This paper reports on spall failure and damage modes in Laser Powder Bed Fusion fabricated Stainless Steel 316L (SS316L) with intentional levels of low-volume (1–5 vol. %) porosity and pore sizes of 200, 350, and 500 μm. The fabricated specimens were subjected to uniaxial-strain plate-impact loading at ∼4.5 GPa, to initiate incipient spall failure. Analysis of velocimetry profiles measured using multi-probe photon-Doppler velocimetry coupled with post-mortem analysis of soft-recovered samples reveals local suppression of spall failure (termed as spall-dominated) as a function of porosity, as the failure mechanism transitions from spall-centered tensile stress dominated to a pore-centered microstructure-dominated damage mode involving void/crack nucleation and growth at pre-existing pores. The critical porosity level where the suppression of spall failure is first observed, as well as the spall location, is dependent on both the volume fraction and the size of the initially fabricated pores. In samples of 500 μm pore size, the suppression of spall failure is observed with as little as 1 vol. % porosity, while samples with smaller pores (200 μm) still experience spall-centered tensile stress dominated failure with higher levels (5 vol. %) of porosity. In the case of pore-centered microstructure-dominated failure, spall damage can occur but the spall plane is shifted toward the rear free surface, or more generally in areas further away from the region with pores. Highly heterogeneous deformation twinning, shear banding, grain rotation, and cracking are observed in the vicinity of pre-existing pores and expected spall failure sites.

Interactions of pre-existing porosity to shock wave propagation and shock compression effects is a subject of considerable interest.1–6 Additive manufacturing (AM) enables the manufacture of controlled distribution of open and closed encapsulated pore geometries, where traditional manufactured materials are often limited to 2D holes or uncontrolled pores formed as process-inherent defects.7,8 A limited number of studies have been conducted to investigate the effect of porosity, both controlled and uncontrolled, on spall failure in AM materials with complex polycrystalline microstructures.6,9–12 These pores range in size from >2 to ∼1000 μm and are randomly or periodically spaced.6,11,12

Experiments by Jones et al. found that the presence of porosity in tantalum increases the Hugoniot Elastic Limit (HEL).9 They postulate that this is because the inherent porosity aids energy dissipation due to pore compression and strain hardening during impact testing.9 The inherent porosity and cracking is generally observed in the initial build layers of AM fabricated materials due to incomplete fusion, and hot tearing under extreme thermal gradients.9 Their presence corresponds to a lack of observed slip banding and increased intra-granular void formation during impact.9 In contrast, pore-free AM fabricated materials show extensive inter-granular void formation and slip banding associated with the spall failure.9 For both porous and pore-free AM materials, the observed spall damage is highly dependent on grain orientation and a large amount of scatter is recorded in measured spall strength values. Materials impacted in the through thickness direction tend to fail along columnar grains and have a much wider damage plane than observed in AM samples impacted in the in-plane direction, or in wrought specimens.9 

Experiments by Cui et al. found that the size and vol. % of porosity in AM Ti-6Al-4V had a significant effect on both the HEL and spall properties.10 Pores ranging in size from 1.8 to 81 μm and 29 to 5.41 vol. % were introduced in Ti-6Al-4V through changes in selective laser melting (SLM) process parameters.10 These pores were randomly distributed throughout the sample, which was subject to plate-impact experiments at 500 and 620 m/s using a copper flyer.10 The authors found that at both impact conditions, there was less damage in specimens with lower levels of porosity, and a noticeable decrease in both the HEL and spall strength.10 The specimen with the largest size pores and the largest amount of porosity (81 μm and 5.41 vol. %) was found to have a slow rise time and the absence of shock plateau, though the release wave timing was found to be similar to those observed in the lower pore volume samples.10 Though the authors did not discuss the observed slow ramp up, the delayed rise times are typical of those reported in the literature for both granular media and porous solids.13–16 

