6 This paper presents a new experimental setup to study dynamic fragmentation of metallic rings manufactured 7 by 3D-printing technology. The ring is inserted over a ductile thin-walled tube which is impacted axially by a 8 conical-nosed cylindrical projectile fired by a single-stage light-gas gun. The diameter of the projectile is larger 9 than the internal diameter of the thin-walled tube, which expands as the projectile advances, pushing radially 10 outwards the metallic ring, that eventually breaks into multiple fragments. The impact velocities considered in 11 the present experimental campaign range from 197 m /s to 385 m /s. The AlSi10Mg ring specimens are printed 12 by Selective Laser Melting technique, with an inner diameter of 14 mm and square cross section of 2 ×2 mm2. 13 To obtain time-resolved information on the mechanics of fragmentation, the number of fractures, and the size of 14 the fragments, the tests have been recorded with two-high speed cameras. A tunnel-shaped soft casing made of 15 polymer foam is placed around the specimen to softly recover the ejected fragments, that have been weighted and 16 sized to determine the statistics of the fragments size distribution. In addition, the predictions of the fragmentation 17 theory of Kipp and Grady [12] for the evolution of the number of fragments with the impact velocity have been 18 compared with the experimental evidence, and an excellent quantitative agreement has been found within the 19 whole range of loading rates investigated. Compared to other available techniques for dynamic fragmentation of 20 rings, in which the expansion of the specimen is driven by electromagnetic or explosive loading, this experimental 21 setup stands out for its simplicity, fast operation, quick assembly, and flexibility to test different engineering 22 materials, which facilitates performing extensive experimental campaigns (34 successful tests have been carried 23 out in this research). To the authors’ knowledge, this paper presents the most comprehensive data set to date on 24 the fragmentation of dynamically expanded printed rings, including the first high-resolution video recordings of 25 the formation of multiple cracks throughout the circumference of the samples, and scanning electron microscopy 26 images of the fractures showing the porous microstructure on the cracks surface. 27 Keywords: 28 Ring expansion, High-speed impact, Dynamic fragmentation, Additively-manufactured metals 29 ∗Corresponding author. Tel. +34 916249588, E-mail address: junietof@ing.uc3m.esFebruary 8, 2023 2 1. Introduction 30 The ring expansion test devised by Niordson [20] was a turning point in the experimental investigation of 31 material behavior at high strain rates. An electromagnetic loading scheme was used to expand copper and alu- 32 minum rings at radial velocities ranging from 40 m /s to 400 m /s. The testing setup consists of a condenser battery 33 discharged into a coil over which the ring is inserted. The coil creates an electromagnetic-field induced current in 34 the ring which interacts with the primary current flowing in the coil, generating repulsive forces between the ring 35 and the coil, leading to a rapid expansion of the specimen. This experimental technique is particularly suitable 36 to test materials which are good electrical conductors. However, the induced current in the ring results in Joule 37 heating effects that significantly increase the temperature of the specimen (note that Cliche and Ravi-Chandar 38 [2] estimated the increase of temperature due to Joule effect in dynamically expanded AZ31B-O rings to be more 39 than 200 K (see Fig. 6c therein)). The inner diameter of the rings tested by Niordson [20] was 140 mm, with 40 axial thickness of 10 mm and radial thickness of 1 mm, so that the radial stress was negligible in comparison with 41 the circumferential stress, and the stress field was mainly uniaxial. The highest strain rate attained in these tests, 42 approximately 5700 s−1, was several times greater than in a conventional Split Hopkinson Tension bar experiment. 43 A salient feature of the electromagnetic loading scheme is that the loading rate is readily controlled through the 44 variation in frequency and intensity of the primary current pulse. Moreover, the radial symmetry of both specimen 45 and loading minimizes the intervention of stress waves along the circumferential direction of the specimen, so that 46 the ring shows practically uniform strain field until deformation is not longer homogeneous at large strains, leading 47 to plastic localization and multiple fractures. 