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Influence of AlSi10Mg particles microstructure on heat conduction during additive manufacturing
International Journal of Heat and Mass Transfer 144 (2019) 118632
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Influence of AlSi10Mg particles microstructure on heat conduction during additive manufacturing Panding Wang a,b, Hongshuai Lei a,1, Xiaolei Zhu c, Haosen Chen a, Daining Fang a,b,1 a
Beijing Key Laboratory of Lightweight Multi-functional Composite Materials and Structures, Beijing Institute of Technology, Beijing 100081, PR China State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, PR China c School of Mechanical and Power Engineering, Nanjing Tech University, Nanjing 210009, PR China b
a r t i c l e
i n f o
Article history: Received 9 January 2019 Received in revised form 1 May 2019 Accepted 22 August 2019 Available online 30 August 2019 Keywords: A. Additive manufacturing B. Hollow particle C. Thermal conductivity D. X-ray micro-computed tomography (lCT) E. Image-based finite element model (FEM)
a b s t r a c t Powder-based metallic additive manufacturing (AM) technology is opening new avenues to fabricate highly complex components from metallic powders. However, most of the powder-scale modeling methods are limited to single track process and ideal particle microstructure. Nevertheless, the presence of hollow particles significantly influences the heat conduction during AM processing and experimental quantification of the heat conduction between hollow particles is extremely challenging. Herein, we have used X-ray micro-computed tomography (lCT) to reconstruct 3D structures of AlSi10Mg particles. The morphology, location and distribution of intact and hollow particles are studied to analyze their role in AM processing. Based on X-ray tomography images, two 3D image-based finite element models of statistically representative particles with imperfect geometry are reconstructed and compared to simulate the thermal conduction in the powder bed. Simulation results shows that thermal conduction is governed not only by cell topology but also by cavities in particles induced by powder production. The calculation results are consistent with the Serial-Parallel Model, which is based on the reconstruction geometry model and statistical results. The results reveal that the presence of cavities in particles significantly influences the thermal conduction and, consequently, reduces the sintered density during selective laser sintering (SLS). Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Powder bed based additive manufacturing (AM) technologies for metallic components, such as selective laser melting (SLM), selective electron beam melting (SEBM) and laser engineering net shaping (LENS), have garnered increasing attention over the past few decades [1–3]. In addition to the fabrication of metallic components with complex geometries, the powder-based AM technologies slice three-dimensional (3D) computer-aided design (CAD) model into a two-dimensional (2D) CAD model with uniform layer thickness. Subsequently, the material is added to each layer to obtain the desired complex geometries. In the SLM/SEBM process, one layer of powder is applied on a preheated platform and, then, the powder bed is selectively melted along the designated scan path [4]. The influence of processing parameters, such as laser powder, building direction, scanning speed and powder feed rate
1 Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100081, China. E-mail addresses: [email protected] (H. Lei), [email protected] (D. Fang)
https://doi.org/10.1016/j.ijheatmasstransfer.2019.118632 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
have been widely discussed, which will crucially impact on properties of fabricated components [5–7]. In a particular component being built, each location is subjected to a complex thermal history, which creates heterogeneous macroscopic and microscopic structure, which is very different from traditional wrought counterparts and the designed CAD models [8–10]. However, rare studies have focused on the influence of powder particle and microstructure on fabrication quality during complex manufacturing processing. The significance of the powder particle varies for different AM technologies. In SLM, all particles undergo melting and the size and distribution of powder particles do not influence the quality of the final product [11]. On the other hand, chemical composition, particle shape, surface morphology and particle size distribution significantly influence the selective laser sintering (SLS) process [11–13]. In SLS processing, chemical composition has a significant impact on the densification of resulting alloy, which implies that the size and distribution of powder particles play a critical role in SLS densification [14]. For instance, powders with a narrow particle size distribution tend to agglomerate, whereas coarsepowders with a broad particle size distribution tend to segregate
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[15]. To date, few reports have visualized and quantified the 3D morphology of particle on AM processing. Furthermore, different techniques are being employed to characterize the particles, used in AM technologies. For instance, scanning electron microscope (SEM) [16,17] is frequently used to observe the surface morphology and measure particle size distribution. Read et al. [18] have utilized SEM and demonstrated that AlSi10Mg particles have an irregular morphology, where several irregular satellite-like particles are attached to the big particles. The irregular-shaped particles affect the powder flowability and melting behavior of powder-bed system during AM processing. Moreover, the particle size distribution, degree of sphericity and the length-to-diameter ratio can be measured by particle size analyzer [19]. However, most of these testing techniques are limited to 2D inspection of particles surface. Recently, high-fidelity X-ray micro-computed tomography (lCT) technique is demonstrated as an effective tool to characterize the 3D morphology of AM-fabricated components [20,21]. 3D structures of cell topology and geometric defects induced by AM are visualized. However, these studies mainly focused on the influence of void and geometrical defects on mechanical properties of solidified structures. Hence, the actual 3D morphologies of particles, used in AM processing, have not been reconstructed by lCT. In most of the experimental and theoretical studies, the particles are considered as ideal spheres with a uniform diameter. The effect of particle morphology on AM process need to be discussed further. However, the actual AM process consists of multiple physical phenomena, such as powder particle packing, heat transfer and phase transformations [19]. Thus, experimental observation of melting and solidification processes is extremely challenging. Therefore, several powder-based mesoscale models have been developed to investigate the complex melting process during AM processing [22–24]. For instance, the powder melting process in SEBM is simulated by a 2D lattice Boltzmann method (LBM), where a raindrop model has been used to generate each layer [23]. Wei et al. [25] used the volume of fluid method and discrete element model (DEM) to simulate the radiation heat transfer in the AlSi10Mg packed bed. Khairallah et al. [22] demonstrates the effect of the recoil pressure and Marangoni convection in laser powder bed fusion of 316L stainless steel using ALE3D massively-parallel multi-physics code. Yan et al. [26] have combined a DEM of powder spreading and a computational fluid dynamics (CFD) model of powder melting to investigate multiple cracks and layers during SEBM processing. Moreover, the finite volume method (FVM) and DEM have also been coupled to elaborate the deposition of powder particles during SLM processing [27]. One