Experiments by Fadida et al. investigated the effects of a single pore of varied size for Laser Powder Bed Fusion (LPBF) Ti-6Al-4V samples in dynamic tension using a split Hopkinson bar setup.11 Single pores with a diameter less than ∼500 μm were found to have a negligible effect on material failure dynamics, with fracture occurring away from the pore, while failure was found to occur in the vicinity of the pore location for those with diameters >500 μm.11 The authors postulate that the critical porosity, where failure is determined by the presence of pores, rather than sample geometry, occurs when the pore diameter is on the order of 0.1–0.15 times the specimen diameter.11 The authors also observe a drastic decrease in total displacement when fracture occurs in the vicinity of the pore rather than in the bulk of the material. High speed camera images capturing the moment of failure and pore rupture for a single 1000 μm pore showed the presence of uncompacted powder, suggesting that temperature rise due to powder compaction is not sufficient to introduce melting at these strain rates and impact conditions.

While much work has been done to develop a constitutive model that describes pore collapse and shock compaction of powders at the continuum level,17,18 there are few experimental studies on materials with controlled low-volume fraction of porosity, with much of the early focus in the field centered on modeling.2–5,19 Furthermore, the interplay of mesoscale features, such as grain boundaries and pores, has rarely been systematically explored.9,20,21

Several studies of the dynamic failure response of full density AM SS316L have been recently performed.22–24 The purpose of the work presented here is to understand the impact of low-volume fraction of porosity on the dynamic spall failure of LPBF SS316L, with a focus on the incipient spall state. In particular, we characterize the presence and location of the spall plane and the deformation state in the region surrounding the spall plane, when present, and the collapsed or partially collapsed pre-existing pores in the AM fabricated material. The deformation and failure characteristics observed in post-mortem scanning electron microscopy (SEM) micrographs and electron backscattered diffraction (EBSD) analysis is systematically related to spall signatures captured in time-resolved velocimetry profiles measured using photon-Doppler velocimetry (PDV). The results suggest that the size of pores as well as their overall pore volume fraction have a profound influence on the observed failure mode in terms of whether spall failure occurs or not, its location, and the post-impact deformation and damage state.

A set of 12.7 mm diameter SS316L cylinders were printed in an inert argon environment using the SLM280 system at Y-12 National Security Complex in Oak Ridge, TN, with process parameters listed in Table I.

TABLE I.

SLM280 process parameters for fabrication of SS316L cylinders.

ParameterValues
Laser power 190 W 
Laser speed 750 mm/s 
Hatch rotation angle 67° 
Hatch distance 0.12 mm 
Layer thickness 0.03 mm 
Platform temperature 200 °C 
ParameterValues
Laser power 190 W 
Laser speed 750 mm/s 
Hatch rotation angle 67° 
Hatch distance 0.12 mm 
Layer thickness 0.03 mm 
Platform temperature 200 °C 

The cylinders were fabricated with varying levels of intentional porosity (200, 350, and 500 μm, each at 1%, 3%, and 5% by volume) introduced through the Computer Aided Design (CAD) file while print parameters were held constant, allowing for porosity to be isolated from other processing parameters since the thermal history of each part was consistent. Screenshots of CAD files for each fabricated cylinder may be found in Fig. S1 in the supplementary material. The presence of pores in the as-printed cylinders was confirmed for select prints with nano-computed tomography (nano-CT) scans, validating the ability to create materials with controlled and consistent internal porosity consistent with the CAD files (see Fig. S2 in the supplementary material). Table II lists the pore size and volume percent of porosity for each sample fabricated, along with its bulk density and pore characteristics including average number and distance between pores.

TABLE II.

Porosity parameters including relevant measured average bulk densities and average number and distance between pores for each sample disk used for the impact experiments.