48 49 Some years later, Fyfe and Rajendran [4], and Rajendran and Fyfe [22], designed an alternative system to 50 dynamically expand metal rings, which consisted of an exploding wire placed along the axis of a polyethylene 51 hollow cylinder over which the specimen was fitted. Wire vaporization, occurring due to the energy released from 52 high-voltage capacitors, generates a wave disturbance that propagates through the medium surrounding the wire 53 to impinge uniformly on the inner wall of the cylinder, hence inducing an uniform radial cylindrical stress wave into 54 the ring. The tests were performed using aluminum 6061-T6 and annealed copper specimens with internal diameter 55 of 25 .4 mm, width of 3 mm, and different thicknesses ranging from 0 .5 mm to 1 .0 mm. The experiments were 56 conducted at various voltage levels of the capacitor bank, so that increasing the energy release increased the loading 57 rate in the specimen and thus the number of pieces into which the ring broke. For the highest strain rate levels, up 58 to 10 fractures were observed. Moreover, Grady and Benson [6] implemented similar electromagnetic experimental 59 3 arrangement to Niordson [20] and tested OFHC copper and aluminum 1100–O rings to radial velocities up to 60 200 m /s. The samples had a 32 mm inner diameter and a square cross section of 1 mm2, such that the maximum 61 circumferential strain rate attained in the rings was approximately 104s−1(roughly double than in Niordson [20] 62 setup, because the samples tested had a smaller diameter). The time resolved motion of the ring-shaped specimens 63 was recorded with a streak-camera technique, verifying that the expansion process was uniform and stable, with 64 an initial acceleration region followed by an interval of nearly constant velocity, when the nucleation of multiple 65 necks and fractures led to the fragmentation of the samples. Not all the necks developed into fractures. Here, 66 arrested necks are presumed to result from the arrival of a relief stress wave from a nearby fracture that removes 67 the driving force before fracture completion. The fragments were recovered, determining the number and size 68 distributions. The number of fragments and the fracture strain were shown to increase with the expansion velocity 69 for both aluminum and copper samples. 70 71 Altynova et al. [1] performed electromagnetic ring expansion experiments with aluminum 6061 and OFHC 72 copper samples, for radial speeds ranging between 50 m /s and 300 m /s. The ring-shaped specimens had inner 73 and outer diameters of 30 .5 mm and 32 .5 mm, respectively, and different widths varying from 1 mm to 2 mm. 74 Consistent with the results of Grady and Benson [6], the number of necks, the number of fragments and the fracture 75 strain were shown to increase with the expanding velocity. For instance, at an expansion velocity above 200 m /s, 76 the dynamic ductility of aluminum 6061 and OFHC copper rings exceeded the quasi-static value by 60% and 250%, 77 respectively. The improved ductility at large expanding velocities was attributed to inertia effects at high strain 78 rates. Dynamic fragmentation experiments on rings of U6N were carried out by Grady and Olsen [8]. The samples 79 with 30 mm of inner diameter were tested at expansion velocities within the range 50 −300 m /s. The number of 80 fragments, the distributions in fracture spacing and fragment masses, and the strain to fracture were compared 81 with the statistical-based fragmentation theory of Mott [18] and with the energy-based fragmentation theory of 82 Kipp and Grady [12]. These theories postulate that fragmentation of metals under intense tensile impulsive loading 83 occurs due to the activation of material weak points which are scattered throughout the sample (material defects 84 such as pores, cavities and cracks formed during material processing) and determine the distribution of fracture 85 points. The predictions obtained with both theoretical approaches agreed reasonably well with the experimental 86 data that, similarly to the results of Grady and Benson [6], and Altynova et al. [1], for copper and aluminum 87 specimens, showed an increase in the number of fractures and in the fracture strain with the expansion velocity. 88 89 4 Shortly after the paper of Grady and Olsen [8], Zhang and Ravi-Chandar [30] presented the first implemen- 90 tation of the electromagnetic loading scheme of Niordson [20] in which high-resolution, high-speed images of the 91 ring expansion process were acquired showing the formation of multiple necks and fractures. Aluminum 6061-O 92 specimens with inner diameter of 30 .5 mm, and rectangular cross section of thickness 0 .5 mm and length 1 mm, 93 were tested at velocities ranging from 80 to 200 m /s. Following Mott [18] postulates, the distribution of neck 94 spacings and fragment sizes was attributed to the spatial variability of the necking and fracture strains through- 95 out the circumference of the ring, and to the unloading waves released from growing necks and early fractures. 96 It was concluded that the release wave mechanism sets the scale for fragmentation, so that the decrease in the 97 necks spacing and in the fragments size with the increase of the expansion velocity occurs because the unloading 98 engendered by any localization and fracture does not travel far enough quickly to inhibit further localization and 99 fracture at neighboring locations. In a companion paper, Zhang and Ravi-Chandar [31] carried out additional 100 ring expansion experiments with Al 1100-H14 and Cu 101 specimens for expansion velocities ranging from 65 to 101 230 m /s. The tests resulted in statistical distributions of neck spacings and fracture sizes similar to those obtained 102 in the experiments with Al 6061-O rings in Zhang and Ravi-Chandar [30], such that with increasing strain rate, 103 more necks and fractures were nucleated at shorter distances. The same experimental setup was used years later 104 by Cliche and Ravi-Chandar [2] to investigate the fragmentation behavior of annealed AZ31B-O magnesium