6 In this paper, we have developed and demonstrated a novel high-velocity impact experiment to study dynamic 7 fragmentation of additively-manufactured metals. The experiment consists of a light-gas gun that res a conical 8 nosed cylindrical projectile that impacts axially on a thin-walled cylindrical tube fabricated by 3D printing. The 9 diameter of the cylindrical part of the projectile is approximately twice greater than the inner diameter of the 10 cylindrical target, which is expanded as the projectile moves forward, and eventually breaks into fragments. The 11 experiments have been performed for impact velocities ranging from 180 m=s to390 m=s, leading to strain 12 rates in the cylindrical target that vary between 9000 s1and23500 s1. The cylindrical samples tested 13 are printed by Selective Laser Melting out of aluminium alloy AlSi10Mg, using two printing qualities, with two 14 di erent outer diameters, 12 mm and 14 mm, and two di erent wall thicknesses, 1 mm and 2 mm. A salient feature 15 of this work is that we have characterized by X-ray tomography the porous microstructure of selected specimens 16 before testing. Three-dimensional analysis of the tomograms has shown that the initial void volume fraction of 17 the printed cylinders varies between 1 :9% and 6:1%, and the maximum equivalent diameter of the 10 largest pores 18 ranges from 143 µm to 216 µm, for the two di erent printing conditions. Two high-speed cameras have been used to 19 lm the experiments and thus to obtain time-resolved information on the mechanics of formation and propagation 20 of fractures. Moreover, fragments ejected from the samples have been recovered, sized, weighted and analyzed 21 using X-ray tomography, so that we have obtained indications on the e ect of porous microstructure, specimen 22 dimensions and loading velocity on the number and distribution of fragment sizes. To the authors' knowledge, this 23 is the rst paper ever (i) providing a systematic experimental study (34 impact tests) on the fragmentation behavior 24 of printed specimens, and (ii) including 3D reconstructions of dynamic cracks in porous additively-manufactured 25 materials. 26 Keywords: 27 High-velocity impact, Axial penetration, Fragmentation, Additively-manufactured metals, X-ray tomography 28 Corresponding author. Tel. +34 916249588, E-mail address: junietof@ing.uc3m.es Preprint submitted to Elsevier October 17, 2022 2 1. Introduction 29 The ring expansion test developed by Niordson (1965) was a turning point in the experimental research on 30 dynamic localization and fragmentation of metallic materials. In this impact experiment, a circular ring specimen 31 is expanded at large velocities up to two or three hundreds of meters per second by detonation of an explosive 32 charge (Diep et al., 2004) or by application of transient magnetic elds (Grady and Benson, 1983; Altynova et al., 33 1996; Zhang and Ravi-Chandar, 2006). While the magnetic loading technique has become more popular, largely 34 because it is more conducive to a laboratory environment than explosive loading schemes, and loading rates are 35 readily controlled trough variation of the driving current pulse, it shows the drawback that, since it is based on 36 the principle of opposing forces between primary and induced currents, Joule heating e ects occur in the sample 37 material. The strain rates attained in the electromagnetic loading ring expansion experiments generally range 38 from 5 103s1to 5104s1, for specimens with diameter typically varying between 27 mm and 36 mm. For thin 39 rings, the radial stress becomes negligible in comparison with the circumferential stress, so that the stress eld is 40 mainly uniaxial. In addition, the symmetry of the problem nearly eliminates the e ects of wave propagation along 41 the circumferential direction of the specimen, so that the material stretches during loading until homogeneous 42 deformation fails at large strain, leading to the nucleation of multiple necks {in ductile materials{ and subsequent 43 fragmentation. 