Sample number and configurationPore size (μm)Intentional porosity (%)Bulk density (g/cm3)No. of pores in sample (⌀ = 9 mm h = 3 mm)Average center-to-center distance between pores (mm)
Control N/A 7.96 ± 0.00 N/A N/A 
200 μm-1% 200 7.93 ± 0.01 238 0.9 
200 μm-3% 200 7.88 ± 0.06 715 0.6 
200 μm-5% 200 7.91 ± 0.03 1192 0.5 
350 μm-1% 350 7.94 ± 0.01 45 1.6 
350 μm-3% 350 7.92 ± 0.02 134 1.1 
350 μm-5% 350 7.91 ± 0.04 223 0.9 
500 μm-1% 500 7.93 ± 0.05 15 2.3 
500 μm-3% 500 7.93 ± 0.02 46 1.6 
500 μm-5% 500 7.90 ± 0.03 75 1.3 
Sample number and configurationPore size (μm)Intentional porosity (%)Bulk density (g/cm3)No. of pores in sample (⌀ = 9 mm h = 3 mm)Average center-to-center distance between pores (mm)
Control N/A 7.96 ± 0.00 N/A N/A 
200 μm-1% 200 7.93 ± 0.01 238 0.9 
200 μm-3% 200 7.88 ± 0.06 715 0.6 
200 μm-5% 200 7.91 ± 0.03 1192 0.5 
350 μm-1% 350 7.94 ± 0.01 45 1.6 
350 μm-3% 350 7.92 ± 0.02 134 1.1 
350 μm-5% 350 7.91 ± 0.04 223 0.9 
500 μm-1% 500 7.93 ± 0.05 15 2.3 
500 μm-3% 500 7.93 ± 0.02 46 1.6 
500 μm-5% 500 7.90 ± 0.03 75 1.3 

The percent porosity indicated in Table II is based on the intentional porosity present in the inner diameter (9 mm) of the specimen rather than along the global cylinder diameter (12.7 mm), as pores were not printed close to the outer circumference to avoid introducing pore-edge shock wave interactions. The pores were filled with unconsolidated and unmelted powder from the LPBF process, as confirmed by SEM (Fig. 1). The average bulk density (ρ0) of each LPBF SS316L sample was measured using the Archimedes method for machined disks taken from the center of the as-printed cylinders. Each reported density value in Table II was taken from an average of three to four measurements performed on each sample. The higher-than-expected densities for samples, given their pore designations, arise from the presence of the unconsolidated powder in the pores. This unconsolidated powder was assumed to have a negligible effect on the mechanical properties due to the ductility of SS316L, the lack of compaction, and the rapid rate of impact loading.12 

FIG. 1.

SEM image showing an example of an as-fabricated pore taken from a 500 μm-5 vol. % porosity sample.

FIG. 1.

SEM image showing an example of an as-fabricated pore taken from a 500 μm-5 vol. % porosity sample.

Close modal

The calculated number of pores as well as the center-to-center distance between pores is also tabulated in Table II for each sample investigated. The smaller volume per pore for the 200 μm subgrouping indicates that there is an order of magnitude higher number of 200 μm pores than there are the larger 500 μm pores for a given volume percentage.

The LPBF fabricated cylinders were postprocessed using wire electro-discharge machining (EDM) to make disk-shaped samples of diameter 11.43 mm and thickness of 3 mm. The samples were then impacted normal to the in-plane (IP) build direction to create an area of localized tension between build layers. Ultrasonic sound speed measurements were performed on each LPBF SS316L sample disk using transducers oriented normal to the in-plane build direction. Longitudinal wave speed (CL) was measured using a VSP 200 pressure transducer, while shear wave speed (CS) was measured using an SRD50-5 Ultron pressure transducer with an Olympus 5072PR pulser/receiver in the pulse echo configuration and a Tektronix DPO 5104 1 GHz oscilloscope. Based on these measurements, the average values of various elastic constants, including the bulk sound speed (C0), shear modulus (G), bulk modulus (B), Young’s modulus (E), and Poisson's ratio (ν) for each printed sample disk, were calculated using standard equations of elasticity25 and are listed in Table S1 in the supplementary material.