al- 105 loy. Experiments in which the electromagnetic-field induced current circulates in the magnesium specimen were 106 compared with tests in which a copper pusher ring is used to carry the induced current, in order to reduce the 107 Joule heating effects in the magnesium specimen. Samples with inner diameter of 31 .5 mm, length of 0 .5 mm, 108 and two different thicknesses of 0 .5 mm and 2 .286 mm were tested at expanding velocities ranging from 40 m /s to 109 200 m /s. The experiments did not reveal any measurable effect of the expansion velocity and the Joule heating on 110 the ductility of the magnesium rings, suggesting that the onset of necking localization in AZ31B-O is not affected 111 by thermal softening for temperatures below half of the melting point. On the other hand, the increase of the 112 cross section of the specimen boosted the strain developed in the unnecked regions of the ring, probably due to 113 enhanced inertia effects with the increase of the specimen size (inertia increases with the thickness of the sample). 114 Fragmentation behavior of magnesium was also investigated by Kahana et al. [11] expanding AZ31 ring-shaped 115 specimens at strain rates ranging from 6 ·103s−1to 1.2·104s−1. The dimensions of the specimens were 36 mm 116 of outer diameter, 32 .6 mm of inner diameter, and 2 .4 mm of width. The fracture strain of the material increased 117 with the strain rate from 0 .18 to 0 .34, while the sum of necks and fractures raised from 2 to 21. Consistent with 118 the results of Grady and Benson [6] and Altynova et al. [1] for copper and aluminum samples, these experiments 119 5 indicated the increased ductility of AZ31 magnesium alloy at high strain rates (these results stand in contrast with 120 the tests of Cliche and Ravi-Chandar [2] on AZ31B-O rings, which did not show a correlation between the necking 121 strain and the strain rate). 122 123 Ring expansion tests on cold-rolled Cu-ETP copper, aluminum alloy 7075, barrel steel and tungsten heavy 124 alloy were performed by Janiszewski [9] using a similar experimental setup to Grady and Benson [6]. While in the 125 tests with copper and aluminum rings the induced current was beared by the specimen, in the experiments with 126 barrel steel and tungsten alloy an indirect expansion technique using a copper pusher ring was employed to reduce 127 the specimen heating resulting from the high current flow. All the specimens tested had a square cross-sectional 128 area of 1 ×1 mm2, the mean diameter being 32 mm for Cu-ETP copper and aluminum alloy 7075, 33 .4 mm for 129 barrel steel, and 27 .2 mm for tungsten heavy alloy. The experiments, performed for expansion velocities ranging 130 between 65 m /s and 275 m /s, showed the fracture strain to increase monotonically with the loading rate for Cu- 131 ETP copper, barrel steel and tungsten alloy, while in the case of aluminum alloy 7075 the maximum ductility of 132 the specimen corresponded to an intermediate value of the expansion velocity. Very recently, Wood et al. [29] 133 performed electromagnetic ring expansion tests on Inconel 718 specimens fabricated using Laser Melting Powder 134 Bed Fusion technique. A pusher ring made of copper was used to carry the induced current and expand the 135 specimens at strain rates ranging from 8 ·103s−1at the peak radial velocity to 1 .5·103s−1at fracture. The 136 dimensions of the rings were 33 .6 mm of outer diameter, 0 .7 mm of wall thickness and 1 mm of length. The 137 initial void volume fraction of the specimens was estimated using an empirical model which related the printing 138 parameters with the residual porosity, so that the ring expansion tests suggested that increasing the material 139 porosity drops the specimen ductility and increases the number of fragments. Moreover, it was concluded that the 140 increase of the fracture strain with the strain rate is more important as the initial void volume fraction decreases. 141 Electromagnetic ring expansion tests on aluminum alloy 5052 specimens were performed by Ma et al. [14]. The 142 rings had an inner diameter of 65 mm and a square cross section of 1 mm2, and were expanded at radial velocities 143 varying from 60 m /s to 140 m /s, so that the strain rates ranged between 1800 s−1and 3300 s−1. The experiments 144 were recorded with a high-speed camera, showing the formation of multiple necks evenly distributed around the 145 circumference of the specimen, some of these necks ultimately developing into fractures. The number of necks and 146 fragments was shown to increase with the strain rate, so that for the highest radial expansion velocity tested the 147 number of fragments and necks amounted to 9 and 44, respectively. 