should note that modeling and simulation play a critical role in improving the process yield and reducing the producing cost of AM-fabricated complex components [28]. However, most of the powder melting models only consider the ideal spherical particles. The effect of 3D particle morphology on AM process need to be discussed further. Owing to the complex microstructure of particles, the geometric imperfections significantly influence the thermal conduction behavior and quality of the final product. Previously, several experimental and theoretical studies have discussed the influence of powder particle on AM processing. However, the actual 3D morphologies have not been imaged and reconstructed yet. Spierings et al. [29] have attributed the larger void defects in components to the hollow particles during AM processing but, neither experimental not theoretical, results are provided to support their conclusion. The actual AM process during multiple physical phenomena need to be discussed further, considering the actual structure of particles. Herein, for the first time, we aimed to visualize and analyze the 3D structure of hollow particles in AM processing by employing the high-resolution lCT technique. We have scanned and
visualized AlSi10Mg powder by high-resolution lCT to characterize the morphology, location and distribution of particles. The AlSi10Mg material is widely used in aerospace and automotive industry. However, 3D structures of AlSi10Mg particles are complex and lots of cavities appear in the center of particles. Furthermore, two image-based finite element models (FEM) were built in Avizo software package by using the mCT data. The 1st model is based on the 3D reconstruction results containing the internal cavity defects of the particles, whereas the 2nd model filled the internal cavities. The influence of hollow particles on thermal conduction of powders has been studied by comparing the simulation results. In addition, the Serial- Parallel model is generated to provide a citation here for the simulation and explain the effect of hollow particles and the porosity on thermal conduction during AM processing. Lastly, the heat transfer properties of the powder particles have also been discussed. 2. Experimental procedures 2.1. Materials The AlSi10Mg powder supplied by Eos Gmbh Electro Optical Systems and its composition is presented in Table 1. The volumetric content of particles, with an equivalent diameter of >90 lm, is less than 0.5%, as specified by the supplier. 2.2. X-ray micro-computed tomography To scan the actual geometry of AlSi10Mg particles, X-ray microcomputed tomography was performed by using a 225 kV lCT equipment (Beijing Institute of Technology, China). The AlSi10Mg powder was speaded into a glass tube using the flexible rubber recoater blade at room temperature, which is also used to spread a thin layer of powder in the powder platform in AM processing. The diameter of glass tube is 0.8 mm. The lCT experiment was carried out at 80 kV and 35 lA and an area of 0.8 mm 0.8 mm 0.3 mm was scanned, which resulted in an effective spatial pixel size of 0.5 lm of tomography images. 2.3. Data processing The detailed 3D tomographic images were analyzed by using Avizo 9.0 software to evaluate different morphological characteristics of the particles, such as the degree of sphericity, equivalent diameter and cavity volume. The image processing and structural reconstruction process are presented in Fig. 1. The tomography images are pre-processed to extract useful information. First, image enhancement was carried out to remove noise and highlight useful information. In l-CT scanned images of AlSi10Mg particles, the noise is caused by the conversion between light and electricity. In general, it is called ‘‘salt and pepper” noise, which can be removed by using a 3D median filter. Second, the interactive threshold was applied to separate air voids from other phases. The extraction of external contour and the internal boundary is an important step to reconstruct geometric model. Finally, a 3D reconstruction model was built by using the iso-surface extraction technique. Fig. 1 presents the 3D structure of the reconstructed particles, which contains several incomplete particles in the top and bottom surfaces. Also, the particles are linked with each other. In order to characterize the particle morphology, a 3D watershed algorithm was used to separate these particles [30]. Then, the particles were filtered by considering the center of gravity of the intact particles in the range of 0.045 to 0.255 mm in the Z direction. As the equivalent diameter of the particles is lower than 90 lm, as specified by
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P. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118632 Table 1 Chemical composition of AlSi10Mg alloy powder. Element
Si
Mg
Fe
Mn
Ni
Ti
Cu
Al
Composition (wt. %)
11
0.45
0.55
0.45
0.05
0.15
0.04
Bal
diameter of the cavities ranged from 5 to 20 lm and the maximum equivalent diameter is 32.21 lm. Overall, around 19% of particles contain cavities. The volume fraction of cavities can be defined as:
v pore ¼
Fig. 1. The schematic illustration of the reconstruction process, carried out by Avizo.
the supplier, the range of center of gravity of complete particles in the Z direction is determined.
V cav ity V particle
ð1Þ
where Vcavity and Vparticle represent the total volume of cavities and particles, respectively. The volume fraction of cavities is 0.55%. One should note that the hollow particles worsen local thermal conductivity of the powder-bed and negatively influence the sintered density during SLS processing. Moreover, the larger cavities contribute to larger pores in AM-fabricated samples [29]. We have discussed the influence of hollow particles on heat conduction during AM processing and confirmed our results by image-based finite element models and Serial-Parallel model in the following section. 4. Finite element modeling and theoretical prediction method 4.1. Image-based finite element modeling
3. Morphological characterization To evaluate the geometrical characteristics of particles, 0.5 mm voxel size 3D images are segmented in black and other colors, corresponding to void-cells and each AlSi10Mg particle. Fig. 2 presents the particle size distribution of the AlSi10Mg powder, where the average equivalent diameter is 19.7 lm. The CT-scanned particle distribution has been compared with that measured by laser diffraction from supplier, as is shown in Table 2. The particle in tomography image has been separated by 3D watershed algorithm. Thus, the volume fraction of small particles is higher than that measured by laser diffraction. The CT scan result is more accurate. In fact, the equivalent diameter of most particles ranged from 10 to 40 lm and the accumulative volume fraction is 84.85%. The size distribution and average equivalent diameter of the particles have a significant influence on SLS processing. The sintering stress, encountered by the small particles, is significantly higher than the sintering stress of large particles. In SLS processing, fine particle size distribution can increase the sintering response and improve the packing density [31]. The average particle size affects the saturation density [15]. Fig. 3 presents the 3D reconstruction structure of particles with different degrees of sphericity and distribution. It can be readily observed that the AlSi10Mg particles are not ideally spherical. There are about 59.62% particles with a degree of sphericity of <0.9. These particles possess an irregular 3D morphology, where several small satellite-like particles are attached to the larger particles. One should note that the SEM analysis of particle morphology renders large error. In AM processing, the particle morphology significantly influences the powder flowability and melting behavior in powder-bed systems. The utilization of fine additive powders can result in a greatly reduced quantity of the formed liquid phase, whereas the coarse powders increase the amount of liquid phase during SLS processing [32]. The geometric structure of AlSi10Mg powder particles shows that the powder particles contain several cavities (Fig. 4a). Fig. 4b presents the corresponding tomography slice, which shows the cavities in white-color. 3D cavity structure and cavity size distribution are presented in Fig. 4c and d. The average equivalent