Plate-on-plate impact experiments were performed using an 80 mm diameter 7.6 m length single-stage light gas gun at the Georgia Institute of Technology. All samples were impacted at a nominal velocity of ∼250 m/s to investigate the early stages of void nucleation, growth, and coalescence associated with spall damage. A multi-sample target assembly was utilized such that each impact experiment included duplicate samples, one instrumented with single or multiple PDV probes to capture the free surface velocity profiles, and a second sample soft recovered in a catch tank filled with soft rags for post-shock microstructure characterization.

Figure S3 in the supplementary material illustrates a schematic of the plate-impact experiment assembly. A wrought 316LSS disk was utilized as the flyer plate. The sample disks were lapped flat and parallel to within 1 mrad and pressed into a 94 mm diameter 3 mm thick wrought and annealed SS316L target holder which was also lapped flat and parallel to within 1 mrad using 45 μm diamond slurry. The sample disks and target ring holder were machined to hold a class LT2 locational transition fit tolerance per ANSI B4.1-1967. The fit allowed for the samples to be pressed into a target holder surround ring of wrought SS316L, without introducing significant deformation common to a traditional interference fit, while minimizing potential edge effects.

For all PDV measurements, fiber pigtail collimated probes (AC Photonics P/N: CL1P155020B16301) were positioned to collect velocimetry data from the center or slightly off center of each sample [as shown in Fig. S3(b) in the supplementary material] and connected to a mixed multiplex PDV (MPDV) system capable of conventional, time-delayed, and upshifted frequency-based measurements. A 1-km long SMF-28 fiber optic cable creates an ∼5 μs time delay in simultaneous impact events, while frequency separations of ∼200 and ∼400 GHz were used to upshift the frequency of captured signals.

The impact velocity (Vimpact) was measured using a PDV probe positioned orthogonal to and flush with the impact surface of the target plate to measure the projectile arrival time and velocity to an accuracy of 0.1%.26 A series of four electrically charged pins of known spacing were also affixed approximately 50 mm in front of the target to trigger the digitizer used to collect PDV data and to provide a backup for projectile velocity measurement in the event of PDV failure. Signals were collected using a Teledyne Lecroy wave master 813Zi-B 13 GHz Oscilloscope. Analysis of PDV signals was performed using the HiFiPDV program,27 which takes an average of up to 180 potential Short Time Fourier Transforms (STFTs) based on likely window functions, time-bins, and peak determination methods to find the best fit and uncertainty for the velocity at each point in the profile.

As-fabricated samples were obtained from each cylinder as a representative sample to examine microstructure and void details. Soft-recovered, impacted samples were cross-sectioned and metallographically prepared using standard techniques for optical microscopy and EBSD analysis.28 Specimens were mounted in epoxy and polished in incremental steps to a 0.05 μm finish. A 0.05 μm colloidal silica suspension was used to obtain the final polish. EBSD scans were conducted with an EDAX Velocity detector using a step size of 0.3 μm (unless otherwise noted) and analyzed using the TSL OIM software package. Secondary electron SEM micrographs were collected using either a Tescan Mira FE-SEM or a Hitachi SU8230 FE-SEM. Areas of interest were identified by SEM and prepared for transmission electron microscopy (TEM) analysis using focused ion beam (FIB) lift out on a dual-beam FIB-SEM (FEI Nova Nanolab 200). A Pt coating was applied to the region of interest to protect the sample from damage during milling. The region of interest was removed and attached to a Cu half-moon TEM grid. Lastly, the TEM sample was thinned to 150 nm using a Ga ion beam. TEM images were collected using a FEI Tecnai F30 TEM.

Significant grain refinement and some twinning were found to be present in the microstructures surrounding the as-fabricated pores in all samples (see Fig. 2). Residual powder from LPBF fabrication was also present and loosely packed, though original powder packing fractions could not be determined from 2D imaging due to postprocessing steps taken for characterization, mainly cutting, and polishing the sample, which likely caused loss of loose powder.

FIG. 2.

Pre-shock characterization of the as-printed samples. (a) EBSD of an as-fabricated pore taken from 500 μm-5% samples. Arrows show the location of grain refinement at pore edges. (b) Dark field TEM micrograph highlighting twinning at edge of an as-fabricated pore taken from 500 μm-5% samples. Diffraction pattern included as an inset in the image.

