Variation of elastic mechanical properties with texture, porosity, and defect characteristics in laser powder bed fusion 316L stainless steel

Materials Science & Engineering A 763 (2019) 138032

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Variation of elastic mechanical properties with texture, porosity, and defect characteristics in laser powder bed fusion 316L stainless steel

T

E. Garleaa,*, H. Choob, C.C. Slussa, M.R. Koehlerb, R.L. Bridgesa, X. Xiaoc,1, Y. Renc, B.H. Jaredd a

CNS/Y-12 National Security Complex, Oak Ridge, TN, 37831, USA University of Tennessee, Knoxville, TN, 37996, USA c Advanced Photon Source, Argonne National Laboratory, Argonne, IL, 60439, USA d Sandia National Laboratories, Albuquerque, 87185, NM, USA b

A R T I C LE I N FO

A B S T R A C T

Keywords: Resonant ultrasound spectroscopy (RUS) Elastic mechanical properties X-ray synchrotron micro-tomography and diffraction Porosity and texture Stainless steel Laser powder bed fusion

Elastic mechanical properties of 316 L stainless steel samples fabricated using laser powder bed fusion were studied non-destructively through resonant ultrasound spectroscopy. Samples in five different conditions were obtained by varying the laser power from 103 W (the highest density condition) to 68 W (the lowest density condition) at constant laser speed, producing samples with a volume energy density in the 24.5–16.5 J/mm3 range and volumetric porosity in the 0.1–10% range. The observed elastic mechanical properties are discussed taking into consideration the bulk texture developed and quantitative pore characteristics studied using highenergy high-resolution synchrotron X-ray diffraction and X-ray computed micro-tomography, respectively. Furthermore, empirical exponential relationships are provided to express the functional dependence of Young's and shear moduli with porosity.

1. Introduction Powder bed laser fusion has been a fast emerging commercial additive manufacturing (AM) technology originating from the ability to produce high resolution complex features with the conservation of dimensional aspects [1–4]. Some of the important technology challenges affecting microstructure, composition, and mechanical performance in metal AM have been highlighted and reviewed in literature [1,2,5]. For example, rapid solidification can lead to metastable phase transformation and directional heating will result in grain growth with preferred orientation. Repeated thermal cycling was observed to produce microstructure banding. Columnar and equiaxed structures are the most common solidification microstructures in AM, and the relationship between temperature gradient (G) and solidification rate (R) directly affects grain morphology (as G/R) and grain size (as GxR). Even when the AM structures have the same shape and size, significantly different texture can be developed. Formation of texture depends on the local heat flow directions and competitive grain growth and can be favored by the development of coarse grain structures through multiple layers. Scanning speed and layer thickness are major factors that affect the texture because these parameters determine how extensive remelting is to the previous tracks. However, scanning strategy was also reported to

affect the texture. Mechanical behavior of AM samples can be comparable to the standard material; however, anisotropy from the build direction can be present. This originates from a dominant presence of columnar grains aligned along certain directions. Columnar grains are generally coarse and exhibit anisotropic mechanical properties, while equiaxed grains are small and exhibit less anisotropic properties [1,2,5–7]. The most pertinent defects in metal AM are associated with residual stress accumulated during fabrication, along with porosity, and cracking [2,3,8,9]. In particular, numerous models and theoretical relationships have been developed to correlate the volume porosity and Young's modulus for AM applications [10,11]. Ref. [10] reviews the evolution of developments in effective calculation of moduli in porous materials. The conclusion of this review is that most of the property – porosity equations have predictive limitations for design purposes. The limitations originate from lack of rigorous quantitative microstructureproperty correlations for model validation, especially pore characterization. Pore geometry, orientation, and distribution are known factors to produce discrepancies in these models, yet there is little to no data available over a wide range of porosity. Experimentally, mechanical properties of AM parts have been mostly studied by conventional mechanical testing [12–16].

*

Corresponding author. CNS/ Y-12 National Security Complex, P.O. Box 2009 MS 8097, Oak Ridge, TN, 37831-8097, USA. E-mail address: [email protected] (E. Garlea). 1 Current affiliation: National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY, 11973, USA. https://doi.org/10.1016/j.msea.2019.138032 Received 28 March 2019; Received in revised form 11 June 2019; Accepted 13 June 2019 Available online 17 June 2019 0921-5093/ © 2019 Elsevier B.V. All rights reserved.

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76.7, 86.4, 94.6 and 103 W, which gave a total of 10 samples. The build direction (Z) was also marked. All other processing settings were held constant. The cylinders, in as printed condition, were used for high resolution computed tomography (CT) and texture measurements. The discs were machined and polished to mirror finish and were used for determination of elastic mechanical properties using resonant ultrasound spectroscopy (RUS). The sample geometry and size were dictated by the investigative technique; as such, a cylinder was a better geometry for tomography and texture, and a disc was preferred for RUS. Using equation (1) [9] and the printing parameters from above, the volume energy density (VED) for each sample was calculated and summarized in Table 1:

Nevertheless, ultrasonic techniques offer a non-destructive alternative to obtain quantitative elastic mechanical properties [14,17–21]. In particular, resonant ultrasound spectroscopy was employed to determine the elastic modulus as a function of porosity in brittle materials (alumina and hydroxyapatite) [22], was used as a non-destructive evaluation of defects [23], and recently, even to measure the volumetric texture [24]. In this study, the following are reported:

• elastic mechanical properties variation with laser power determined non-destructively using resonant ultrasound spectroscopy • resulting microstructure: grain morphology and grain orientation • volume porosity and pore characteristics as a function of laser power • discussion of the effects of pores size, shape, and orientation on the elastic moduli • functional dependence of Young's and shear moduli with porosity

VED =

P v⋅σ⋅t

(1)