AlSi10Mg particles with cavities have been detected and visualized by high-fidelity lCT technology. It has been observed that the maximum equivalent diameter of cavities was larger than the average equivalent diameter of particles. In the local section, hollow particles heavily affected the thermal conductivity of the powder bed. As a result, the sintered density was influenced by cavities during SLS processing. The influence of hollow particles on local thermal conductivity is discussed here. The 1st FEA model is directly generated from CT tomography images (Fig. 5a), which is named as Model-1. In order to study the influence of hollow particles, another FEA model has also been generated from CT tomography images, where the cavities are filled, as shown in Fig. 5b. The 2nd FEA model is named as Model-2. During AM processing, the thickness of each printed layer is about 30 lm [16]. Thus, a region of interest (200 lm 150 lm 86 lm) is meshed to simulate the thermal conduction in powder-bed, which is shown by yellowcolor in Fig. 5a–c. The particle with the largest cavity is in the selected ROI. The surface mesh has been generated in Avizo 9.0 software by using the iso-surface extraction technique, consisting of triangles, which fit the boundary of the solid phase. The surface mesh was simplified to reduce the number of nodes and triangles while preserving a good description of the surface and cavities of the particles. Finally, the tetrahedral mesh was directly generated from the Triangular-facet mesh (Fig. 6). The positions of the cross-sections are shown in blue-color in Fig. 6a and c. Static thermal conduction simulations are carried out on the basis of the ABAQUS/standard code. The meshes are generated with the element-type DC3D4, as shown in Table 3. The top surface of the sample refers to the hot-wall boundary with a temperature of 393 K, whereas the bottom surface of the sample represents the cold-wall boundary with a temperature of 293 K. As for the simulation of thermal conductivity in powder bed, the conductivity is isotropic and the aspect is very high, e.g., a large but thin region. Thus, the thermal boundary conditions of other four surrounding surfaces are thermal insulation. The thermal conductivity of AlSi10Mg material and the air is 203.5 W/(m K) and 0.025 W/(m K), respectively. The specific heat and density of the metallic matrix are 880 J/(kg K) and 2700 kg/m3. In FEM simulations, only
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Fig. 2. The particle size distribution.
Table 2 Statistical information of particle distribution measured by laser diffraction from supplier and CT scan. Equivalent diameter
Particle volume fraction (Laser diffraction)
Particle volume fraction (CT scan)
<29.41 lm <47.38 lm <72.85 lm <90 lm
10% 50% 90% 100%
60.94% 99.25% 100% 100%
heat conduction between particles and air is considered. The heat convection between the solid phase and the radiations is beyond the scope of current study. 4.2. Theoretical model of thermal conductivity Thermal conductivity (kpowder) is an important property of the powder materials, which can be defined as:
kpowder ¼
q DT=H
ð2Þ
where q refers to the heat flux, W/m2, DT represent the temperature difference (K) and H corresponds to the sample thickness (m). As shown in CT scans and the reconstructed structure of particles (Fig. 5), the particles are linked to each other. The general contact is surface to surface. Thus, in thermal conduction simulations, the samples are simplified to porous materials, where the porosity can be defined as:
Vg ¼
V v oid V domain
ð3Þ
where Vvoid refers to the total volume of void defects in domain volume. Vdomain represents the domain volume. The measured porosity of Model-1 is 54.11%. The porosity of Model-2 is 49.77% after the cavities were filled. According to the relationship between air and metal phase, the theoretical models of porous materials to predict the thermal conductivity can be divided into two types: Serial-
Fig. 3. (a) 3D reconstruction structure of AlSi10Mg particles with various degrees of sphericity and (b) the degree of sphericity distribution.
P. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118632
Fig. 4. (a) Local cavities in AlSi10Mg particles, (b) tomographic slice, (c) 3D reconstruction structure of cavities in particles and (d) the cavity size distribution.
Fig. 5. (a) CT scanned tomographic slice, (b) tomographic slice with filled-cavities and (c) the region of interest (ROI).
5
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Fig. 6. Image-based finite element models: (a) Model-1, (b) cross-section of Model-1, (c) Model-2 and (d) cross-section of Model-2.
Table 3 Characteristics of the generated mesh volumes of AlSi10Mg particles. Model
Number of nodes
Number of elements
Mesh type
Average element size (lm)
Porosity (%)
Model-1 Model-2
80,003 91,814
320,051 387,010
DC3D4 DC3D4
3 3
54.11% 49.77%
Parallel model and Parallel-Serial model (Fig. 7) [33]. The expressions for both models can be given as:
2 1 Serial - Parallel model : kpowder ¼ km 1 V3g þ kair V 3g
Parallel - Serial model : kpowder ¼
2 1 V3g 2
1 þ Vg V3g
km
ð4Þ
ð5Þ
where km and kair refer to the thermal conductivity of metal phase and air, respectively. 5. Results and discussion 5.1. Simulation results and discussion The temperature and heat flux distributions, predicted by two image-based FEMs, are presented in Fig. 8. The equivalent thermal conductivity of AlSi10Mg powder is calculated by heat flux distribution (Fig. 8b and d) and Eq. (2). Feng et al. [34] have compared the experimental and calculation results and suggested that the thermal conductivity of porous materials is decreased with increasing porosity. Herein, Model-2 has a lower porosity than Model-1 due to filled-cavities. As is shown in Fig. 8b and d, the maximum heat flux of Model-2 is 20.59% higher than Model-1.
Moreover, the simulation predicted thermal conductivity factors from Model-1 and Model-2 are 63.77 W/(m K) and 79.18 W/(m K), respectively. It is worth noting that the presence of cavities reduced the thermal conductivity factors by 24.16% in power bed, which reduced the sintered density of SLS-processed parts, as demonstrated by Olakanmi et al. [14]. In the present study, the influence of 3D particles morphology on thermal conductivity is discussed by comparing two imagebased FEM results. The results revealed that the particles possess complex structure and large-sized cavities exist in the center of particles. We have compared the simulation results of intact particles with filled-cavities and observed that the irregular and hollow particles lead to a reduction of 24.16% in thermal conductivity of the power bed. This decrease is mainly caused by higher porosity in particle powder, considering cavities in the center of particles. 5.2. Theoretical calculations The effect of porosity on thermal conductivity are discussed through theoretical calculations. Table 4 presents the error analysis of thermal conductivity between image-based FEM results and theoretical calculations. The absolute value of the error, obtained from Eq. (5), is about 7.2%, which is much less than Eq. (4). The Serial-Parallel model can better calculate the thermal conductivity of particles, as is shown in Table 4. In two theoretical models, the
P. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118632
7
Fig. 7. The porous structure theoretical models: (a) Serial-Parallel model and (b) Parallel-Serial model.