FIG. 2.

Pre-shock characterization of the as-printed samples. (a) EBSD of an as-fabricated pore taken from 500 μm-5% samples. Arrows show the location of grain refinement at pore edges. (b) Dark field TEM micrograph highlighting twinning at edge of an as-fabricated pore taken from 500 μm-5% samples. Diffraction pattern included as an inset in the image.

Close modal

A Zeiss Xradia 520 Versa X-ray Microscope (XRM) at the University of Colorado Boulder was used to analyze incipient spall generated voids and damage in select post-impact instrumented samples. The 3D models were processed using a series of Otsu method splits within the Dragonfly image analysis software,29 allowing for automated image thresholding of pores and cracks in the material.

PDV measurements were used to obtain free surface velocity profiles during plate-impact experiments conducted on LPBF SS316L samples containing intentional pores of three different sizes and volume fractions at ∼250 m/s. The impact velocity corresponds to a calculated peak shock pressure, σpeak of 4.7–5.1 GPa (based on σpeak = ρ0UsUp, where Us and Up are shock and particle velocities).30 For each impact experiment, the particle velocity, Up,25 was calculated considering the non-symmetric impedance conditions arising from mismatched C0 and ρ0 between the wrought SS316L flyer and LPBF SS316L target samples. However, the values were not found to be statistically significantly different from Up values calculated considering symmetric impact conditions, where Up = 0.5*Vimpact.25 

The shock velocity Us for each impact experiment was calculated using elastic and shock wave arrival timings from the measured free surface velocity data, along with values of the longitudinal sound speed CL obtained from ultrasound measurements. The shock-compressed width of the sample (x) was also calculated by measuring time (t1) from the initial velocity rise from zero to a local slope minimum, indicating the arrival of the longitudinal elastic wave and the HEL at the rear free surface of the sample (x = CL*t1). The full width half maximum (FWHM) of the shock wave from t1 to the peak velocity was used to determine the arrival time of the shock front at time t2. These idealized arrival times are illustrated graphically by plotting the location of shock and elastic wave fronts through time in the distance–time plot shown in Fig. 3(a). An example of a free surface wave profile traveling through a fully dense AM steel is shown in Fig. 3(b) where the arrival of the elastic and shock waves at the rear free surface is designated by time t1 and t2, respectively, in Figs. 3(a) and 3(b).

FIG. 3.

(a) Distance–time (X–T) diagram showing the location of the shock and elastic wave front through time in a fully dense SS316L AM sample representing geometries used in the present study. The predicted spall region is circled. (b) Example of free surface wave profile traveling through a fully dense material. The arrival of CL, Us, elastic release, and spall pullback is designated by times t1 to t4. Velocity profiles exhibit an initial rise corresponding to the elastic wave front followed by a slower rise as the material experiences elastic–plastic yielding and approaches the peak state. The rise times and the corresponding peak state of the wave propagating through the material are found to vary considerably with porosity. Following the peak state, the pressure is released, and the wave begins to decelerate before a pullback in the velocity signal is detected, as reflected wave fronts from the free surface of the flyer and the sample interact to produce regions of localized tension and spall failure. The arrival of the idealized elastic release and spall pullback signals at the rear free surface corresponds to times t3 and t4 as shown in (a) and (b).

FIG. 3.

(a) Distance–time (X–T) diagram showing the location of the shock and elastic wave front through time in a fully dense SS316L AM sample representing geometries used in the present study. The predicted spall region is circled. (b) Example of free surface wave profile traveling through a fully dense material. The arrival of CL, Us, elastic release, and spall pullback is designated by times t1 to t4. Velocity profiles exhibit an initial rise corresponding to the elastic wave front followed by a slower rise as the material experiences elastic–plastic yielding and approaches the peak state. The rise times and the corresponding peak state of the wave propagating through the material are found to vary considerably with porosity. Following the peak state, the pressure is released, and the wave begins to decelerate before a pullback in the velocity signal is detected, as reflected wave fronts from the free surface of the flyer and the sample interact to produce regions of localized tension and spall failure. The arrival of the idealized elastic release and spall pullback signals at the rear free surface corresponds to times t3 and t4 as shown in (a) and (b).