2.2. Resonant ultrasound spectroscopy for elastic moduli calculation 2. Experimental details Discs were machined to a final dimension of 18 mm diameter and 2 mm height and a mirror surface finished on top and bottom. The surface of the disc circumference remained unpolished. The commercially available equipment for RUS (RUSpec, Magnaflux, IL) was employed for this study at room temperature using the three transducers configuration. The five discs were built with the thickness along the build direction. In the case of polycrystalline materials, the RUS technique provides an average measurement over all grains in the bulk, regardless of grain orientation or size. However, the texture affects the structural symmetry of the sample, and the vibrational modes activated. The texture effect is taken into consideration during the data analysis process by choosing to fit the data with the cubic mode. In this study, both the isotropic (no texture) and the cubic (texture materials) modes were employed to analyze experimental data. The isotropic mode has two independent stiffnesses (C11 and C44), while the cubic mode has three independent elastic stiffnesses (C11, C12, and C44) that are used for calculation of elastic moduli. From the known sample dimensions, geometry and density, a set of elastic constants are predicted to give the calculated (predicted) spectrum. This is followed by the collection of the measured frequencies for the specific sample that constitute the experimental spectrum. A multidimensional algorithm (Quasar International, Albuquerque, NM) that minimizes the root-mean-square (RMS) error between the measured and calculated resonant peaks enables the determination of the elastic constants from a single frequency scan. Measurements were taken for each sample in the 0–350 kHz frequency range. Goodness of fit was estimated using the RMS error

2.1. Samples and fabrication process Samples were printed in 316 L stainless steel using a 3D Systems ProX DMP 200 laser powder bed fusion system. The 316 L powder was characterized using an FEI Aspex 1020 scanning electron microscope with automated feature analyses. It had an average particle diameter of 16.7 μm with a 10% particle size distribution (D10) size of 8.2 μm and a 90% particle size distribution (D90) size of 27.6 μm. Powder composition was quantified on the Aspex using energy-dispersive x-ray spectroscopy (EDS) to be 59.6% Fe, 18.73% Cr, 8.36% Ni, 1.19% Mn, 1.69% O2, 0.01% Si and 0.009% Al. Powder use was not tracked precisely for these parts but was on the order of 20–25 reuse cycles. Samples were printed using a 30 μm powder layer thickness (t) with a 1400 mm/s laser scan velocity (v) and a 50 μm cross feed or hatch spacing. The laser beam diameter (σ) at focus was approximately 100μm. 3D Systems standard “hexagons” scan pattern was used to print the parts where the laser raster scans back and forth within 10 mm diameter circumscribed hexagon islands that are stitched together to generate part layers, Fig. 1 (a). The build chamber temperature during printing was roughly 40 °C with an oxygen content that fluctuated about 1000 ppm O2. Two sample geometries were printed together in a single build cycle, as visible in the schematic in Fig. 1 (b). The first sample geometry was 30 mm in diameter and 3 mm tall discs, whereas the second sample geometry was 1.5 mm diameter and 7 mm tall cylinders. Five samples of each geometry were fabricated using five different laser powers (P), 68,

Fig. 1. Schematic showing a) hexagon laser scan pattern for sample printing and b) the two sample geometries and their relationship during fabrication. Hexagon sections are scanned in some randomized sequence that cannot be control by the user. Not drawn to scale. 2

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Table 1 Summary of the elasticity of the disc samples with respect to the printing parameters for both isotropic and cubic (in bold) modes used to process the RUS data analysis. Laser Power (W)

VED (J/mm3)

Archimedes density (g/cm3)

E (GPa)

B (GPa)

G (GPa)

ν

longitudinal velocity mm/μs

shear velocity mm/μs

RMS %

RUS mode

103

24.5

7.91

7.891

1.657

isotropic

94.6

22.5

7.891

1.01

cubic

85.5

20.4

7.819

1.084

isotropic

85.5

20.4

7.819

0.61

cubic

76.7

18.3

7.58

0.588

isotropic

76.7

18.3

7.58

0.384

cubic

68

16.2

7.324

3.198 ± 0.01 3.021 ± 0.05 2.921 ± 0.03 2.998 ± 0.03 2.929 ± 0.02 2.902 ± 0.02 2.871 ± 0.01 2.768 ± 0.02

cubic

22.5

5.423 ± 0.13 5.616 ± 0.02 5.474 ± 0.09 5.494 ± 0.06 5.454 ± 0.06 5.479 ± 0.03 5.28 ± 0.03 5.27 ± 0.02 4.888 ± 0.03

0.319

94.6

0.275 ± 0.007 0.260 ± 0.0008 0.281 ± 0.005 0.303 ± 0.003 0.284 ± 0.003 0.300 ± 0.002 0.283 ± 0.002 0.289 ± 0.001 0.264 ± 0.002

isotropic

7.91

71 ± 1.8 80 ± 0.3 71 ± 1.2 66 ± 0.7 69 ± 0.8 66 ± 0.4 63 ± 0.4 62 ± 0.2 55 ± 0.4

2.449

24.5

135 ± 3.3 165 ± 0.5 139 ± 2.3 132 ± 1.3 137 ± 1.5 133 ± 0.8 125 ± 0.7 122 ± 0.5 98 ± 0.6

3.019 ± 0.07

103

182 ± 4.5 202 ± 0.7 182 ±3 173 ± 1.8 178 ±2 172 ±1 162 ±1 160 ± 0.6 139 ±1

0.675

isotropic

between the measured and calculated peaks. The first 40 resonant peaks were fit for each sample.

2.4. Metallography The material left after each disc's diameter reduction, from 30 mm to 18 mm in diameter, was used for metallography. Three specimens were prepared for each condition, consisting of top view (bottom and top of the sample) and side view (cross section to view layers along the build direction). After cold mounting each AM sample individually in epoxy, the metallographic specimen preparation began by wet grinding with 220 grit silicon carbide paper. Each subsequent grinding utilized incrementally finer grit to 2400. After wet grinding, the specimens were mechanically polished incrementally with diamond suspension from 6 to 1 μm. After mechanical polish, the specimens were given a final vibratory polish with 0.3 μm alumina. Specimen were examined on a Leica DMI 5000 M metallograph and images recorded under bright field illumination. The specimens were electro-etched with 10% oxalic acid at 3 V DC for 60 s and additional images were recorded under bright field illumination.