148 149 6 An alternative to performing ring fragmentation tests using electromagnetic loading schemes is employing gas 150 guns. Mechanical loading systems are generally more conducive to a laboratory environment, as they do not 151 require the employment of large currents – up to 20 kA are needed to accelerate samples with sub-millimeter wall 152 thickness to 200 m /s – and do not have the problem of the specimen being affected by Joule heating effects. Note 153 also that extending the electromagnetic loading technique to larger specimens requires more current, and with 154 higher currents the resistive heating thermally softens or even partially melts the sample, imposing a limitation to 155 the range of sample sizes that can be tested with this technique [10]. Moreover, as inertia effects are proportional 156 to the sample thickness squared [32], there is a need for testing larger samples to obtain further insights into 157 the effect of inertia on dynamic fragmentation. Note that once inertia starts to play a role, the fragmentation 158 mechanics depend on both material behaviour and specimen size (the fragmentation is no longer characteristic of a 159 specimen but a structure). Stepanov and Babutskii [24] used a pneumatic solid fuel impact machine to investigate 160 the fragmentation of metal rings subjected to dynamic expansion at radial velocities up to 500 m /s. Two different 161 configurations were developed. In the first arrangement, the pneumatic impact machine was used to launch a 162 conical projectile which penetrates axially the ring, the inner diameter of the specimen being smaller than the 163 diameter of the base of the conical striker, so that the ring expands during the impact and ultimately breaks into 164 pieces. In the second configuration, the ring is launched onto the striker, which is fixed. Note that the limitation in 165 size of the specimens is that the diameter of the rings has to be smaller than the diameter of the gun barrel bore. 166 Ring samples of different hardnesses (97 HV and 195 HV) with an outer diameter of 80 and 64 mm and a wall 167 thickness of 4 and 3 mm, respectively, were tested. The experimental results showed that the number of fragments 168 increases with increasing deformation velocity (consistent with all previous works cited in this introduction), and 169 that the material with greater hardness breaks into a larger number of fragments. Gant et al. [5] developed a 170 new experimental setup using a single-stage gas gun to study the fragmentation of metallic rings under dynamic 171 radial expansion. The test consists of launching a steel ogival-nosed projectile onto a high-density polyethylene 172 disk which is crushed onto a steel anvil, deforming and imparting radial momentum to a metal ring which expands 173 at high strain rate and ultimately breaks into pieces. The ejected fragments were collected with a polymer foam 174 casing surrounding the specimen. The rings tested had 40 mm of diameter and 1 mm2of square cross section. 175 The experiments were performed using mild steel and aluminum alloy specimens, and recorded with a high-speed 176 camera. The impact velocity of the projectile and the expansion velocity of the ring were measured with Photon 177 Doppler Velocimetry probes. It was shown that for a given projectile velocity of 150 m /s, the maximum radial 178 velocity of the aluminum rings is 40% larger, while the mild steel specimens show less number of fragments and 179 7 greater strain at fracture. Note that similar experimental arrangements to Stepanov and Babutskii [24] and Gant 180 et al. [5] were used by Winter and Prestidge [28], Vogler et al. [26] and Jones et al. [10], among others, to study 181 dynamic fragmentation of metallic thin-walled cylinders. 182 183 In this paper, guided by the works cited in previous paragraph, we have developed and demonstrated a novel 184 experiment which consists of an additively-manufactured ring specimen inserted over the edge of a ductile thin- 185 walled tube (also referred to as hollow cylinder or pusher along this paper) which is impacted axially by a conical- 186 nosed cylindrical projectile (also referred to as striker along this paper) fired by a single-stage gas gun. The 187 cylindrical part of the projectile has a diameter approximately double than the inner diameter of the thin-walled 188 tube, which expands as the projectile moves forward, pushing radially outward the metal ring, which ultimately 189 breaks into multiple fragments. Compared to electromagnetic loading schemes, this experiment is a simple setup, 190 which is fast to operate and assemble, and thus it is suitable to perform extensive experimental campaigns. The 191 main practical limitation is that the inner diameter of the ductile hollow cylinder used as a pusher has to be smaller 192 than the bore of the gun barrel. To the authors’ knowledge, this paper presents the more comprehensive data set 193 to date on the fragmentation of dynamically expanded printed rings. 194 2. Experimental setup 195 The experimental setup adapts the configuration recently developed by Nieto-Fuentes et al. [19] for the axial 196 penetration of thin-walled cylinders to perform ring expansion tests. The actual setup is shown in Figures 1 197 and 2, with arrows and numbers indicating the main items of the setting, while the schematic of Fig. 3 shows 198 the principle of operation of the experiment. The AlSi10Mg ring specimens were additively-manufactured by the 199 company Materialise [15] by Selective Laser Melting (SLM) using two printing qualities, standard andperformance , 200 with nominal porosity of 3% and 0 .5% [15], respectively. However, note that the tomography analysis performed 201 by Nieto-Fuentes et al. [19] with as-printed thin-walled cylinders revealed that the porosity is actually larger, up 202 to 6% and 2%, respectively. The experiments of Nieto-Fuentes et al. [19] —see Fig. 7 therein— also showed 203 that the voids are largely