Close modal

The measured free surface velocity profiles for each sample type with 200-, 350-, and 500-μm pores and different porosity fractions, along with the fully dense control sample, are shown in Figs. 4–6, respectively. Tables S2–S4 in the supplementary material list the measured and calculated values obtained from the presented velocity profiles. The samples are grouped and presented by pore size for clarity in the discussion of the results.

FIG. 4.

PDV profiles for samples with 200 μm pores and % volume porosity of between 1%, 3%, and 5%. Velocity profiles are plotted along with that of an IP build direction pore-free control sample. The HEL of each sample is captured at ∼0.18 μs and is enlarged for clarity in the included inset.

FIG. 4.

PDV profiles for samples with 200 μm pores and % volume porosity of between 1%, 3%, and 5%. Velocity profiles are plotted along with that of an IP build direction pore-free control sample. The HEL of each sample is captured at ∼0.18 μs and is enlarged for clarity in the included inset.

Close modal
FIG. 5.

PDV profiles for samples with 350 μm pores and % volume porosity of 1% and 5%. Velocity profiles are plotted along with that of an IP build direction pore-free control sample. The HEL of each sample is captured at ∼0.2 μs and is enlarged for clarity in the included inset.

FIG. 5.

PDV profiles for samples with 350 μm pores and % volume porosity of 1% and 5%. Velocity profiles are plotted along with that of an IP build direction pore-free control sample. The HEL of each sample is captured at ∼0.2 μs and is enlarged for clarity in the included inset.

Close modal
FIG. 6.

PDV profiles for samples with 500 μm pores and % volume porosity of between 1% and 5%. Velocity profiles are plotted along with that of an IP build direction pore-free control sample. The HEL of each sample is captured at ∼0.2 μs and is enlarged for clarity in the included inset.

FIG. 6.

PDV profiles for samples with 500 μm pores and % volume porosity of between 1% and 5%. Velocity profiles are plotted along with that of an IP build direction pore-free control sample. The HEL of each sample is captured at ∼0.2 μs and is enlarged for clarity in the included inset.

Close modal

A four-part set of numbers and letters is used to convey information about each velocity profile and test conditions. The first number designates the size of a pore (200, 350, or 500 μm), while the second dictates the volume percentage of porosity. The third part designates the “shot number” for the gas gun experiment with the first two numbers indicating the year and the second two numbers indicating the order. Finally, the fourth number and letter combination indicates the signal channel and type within the multiplex PDV setup used to capture the velocity profile. A CC designation denotes signals captured by conventional PDV, while those with a CD designation were captured using a multiplexed time-delay PDV and those with a UC designation were captured with a multiplexed upshifted PDV signal. UCA or UC designates an upshift of 200 GHz while a designation of UCB indicates an upshift of 400 GHz. The ability to leverage up to ten velocity profiles in a single impact experiment through multiplexing allows for the placement of several probes on a single sample, enabling spatial monitoring of the material response, unlike what may be typically achieved with a single probe. These probes reveal a highly heterogeneous response to impact for all pore sizes.30 In particular, the plastic-wave rise time for the captured velocity profiles is found to vary considerably within the probed samples (see signals 2202-CC3 and CC4, as well as 2105-CC1 CC2, UC3A, and UC3B in Fig. 5 as examples). Local pore-to-probe interactions are hypothesized to be the cause of these disparate rise times.