44 45 Since the pioneering work of Niordson (1965), only few laboratories have mastered the ring expansion testing 46 technique. For instance, Grady and co-workers (Grady and Benson, 1983; Grady and Olsen, 2003) performed 47 experiments with OFHC copper, aluminum 1100{O and U6N specimens, with 30 32 mm in diameter and 48 0:751 mm in thickness of square cross section, expanding to radial velocities ranging over 50 300 m=s. The 49 experiments revealed that the fracture strain of the specimens, the number of necks and the number of fragments all 50 increase with the expansion velocity, the number of fragments being less than the number of necks. Following the 51 concepts of fragmentation statistics put forth by Mott (1947), Grady and Benson (1983) stated that the arrested 52 necks result from the arrival of relieving stress waves from a nearby fractures that remove the driving force before 53 fracture is completed. Moreover, Altynova et al. (1996) carried out ring expansion tests with solutionized Al6061, 54 Al6061{T6, and OFHC Cu specimens, with similar dimensions to the samples used by Grady and Benson (1983), 55 and tested within the same range of radial velocities. Altynova et al. (1996) reported that the strains to failure 56 of the three materials increase continuously with increasing velocity, and attributed the increase in ductility to 57 inertia and changes in material constitutive behavior at high strain rates. As Molinari and collaborators would 58 3 later con rm using perturbation analyses (Fressengeas and Molinari, 1985, 1994; Mercier and Molinari, 2003, 59 2004), inertia a ects ductility because the necking development is impeded due to the circumferential acceleration 60 that stabilizes plastic ow and opposes to localization. Altynova et al. (1996) showed that at expansion velocities 61 greater than 200 m =s the ductility of the samples exceed the quasi-static value by 60, 150, and 250% for OFHC Cu, 62 solutionized Al6061, and Al6061{T6, respectively. Years later, Zhang and Ravi-Chandar (2006) performed ring 63 expansion experiments using Al6061{O specimens with rectangular cross section of thickness 0 :5 mm and length of 64 1 mm, at velocities ranging from 80 to 200 m =s, and photographed the tests using a high-speed camera obtaining 65 time-resolved images of the necking and fragmentation processes. Consistent with the earlier results of Grady and 66 co-workers (Grady and Benson, 1983; Grady and Olsen, 2003) and Altynova et al. (1996), the experiments of Zhang 67 and Ravi-Chandar (2006) showed that the number of necks and fragments increases rapidly with the expanding 68 speed of the ring, and that the resulting distributions of neck and fragment sizes are governed by the statistical 69 material property and microstructure variations (which activate the nucleation of necks in speci c locations), 70 and by the propagation of the unloading or release waves from early growing necks and fractures. Shortly after, 71 Zhang and Ravi-Chandar (2008) published additional ring expansion experiments with samples of the same size 72 made of Al1100{H14 and Cu101. The tests yielded statistical distributions of neck spacings and fragment sizes 73 similar to those obtained in the experiments performed with Al6061{O rings in Zhang and Ravi-Chandar (2006) 74 (for the same range of loading velocities), such that with increasing strain rate, more necks were nucleated at 75 shorter distances. Janiszewski (2012) performed ring expansion experiments with cold-rolled copper Cu-ETP, 76 Al7075, barrel steel and tungsten alloy samples with diameters varying from 27 :2 mm to 33 :4 mm and square 77 cross section of 1 mm thickness. The experiments were recorded with a high-speed camera to obtain real-time 78 observations of the necking and fragmentation processes, and to determine the expanding velocities attained in 79 the experiments, that ranged from 85 m =s to 235 m =s. Consistent with earlier experimental data of Altynova 80 et al. (1996), the ductility of the samples, that was estimated with a simple relation between the initial cross 81 section area of the specimen and the cross sectional area in the uniform strain portions of the recovered fragments, 82 was shown to increase monotonically with expanding velocity (for all materials tested with exception of Al7075). 83 Recently, Cliche and Ravi-Chandar (2018) carried out electromagnetically driven expanding ring experiments to 84 investigate the high strain rate behavior of AZ31B-O magnesium alloy. Some of the experiments were performed 85 using an indirect expansion technique in which a copper pusher ring carries the electric current and launches the 86 magnesium specimen, which remains largely free of Joule e ect heating. In the remaining tests, the magnesium 87 specimen carried the current, being heated by the Joule e ect, as in the earlier tests of Altynova et al. (1996) and 88 4 Zhang and Ravi-Chandar (2006, 2008). The inner radius of the magnesium specimens was xed at 15 :75 mm, while 89 two di erent thicknesses, 0 :5 mm and 2 :286 mm, were considered to explore the in uence of the cross sectional 90 aspect ratio of the samples in the statistics of neck development and fragmentation. The tests, that were performed 91 for expansion velocities ranging from 50 m =s to 200 m=s, did not reveal any measurable e ect of the strain rate 92 and the Joule heating on the ductility of the