spherical, with 90% of the pores having diameter smaller than 20 µm for both standard 204 andperformance samples. Moreover, the standard samples were shown to have 4% of the voids with diameter 205 greater than 50 µm, while this percentage decreases down to 1 .5% in the case of the performance specimens. The 206 largest pores were located near the surface of the samples. The average surface roughness of the rings provided 207 by Materialise [15] for standard andperformance samples was Ra= 10.75µm and Ra= 7.0µm. These values 208 8 are very similar to in-house experimental measurements obtained with an optical profilometer ZETA 20 3D. The 209 rings tested in this paper have an outer diameter of 18 mm and a square cross section of 2 ×2 mm2. We are aware 210 that for these specimen dimensions, the effect of curvature in the deformation behavior of the ring may not be 211 negligible [17]. On the other hand, we have performed finite element calculations showing that the stress and strain 212 fields in the ring are rather uniform during the expansion (the results are not included in the paper for the sake of 213 brevity). The pusher is made of AISI 316L steel, having an initial length of 40 mm, inner diameter of 14 mm and 214 thickness of 2 mm. Note that AISI 316L steel is significantly more ductile than the additively-printed materials 215 so that the first failure of the pusher occurs after the complete fragmentation of the ring specimens. A thin layer 216 of grease is inserted between the ring and the pusher to reduce friction effects during the tests. The opposite end 217 of the pusher to which the ring is mounted is inserted into a pyramidal support printed out of polylactide (PLA) 218 thermoplastic polyester. The pyramidal support has 8 thin petals that embrace the pusher, extending until the 219 rear part of the ring, so that the specimen does not move axially due to the air flow coming from the gas gun 220 that precedes the arrival of the projectile. The pyramidal support sits on a XYZ assembly which integrates an XY 221 precision table with a height regulator jack in order to ensure the alignment of the cylindrical specimen with the 222 gun barrel before testing, so that the striker impacts uniformly on the inner perimeter of the pusher, and the ring 223 expands radially. The XYZ assembly is screwed to an aluminium structure which is fixed to the laboratory floor 224 (see Fig. 1), such that the position of the pyramidal support which holds the hollow cylinder is the same in all 225 tests. Fine-tuning of the projectile trajectory is carried out using a laser that is passed through the gun barrel and 226 the axis of the hollow cylinder before the experiment. However, for ≈20% of the impact experiments performed, 227 the flight of the projectile slightly deviated from a straight trajectory, with the first contact between projectile and 228 pusher occurring on one side of the thin-walled tube. The tests in which the impact deviation was greater than 229 0.2 mm were discarded from the present test series (i.e., they are not included in Table 1). The striker was made 230 out of quenched and tempered 42CrMo4 alloy, and it is 64 mm long, with a 1 .55 mm nose radius, 40◦apex angle, 231 and a 24 mm diameter base (see Figure 2 in Nieto-Fuentes et al. [19]). A cup-type cylindrical sabot of 24 .5 mm 232 diameter and 100 mm long, printed out of PLA thermoplastic polyester, was inserted in a 20 mm long and 10 mm 233 diameter pin machined at the projectile base (see Figure 2 in Nieto-Fuentes et al. [19]). The total mass of the 234 assembly striker/sabot is 157 g. 235 236 The experiments have been performed at 4 different impact velocity ranges: 197 m /s≤vz≤218 m /s, 237 246 m /s≤vz≤259 m /s, 317 m /s≤vz≤338 m /s and 363 m /s≤vz≤385 m /s. The 25-mm bore barrel 238 9 gas gun (manufactured by Thiot Ingenierie ) was driven by helium, with the firing pressure in the reservoir being 239 P= 22 bar and 95 bar for the lowest and highest impact velocity tested, respectively. The radial expansion velocity 240 of the ring is computed as vr=vzsin(2α) 2, under the assumption that the pusher and the ring move perpendicular 241 to the conical-nose of the projectile. Note that α= 70◦is the angle formed between the perpendicular and axial 242 directions of the striker cone (see Figure 2 in Nieto-Fuentes et al. [19]). The nominal circumferential strain rate in 243 the specimen ˙ εθ, computed as the radial expansion velocity over the initial inner radius of the ring, varies between 244 8000 s−1and 15000 s−1(similar range of strain rates was attained by Kahana et al. [11] using the electromagnetic 245 expansion method, see Section 1). The tests have been recorded with two-high speed cameras Photron Fastcam 246 SA-Z 2100K, using a frame rate of 200000 fps, a resolution of 256 px ×232 px, and a shutter speed of 1 /2880000 s. 247 Two lampheads provided the lighting required to film the experiments, the video recordings giving time-resolved 248 information on the mechanics of fragmentation, the number of fractures and the size of the fragments (see Section 249 3). The impact velocity has been also measured using the video footage of the high-speed cameras which were 250 calibrated before each test by setting a reference length to determine the pixel size, which allowed computing 251 the distance traveled by the projectile within a given time interval (and thus obtaining the impact velocity). A 252 tunnel-shaped aluminum casing lined with a polymer foam has been placed around the specimen to trap the ejected 253 fragments, that have been weighted and sized to determine the statistics of the fragments size distribution. The 254 fracture surfaces of selected fragments have been analyzed using scanning electron microscopy (SEM) in order to 255 obtain information on the failure mechanisms and the porous microstructure of the specimens. 