2.3. Synchrotron high resolution computed micro-tomography for porosity and diffraction for texture studies on cylinders High-resolution synchrotron X-ray computed micro-tomography measurements were performed at beamline 2BM at the Advanced Photon Source (APS) at Argonne National Laboratory. The instrument uses an approximately 60 keV white beam and the beam was collimated to 1.6 mm wide and 1.4 mm tall (shown in green box in Fig. 1) to illuminate the cylinder at approximately 2 mm from its bottom. This way, as it is visible in the Results section, there is about 0.7 mm overlap in the Z direction between the fabrication of discs and cylinders. A second exposure was measured on top of exposure 1 (shown by the blue box in Fig. 1) that overlaps exposure 1 by 0.1 mm. The nominal pixel pitch of the detector is 0.65 μm. Each sample was rotated over 180° with 50msec exposure time for each projection. Using TomoPy, an APS software package [25], the 1500 radiographic projections collected in an HDF file format were reconstructed into 2130 TIFF images. Fiji, an open-source software [26], was then used to convert the 32-bit TIFF images to high quality 8-bit JPEG images. Finally, Simpleware ScanIP, a commercial software for three dimensional (3D) image segmentation and processing, was used for statistical analysis of porosity. A volume of 0.7332 x 0.9197 × 1.3845 mm (0.9336 mm3) for quantitative statistical analysis was cropped for each exposure. Synchrotron X-ray diffraction measurements were performed to study constituent phases and crystallographic texture of as-printed cylinders at beamline 11-ID-C at APS. The wavelength was 0.1173 Å and the incident beam size was collimated to 500 μm × 500 μm for volumetric measurements. The texture data were collected at approximately 2 mm from the bottom of the cylinder (shown by the green box in Fig. 1) by rotating the specimen around the cylinder axis from 0° to 90° at 30° interval. The raw data collected as Debye-Scherrer rings were converted into diffraction patterns using the Fit2D software [27]. Rietveld refinements were then performed for texture analysis using the Material Analysis Using Diffraction (MAUD) software [28], and the pole figures were generated using the MTEX toolbox in MATLAB [29]. Similar micro-tomography and texture studies were conducted by the same authors at APS and additional details are available in Ref. [9].

3. Results 3.1. Cylinder porosity and texture Samples printed using a laser powder bed fusion system at five different laser energies were examined for density/porosity. In Fig. 2, 3D renderings of sample volume studied by micro-tomography at APS are shown for two exposures. A defined volume of 0.9336 mm3 was cropped for the quantitative analysis of porosity, which was perofmred using the ScanIP software. The stainless steel matrix is removed from the renderings and only the identified defects are shown in red. Note that defects smaller than 5 μm were ignored. It is apparent that as the laser power decreases from 103 W to 68 W, there is a monotonic increasing in porosity from 0.106, 0.476, 1.43, 4.6, to 9.63%. In the figure, the porosity from exposure 2 is included as a comparison. The second exposure showed consistently lower porosity than exposure 1. Fig. 3 shows the cylinder porosity variation with the laser power and is compared to that of discs. The cylinders’ porosity was calculated from the data collected at APS and shown in Fig. 2. The measured density in the graph is the Archimedes density that was measured for each disc in its final polished surface condition. The error bar is included although it is hardly observable. Porosity for the discs was obtained from the measured Archimedes density using the formula from Ref. [22]: P = 1-ρ/ρth, 3

(2)

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Fig. 2. Micro-tomography 3D rendering of the sample volume measured for exposures 1 and 2 showing the pores in red for cylinders fabricated at variable laser power: a) 103 W, b) 94.6 W, c) 85.5 W, d) 76.6 W and e) 68 W. Volumetric porosity is reported for each exposure in %. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

While the grain morphology was not significantly affected by the changes in the laser power, the microstructure shows preferential orientation for certain families of grains. Fig. 5 shows the pole figures (PF) for four different families of grains: Fe (111), Fe (200), Fe (220), and Fe (311), obtained from synchrotron X-ray diffraction study. The bulk crystallographic texture is monitored as a function of the laser energy. For the pole figures, the units are in multiple of random distribution (m.r.d.). The build direction is at the center of the pole figure, which is the direction normal to the page. The high localized intensities on the PF represent the preferred orientations of the grain's pole, meaning certain families of grains are aligned in a crystallographic order. Sample 103 W has the most intense points, and the intensity fades away as the laser power decreases. As expected for cubic materials, the solidification growth direction is (200) [2], [9]. Fig. 6 shows the maximum intensity for Fe (200) from Fig. 5, plotted as a function of the laser power. In polycrystalline materials, competitive growth during solidification takes place when dendrites positioned in easy-growth directions align with the maximum heat flow direction. As such, the (100) direction is the easy growth direction for stainless steels [2]. The high-density samples, which correspond to the high laser power cases of 103 W and 94.6 W, have the strongest growth texture along the build direction. The texture diminishes as the laser power decreases, and the lowest density case (68 W) exhibits random grain orientation. Also from the X-ray diffraction measurements, it was confirmed that in all cases there is only one phase present, the FCC (austenitic) phase.

Fig. 3. Measured Archimedes density (RUS discs) and porosity variation with the laser power in the discs and cylinders.

where ρth = 7.99 g/cm3. The density increases with the increase in the laser energy, while porosity follows an opposite trend. There is an overlap between porosity and density for the 76.7 W case. The two sample types, cylinders and discs, exhibit overall good agreement in porosity. 3.2. Microstructure and texture

3.3. Elastic moduli variation with laser power

In Fig. 4 (a-f), optical micrographs are presented at low, intermediate, and high magnifications taken on metallographic specimens prepared using material from the large discs machined into RUS samples. Top views of the sample (a-c) and side views of the cross section parallel to the build direction (d-f) are shown. Density of pores increases as the laser power decreases, consistent with observations in Figs. 2 and 3. Pores can be observed as well as the laser scan pattern and morphology of the melt pools. Microstructure is very similar for all five samples without obvious differences from the variation in laser power. The cross section exhibits the typical fish scale structure. Columnar grains are predominantly observed passing the melt pool boundaries rather than following the curvature of the melt pool. For the 103 W case, large columnar structures extend through layers almost parallel with the build direction. Equiaxed grains are not visible.