magnesium samples. In contrast, the increase of the cross section 93 size of the specimen boosted the strain developed in the unnecked regions of the ring due to the increasing time 94 taken for the localization to develop across the thickness of the samples. Moreover, Cliche and Ravi-Chandar 95 (2018) interpreted the experimentally observed distributions of neck spacings and fragment sizes using a simple 1D 96 implementation of the fragmentation model of Mott (1947), and suggested that the inherent scatter in the strain to 97 fracture of the material, which materializes in a distribution of punctual defects with low failure strain, determines 98 the number and size of the necks and fragments formed along the circumference of the rings. The higher the strain 99 rate of the tests, the more the distribution of defects is activated towards higher strain to failure values, explaining 100 the increase in the number of fragments as the expansion velocity increases. 101 102 The fragmentation of metallic materials has also been investigated by means of the rapid radial expansion of 103 cylindrical shells (Wesenberg and Sagartz, 1977; Goto et al., 2008; Hiroe et al., 2008; Zhang and Ravi-Chandar, 104 2010) and hemispherical shells (Mercier et al., 2010), in which the fragmentation of the samples is preceded by the 105 formation of necking bands {in ductile materials{ which are generally aligned with the direction of zero stretch (Hill, 106 1952; Zhang and Ravi-Chandar, 2010; Mercier et al., 2010). For instance, Wesenberg and Sagartz (1977) carried 107 out electromagnetic expansion of Al6061{T6 cylinders 102 mm long, 127 mm in outer diameter, and 1 :27 mm 108 in thickness, at initial strain rates of 104s15102s1. The experiments were recorded using a high-speed 109 camera, and the fragments were collected, reassembled and weighted after the tests, to determine the distribution 110 of fragment sizes. There was a small range of preferred wavelengths, i.e. fragment sizes, into which the 6061 T6 111 cylinders fractured, in agreement with the theoretical distribution of fragments derived from the statistical theory 112 of Mott (1947). Years later, Goto et al. (2008) explosively drove to fragmentation long cylinders fabricated from 113 AerMet 100 alloy and AISI 1018 steel, with outer diameter of 50 :8 mm, wall thickness of 3 mm and axial length 114 of 203:2 mm, so that the loading path was close to plane strain. A part of the tests was monitored using high- 115 speed diagnostics, including high-speed cameras, ash radiography and velocimetry of the outer surface of the 116 specimen during expansion, and in the remaining tests soft-recovery of the fragments was performed, in order to 117 determine the distribution of mass sizes and failure strains. The strain rate attained during the experiments was 118 5 comprised between 104s1and 105s1, and the failure strain was found to be 0 :220:03 for AerMet 100 alloy and 119 0:460:07 for AISI 1018 steel. Moreover, Hiroe et al. (2008) explosively expanded to fragmentation cylindrical 120 metallic specimens made of 304 stainless steel, Al5052 and two di erent types of carbon steel. While the length of 121 the cylinders was xed at 100 mm, di erent outer diameters varying between 34 mm and 40 mm were investigated, 122 and also various wall thicknesses ranging from 1 :65 mm to 6 mm. The strain rates attained in the tests ranged 123 between 0:5104s1and 5104s1. The experiments were recorded with a high-speed camera, and it was observed 124 that the fractures of the cylinders generally occurred parallel to the axis. The investigation on recovered fragments 125 revealed that the number of fragments is greater for the thinner-walled cylinders that are expanded at higher 126 strain rates. Mercier et al. (2010) used explosive charges to expand hemispherical shells with radius of 50 mm and 127 thickness of 3 mm, made of copper and tantalum, at strain rates of 104s1. The experiments were recorded 128 with a high-speed camera to monitor the formation of multiple necks and the subsequent fragmentation of the 129 specimens. The displacement of the hemispherical shells was not constrained in their equatorial plane, and thus 130 the motion of the specimens during loading was not perfectly spherical , so that a small layer of the shells located 131 near the equatorial plane was subjected to plane strain conditions, promoting early formation of multiple necking 132 bands, parallel to each other, which eventually triggered the fragmentation of the samples. The mechanisms which 133 control the formation of the necks were studied using a linear stability analysis and a dimensionless parameter 134 which collects the joint e ects of strain rate sensitivity, strain hardening and thermal softening of the material, so 135 that Mercier et al. (2010) derived analytical predictions for the number of necks and the average neck spacing that 136 were in agreement with the experimental evidence. 