Fig. 8. The temperature distribution (a, c) and heat flux distribution (b, d) of Model-1 (a and b) and Model-2 (c and d).
parallel model shows that the matrix phase is continuously distributed at a range of temperature drop, whereas the serial model shows that the solid phase particles do not contact each other, but they only decrease the thickness of heat through the fluid phase in the pores. One should note that the parallel model does not match well with the actual situation, whereas the serial model is close to the actual circumstances. In Serial-Parallel model, the parallel part shows the heat conduction between matrixes, whereas the serial part represents the heat conduction between fluids in the pores. Therefore, the results of Serial-Parallel model are consistent with the image-based FEM simulations. Serial-Parallel model connects the porosity with equivalent thermal conductivity. Based on Serial-Parallel model and the porosity of the powder bed with the value of 45.85%, the equivalent thermal conductivity of the whole powder bed is calculated to be 82.5 W/(m K). The predicted thermal conductivity of the powder bed to solid bulk thermal conductivity is defined as:
mb ¼
kbed kbulk
ð6Þ
where kbed is the predicted thermal conductivity of the powder bed and kbulk is the solid bulk thermal conductivity. The effective thermal conductivity of the AlSi10Mg powder bed to solid bulk thermal conductivity tb = 40.54%. Wei [35] et al. used the transient hot wire method to test the thermal conductivties of Inconel 718, 17–4 stainless steel, Inconel 625, Ti-6Al-4 V and 316L strainless steel powder bed. The thermal conductivities are less than 1/100th of the solid bulk thermal conductivities. However, more cavities exist in AlSi10Mg particles. The effective thermal conductivity of the AlSi10Mg powder bed to solid bulk thermal conductivity is ranged from 60% to 100% [36,37], which depends on the porosity of the powder bed. Zhou et al. [38] has compared the predicted bed effective thermal conductivity with those measured by experiments. When the ratio of the
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P. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118632
Table 4 Error analysis between image-based FEM results and theoretical calculations. Particle
Model-1 Model-2
Thermal conductivity, W/(m K)
Absolute error, %
Image-based FEM
Eq. (4)
Eq. (5)
Eq. (4)
Eq. (5)
63.77 79.18
68.4 75.7
78.0 87.0
7.2% 4.4%
22.2% 9.9%
thermal conductivity of solid bulk to that of fluid is 31.62, tb is 17.39%. In Sih’s experimental study [39,40], tb is assumed to be 60%. Moreover, the theoretical calculations are used to predict the thermal conductivity of hollow particles and particles with filledcavities. It can be readily observed that the theoretical calculations of hollow particles are more accurate than the predictions based on ideal particles with filled-cavities. Comparing image-based FEM results and theoretical calculations, the thermal conductivity is not only influenced by the porosity of particle powder, but also by the 3D particle morphology. Simplified theoretical predictions have large errors. 6. Conclusions In summary, we have demonstrated a novel method to investigate the influence of particles shape and structure on heat conduction during additive manufacturing (AM). X-ray micro-computed tomography (lCT) was used to reconstruct 3D geometry of AlSi10Mg particles. The statistical results of particle distribution measured by CT scans is more accurate compared with that measured by SEM and laser diffraction. Because each particle is separated by 3D watershed algorithm. Moreover, lCT offers a new opportunity to visualize the hollow particles. The thermal conductivity of particles is calculated by imagebased finite element methods (FEMs) and theoretical calculations. The comparison of two image-based FEM simulations quantitatively revealed the influence of hollow particles on thermal conductivity. The cavities reduced the heat conductivity of power bed. Moreover, the energy consumption in AM processing is higher correspondingly, which influenced the mechanical properties of samples after curing. The following conclusions can be drawn from the current study: (1) The 3D structure of particles is complex and large cavities exist in the center of particles. (2) The cavity-containing powder particles could be simplified into porous materials to study the heat conduction in powder-bed. The Serial-Parallel model can better calculate the thermal conductivity of AlSi10Mg particles. (3) The thermal conductivity is not only influenced by the porosity of particle powder, but also by the 3D particle morphology. (4) Compared to the filled-cavity particles, the hollow particles resulted in a decrease of 24.16% in the thermal conductivity of the powder bed. One should note that the presence of cavities reduces the sintered density of SLS-processed components. With 3D structure of particles reconstructed in this paper, a new method was proposed to discuss the particle behavior in the actual AM process. Reconstructed particle microstructure used in this paper could make improvement in previous simulation works to track the AM processing. The research on the heat conductivity of powder bed in this paper is part of the preliminary work of the further research on the effect of hollow particles on powder spreading and powder melting using image-based finite element model.
Declaration of Competing Interest The authors declared that there is no conflict of interest.
Acknowledgements This work is supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (11521202), National Natural Science Foundation of China (11872012), the National Key Research and Development of China (2018YFC0810300), the Young Elite Scientists Sponsorship Program, and the Natural Science Foundation for Colleges and Universities of Jiangsu Province of China grant (16KJB130003).