The measured velocity profiles of LPBF SS316L specimens with intentionally fabricated 200 μm pores at 1, 3, and 5 vol. % are presented in Fig. 4, along with the wave profile for the control fully dense AM sample without porosity. As the volume percent of porosity increases, the shock speed (Us) generally slows, resulting in longer initial rise times. Furthermore, the samples with porosity do not reach a steady shock state or plateau, unlike the control sample, due to the arrival of the release (unloading) wave followed by material decompression. The 200 μm pore size samples with 1% and 3% porosity experience a slope change during the initial rise at a velocity corresponding to the HEL of the SS316L steel, and again at ∼140 m/s. The slope change at ∼140 m/s is also captured for the 5% porosity sample in the (200 μm-5%-2202-CC3) profile. On the other hand, the 5% porosity sample (200 μm-5%-2202-CC4) shows slope change only corresponding to the HEL, due to the significantly longer plastic-wave rise time. The cause of this slope change at the higher velocity is not well understood, but we hypothesize that it may correspond to shock induced densification of the previously unconsolidated SS316L powder in the pores upon complete pore collapse. However, further experimentation is required to confirm the cause of this slope change.

Compared to the control sample with no porosity, the HEL is lower for all porous samples (see Fig. 4, inset and Table S2 in the supplementary material). The change in the free surface velocity (ΔUfs) measured from peak to trough of pullback is used to calculate the spall strength (σspall), which is found to vary with porosity. The 200 μm-1% pore sample has a higher spall strength than the IP control sample (Table S2 in the supplementary material) while the 200 μm-3% and 200 μm-5% pore samples have slightly lower spall strengths. The rate of decompression on initial wave release (u̇1) was found to be identical (0.38 mm/μs2) for both 200 μm-5% signals (2202-CC3 and 2202-CC4), although the velocity profiles for the 200 μm-5 vol. %-2202-CC4 sample show a rapid initial unloading rate of ∼1.00 mm/μs2. For all 200 μm pore samples, the rate of decompression falls between 0.38 and 0.45 mm/μs2, even in those signals which have a bilinear slope on wave release.

While the rate of decompression (u̇1) and the corresponding decompression strain rate ( ε ˙) for initial wave release are similar for all 200 μm pore signals, the recorded pullback signatures following spall failure are heterogeneous, and the rates of recompression (u̇2) are not easily grouped together (see Table S2 in the supplementary material), suggesting that highly localized damage kinetics are present from sample to sample and even within the same sample. The 200 μm-5%-2202-CC3 and 200 μm-5%-2202-CC4 velocity profiles highlight this variability and possible heterogeneous material responses with recompression rates of 0.09 and 0.20 mm/μs2, respectively. It should be noted that the recompression rate for the control AM sample and the 200 μm-1% sample is the same, suggesting that similar damage responses exist in these samples, and the role of porosity on resulting spall damage is relatively minor for these 1% porosity and 200 μm pore size samples.

Figure 5 shows velocity profiles measured for LPBF SS316L with 350 μm pores at 1 and 5 vol. % pre-existing porosity levels. Note that the velocity profile was not captured for the 350 μm-3% specimen, although a soft-recovered sample was obtained for post-mortem characterization. The machined section for the instrumented 350 μm-3% specimen was taken from the edge of the printed cylinder where no pores were present (see Fig. S1 in the supplementary material for example). Table S3 in the supplementary material lists the parameters obtained from the measured velocity profiles shown in Fig. 5. The 350 μm pore samples experience similar strain rates as the 200 μm pore samples, on initial unloading, though a steady state shock wave is not attained as the peak of shock front arrival coincides with the arrival of the release wave. For four of the six considered velocity profiles, the release wave has a decompression rate, u̇1 slope of 0.43 mm/μs2.

The initial elastic and plastic wave arrival trends are not as clearly defined for these 350 μm pore size samples compared to the 200 μm pore samples. This is thought to be a result of fewer overall pores in the sample due to the larger individual volume of each pore, resulting in a more heterogeneous mesoscale structure and overall shock response. The effects of local heterogeneities are best captured in the PDV data obtained from the four probes affixed to the back free surface of one sample (350 μm-1%-2105) displaying differing rise times, and decompression and recompression slopes.