137 138 However, the complexity of performing fragmentation tests of rings, cylinders and hemispheres, either with 139 explosives or with electromagnetic loading, has recently led to the development of alternative techniques to conduct 140 fragmentation experiments using gas guns. The idea is to have tunable experimental setups which provide greater 141 control over the strain rates in the specimen and extended exibility to carry out tests in a laboratory environment, 142 decreasing the risk for deployment of instrumentation for test monitoring. For instance, Rao et al. (2020) studied 143 the fragmentation of metallic cylindrical shells by launching with a gas gun a polycarbonate projectile that impacts 144 a mild steel ogive placed inside the target, making the polycarbonate projectile to ow over the ogive, thus causing 145 radial expansion and fragmentation of the test cylinder. The cylindrical targets, made of EN3 mild steel and 146 304 stainless steel, were 600 mm long. Specimens with wall thickness of 2, 3 and 4 mm were tested in order 147 to investigate the e ect of specimen size and expansion velocity in the fragmentation process. The strain rates 148 6 attained in the tests varied between 0 :5104s1and 2:5104s1. Soft recovery of the fragments showed that 149 decreasing the wall thickness of the cylinders increases the number of fragments, while decreasing their size and 150 mass, and this was attributed to thinner casings being subjected to higher strain rates. Moreover, Neel et al. 151 (2020) developed the so-called conical impact fragmentation test, a novel experimental arrangement to perform 152 high strain rate fracture characterization of metallic materials. The setup consists of a conical specimen red with 153 a gas gun which is impacting a mating conical target, similar in geometry to a funnel (in the authors' words), at 154 nominal velocities of 1 2 km=s. Three tests were performed as proof of concept using specimens made of 1018 155 steel. Time-resolved velocity measurements obtained from the free outer surface of the conical target were used 156 to validate simulations which revealed that, when compared with other laboratory techniques like the explosively 157 driven cylinder expansion, the conical impact fragmentation test allows to obtain constant strain rate in the 158 specimen and improved spatial uniformity of strain history. 159 160 In this paper, motivated by the recent works of Rao et al. (2020) and Neel et al. (2020), we have developed 161 and demonstrated a novel fragmentation experiment which uses a light-gas gun to re a conical projectile that 162 impacts axially on a cylindrical tube which is expanded until multiple fractures appear along the circumference of 163 the specimen. The impact velocities have been varied from 180 m=s to380 m=s, leading to strain rates in 164 the cylindrical target that range between 9000 s1and23500 s1. We have tested additively-manufactured 165 samples made of aluminum alloy AlSi10Mg, printed with two di erent qualities ( standard and performance ), with 166 two di erent outer diameters, 12 mm and 14 mm, and two di erent wall thicknesses, 1 mm and 2 mm. We 167 have characterized by X-ray tomography the porous microstructure of selected specimens before testing. Three- 168 dimensional analysis of the tomograms has shown that the initial void volume fraction of the printed cylinders 169 varies between 1 :9% and 6:1%, and the maximum equivalent diameter of the 10 largest pores ranges from 143 µm 170 to 216 µm, for two di erent printing conditions. The experiments have been recorded with two high-speed cameras 171 to obtain time-resolved information on the nucleation and propagation of fractures. In addition, fragments ejected 172 from the samples have been recovered, sized and weighted, so that we have obtained fragments size distributions 173 for all tests performed. Moreover, additional X-ray tomography studies performed on recovered fragments have 174 provided indications on the evolution of the porous microstructure in the experiments, showing that the voids 175 deform during loading, and serve as preferential locations for the cracks propagation. To the authors' knowledge, 176 this is the most comprehensive investigation published so far on the dynamic fragmentation behavior of additively- 177 manufactured metals. 