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[29] A.B. Spierings, N. Herres, G. Levy, Influence of the particle size distribution on surface quality and mechanical properties in AM steel parts, Rapid Prototyping J. 17 (2011) 195–202. [30] G. Lin, U. Adiga, K. Olson, J.F. Guzowski, C.A. Barnes, B. Roysam, A hybrid 3D watershed algorithm incorporating gradient cues and object models for automatic segmentation of nuclei in confocal image stacks, Cytometry 56A (2003) 23–36. [31] R. German, M. Sintering, Theory and Practice, John Willey & Sons. Inc, New York, 1996. [32] R.N. Lumley, G.B. Schaffer, The effect of solubility and particle size of liquid phase sintering, Scripta Mater. 35 (1996). [33] Y. Sugimura, J. Meyer, M.Y. He, H. BartSmith, J. Grenstedt, A.G. Evans, On the mechanical performance of closed cell Al alloy foams, Acta Mater. 45 (1997) 5245–5259. [34] Y. Feng, Z. Zhu, N. Tao, H. Zhen, Thermal conductivity of closed-cell aluminum alloy foam, Acta Metall. Sin. 39 (2003) 817–820. [35] L.C. Wei, L.E. Ehrlich, M.J. Powell-Palm, C. Montgomery, J. Beuth, J.A. Malen, Thermal conductivity of metal powders for powder bed additive manufacturing, Additive Manuf. 21 (2018) 201–208. [36] F. Thummler, R. Oberacker, Introduction to Powder Metallurgy, vol. 346, Oxford Science Publications, 1993. [37] Y. Li, D. Gu, Parametric analysis of thermal behavior during selective laser melting additive manufacturing of aluminum alloy powder, Mater. Des. 63 (2014) 856–867. [38] Z.Y. Zhou, A.B. Yu, P. Zulli, Particle scale study of heat transfer in packed and bubbling fluidized beds, Aiche J. 55 (2009) 868–884. [39] S.S. Sih, J.W. Barlow, The prediction of the emissivity and thermal conductivity of powder beds, Particulate Sci. Technol. 22 (2004) 427–440. [40] C. Li, M.F. Gouge, E.R. Denlinger, J.E. Irwin, P. Michaleris, Estimation of part-topowder heat losses as surface convection in laser powder bed fusion, Additive Manuf. 26 (2019) 258–269.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Influence of AlSi10Mg particles microstructure on heat conduction during additive manufacturing Panding Wang a,b, Hongshuai Lei a,1, Xiaolei Zhu c, Haosen Chen a, Daining Fang a,b,1 a
Beijing Key Laboratory of Lightweight Multi-functional Composite Materials and Structures, Beijing Institute of Technology, Beijing 100081, PR China State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, PR China c School of Mechanical and Power Engineering, Nanjing Tech University, Nanjing 210009, PR China b
a r t i c l e
i n f o
Article history: Received 9 January 2019 Received in revised form 1 May 2019 Accepted 22 August 2019 Available online 30 August 2019 Keywords: A. Additive manufacturing B. Hollow particle C. Thermal conductivity D. X-ray micro-computed tomography (lCT) E. Image-based finite element model (FEM)
a b s t r a c t Powder-based metallic additive manufacturing (AM) technology is opening new avenues to fabricate highly complex components from metallic powders. However, most of the powder-scale modeling methods are limited to single track process and ideal particle microstructure. Nevertheless, the presence of hollow particles significantly influences the heat conduction during AM processing and experimental quantification of the heat conduction between hollow particles is extremely challenging. Herein, we have used X-ray micro-computed tomography (lCT) to reconstruct 3D structures of AlSi10Mg particles. The morphology, location and distribution of intact and hollow particles are studied to analyze their role in AM processing. Based on X-ray tomography images, two 3D image-based finite element models of statistically representative particles with imperfect geometry are reconstructed and compared to simulate the thermal conduction in the powder bed. Simulation results shows that thermal conduction is governed not only by cell topology but also by cavities in particles induced by powder production. The calculation results are consistent with the Serial-Parallel Model, which is based on the reconstruction geometry model and statistical results. The results reveal that the presence of cavities in particles significantly influences the thermal conduction and, consequently, reduces the sintered density during selective laser sintering (SLS). Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Powder bed based additive manufacturing (AM) technologies for metallic components, such as selective laser melting (SLM), selective electron beam melting (SEBM) and laser engineering net shaping (LENS), have garnered increasing attention over the past few decades [1–3]. In addition to the fabrication of metallic components with complex geometries, the powder-based AM technologies slice three-dimensional (3D) computer-aided design (CAD) model into a two-dimensional (2D) CAD model with uniform layer thickness. Subsequently, the material is added to each layer to obtain the desired complex geometries. In the SLM/SEBM process, one layer of powder is applied on a preheated platform and, then, the powder bed is selectively melted along the designated scan path [4]. The influence of processing parameters, such as laser powder, building direction, scanning speed and powder feed rate
1 Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100081, China. E-mail addresses: [email protected] (H. Lei), [email protected] (D. Fang)
https://doi.org/10.1016/j.ijheatmasstransfer.2019.118632 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
have been widely discussed, which will crucially impact on properties of fabricated components [5–7]. In a particular component being built, each location is subjected to a complex thermal history, which creates heterogeneous macroscopic and microscopic structure, which is very different from traditional wrought counterparts and the designed CAD models [8–10]. However, rare studies have focused on the influence of powder particle and microstructure on fabrication quality during complex manufacturing processing. The significance of the powder particle varies for different AM technologies. In SLM, all particles undergo melting and the size and distribution of powder particles do not influence the quality of the final product [11]. On the other hand, chemical composition, particle shape, surface morphology and particle size distribution significantly influence the selective laser sintering (SLS) process [11–13]. In SLS processing, chemical composition has a significant impact on the densification of resulting alloy, which implies that the size and distribution of powder particles play a critical role in SLS densification [14]. For instance, powders with a narrow particle size distribution tend to agglomerate, whereas coarsepowders with a broad particle size distribution tend to segregate