Comparison of collected resonant spectra using RUS are shown in Fig. 7 for all five discs fabricated with different laser energy and plotted as amplitude vs. frequencies. The beginning of the experimental spectra from about 2 kHz to 116 kHz are included to highlight the direct effects of the fabrication process on the resonant spectra. The main observations as the laser power increases are a progressive larger splitting of the first frequency peak and a general trend of frequency peaks shifting toward lower frequency. The peak splitting is associated with a change in the sample's axial symmetry, which in turn affects the vibrational modes. When an axially symmetric sample vibrates, its vibrational modes have the same frequency and appear to be a single resonance. However, when the symmetry is broken, the effective diameter is 4

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Fig. 4. Optical micrographs at low magnification, intermediate magnification, and high magnification as a-c) top view and d-f) cross section, respectively, showing the presence of porosity in the microstructure, laser scan pattern and melt pool characteristics.

5

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Fig. 4. (continued)

6

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Fig. 5. Comparison of pole figures with varying laser power for four families of grain: (111), (200), (220), and (311): a) 103 W, b) 94.6 W, c) 85.5 W, d) 76.6 W and e) 68 W. Units are in multiple of random distribution (m.r.d.). Center of the pole figure, which is the direction normal to the page, is the build direction.

developed texture and peak intensity variation in Figs. 5 and 6. The texture effect is accounted for in the spectral data analysis by employing the cubic mode. Nevertheless, the presence of defects, when distributed in an inhomogeneous way in the bulk, can also affect the structural symmetry of the sample, and this effect is discussed later in

reduced for one of the vibrational modes, decreasing its frequency. Thus, both modes are seen and the size of the split is proportional to the size of the defect [17]. In this case, the symmetry is broken due to the strong texture developed in the high density cases. The peak split evolution is in great agreement with the trend observed in the 7

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Fig. 6. Maximum intensity of the pole figure obtained for Fe (200) family of grains with variation of laser power.

Fig. 8. Young's modulus variation with density for the five samples printed at different laser power.

187 GPa for was reported for wrought stainless steel [13]. The variations in the mechanical properties for conventional steel are evident due to testing materials having different starting microstructures. The experimental results obtained here are compared to those from Ref. [14], which are included in the graph, although samples were printed with different parameters. Specifically, in Ref. [14], the laser density energy for the highest density sample was 81.29 J/mm3 and varied from 174.19 J/mm3 to 41.47 J/mm3, whereas in our case the VED is 24.5 J/mm3 for the highest density sample, and varies from 24.5 J/mm3 to 16.2 J/mm3. However, these results are included because they were also obtained by ultrasonic measurements using a pulse echo precision thickness gauge. It is noted that there is an inexplicable limited data available in the open literature on non-destructive (e.g., ultrasonic) mechanical behavior studies of AM. Mechanical properties from the conventional testing have often been significantly lower. As a comparison, also from Ref. [14], the average modulus of 139 ± 47 GPa was obtained from tensile testing, and the high error was believed to be due to machine sensitivity. A value of 180 GPa was reported for a 316 L sample produced by direct metal laser sintering [13]. Moreover, Young's modulus varied from 150 GPa to 200 GPa, and the higher values were reached after a preheating process was employed prior to the tensile testing [16]. In Fig. 8 and Table 1, it can be observed that the 103 W disc has a very small error bar when the RUS cubic mode is used for the calculation of E, 202 ± 0.5 GPa, which changes to 182 ± 4.5 GPa for the isotropic mode when the texture effect is not accounted for. A similar trend is observed for the 94.5 W and 85.5 W cases, when the RMS error decreases by approximately 0.6% when the texture is taken into consideration in the calculation of E; however, it is not as significant as the 103 W case. The 76.7 W sample has a small error for both modes, suggesting that if some grains with preferred orientations are present, they are in a small enough number to play no significant role in elasticity. Indeed, E is very similar for both modes. The 68 W sample has a random texture and only a slight frequency peak split, Fig. 7; therefore, only the isotropic mode was used to analyze the RUS data. Similarly, Fig. 9 and Fig. 10 present shear moduli (G) and Poisson's ratio (ν) variations with Archimedes density for the five samples when both modes were used to analyze the resonant spectra. Results from Ref. [14] are again included in the graphs for comparison, and G = 77 GPa and ν = 0.29 are used for the standard stainless steel 316 L. All three sets of data follow the same trend as a function of density. There is a significant change in G and ν from the “cccci” mode between the 103 W and 94.6 W discs, while the “iiiii” mode yields larger error bars. The longitudinal and shear velocities are shown in Fig. 11, following

Fig. 7. First part of RUS spectra for the five samples printed at different laser powers (103 W–68 W). Resonant spectrum is plotted as amplitude in arbitrary units vs. frequency in kHz.

the paper. Shifts in the resonant frequencies to lower values are associated with a decrease in the Young's modulus (E), and this phenomenon is more evident at higher frequencies [17]. For the frequency range shown here, a more significant frequency peak shift is evident for the low power samples, 76.7 W and 68 W samples, which are also the samples with increased porosity, and thus with expected smaller elastic modulus. Furthermore, based on the correlation between the observations in the RUS spectra and texture evolution, the spectra are analyzed through two approaches, employing both the cubic and isotropic modes. For the first approach, elastic moduli for the 103 W, 94.6 W, 85.5 W and 76.7 W samples were determined using the cubic mode; the isotropic mode was only used for the 68 W sample. The results for the first approach are designated with “cccci” in Fig. 8. The second approach employed the isotropic mode for all samples and is designated as “iiiii” in Fig. 8. A summary of the obtained results is available in Table 1. The Young's modulus variation is presented in Fig. 8 as a function of the Archimedes density. Results from both approaches, cccci and iiiii, are included for comparison. The RMS error was transformed from % to GPa and is included for each data point. The value of 210 GPa is used for the Young's modulus of standard steel, similar to Ref. [14], represented as the black cube symbol in the figure. However, using the RUS technique we obtained a value of 193 GPa for conventional 316 L stainless steel which was in extruded condition. Additionally, a value of 8