256 3. Results 257 This section presents the main results of the impact experimental campaign, including high-resolution snapshots 258 of the fragmentation process, post-mortem analysis of fragment sizes, and scanning electron microscopy images 259 of fracture surfaces. The dynamic fragmentation campaign comprises 34 successful experiments, out of which 19 260 correspond to specimens printed with quality standard , which are designated by Ring-Alu-S-1, ..., Ring-Alu-S-20, 261 and the remainder correspond to samples with quality performance , which are referred to as Ring-Alu-P-1, ..., 262 Ring-Alu-P-17 (note that results for samples Ring-Alu-S-19, Ring-Alu-P-9 and Ring-Alu-P-14 were discarded, as 263 the striker did not impact axially on the hollow cylinder based on the standard established in Section 2). Section 264 3.1 compares two tests performed at similar impact velocity on standard andperformance specimens to identify 265 the mechanisms of fragmentation of the rings, and Section 3.2 investigates the influence of impact velocity on the 266 number and the size distribution of the fragments, and compares the results with the predictions of the theory of 267 10 Figure 1: Experimental setup: (1) high-speed camera 1, (2) high-speed camera 2, (3) XY precision table, (4) height regulator jack, (5) tunnel-shaped aluminum casing (the foam has been removed to lighten the picture), (6) lampheads and (7) aluminium structure screwed to the laboratory floor. 11 Figure 2: Experimental setup: (5) tunnel-shaped aluminum casing (the foam has been removed to lighten the picture), (8) pyramidal support, (9) conical-nosed cylindrical projectile, (10) gun barrel, (11) pusher and (12) ring specimen. Figure 3: Schematic of the setup showing the principle of operation of the experiment. The ring is inserted over a thin-walled tube which is impacted axially by a conical-nosed cylindrical projectile fired by a single-stage gas gun. The diameter of the projectile is larger than the internal diameter of the thin-walled tube, which expands as the projectile advances, pushing radially outwards the metallic ring, that eventually breaks into multiple fragments. Main items of the setting: (3) XY precision table, (4) height regulator jack, (8) pyramidal support, (9) conical-nosed cylindrical projectile, (10) gun barrel, (11) pusher, (12) ring specimen and (13) sabot. 12 Kipp and Grady [12]. 268 Table 1 includes for all successful tests performed: specimen identification, outer diameter of the ring ( Dext), 269 initial thickness ( t0), initial width ( w0), impact velocity ( vz), estimated nominal circumferential strain rate ( ˙ εθ), 270 average fragment length (along the circumferential direction of the specimen) with standard deviation ( Lθ±SD), 271 average fragment thickness (along the radial direction of the specimen) with standard deviation ( t±SD), average 272 fragment width (along the axial direction of the specimen) with standard deviation ( w±SD), average fragment 273 mass with standard deviation ( m±SD), number of fragments based on the video recordings ( Nv), number of 274 fragments recovered ( Nr) and percentage of mass recovered with respect to the complete ring ( ˆ m). Despite in 275 some experiments we recover all the visible fragments, the mass of the fragments never matches the mass of 276 the ring before testing, most likely due to material particles and debris ejected during cracks formation and 277 fragmentation (see Figures 8 and 13). A complete summary with separate data for each specimen, including the 278 length, thickness, width and weight of each fragment recovered is provided in Appendix A. Following the same 279 systematic procedure employed by Nieto-Fuentes et al. [19], the length, thickness, and width of each fragment was 280 measured in three different positions using a digital caliper with 0 .01 mm of resolution. The mean value of the 281 three measurements corresponds to Lθ,tandw, in the data sets of Appendix A. The average of all the values of 282 Lθ,t, and wobtained per tested ring gives the average fragment length Lθ, the average fragment thickness t, and 283 the average fragment width wincluded in Table 1. Moreover, Appendix B includes post-mortem photographs of 284 the recovered fragments corresponding to all specimens tested. Fragments are arranged in a layout that recreates 285 the ring before testing. 