178 7 2. Experimental methodology 179 This section describes the novel high-velocity impact experiment devised to study dynamic fragmentation of 180 additively-manufactured thin-walled tubes. The cylindrical samples were made of AlSi10Mg alloy and printed using 181 Selective Laser Melting (SLM) technique by Materialise (2022). This material generally shows limited ductility 182 that rarely exceeds 5% in tension (Nalli et al., 2021; Laursen et al., 2020). A key feature of the experimental 183 methodology is that compared to dynamic fragmentation experiments in which the sample is loaded by controlled 184 detonation of an explosive or by electromagnetic forces, the setup presented in this work is remarkable for its 185 simplicity and rapid operation. Moreover, X-ray computed tomography scans of the porous microstructure of 186 selected specimens were performed to determine the void volume fraction and the spatial and size distributions of 187 voids in the thin-walled tubes. In addition, post-mortem tomograms of recovered fragments were also performed 188 to gain insights into the in uence of voids on the initiation of the fractures and the path of the cracks. 189 2.1. Impact testing 190 The experiment consists of a 25-mm bore single-stage helium-driven gun, located at the Impact Laboratory of 191 the Carlos III University of Madrid, ring a conical-nosed cylindrical projectile that impacts axially on a tubular 192 specimen { see an overview of the experimental setup in Figure 1. The tests were performed for impact velocities 193 within the range 180 m =s.vz.390 m=s,vzbeing the projectile axial velocity. 194 The conical nosed projectile (also referred to as striker along this manuscript), machined out of a 42CrMo4 195 (quenched and tempered) alloy steel bar, has a spherically blunted tip to minimize aerodynamic drag and to insure 196 a stable motion during the projectile ight. The projectile is 64 mm long, with a 1 :55 mm nose radius, 40apex 197 angle, and a 24 mm diameter base { see Figure 2. In order to maintain the projectile centered with respect to 198 the gun barrel, such that the projectile impacts axially on the tubular specimen, a cup-type cylindrical sabot of 199 24:8 mm diameter and 100 mm long, made of printed polylactide (PLA), was inserted in a 20 mm long and 10 mm 200 diameter pin machined at the projectile base { see the indication in Figure 2. The total mass of the assembly 201 projectile-sabot was 157 g. While the gas gun is capable of propelling a mass of 30 g up to 1 km =s, for 157 g the 202 limit velocity is 400 m=s (i.e., the maximum impact velocity attained in the experimental campaign). 203 The impacted cylindrical samples are 40 mm long, such that one end of the specimen is mounted on a printed 204 PLA support (hereinafter referred to as clamped end), while the other end is cantilevered (hereinafter referred to 205 as impacted end) { see Figure 3. The PLA support is seated on a XYZ assembly formed by an XZ precision table 206 and a height regulator jack, allowing to align the cylindrical specimen's axis with that of the gun barrel before 207 testing. Specimens with two di erent outer diameters, 12 mm and 14 mm, and two di erent wall thicknesses, 208 8 1 mm and 2 mm, were tested. Note that the caliber of the gas gun imposes a limitation on the size of the impacted 209 samples, as the diameter base of the striker has to be larger than the inner diameter of the cylinders in order for 210 them to expand during the penetration process. 211 Upon impact, the stationary hollow cylinder is axially penetrated by the ying projectile, expanding it sym- 212 metrically until the formation and propagation of multiple cracks leads to the fragmentation of the specimen (the 213 diameter of the cylindrical part of the projectile is approximately twice greater than the inner diameter of the 214 cylindrical target). The nominal circumferential strain rate on the cylinder is estimated as _ "=vr r, wherevris the 215 radial expansion velocity and ris the specimen radius at half thickness. The radial expansion velocity is computed 216 asvr=vzsin(2 ) 2{ where the angle is indicated in Figure 2 { under the assumption that the deforming cylinder 217 moves perpendicular to the conical nose of the projectile, so that _ "varies from 9000 s1to23500 s1for 218 the range of impact velocities tested. This is the same range of strain rates generally attained in electromagnetic 219 driven expanding cylinder tests, see Section 1. Moreover, while this experiment does not show the drawback of 220 Joule heating e ects, as it is the case for cylinder expansion tests performed using electromagnetic loading, see the 221 rst paragraph of Section 1, the friction between striker and specimen may have an e ect on the fragmentation 222 process (which is dicult to assess). The impact experiments were recorded with two high-speed cameras Photron 223 Fastcam SA-Z 2100K using a frame rate of 200 kfps for a window resolution of 256 232 px, with a shutter speed 224 of 1=2880000 s. Two 1800-W open face lampheads were used to provide the lighting required to obtain clear-cut, 225 high-quality images. The recordings were employed to compute the impact velocity by setting a reference length 226 before the test and computing the time needed by the projectile to cover this length in the video footage. 