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influenced significantly by a low number of pores; however, they were observed to gradually decrease with increasing porosity [30]. In addition to the data graphed here, Table 1 also includes the bulk moduli (B) variation with laser energy. 3.4. Porosity and pore characteristics 3.4.1. Porosity A detailed analysis of the pore characteristics are discussed. Fig. 2 shows 3-D renderings to illustrate the porosity present in each cylinder over a total sample volume of approximately 2 mm3, measured in the two exposures. Table 2 and Table 3 are a summary of the pores statistics and characteristics for the five cylinders as they developed during fabrication. Only exposure 1 is analyzed in detail and discussed here because this part of the cylinder was printed at the same time with the RUS discs. Included in Table 2 are the total number of pores, the total volume of pores, the maximum and average pore volume, and the total, average, and maximum pore surface area present in the 0.9336 mm3 volume of stainless steel. The size and shape of the pores, represented as the size of the pore's major axis and the aspect ratio between the minor to major pore's axes, are detailed in Table 3. The average angle between the major pore axis and build direction is also included. The number of pores increases almost linearly with decreasing laser power from 103 W to 76.7 W, at which point a saturation of 5720 pores occurs. The 68 W sample has a significantly lower number of pores, approximately 3700; however, Fig. 12 shows that the pore volume is the largest for this case. The size of the pore's major axis increases almost linearly with the decrease in the laser power to a maximum of 1.4 mm for the 68 W sample, Fig. 13. However, the average size of pore's major axis, Table 3, saturates at 0.02 mm for the 76.7 W sample and then decreases to 0.017 mm for the 68 W sample, which means that there are only a few pores with larger major axis in this sample than in the 76.7 W sample. Therefore, with the exception of the 68 W case, the porosity increases due to an increased number of pores and increased pore sizes. For the 68 W case, the number of pores decreases significantly, but their volume and surface area are the largest.

Fig. 9. Shear modulus variation with density for the five samples printed at different laser power.

3.4.2. Pore size In terms of the pore size distribution, Fig. 14 shows multiple histograms of the pore's major axis size distribution. Overall, the majority of pores for the 103 W sample have the major axis in the 0–10 μm range, in the 0–20 μm range for sample the 94.6 W sample, in the 0–20 μm and 20–40 μm ranges for the 85.5 W sample, in the 0–50 μm range for 76.7 W sample, and in the 0–100 μm range for the 68 W sample.

Fig. 10. Poisson's ratio variation with density for the five samples printed at different laser power.

the same trends [14]. Longitudinal waves are the waves that move the atoms parallel to the direction in which the wave travels, whereas shear waves have complex displacements both parallel and perpendicular to the direction of propagation [17]. Ultrasonic wave velocity is not

3.4.3. Pore shape Furthermore, details about pores shape are depicted in Fig. 15(a-c)

Fig. 11. (a) Longitudinal and (b) shear velocity as a function of density for the five samples printed at different laser power. 9

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Table 2 Summary of pore statistics and characteristics from exposure 1 for the five cylinders considered. Laser Power (W)

Total number of pores (count)

Total volume of defects (mm3)

Porosity (%)

Avg. Pore Volume (mm3)

Max. pore volume (mm3)

Total Surface Area (mm2)

Avg. Surface Area (mm2)

Max. Surface Area (mm2)

103 94.6 85.5 76.7 68

2160 4160 4800 5720 3690

9.92E-04 0.00445 0.0133 0.0435 0.0898

0.106 0.476 1.43 4.66 9.63

4.60E-07 1.07E-06 2.77E-06 7.61E-06 2.43E-05

5.63E-05 2.62E-04 8.70E-04 0.00885 0.085

0.87281 2.79008 6.94008 19 37.6

4.05E-04 6.70E-04 0.00145 0.00333 0.0102

0.0237 0.103 0.365 3.34 34.1

Table 3 Summary of pore size, shape, and orientation from exposure 1 for the five cylinders considered. Laser Power (W)

Avg. Major axis (mm)

Avg. Aspect Ratio (minor to major)

Min. Aspect Ratio (minor to major)

Max. Aspect Ratio (minor to major)

Avg. Angle

103 94.6 85.5 76.7 68

0.0124 0.0139 0.0181 0.0214 0.0176

0.473 0.58 0.518 0.493 0.484

0.0767 0.105 0.094 0.0579 0.0465

0.85 0.967 0.974 0.989 0.98

83.7 74.3 73.7 71.9 71.1

Fig. 14. Pore's major axis size distribution for the five cylinders fabricated with variable laser power, calculated from exposure 1. Fig. 12. Total number of pores and total volume of pores as a function of the laser power in the cylindrical samples calculated from exposure 1.

of the major axis, the pores evolve from ellipsoids to elongated ellipsoids to flat. Similarly, as the aspect ratio increases from 0.5 towards 1, the ellipsoidal shape becomes more spherical. Looking at Fig. 15(a), the 94.6 W sample has a bimodal distribution of pore shape, represented as a peak at an aspect ratio of approximately 0.5 that is similar to the 103 W sample, and an even larger peak at an aspect ratio of 0.8. This means that, while most of the pores for the 103 W sample are ellipsoids, the 94.6 W sample has a similar number of ellipsoid pores as it does pores in the ellipsoid - sphere range. When comparing the aspect ratio of the 103 W sample to the 68 W sample, Fig. 15(b), it is seen that the 68 W sample also has a bimodal distribution of pore shape, but in this case most of the pores are in the ellipsoidal – flat range. It is noted again that these two samples have the most similar total numbers of pores. The 94.6 W, 85.5 W and 76.7 W samples are shown in Fig. 15(c). All three samples display a bimodal pore distribution. The 76.7 W sample has the largest number of pores, and the majority of those pores fall into the ellipsoidal-flat range, similar to the 85.5 W sample. However, there are many pores in the ellipsoidal-sphere range as well. Another way to understand the porosity is to plot the pore shape, represented as the aspect ratio between the minor and major axes, as a function of the pore size, which is shown as the pore's major axis, Fig. 16. Graphs for the 103 W and 94.6 W cylinders are plotted with the same scale range, while the 85.5 W, 76.7 W and 68 W samples have the same scale range. Consistently, larger pores correspond to the ellipsoidflat aspect ratio range, while smaller pores correspond to the spheroid shape. It is noted again that the 103 W sample is the only sample

