing of strong and ductile Ti-6Al-4V by selective laser melting via in situ martensite decomposition. Acta Mater. 85, 74–84. Yang, Y., Gu, D., Dai, D., Ma, C., 2018. Laser energy absorption behavior of powder particles using ray tracing method during selective laser melting additive manufacturing of aluminum alloy. Mater. Des. 143, 12–19. Yin, J., Peng, G., Chen, C., Yang, J., Zhu, H., Ke, L., Wang, Z., Wang, D., Ma, M., Wang, G., Zeng, X., 2018. Thermal behavior and grain growth orientation during selective laser melting of Ti-6Al-4V alloy. J. Mater. Process. Technol. 260, 57–65.

Ahmadi, A., Mirzaeifar, R., Moghaddam, N.S., Turabi, A.S., Karaca, H.E., Elahinia, M., 2016. Effect of manufacturing parameters on mechanical properties of 316L stainless steel parts fabricated by selective laser melting: a computational framework. Mater. Des. 112, 328–338. Boley, C.D., Khairallah, S.A., Rubenchik, A.M., 2015. Calculation of laser absorption by metal powders in additive manufacturing. Appl. Opt. 54, 2477–2482. Boley, C.D., Mitchell, S.C., Rubenchik, A.M., Wu, S.S.Q., 2016. Metal powder absorptivity: modeling and experiment. Appl. Opt. 55 (23), 6496–6500. Born, M., Wolf, E., 2013. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Pergamon Press, Oxford, pp. 38–51. Calignano, F., 2014. Design optimization of supports for overhanging structures in aluminum and titanium alloys by selective laser melting. Mater. Des. 64, 203–213. Dingle, K., S W Lamb, J., Lázaro-Camí, J.A., 2013. Knudsen’s law and random billiards in irrational triangles. Nonlinearity 26, 369–388. Friedman, G., 2011. Particle Pack User’s Manual. Lawrence Livermore National Laboratory, LLNL-SM-458031. Günther, J., Leuders, S., Koppa, P., Tröster, T., Henkel, S., Biermann, H., Niendorf, T., 2018. On the effect of internal channels and surface roughness on the high-cycle fatigue performance of Ti-6Al-4V processed by SLM. Mater. Des. 143, 1–11. Gusarov, A.V., Kruth, J.P., 2005. Modelling of radiation transfer in metallic powders at laser treatment. Int. J. Heat Mass Transf. 48, 3423–3434. Huang, Y.L., Liang, G.Y., Su, J.Y., Li, J.G., 2004. Interaction between laser beam and powder stream in the process of laser cladding with powder feeding. Modell. Simul. Mater. Sci. Eng. 13, 47. Klassen, A., Bauereiß, A., Körner, C., 2014. Modelling of electron beam absorption in complex geometries. J. Phys. D Appl. Phys. 47 (6). Lu, H.G., 1998. Guide to Powder Technology. Tongji University Press, Shanghai. Mazur, M., Leary, M., Sun, S., Vcelka, M., Shidid, D., Brandt, M., 2016. Deformation and

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