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[15]. To date, few reports have visualized and quantified the 3D morphology of particle on AM processing. Furthermore, different techniques are being employed to characterize the particles, used in AM technologies. For instance, scanning electron microscope (SEM) [16,17] is frequently used to observe the surface morphology and measure particle size distribution. Read et al. [18] have utilized SEM and demonstrated that AlSi10Mg particles have an irregular morphology, where several irregular satellite-like particles are attached to the big particles. The irregular-shaped particles affect the powder flowability and melting behavior of powder-bed system during AM processing. Moreover, the particle size distribution, degree of sphericity and the length-to-diameter ratio can be measured by particle size analyzer [19]. However, most of these testing techniques are limited to 2D inspection of particles surface. Recently, high-fidelity X-ray micro-computed tomography (lCT) technique is demonstrated as an effective tool to characterize the 3D morphology of AM-fabricated components [20,21]. 3D structures of cell topology and geometric defects induced by AM are visualized. However, these studies mainly focused on the influence of void and geometrical defects on mechanical properties of solidified structures. Hence, the actual 3D morphologies of particles, used in AM processing, have not been reconstructed by lCT. In most of the experimental and theoretical studies, the particles are considered as ideal spheres with a uniform diameter. The effect of particle morphology on AM process need to be discussed further. However, the actual AM process consists of multiple physical phenomena, such as powder particle packing, heat transfer and phase transformations [19]. Thus, experimental observation of melting and solidification processes is extremely challenging. Therefore, several powder-based mesoscale models have been developed to investigate the complex melting process during AM processing [22–24]. For instance, the powder melting process in SEBM is simulated by a 2D lattice Boltzmann method (LBM), where a raindrop model has been used to generate each layer [23]. Wei et al. [25] used the volume of fluid method and discrete element model (DEM) to simulate the radiation heat transfer in the AlSi10Mg packed bed. Khairallah et al. [22] demonstrates the effect of the recoil pressure and Marangoni convection in laser powder bed fusion of 316L stainless steel using ALE3D massively-parallel multi-physics code. Yan et al. [26] have combined a DEM of powder spreading and a computational fluid dynamics (CFD) model of powder melting to investigate multiple cracks and layers during SEBM processing. Moreover, the finite volume method (FVM) and DEM have also been coupled to elaborate the deposition of powder particles during SLM processing [27]. One should note that modeling and simulation play a critical role in improving the process yield and reducing the producing cost of AM-fabricated complex components [28]. However, most of the powder melting models only consider the ideal spherical particles. The effect of 3D particle morphology on AM process need to be discussed further. Owing to the complex microstructure of particles, the geometric imperfections significantly influence the thermal conduction behavior and quality of the final product. Previously, several experimental and theoretical studies have discussed the influence of powder particle on AM processing. However, the actual 3D morphologies have not been imaged and reconstructed yet. Spierings et al. [29] have attributed the larger void defects in components to the hollow particles during AM processing but, neither experimental not theoretical, results are provided to support their conclusion. The actual AM process during multiple physical phenomena need to be discussed further, considering the actual structure of particles. Herein, for the first time, we aimed to visualize and analyze the 3D structure of hollow particles in AM processing by employing the high-resolution lCT technique. We have scanned and
visualized AlSi10Mg powder by high-resolution lCT to characterize the morphology, location and distribution of particles. The AlSi10Mg material is widely used in aerospace and automotive industry. However, 3D structures of AlSi10Mg particles are complex and lots of cavities appear in the center of particles. Furthermore, two image-based finite element models (FEM) were built in Avizo software package by using the mCT data. The 1st model is based on the 3D reconstruction results containing the internal cavity defects of the particles, whereas the 2nd model filled the internal cavities. The influence of hollow particles on thermal conduction of powders has been studied by comparing the simulation results. In addition, the Serial- Parallel model is generated to provide a citation here for the simulation and explain the effect of hollow particles and the porosity on thermal conduction during AM processing. Lastly, the heat transfer properties of the powder particles have also been discussed. 2. Experimental procedures 2.1. Materials The AlSi10Mg powder supplied by Eos Gmbh Electro Optical Systems and its composition is presented in Table 1. The volumetric content of particles, with an equivalent diameter of >90 lm, is less than 0.5%, as specified by the supplier. 2.2. X-ray micro-computed tomography To scan the actual geometry of AlSi10Mg particles, X-ray microcomputed tomography was performed by using a 225 kV lCT equipment (Beijing Institute of Technology, China). The AlSi10Mg powder was speaded into a glass tube using the flexible rubber recoater blade at room temperature, which is also used to spread a thin layer of powder in the powder platform in AM processing. The diameter of glass tube is 0.8 mm. The lCT experiment was carried out at 80 kV and 35 lA and an area of 0.8 mm 0.8 mm 0.3 mm was scanned, which resulted in an effective spatial pixel size of 0.5 lm of tomography images. 2.3. Data processing The detailed 3D tomographic images were analyzed by using Avizo 9.0 software to evaluate different morphological characteristics of the particles, such as the degree of sphericity, equivalent diameter and cavity volume. The image processing and structural reconstruction process are presented in Fig. 1. The tomography images are pre-processed to extract useful information. First, image enhancement was carried out to remove noise and highlight useful information. In l-CT scanned images of AlSi10Mg particles, the noise is caused by the conversion between light and electricity. In general, it is called ‘‘salt and pepper” noise, which can be removed by using a 3D median filter. Second, the interactive threshold was applied to separate air voids from other phases. The extraction of external contour and the internal boundary is an important step to reconstruct geometric model. Finally, a 3D reconstruction model was built by using the iso-surface extraction technique. Fig. 1 presents the 3D structure of the reconstructed particles, which contains several incomplete particles in the top and bottom surfaces. Also, the particles are linked with each other. In order to characterize the particle morphology, a 3D watershed algorithm was used to separate these particles [30]. Then, the particles were filtered by considering the center of gravity of the intact particles in the range of 0.045 to 0.255 mm in the Z direction. As the equivalent diameter of the particles is lower than 90 lm, as specified by
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P. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118632 Table 1 Chemical composition of AlSi10Mg alloy powder. Element
Si
Mg
Fe
Mn
Ni
Ti
Cu
Al
Composition (wt. %)
11
0.45
0.55
0.45
0.05
0.15
0.04
Bal
diameter of the cavities ranged from 5 to 20 lm and the maximum equivalent diameter is 32.21 lm. Overall, around 19% of particles contain cavities. The volume fraction of cavities can be defined as:
v pore ¼
Fig. 1. The schematic illustration of the reconstruction process, carried out by Avizo.
the supplier, the range of center of gravity of complete particles in the Z direction is determined.