286 13Table 1: The dynamic fragmentation experimental campaign comprises 34 experiments: specimen label, external diameter ( Dext), initial thickness ( t0), initial width (w0), impact axial velocity ( vz), estimated nominal circumferential strain rate ( ˙ εθ), average fragment length with standard deviation ( Lθ±SD), average fragment thickness with standard deviation ( t±SD), average fragment width with standard deviation ( w±SD), average fragment mass with standard deviation ( m±SD), number of fragments based on video recordings ( Nv), number of fragments recovered ( Nr) and percentage of mass recovered with respect to the complete ring ( bm). Specimen Dext(mm) t0(mm) w0(mm) vz(m/s) ˙εθ(s−1)Lθ±SD (mm) t±SD (mm) w±SD (mm) m±SD (g) NvNrbm(%) Ring-Alu-S-1 18.08 2.00 1.76 246.4 9849.7 7.27 1.39 1.90 0.01 1.79 0.01 0.049 0.011 8 6 60.76 Ring-Alu-S-2 18.08 1.98 1.77 324.7 12961.6 6.02 1.70 1.88 0.01 1.80 0.02 0.041 0.012 9 5 42.32 Ring-Alu-S-3 18.03 1.96 1.85 385.0 15394.9 6.19 1.61 1.90 0.01 1.81 0.02 0.043 0.012 9 5 45.03 Ring-Alu-S-4 18.08 1.96 1.89 205.5 8190.1 9.96 3.70 1.90 0.02 1.78 0.01 0.070 0.026 8 5 72.67 Ring-Alu-S-5 18.07 1.97 1.75 217.9 8695.8 10.10 3.46 1.89 0.01 1.69 0.03 0.065 0.020 6 5 66.99 Ring-Alu-S-6 18.07 1.95 1.78 258.0 10286.2 8.67 2.94 1.91 0.02 1.70 0.04 0.061 0.023 8 4 51.26 Ring-Alu-S-7 18.05 1.96 1.86 327.0 13060.9 7.07 2.49 1.90 0.01 1.82 0.04 0.053 0.021 10 6 66.61 Ring-Alu-S-8 18.05 1.94 1.87 363.2 14491.9 5.61 2.04 1.88 0.03 1.81 0.04 0.041 0.015 10 9 77.05 Ring-Alu-S-9 18.08 1.97 1.8 203.3 8107.5 7.65 2.90 1.93 0.03 1.93 0.03 1.798 0.011 6 4 53.90 Ring-Alu-S-10 17.92 1.90 2.1 211.7 8490.5 9.11 3.79 1.82 0.02 1.82 0.02 2.000 0.012 6 6 98.73 Ring-Alu-S-11 17.91 1.91 2.0 258.3 10375.1 7.29 2.21 1.84 0.02 1.84 0.02 1.971 0.008 8 8 98.93 Ring-Alu-S-12 17.91 1.90 2.1 259.3 10405.8 8.28 2.13 1.80 0.02 1.80 0.02 1.999 0.010 7 7 97.48 Ring-Alu-S-13 17.94 1.91 2.1 338.7 13580.2 6.44 1.29 1.82 0.02 1.82 0.02 1.979 0.019 10 8 83.09 Ring-Alu-S-14 17.89 1.89 2.1 334.5 13436.4 7.38 2.15 1.82 0.01 1.82 0.01 2.008 0.011 9 8 95.62 Ring-Alu-S-15 17.94 1.89 2.1 367.5 14718.0 6.02 1.34 1.80 0.02 1.80 0.02 1.991 0.012 10 9 87.66 Ring-Alu-S-16 17.91 1.91 2.0 369.3 14831.5 6.11 1.79 1.80 0.02 1.80 0.02 1.976 0.008 11 9 96.59 Ring-Alu-S-17 17.92 1.87 2.1 368.8 14770.8 6.12 2.00 1.80 0.02 1.80 0.02 1.991 0.010 10 7 73.64 Ring-Alu-S-18 17.87 1.86 2.1 331.7 13316.1 5.38 2.40 1.81 0.01 1.81 0.01 2.016 0.012 10 7 59.92 Ring-Alu-S-20 17.91 1.90 2.1 207.2 8318.9 11.26 3.93 1.85 0.03 1.85 0.03 2.014 0.015 5 5 99.79 Ring-Alu-P-1 18.18 2.04 1.95 204.5 8143.0 16.21 2.59 1.97 0.01 1.87 0.03 0.133 0.018 4 3 71.00 Ring-Alu-P-2 18.18 2.07 1.97 254.0 10136.1 7.74 2.64 1.95 0.02 1.95 0.02 1.876 0.015 8 7 77.92 Ring-Alu-P-3 18.14 2.05 1.93 322.8 12897.3 7.56 1.57 1.94 0.04 1.94 0.04 1.860 0.019 7 7 87.86 Ring-Alu-P-4 18.19 2.06 1.97 371.5 14806.2 6.90 2.60 1.90 0.02 1.90 0.02 1.865 0.012 8 8 87.68 Ring-Alu-P-5 18.16 2.03 1.92 197.1 7855.7 11.60 3.40 1.95 0.03 1.95 0.03 1.842 0.032 5 5 85.55 Ring-Alu-P-6 18.10 2.00 1.94 247.2 9870.6 8.74 2.83 1.96 0.02 1.96 0.02 1.881 0.032 7 7 88.92 Ring-Alu-P-7 18.70 2.30 1.99 334.2 13094.0 8.64 2.67 1.95 0.02 1.95 0.02 1.900 0.028 7 7 93.18 Ring-Alu-P-8 18.18 2.06 2.03 371.9 14828.9 6.75 2.62 1.93 0.02 1.93 0.02 1.923 0.017 9 6 77.39 Ring-Alu-P-10 18.02 2.01 2.27 367.6 14756.9 5.54 1.44 1.91 0.02 1.91 0.02 2.204 0.026 11 10 86.17 Ring-Alu-P-11 18.00 2.01 2.23 328.3 13196.7 8.36 1.81 1.93 0.03 1.93 0.03 2.141 0.015 7 7 99.46 Ring-Alu-P-12 18.01 2.01 2.25 252.5 10140.4 10.46 3.14 1.92 0.03 1.92 0.03 2.180 0.011 6 5 90.99 Ring-Alu-P-13 17.98 1.99 2.22 253.6 10195.6 11.05 3.68 1.93 0.01 1.93 0.01 2.176 0.014 5 5 97.67 Ring-Alu-P-15 17.96 2.00 2.19 204.0 8217.5 9.76 2.76 1.89 0.03 1.89 0.03 2.158 0.012 6 6 99.46 Ring-Alu-P-16 17.95 1.99 2.22 368.2 14824.9 7.81 2.68 1.90 0.02 1.90 0.02 2.204 0.021 8 7 93.68 Ring-Alu-P-17 17.99 1.98 2.22 317.6 12746.8 8.24 2.97 1.90 0.01 1.90 0.01 2.143 0.019 7 6 85.56 14 3.1. Salient results 287 Figure 4 shows snapshots of the impact test on specimen Ring-Alu-S-4. The ring was printed with quality 288 standard . The notation t <0 and t >0 is used to determine pre- and post-impact loading times, respectively, 289 so that t = 0 µs corresponds to the impact time. The striker velocity is vz= 205 .5 m/s (the firing pressure was 290 P= 22.7 bar). The corresponding estimated strain rate is ≈8190 s−1. This experiment lies within the impact 291 velocity range 1 (see Section 2), and it has been chosen to illustrate the impact process because of the quality 292 of the image recording and the clear identification of the fracture sites. The snapshots on the left were taken by 293 camera 1, while those on the right side correspond to camera 2, see Figure 1. 294 The first pair of images, snapshots (a)-(b), is taken for t = −75µs and shows the striker approaching the pusher 295 over which the ring specimen is inserted. Notice the alignment of the projectile trajectory with the axis of the 296 hollow cylinder. Snapshots (c)-(d) correspond to the time of impact, t = 0 µs. The uniform contact of the projectile 297 nose on the inner circumference of the hollow cylinder is essential for the radial expansion of the specimen, so that 298 the strain field throughout the ring is (largely) homogeneous during loading. After the impact, the projectile 299 penetrates the hollow cylinder, expanding it, and pushing radially outward the metal ring, see images (e)-(f). The 300 specimen deforms as the projectile moves forward so that the first three cracks nucleate at t = 30 µs, see the 301 colored arrows and numbering in snapshot (e). Notice that the three first cracks nucleate in the same region. 