Fig. 13. Total number of pores and the maximum major axis as a function of the laser power, in the cylindrical samples calculated from exposure 1.

as histograms of the aspect ratio between minor to major pore axes. In each figure, a schematic of pore shape is included and for an aspect ratio (minor axis/major axis) of 0.5 the pores are ellipsoids. As the aspect ratio decreases from 0.5 towards 0, corresponding to an increase

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Fig. 15. Pore distribution for aspect ratio (pore's minor to major axes) for samples a) 103 W and 94.6 W, b) 103 W and 68 W, c) 94.6 W, 85.5 W and 76.7 W. Data are calculated from exposure 1.

frequency peak shift in the resonant spectra is due to a decrease in the elastic modulus [17], which in turn is known to have an exponential variation with porosity [11,22,30]. The Young's modulus for the 103 W sample is the closest of all samples to that of the standard 316 L but drops significantly about 30 GPa (15%) when the laser power is decreased to 94.6 W, whereas the porosity increases five times from 0.1% to approximately 0.5%, Table 2. The significant drop in the elastic moduli for the 94.6 W sample is unexpected based solely on the slight reduction in density and cannot be fully explained by the texture and resonant spectrum characteristics that indicate strong texture in the bulk. However, there are distinct differences between the two samples in the number of pores and the distribution of pore size, shape, and orientation. Specifically, 1) the number of pores doubles when the laser power is dropped from 103 W to 94.6 W; 2) pores are twice as large for 94.6 W; 3) both samples have about the same number of pores with ellipsoid shape, but the 94.6 W sample also has nearly as many pores in the ellipsoid-sphere shape range; 4) most pores in 103 W sample are almost perfectly perpendicular to the build direction (average 83.7°) whereas the 94.6 W sample has more of a gradual distribution in pore orientation from perpendicular to parallel. The 85.5 W, 76.7 W and 68 W samples have the expected elastic moduli based upon their densities. In particular, the 76.7 W and 68 W samples show no evidence of a texture effect on the elastic mechanical behavior and no effect from the bimodal shape distribution of pores as they exhibit the same elastic properties for both isotropic and cubic modes of calculation. Finally, the variation in elastic moduli with density can be further analyzed to provide an empirical relationship to express the functional dependence with porosity. Specifically, the Young's and shear moduli

without pores with aspect ratio greater than 0.8. 3.4.4. Pore orientation Fig. 17 shows the pore distribution for the angle between the pore's major axis and build direction. Most of the pores are perpendicular to the build direction. As the orientation becomes more parallel to the build direction, the number of pores decreases. This trend is followed by all samples with the exception of sample the 103 W sample, which has more than half of the pores orientated at approximately 87°, resulting in the average of 83.7° shown in Table 3. For the remaining four samples, the mean angle decreases consistently. 4. Discussion Stainless steel 316 L samples were fabricated using laser powder bed fusion technology at a constant laser speed of 1400 mm/s and variable laser power from 68 W to 103 W, resulting in a volume energy density in the range of 16.2–24.5 J/mm3, and volumetric porosity of 0.1–9.6%. The elastic moduli were studied non-destructively using resonant ultrasound spectroscopy, and their variation with the laser power is discussed, taking into consideration the microstructure developed, volume porosity, and pore characteristics. The specific fingerprints in the resonant spectra, such as frequency peak split and separation and frequency peak shift (Fig. 7) are consist with the texture evolution (Figs. 5 and 6) and the variation in volume porosity (Fig. 3). As such, the frequency peak separation is associated with strong texture for the 103 W case, and only a slight peak split is observed in the sample with random texture, the 68 W sample. In turn, the strong texture yields a value of 202 GPa for the highest density sample, which is the closest to the standard value of 210 GPa. The 11

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Fig. 16. Pore size (represented by the major axis) as a function of pore shape (represented by the aspect ratio of the minor to major axes) for the cylinders printed with the laser energy: 103 W, 94.6 W, 85.5 W, 76.7 W, and 68 W. Data are calculated from exposure 1.

Fig. 17. Pore distribution as a function of the angle between the pore major axis and build direction for the a) 103 W and 94.6 W, b) 103 W and 68 W, and c) 94.6 W, 85.5 W and 76.7 W samples. Data are processed from exposure 1. 12

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Fig. 18. Exponential fit of Young's modulus as a function of volume fraction porosity that was calculated using either cubic (c) or isotropic (i) RUS modes: a) cccci, b) iiiii, and c) ciiii. Exponential fit of shear modulus as a function of the volume fraction porosity that was calculated using either cubic or isotropic RUS modes: d) cccci, e) iiiii, and f) ciiii.

data can be fitted with an empirical exponential function, equations (3) and (4), where E0 is Young's modulus at the highest density (zero porosity), and bE is a measure of the rate at which E decreases as the porosity, P, increases [22]. Similarly to E, equation (4) can be written for the shear modulus (G).

E = E0 exp(−bE ⋅P )

(3)

G = G0 exp(−bG ⋅P )

(4)

consistency shown for the high density samples for both Ref [14] and this work to exhibit a low value in ν. Poisson's ratio is believed to be more influenced by the pore morphology than the pore concentration, and irregular variation with porosity was observed [22,31,32]. The ν is lower than the standard steel value for the high density case, the 103 W sample, which has 0.106% porosity. This sample is the only sample without ellipsoid-sphere shape pores and with almost all pores perpendicular to the build direction. The 68 W sample has a 9.6% porosity, a somewhat similar pore shape distribution, and exhibits a low Poisson's ratio, but this is expected due to the significant increase in porosity.