V cav ity V particle
ð1Þ
where Vcavity and Vparticle represent the total volume of cavities and particles, respectively. The volume fraction of cavities is 0.55%. One should note that the hollow particles worsen local thermal conductivity of the powder-bed and negatively influence the sintered density during SLS processing. Moreover, the larger cavities contribute to larger pores in AM-fabricated samples [29]. We have discussed the influence of hollow particles on heat conduction during AM processing and confirmed our results by image-based finite element models and Serial-Parallel model in the following section. 4. Finite element modeling and theoretical prediction method 4.1. Image-based finite element modeling
3. Morphological characterization To evaluate the geometrical characteristics of particles, 0.5 mm voxel size 3D images are segmented in black and other colors, corresponding to void-cells and each AlSi10Mg particle. Fig. 2 presents the particle size distribution of the AlSi10Mg powder, where the average equivalent diameter is 19.7 lm. The CT-scanned particle distribution has been compared with that measured by laser diffraction from supplier, as is shown in Table 2. The particle in tomography image has been separated by 3D watershed algorithm. Thus, the volume fraction of small particles is higher than that measured by laser diffraction. The CT scan result is more accurate. In fact, the equivalent diameter of most particles ranged from 10 to 40 lm and the accumulative volume fraction is 84.85%. The size distribution and average equivalent diameter of the particles have a significant influence on SLS processing. The sintering stress, encountered by the small particles, is significantly higher than the sintering stress of large particles. In SLS processing, fine particle size distribution can increase the sintering response and improve the packing density [31]. The average particle size affects the saturation density [15]. Fig. 3 presents the 3D reconstruction structure of particles with different degrees of sphericity and distribution. It can be readily observed that the AlSi10Mg particles are not ideally spherical. There are about 59.62% particles with a degree of sphericity of <0.9. These particles possess an irregular 3D morphology, where several small satellite-like particles are attached to the larger particles. One should note that the SEM analysis of particle morphology renders large error. In AM processing, the particle morphology significantly influences the powder flowability and melting behavior in powder-bed systems. The utilization of fine additive powders can result in a greatly reduced quantity of the formed liquid phase, whereas the coarse powders increase the amount of liquid phase during SLS processing [32]. The geometric structure of AlSi10Mg powder particles shows that the powder particles contain several cavities (Fig. 4a). Fig. 4b presents the corresponding tomography slice, which shows the cavities in white-color. 3D cavity structure and cavity size distribution are presented in Fig. 4c and d. The average equivalent
AlSi10Mg particles with cavities have been detected and visualized by high-fidelity lCT technology. It has been observed that the maximum equivalent diameter of cavities was larger than the average equivalent diameter of particles. In the local section, hollow particles heavily affected the thermal conductivity of the powder bed. As a result, the sintered density was influenced by cavities during SLS processing. The influence of hollow particles on local thermal conductivity is discussed here. The 1st FEA model is directly generated from CT tomography images (Fig. 5a), which is named as Model-1. In order to study the influence of hollow particles, another FEA model has also been generated from CT tomography images, where the cavities are filled, as shown in Fig. 5b. The 2nd FEA model is named as Model-2. During AM processing, the thickness of each printed layer is about 30 lm [16]. Thus, a region of interest (200 lm 150 lm 86 lm) is meshed to simulate the thermal conduction in powder-bed, which is shown by yellowcolor in Fig. 5a–c. The particle with the largest cavity is in the selected ROI. The surface mesh has been generated in Avizo 9.0 software by using the iso-surface extraction technique, consisting of triangles, which fit the boundary of the solid phase. The surface mesh was simplified to reduce the number of nodes and triangles while preserving a good description of the surface and cavities of the particles. Finally, the tetrahedral mesh was directly generated from the Triangular-facet mesh (Fig. 6). The positions of the cross-sections are shown in blue-color in Fig. 6a and c. Static thermal conduction simulations are carried out on the basis of the ABAQUS/standard code. The meshes are generated with the element-type DC3D4, as shown in Table 3. The top surface of the sample refers to the hot-wall boundary with a temperature of 393 K, whereas the bottom surface of the sample represents the cold-wall boundary with a temperature of 293 K. As for the simulation of thermal conductivity in powder bed, the conductivity is isotropic and the aspect is very high, e.g., a large but thin region. Thus, the thermal boundary conditions of other four surrounding surfaces are thermal insulation. The thermal conductivity of AlSi10Mg material and the air is 203.5 W/(m K) and 0.025 W/(m K), respectively. The specific heat and density of the metallic matrix are 880 J/(kg K) and 2700 kg/m3. In FEM simulations, only
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Fig. 2. The particle size distribution.
Table 2 Statistical information of particle distribution measured by laser diffraction from supplier and CT scan. Equivalent diameter
Particle volume fraction (Laser diffraction)
Particle volume fraction (CT scan)
<29.41 lm <47.38 lm <72.85 lm <90 lm
10% 50% 90% 100%
60.94% 99.25% 100% 100%
heat conduction between particles and air is considered. The heat convection between the solid phase and the radiations is beyond the scope of current study. 4.2. Theoretical model of thermal conductivity Thermal conductivity (kpowder) is an important property of the powder materials, which can be defined as:
kpowder ¼
q DT=H
ð2Þ
where q refers to the heat flux, W/m2, DT represent the temperature difference (K) and H corresponds to the sample thickness (m). As shown in CT scans and the reconstructed structure of particles (Fig. 5), the particles are linked to each other. The general contact is surface to surface. Thus, in thermal conduction simulations, the samples are simplified to porous materials, where the porosity can be defined as:
Vg ¼
V v oid V domain
ð3Þ
where Vvoid refers to the total volume of void defects in domain volume. Vdomain represents the domain volume. The measured porosity of Model-1 is 54.11%. The porosity of Model-2 is 49.77% after the cavities were filled. According to the relationship between air and metal phase, the theoretical models of porous materials to predict the thermal conductivity can be divided into two types: Serial-
Fig. 3. (a) 3D reconstruction structure of AlSi10Mg particles with various degrees of sphericity and (b) the degree of sphericity distribution.
P. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118632
Fig. 4. (a) Local cavities in AlSi10Mg particles, (b) tomographic slice, (c) 3D reconstruction structure of cavities in particles and (d) the cavity size distribution.
Fig. 5. (a) CT scanned tomographic slice, (b) tomographic slice with filled-cavities and (c) the region of interest (ROI).
5
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Fig. 6. Image-based finite element models: (a) Model-1, (b) cross-section of Model-1, (c) Model-2 and (d) cross-section of Model-2.
Table 3 Characteristics of the generated mesh volumes of AlSi10Mg particles. Model
Number of nodes
Number of elements
Mesh type
Average element size (lm)
Porosity (%)
Model-1 Model-2
80,003 91,814
320,051 387,010
DC3D4 DC3D4
3 3
54.11% 49.77%
Parallel model and Parallel-Serial model (Fig. 7) [33]. The expressions for both models can be given as:
2 1 Serial - Parallel model : kpowder ¼ km 1 V3g þ kair V 3g
Parallel - Serial model : kpowder ¼
2 1 V3g 2
1 þ Vg V3g
km
ð4Þ
ð5Þ
where km and kair refer to the thermal conductivity of metal phase and air, respectively. 5. Results and discussion 5.1. Simulation results and discussion The temperature and heat flux distributions, predicted by two image-based FEMs, are presented in Fig. 8. The equivalent thermal conductivity of AlSi10Mg powder is calculated by heat flux distribution (Fig. 8b and d) and Eq. (2). Feng et al. [34] have compared the experimental and calculation results and suggested that the thermal conductivity of porous materials is decreased with increasing porosity. Herein, Model-2 has a lower porosity than Model-1 due to filled-cavities. As is shown in Fig. 8b and d, the maximum heat flux of Model-2 is 20.59% higher than Model-1.