302 This could be explained by the fact that the ring microstructure is not homogeneous (inhomogeneous spatial 303 distribution of voids throughout the circumference of the ring, see Nieto-Fuentes et al. [19]). Three additional 304 fractures at different locations of the ring are indicated in images (g)-(h). Note that the arrows with the same 305 color and number in the images recorded by cameras 1 and 2 correspond to the same crack. The fragmentation 306 has already been completed for t = 50 µs, with the formation of eight fragments of various sizes which are 307 ejected radially outwards, moving as rigid bodies. The total time for the fragmentation process is less than 20 µs. 308 Similar fragmentation time was obtained by Zhang and Ravi-Chandar [30] for aluminum 6061-O rings expanded 309 at strain rates in the range 4000 −10000 s−1. Note that the duration of the experiment and of the fragmentation 310 process is in both cases much larger than the propagation time of (elastic) stress waves across the thickness of 311 the specimen ( ≈0.4µs). This indicates that each section of the ring is in equilibrium in the radial direction (this 312 is not the case in the circumferential direction since the time of propagation of a stress wave along the specimen 313 circumference is about 10 µs, which is consistent with the duration of the fragmentation process). The recovered 314 fragments, arranged in a layout that recreates the ring before testing, are shown in Figure 5. They have different 315 lengths, ranging from 14 .31 mm for fragment 1, to 5 .01 mm for fragment 5 (see Table A.4). Based on the video 316 15 recordings, three fragments are missing, which correspond to 27 .33% of the total mass of the specimen, i.e., the 317 missing fragments are relatively small. Following Cliche and Ravi-Chandar [2], the location of the fracture sites 318 is most likely determined by the activation of geometrical and material defects (large pores and printing defects 319 are observed in the fractography analysis of the fracture surfaces, see Figure 6), and the size of the fragments by 320 the distance traveled by the relieving stress waves released by early fractures. The fragmentation mechanisms for 321 printed AlSi10Mg, which has a relatively low tensile ductility (see discussion below), seem to be consistent with the 322 statistical fragmentation theories of Mott [18] and Grady et al. [7], rather than to the stability analysis approach 323 of Molinari and co-workers [3, 16, 17], which is suitable for materials with large ductility in which the formation of 324 multiple necks precedes fragmentation. Moreover, note that the cross-sectional area of the post-mortem specimen 325 Ring-Alu-S-4 is relatively uniform, being ≈91% in average of the initial cross section. Hence, assuming volume 326 conservation, the average logarithmic circumferential strain in the tested specimen is εθ≈0.09 (recall that this 327 material shows relatively low tensile ductility, e.g., see Soni et al. [23]). No necks are observed and the fractures 328 are not preceded by a local reduction of the thickness. These observations are consistent with the fragmentation 329 patterns observed by Nieto-Fuentes et al. [19] in the axial penetration of additively-manufactured AlSi10Mg thin- 330 walled tubes. Figure 6 shows high-magnification SEM micrographs of the fracture surface indicated in Figure 331 5 with a yellow arrow. The analysis is focused on the areas of the fracture surface denoted by A and B, see 332 subplot (a). A considerable amount of pores is observed, most of them having a nearly circular section, with sizes 333 ranging from a few micrometers up to ≈90µm in diameter, see the white arrows in subplots (b), ..., (g). Recall 334 that Nieto-Fuentes et al. [19] performed X-ray tomography measurements on additively-manufactured AlSi10Mg 335 thin-walled tubes of 1 mm thickness printed with quality standard , and estimated the initial porosity to be ≈6%. 336 Most of the pores are solidification defects formed during the manufacturing process – mainly lack of fusion and 337 gas porosity – and they do not seem to have nucleated/growth during the deformation of the specimen, especially 338 the larger ones (yet, some of them show internal cracks, see the green arrows in subplots (e)-(f)). The fracture 339 surface is a succession of circular cross-sectional cavities connected by ductile fracture areas, e.g., see red arrows 340 in subplots (b), ..., (g). The fracture surfaces looked alike for other fragments, however, the corresponding SEM 341 micrographs are not shown for the sake of brevity. 342 343 Figure 7 shows a sequence of images of the test on specimen Ring-Alu-P-5. The ring was printed with quality 344 performance . This test is selected for the analysis because the impact velocity is vz= 197 .1 m/s, i.e., only 4% 345 lower than for Ring-Alu-S-4 – the test on specimen Ring-Alu-P-5 also lies within the impact velocity range 1. 346 16 Figure 4: Sequence of images of the impact test for specimen Ring-Alu-S-4 for different loading times: (a)-(b) t = −50µs, (c)-(d) t = 0 µs, (e)-(f) t = 30 µs, (g)-(h) t = 35 µs and (i)-(j) t = 50 µs. Images obtained by camera 1 are on the left side of the sequence, while those obtained by camera 2 are on the right side. The impact velocity is vz= 205 .5 m/s. The arrows with the same color and number in the images recorded by cameras 1 and 2 correspond to the same crack. For interpretation of the