227 In order to collect the fragments ejected from the impact, a neoprene curtain was located behind the specimen. 228 Due to the large air ow leaving the gas gun, it was observed that most of the fragments were ying in the axial 229 direction towards the stopping curtain, thus most of them could be recovered. Considering the soft nature of 230 the collecting device, and given that no casing around the specimen was used, it was ensured that no further 231 fragmentation occurred after the impact. The recovered fragments were sized and weighted, and the in uence of 232 impact velocity, specimen dimensions, and porous microstructure on the fragmentation behavior of the printed 233 samples was studied { see Section 3. 234 2.2. Porosity measurements 235 Four samples have been investigated using X-ray tomography analysis: Alu-S-D12-t1-3, Alu-S-D12-t1-4, Alu- 236 P-D12-t1-3 and Alu-P-D12-t1-4. The notation used for the specimens designation is as follows: Alu refers to the 237 material (AlSi10Mg), the following letter denotes the printing quality (S refers to standard and P to performance ), 238 9 Figure 1: Experimental setup for axial penetration testing of thin-walled hollow cylinders. Identi cation of gun barrel, high-speed cameras, lampheads, specimen support, XZ table, and height regulator jack. Figure 2: Cone-shaped 42CrMo4 steel projectile. Millimeter graph paper is used as a reference for the dimensions. 10 Figure 3: 3D printed AlSi10Mg hollow cylinder specimen, mounted on the PLA support before the test. the next three alphanumeric characters indicate the outer diameter of the cylinder (12 mm or 14 mm), the following 239 two alphanumeric characters correspond to the cylinder wall thickness (1 mm or 2 mm) and the last digit stands 240 for the impact velocity (1, 2, 3 and 4 correspond to 180 m=s,240 m=s,320 m=s or390 m=s). The 241 complete list of the impacted samples is included in Table 2, Section 3.1. 242 X-ray Computed Tomography (XCT) measurements of each of the four samples were carried out in a Nanotom 243 160NF tomograph (General Electric-Phoenix) located at IMDEA Materials Institute. The cylindrical samples 244 (before testing) and their fragments (after impact) were measured using 130 kV, 60 µA, and a Tungsten (W) 245 target with 0 :2 mm of Cu lter. For each tomographic inspection about 3000 radiographs were acquired for 360246 rotation using 2 virtual detector mode, i.e., the detector was shifted 40perpendicular to the beam axis to acquire 247 2 images that were partially overlapped to create one projection. The exposure time was set to 750 ms and 8 248 radiographs were averaged for each projection, leading to 11 hours measurement time. The source-object distance 249 was 19 mm and the source-detector distance was 316 :7 mm, yielding a 16.7 magni cation with a reconstruction 250 voxel size of 3 33µm3. The reconstruction of the tomograms was carried out using an algorithm based on the 251 ltered back-projection procedure for Feldkamp cone beam geometry (Feldkamp et al. (1984)). In addition, the 252 analysis of the 3D reconstructed images was performed using the open source software ImageJ (Schneider et al. 253 (2012)) and the commercial software Avizo version 2021 :1 (Avizo, 2021). 254 The XCT measurements before testing correspond to the impacted end of the cylinders, for a total length of 255 5:4 mm, including the whole perimeter of the samples. The selected volumes enable to record sucient number 256 of voids to obtain statistically signi cant results which are representative of the actual porosity distribution in the 257 materials. Figure 4 shows tomography images of a cross section perpendicular to the main axis of the cylinders for 258 11 the four samples analyzed, obtained at a distance of 1 mm from the impacted end. The inset shows a detail of the 259 porosity distribution in a portion of the slice. The voids appear in the form of dark spots, with a roughly circular 260 area. For the performance samples, the porosity is mostly concentrated near the outer and inner surfaces of the 261 specimens (Marvi-Mashhadi et al., 2021), having noticeably more porosity (size and number of pores) the samples 262 printed with quality standard . Koutiri et al. (2018), among others, stated that the