Moreover, the simulation predicted thermal conductivity factors from Model-1 and Model-2 are 63.77 W/(m K) and 79.18 W/(m K), respectively. It is worth noting that the presence of cavities reduced the thermal conductivity factors by 24.16% in power bed, which reduced the sintered density of SLS-processed parts, as demonstrated by Olakanmi et al. [14]. In the present study, the influence of 3D particles morphology on thermal conductivity is discussed by comparing two imagebased FEM results. The results revealed that the particles possess complex structure and large-sized cavities exist in the center of particles. We have compared the simulation results of intact particles with filled-cavities and observed that the irregular and hollow particles lead to a reduction of 24.16% in thermal conductivity of the power bed. This decrease is mainly caused by higher porosity in particle powder, considering cavities in the center of particles. 5.2. Theoretical calculations The effect of porosity on thermal conductivity are discussed through theoretical calculations. Table 4 presents the error analysis of thermal conductivity between image-based FEM results and theoretical calculations. The absolute value of the error, obtained from Eq. (5), is about 7.2%, which is much less than Eq. (4). The Serial-Parallel model can better calculate the thermal conductivity of particles, as is shown in Table 4. In two theoretical models, the
P. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118632
7
Fig. 7. The porous structure theoretical models: (a) Serial-Parallel model and (b) Parallel-Serial model.
Fig. 8. The temperature distribution (a, c) and heat flux distribution (b, d) of Model-1 (a and b) and Model-2 (c and d).
parallel model shows that the matrix phase is continuously distributed at a range of temperature drop, whereas the serial model shows that the solid phase particles do not contact each other, but they only decrease the thickness of heat through the fluid phase in the pores. One should note that the parallel model does not match well with the actual situation, whereas the serial model is close to the actual circumstances. In Serial-Parallel model, the parallel part shows the heat conduction between matrixes, whereas the serial part represents the heat conduction between fluids in the pores. Therefore, the results of Serial-Parallel model are consistent with the image-based FEM simulations. Serial-Parallel model connects the porosity with equivalent thermal conductivity. Based on Serial-Parallel model and the porosity of the powder bed with the value of 45.85%, the equivalent thermal conductivity of the whole powder bed is calculated to be 82.5 W/(m K). The predicted thermal conductivity of the powder bed to solid bulk thermal conductivity is defined as:
mb ¼
kbed kbulk
ð6Þ
where kbed is the predicted thermal conductivity of the powder bed and kbulk is the solid bulk thermal conductivity. The effective thermal conductivity of the AlSi10Mg powder bed to solid bulk thermal conductivity tb = 40.54%. Wei [35] et al. used the transient hot wire method to test the thermal conductivties of Inconel 718, 17–4 stainless steel, Inconel 625, Ti-6Al-4 V and 316L strainless steel powder bed. The thermal conductivities are less than 1/100th of the solid bulk thermal conductivities. However, more cavities exist in AlSi10Mg particles. The effective thermal conductivity of the AlSi10Mg powder bed to solid bulk thermal conductivity is ranged from 60% to 100% [36,37], which depends on the porosity of the powder bed. Zhou et al. [38] has compared the predicted bed effective thermal conductivity with those measured by experiments. When the ratio of the
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P. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118632
Table 4 Error analysis between image-based FEM results and theoretical calculations. Particle
Model-1 Model-2
Thermal conductivity, W/(m K)
Absolute error, %
Image-based FEM
Eq. (4)
Eq. (5)
Eq. (4)
Eq. (5)
63.77 79.18
68.4 75.7
78.0 87.0
7.2% 4.4%
22.2% 9.9%
thermal conductivity of solid bulk to that of fluid is 31.62, tb is 17.39%. In Sih’s experimental study [39,40], tb is assumed to be 60%. Moreover, the theoretical calculations are used to predict the thermal conductivity of hollow particles and particles with filledcavities. It can be readily observed that the theoretical calculations of hollow particles are more accurate than the predictions based on ideal particles with filled-cavities. Comparing image-based FEM results and theoretical calculations, the thermal conductivity is not only influenced by the porosity of particle powder, but also by the 3D particle morphology. Simplified theoretical predictions have large errors. 6. Conclusions In summary, we have demonstrated a novel method to investigate the influence of particles shape and structure on heat conduction during additive manufacturing (AM). X-ray micro-computed tomography (lCT) was used to reconstruct 3D geometry of AlSi10Mg particles. The statistical results of particle distribution measured by CT scans is more accurate compared with that measured by SEM and laser diffraction. Because each particle is separated by 3D watershed algorithm. Moreover, lCT offers a new opportunity to visualize the hollow particles. The thermal conductivity of particles is calculated by imagebased finite element methods (FEMs) and theoretical calculations. The comparison of two image-based FEM simulations quantitatively revealed the influence of hollow particles on thermal conductivity. The cavities reduced the heat conductivity of power bed. Moreover, the energy consumption in AM processing is higher correspondingly, which influenced the mechanical properties of samples after curing. The following conclusions can be drawn from the current study: (1) The 3D structure of particles is complex and large cavities exist in the center of particles. (2) The cavity-containing powder particles could be simplified into porous materials to study the heat conduction in powder-bed. The Serial-Parallel model can better calculate the thermal conductivity of AlSi10Mg particles. (3) The thermal conductivity is not only influenced by the porosity of particle powder, but also by the 3D particle morphology. (4) Compared to the filled-cavity particles, the hollow particles resulted in a decrease of 24.16% in the thermal conductivity of the powder bed. One should note that the presence of cavities reduces the sintered density of SLS-processed components. With 3D structure of particles reconstructed in this paper, a new method was proposed to discuss the particle behavior in the actual AM process. Reconstructed particle microstructure used in this paper could make improvement in previous simulation works to track the AM processing. The research on the heat conductivity of powder bed in this paper is part of the preliminary work of the further research on the effect of hollow particles on powder spreading and powder melting using image-based finite element model.
Declaration of Competing Interest The authors declared that there is no conflict of interest.
Acknowledgements This work is supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (11521202), National Natural Science Foundation of China (11872012), the National Key Research and Development of China (2018YFC0810300), the Young Elite Scientists Sponsorship Program, and the Natural Science Foundation for Colleges and Universities of Jiangsu Province of China grant (16KJB130003).
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