The elastic moduli, E and G and exponential fitting curves can be seen in Fig. 18. The porosity of the discs is expressed as the volume fraction porosity. The RUS data were analyzed utilizing the two modes “cccci” and “iiiii” and the results are summarized in Table 1. A third combination (“ciiii”) is included in which only the 103 W sample was analyzed with the cubic mode, and the rest of four discs were analyzed with the isotropic mode. The results from the exponential fits are summarized in Table 4. The coefficient of determination, R2, is the lowest for the “cccci” case and highest for the “iiii” case. However, the 103 W sample cannot be isotropic due to its strong texture and unimodal pore distribution. The “ciiii” fit yields a value of 210 GPa for E0 that is equal to the value for the standard steel, but G0 is 83 GPa and larger than the value for the standard steel. R2 for “ciiii” is greater than 0.95. In regard to the Poisson's ratio, it is interesting to note the

5. Conclusions 316 L stainless steel specimens were fabricated by laser powder bed fusion technology with variable laser power of 103 W, 94.6 W, 85.5 W, 76.7 W and 68 W at a constant laser speed of 1400 mm/s, yielding samples with porosity varying from 0.1 to 9.6%. The effects of the processing conditions on elasticity, porosity, and microstructure were investigated. 5.1. The following conclusions can be presented

• Microstructure

Table 4 Exponential fit parameters for E and G when RUS data are analyzed with either a cubic (c) or isotropic (i) mode for the first for discs: 103 W, 94.6 W, 85.5 W and 76.7 W. Sample 68 W was always treated as isotropic. Parameter\RUS mode

cccci

iiiii

ciiii

E0 bE R2 G0 bG R2

205 ± 8 −4.9 ± 0.98 0.86367 80 ± 4 −5 ± 1.28 0.79367

195 ± 4 −3.9 ± 03 0.96942 75 ± 1.1 −3.7 ± 0.2 0.98145

210 ± 3.6 −5 ± 0.4 0.97274 83 ± 1.8 −5.18 ± 0.5 0.9583

• •

13

showed no significant difference in grain morphology; however, preferred grain orientation was developed, and the texture become stronger as the laser power increased. Microstructure was studied by optical microscopy and synchrotron bulk X-ray diffraction. Porosity increases with the decrease in density as the laser power decreases. Pore characteristics were studied by synchrotron X-ray tomography yielding a 0.65 μm resolution. Mechanical elastic properties were studied using resonant ultrasound spectroscopy and the spectra show two specific characteristics: the first frequency peak splits and separates in a manner consistent with the development of texture or inhomogeneous porosity distribution; frequency peaks shift toward lower frequencies, which correlates to a decrease of the elastic moduli and is consistent

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Acknowledgements

with the variation in porosity.

• The high density case, the 103 W sample, has elastic moduli close to that of a standard 316 L stainless steel. • There is a significant reduction in Young's modulus of approximately • •

•

E. G. acknowledges Prof. M. Radovic at Texas A&M University for the discussion on the RUS data. This work was performed under the auspices of the U.S. Department of Energy by Consolidated Nuclear Security, LLC (CNS) under Contract DE-NA-0001942. Fabrication of samples was performed at Sandia National Laboratories. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357.

15% from the 103 W sample to the 94.6 W sample, whereas the porosity increases about 5 times. This change is believed to be due to specific differences in porosity and pore characteristics between the two samples. Poisson's ratio has an inconsistent variation with the density which is believed to be due to the pore characteristics more than volume porosity. Pores are quantitatively characterized for size, shape, and orientation with the following observations: o The number of pores increases with the decrease in laser power and saturates at 76.7 W; however, the pore volume, surface area, and major axis increase monotonically from the 103 W–68 W conditions. o The lowest density case, the 68 W sample, has a significantly smaller number of pores than the 76.7 W sample (higher density sample) but the larger pores in the 68 W sample result in it having the highest volume porosity. o As the laser power decreases from 103 W to 76.7 W, porosity increases due to the increase in pore number and pore size. o Sample 103 W has most of the pores in ellipsoidal shape orientated at an average angle of 83.7°, which could be associated with the strong texture for this sample. Sample 94.6 W has the orientation of pores gradually distributed over the 0–90° range with a mean angle of 74.3°. o The 103 W sample contains pores that are mostly ellipsoids, while the 94.6 W sample consists of roughly 50% of pores similar in shape to those found in the 103 W sample and 50% of pores ellipsoidal-spherical in shape. The pores in the 94.6 W samples have the major axis twice as large as those found in the 103 W sample. o Sample 103 W has a smaller Poisson's ratio than expected and is the only sample without a bimodal pore shape distribution, having only ellipsoidal pores and none into the ellipsoidal – sphere range. The elastic mechanical properties are mostly affected by the texture through the grain orientation, pore direction in relationship to the build direction, and pore shape.