concentration of pores below 263 the surface of SLM printed parts is caused by the inadequate connection of the hatching of the sample volume with 264 the contour of the part. The overall void volume fraction for Alu-S-D12-t1-3, Alu-S-D12-t1-4, Alu-P-D12-t1-3 265 and Alu-P-D12-t1-4 is 6 :1%, 6:1%, 1:9% and 2%, respectively (i.e., the porosity in the performance samples is 266 approximately three times less). Notice that the specimens printed with the same quality have similar overall void 267 volume fractions (the term overall is used to denote the void volume fraction of the whole specimen). In addition, 268 note that the maximum equivalent diameter of the 10 largest pores for the standard samples is 216 µm, decreasing 269 to 143 µm for the performance quality. 270 Figure 4: X-ray computed tomography images of a cross section perpendicular to the main axis of the cylinders. Results corresponding to the four samples analyzed: (a) Alu-S-D12-t1-3, (b) Alu-S-D12-t1-4, (c) Alu-P-D12-t1-3 and (d) Alu-P-D12-t1-4. All images correspond to a cross section of the tube located at approximately 1 mm from the impacted end. 12 Figure 5 displays 3D reconstructions of the porous microstructure showing the 3D distribution of all the pores 271 in a portion of the scanned cylinder { see the shadowed region in Figure 5(a). The color coding of the voids 272 corresponds with the void volume in µm3. Figures 5(b) and 5(c) show two views of the porosity distribution 273 in sample Alu-S-D12-t1-4. The number of large voids in this specimen is roughly homogeneously distributed in 274 the represented sub-volume, while for its performance counterpart (Alu-P-D12-t1-4), the largest voids are located 275 near the free surfaces, see Figures 5(c) and 5(d) { this is also observed in the 2D X-ray cross-section images 276 shown in Figures 4(c) and 4(d). It is also evident the di erence in void sizes of both samples: the largest void 277 volume/diameter in the standard sample is almost 3 =1:4 times larger than the largest void in the performance one. 278 Moreover, note that the pore diameters near the outer and inner surfaces of the Alu-P-D12-t1 cylinders are up 279 to 8 times greater than the voids in the midsection of the thickness, indicating strong gradients in the local void 280 volume fraction along the thickness of the samples (i.e., the large voids near the surfaces are mainly responsible for 281 theoverall porosity of the performance cylinders). In contrast, the results presented in Figure 6 corresponding to 282 samples Alu-S-D12-t1-3 and Alu-P-D12-t1-3 show that the local void volume fraction is relatively uniform along 283 the axial and circumferential directions of the samples (the term local is used to denote the void volume fraction 284 at a cross section of the specimen). The same trends have been obtained for Alu-S-D12-t1-4 and Alu-P-D12-t1-4, 285 while the results are not shown for the sake of brevity. 286 A quantitative assessment of the distribution of void shapes and sizes in specimens Alu-S-D12-t1-3 and Alu-P- 287 D12-t1-3 is shown in Figure 7. The sphericity factor S, Figure 7(a), representing the ratio of the surface area of a 288 sphere to the surface area of the void, is computed as S=3r 36V2 A3, whereVandAare the volume and the surface 289 area of each pore, respectively. The value of Sis greater than 0 :9 for 70% and 78% of the voids in the samples 290 printed with standard andperformance qualities, respectively (similar results are obtained for Alu-S-D12-t1-4 and 291 Alu-P-D12-t1-4). Assuming that the voids are spherical { which seems to be a reasonable premise attending to the 292 computed sphericity factors { the calculation of the pore size distribution, Figure 7(b), shows that the equivalent 293 diameter of 90% of the voids is less than 20 µm for both standard and performance samples (similar results 294 are obtained for Alu-S-D12-t1-4 and Alu-P-D12-t1-4). On the other hand, note that the specimen Alu-S-D12- 295 t1-3 contains larger pores, e.g., 4% of the voids for the standard specimen have an equivalent diameter greater 296 than 50 µm, while this percentage decreases down to 1 :5% in the case of the Alu-P-D12-t1-3. The corresponding 297 mean () and standard deviation ( SD) for the experimental distribution of voids equivalent diameter for samples 298 Alu-S-D12-t1-3 and Alu-P-D12-t1-3 is given in Table 1. 299 300 13 Figure 5: 3D reconstructions of X-ray computed tomography scans showing all the pores within an arbitrary portion (4 :7 mm long, and1 mm of arc distance) at the impacted end of the cylinders, corresponding to the shadowed region in (a). Results corresponding to samples: (b)-(c) Alu-S-D12-t1-4, and (c)-(d) Alu-P-D12-t1-4. For interpretation of the