References [1] W.E. Frazier, Metal additive manufacturing: a review, J. Mater. Eng. Perform. 23 (2014) 1917–1928. [2] T. DebRoy, H.L. Wei, J.S. Zuback, T. Mukherjee, J.W. Elmer, J.O. Milewski, A.M. Beese, A. Wilson-Heid, A. De, W. Zhang, Additive manufacturing of metallic components- Process, structure and properties, Prog. Mater. Sci. 92 (2018) 112–224. [3] H.-W. Mindt, O. Desmaison, M. Megahed, A. Peralta, J. Neumann, Modeling of powder bed manufacturing defects, Mater. Eng. Perform. 27 (2018) 32–43. [4] D. Herzog, V. Seyda, E. Wycisk, C. Emmelmann, Additive manufacturing of metals, Acta Mater. 117 (2016) 371–392. [5] S. Al-Bermani, M. Blackmore, W. Zhang, I. Todd, The origin of microstructural diversity, texture, and mechanical properties in electron beam melted Ti-6Al-4V, Metall. Mater. Trans. A 41A (2010) 3422–3434. [6] A.A. Antonysamy, J. Meyer, P.B. Prangnell, Effect of build geometry on the β-grain structure and texture in additive manufacture of Ti-6Al-4V byselective electron beam melting, Mater. Char. 84 (2013) 153–168. [7] L. Thijs, F. Verhaeghe, T. Craeghs, J. Van Humbeeck, J.-P. Kruth, A study of the microstructural evolution during selective laser melting of Ti–6Al–4V, Acta Mater. 58 (9) (2010) 3303–3312. [8] J.A. Cherry, H.M. Davies, S. Mehmood, N.P. Lavery, S.G.R. Brown, J. Sienz, Investigation into the effect of process parameters on microstructural and physical properties of 316 stainless steel parts by selective laser melting, Int. J. Adv. Manuf. Technol. 76 (2015) 869–879. [9] H. Choo, K.-L. Sham, J. Bohling, A. Ngo, X. Xiao, Y. Ren, P.J. Depond, M.J. Matthews, E. Garlea, Effect of laser power on defect, texture, and microstructure of a laser powder bed fusion processed 316 stainless stell, Mater. Des. 164 (2019). [10] J.A. Choren, S.M. Heinrich, M.B. Silver-Thorn, Young's modulus and volume porosity relatinships for additive manufacturing applications, J. Mater. Sci. 48 (2013) 5103–5112. [11] A.P. Roberts, E.J. Garboczi, Elastic properties of model porous ceramics, J. Am. Ceram. Soc. 83 (2000) 3041–3048. [12] J.J. Lewandowski, M. Seifi, Metal additive manufacturing: a review of mechanical properties, Annu. Rev. Mater. Res. 46 (2016) 151–186. [13] T.M. Mower, M.J. Long, Mechanical behavior of additive manufactured, power-bed laser-fused materials, Mater. Sci. Eng. A 651 (2016) 198–213. [14] N.P. Lavery, J. Cherry, S. Mehmood, H. Davies, B. Girling, E. Sackett, S.G.R. Brown, J. Sienz, Effects of hot isostatic pressing on the elastic modulus and tensile properties of 316L parts made by powder bed laser fusion, Mater. Sci. Eng. A 693 (2017) 186–213. [15] N. Chawla, X. Deng, Microstructure and mechanical behavior of porous sintered steels, Mater. Sci. Eng. A 390 (2005) 98–112. [16] B. Zhang, L. Dembinski, C. Coddet, The study of the laser parameters and environment variables effect on mechanical properties of high compact parts elaborated by selective laser melting 316 L powder, Mater. Sci. Eng. A 584 (2013) 21–31. [17] A.A. Migliori, J.L. Sarrao, Resonant Ultrasound Spectroscopy: Applications to Physics, Materials Measurements, and Nondestructive Evaluation, John Wiley, New York, NY, 1997. [18] M. Radovic, E. Lara-Curzio, L.L. Riester, M. Radovic, E. Lara-Curzio, L. Riester, Comparison of different experimental techniques for determination of elastic properties of solids, Mater. Sci. Eng. A 368 (2004) 56–70. [19] M.A. Steiner, E. Garlea, J. Creasy, A. DeMint, S.R. Agnew, Temperature dependent elastic properties of γ-phase U–8 wt% Mo, J. Nucl. Mater. 500 (2018). [20] J.A. Slotwinski, E.J. Garboczi, K.M. Hebenstreit, Porosity measurements and analysis for metal additive manufacturing process control, J. Res. National. Inst. Standard. Technol. 119 (2014) 494–528. [21] E. Garlea, M. Radovic, P. Liaw, High-temperature dependency of elastic mechanical behavior of two wrought magnesium alloys AZ31B and ZK60A studied by resonantultrasound spectroscopy, Mater. Sci. Eng., A 758 (2019) 86–95. [22] F. Ren, E.D. Case, A. Morrison, M. Tafesse, M.J. Baumann, Resonanat ultrasound

Disclaimer and copyright notice Neither the United States Government nor any agency thereof, nor CNS, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility to any non-governmental recipient hereof for the accuracy, completeness, use made, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency or contractor thereof, or by CNS. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency or contractor (other than the authors) thereof. This document has been authored by Consolidated Nuclear Security, LLC, under Contract DE-NA-0001942 with the U.S. Department of Energy/ National Nuclear Security Administration, or a subcontractor thereof. The United States Government retains and the publisher, by accepting the document for publication, acknowledges that the United States Government retains a nonexclusive, paid up, irrevocable, worldwide license to publish or reproduce the published form of this document, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, or allow others to do so, for United States Government purposes. 14

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E. Garlea, et al.

[23] [24]

[25] [26]

[27] A.P. Hammersley, FIT2D: a multi-purpose data reduction, analysis and visualization program, J. Appl. Crystallogr. 49 (2016) 646–652. [28] L. Lutterotti, Maud: a rietveld analysis program designed for the internet and experiment integration, Acta Crystallogr. A: Foundations of Crystallography 56 (2000). [29] F. Bachmann, R. Hielscher, H. Schaeben, Texture analysis with MTEX-free and open source software toolbox, Solid State Phenom. 160 (2010) 63–68. [30] M. Fukuhara, T. Wada, A. Inoue, Ultrasonic characteristics of porous Pd42.5Cu30Ni7.5P20 glassy alloys, J. Appl. Phys. 102 (2007). [31] M.L. Dunn, H. Ledbetter, Poisson's ratio of porous and microcracked solids: theory and application to oxide superconductors, J. Mater. Res. 10 (11) (1995) 2715–2722. [32] Y.H. Zhao, G.P. Tandon, G.J. Weng, Elastic moduli for a class of porous materials, Acta Mech. 76 (1989) 105–130.

spectroscopy measurement of Young's modulus and Poisson's ratio as a function of porosity for alumina and hydroxyapatite, Phil. Mag. 89 (11) (2009) 1163–1182. K. Flynn, M. Radovic, Evaluation of defects in materials using resonant ultrasound spectroscopy, J. Mater. Sci. 46 (2011) 2548–2556. B. Lan, M.A. Carpenter, W. Gan, M. Hofmann, F.P.E. Dunne, M.J.S. Lowe, Rapid measurement of volumetric texture using resonant ultrasound spectroscopy, Scripta Mater. 157 (2018) 44–48. D. Gürsoy, F. De Carlo, X. Xiao, C. Jacobsen, TomoPy: a framework for the analysis of synchrotron tomographic data, J. Synchrotron Radiat. 21 (5) (2014) 1188–1193. J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D.J. White, V. Hartenstein, K. Eliceiri, P. Tomanacak, A. Cardona, Fiji: an open-source platform for biological-image analysis, Nat. Methods 9 (7) (2012) 676–682.

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