Bi-linear slopes are observed for the recompression rate (u̇2) more frequently than for the 200 μm pore sample grouping, with initial rates of ∼0.27–0.33 mm/μs2 followed by slower rates of 0.16–0.22 mm/μs2 for three of the six considered velocity profiles (see Table S3 in the supplementary material). However, this is not always the case, with the 350 μm-1%-2105-UC3A sample showing rates of 0.33 mm/μs2 followed by 0.45 mm/μs2 on recompression. Additionally, the 350 μm-5-2202-CC1 velocity profile has a linear recompression slope of 0.19 mm/μs2. The 350 μm-1%-2105-CC2 sample recompression curve was too noisy to determine the slope.

A well-defined HEL is noted for some but not all samples, as revealed by the velocity profiles for 1% and 5% of 350 μm pore samples in Fig. 5. The profiles appear to vary considerably even for the same sample, e.g., as seen from the multiple profiles for the 350 μm-1vol. % sample. Furthermore, the arrival of both the elastic and plastic waves is delayed with frequent slope changes in the initial rise, complicating the designation of the HEL in some profiles. For example, the 350 μm-1%-2105-CC1 velocity profile shows a slope change at ∼80 and ∼140 m/s, while the 350 μm-1%-2105-UC3A velocity profile has only one distinct slope change at the HEL (∼40 m/s), but the rise time is comparatively much slower.

The recorded pullback signatures following spall failure share similar rates of recompression (u̇2). Most notably, four of the five captured velocity profiles experience a recompression rate of between 0.27 and 0.33 mm/μs2 on initial reloading. Each of these four profiles has a bilinear slope with three of the profiles showing a decrease in recompression rate as reloading continues (between 0.16 and 0.17 mm/μs2) and one profile showing an acceleration in recompression rate (0.45 mm/μs2). This suggests that initial damage accumulation is surprisingly homogenous at this pore size, but that after this initial stage, damage can either accelerate or dampen depending on the local wave interactions.22 It should be noted that the 350 μm-5%-2202-CC1 velocity profile does not show a recompression slope change and illustrates consistent slow damage accumulation following pullback. This possibly is indicative of a velocity profile measured by a probe that is not aligned with a pore in the bulk of the material and is consistent with observations with the 350 μm-5%-2202-CC1 velocity profile, which has an initially fast rise time, similar to that observed in the IP control sample.

Velocity profiles for LPBF SS316L samples with 500 μm pores at 1, 3, and 5 vol. % are displayed in Fig. 6. Given the larger volume of a single 500 μm pore, a relatively small number of pores are expected in the bulk. As with the 200 and 350 μm pore sizes, an increase in pore volume percent is seen to correlate to a slower overall shock wave rise time of the propagating wave.

Calculations from velocity profiles in Fig. 6 are tabulated in Table S4 in the supplementary material and reveal an initial increase in the HEL as porosity increases from 1% to 3%, followed by a decrease in the HEL at 5% porosity. On the other hand, a clear decrease in spall strength is observed as the volume percent of porosity is increased. Slopes corresponding to the decompression strain rates (1) reveal a highly local response with no clear pattern present between individual samples of different pore sizes and porosity levels. The decompression slopes are found to be linear or bi-linear, with slope changes resulting in either faster or slower decompression rates. These results reveal that the deformation response of LPBF SS316L during shock loading is highly heterogeneous and likely localized based on pore location(s) relative to the placement of the PDV probe.

The recompression response following the spall pullback is also heterogeneous, although the recompression strain rate of ∼0.29–0.32 mm/μs2 is commonly observed in all but one velocity profile for 500 μm samples across all porosity levels (see Table S4 in the supplementary material). A similar recompression rate was observed in the 350 μm-1%-2105-UC3B, 350 μm-1%-2105-CC1, and 350 μm-5%-2202-CC2 velocity profiles and in none of the 200 μm velocity profiles, suggesting a failure mechanism which is activated more readily when larger pores are present. One potential reason for the surprisingly consistent slope across increasingly heterogeneous samples could be attributed to continued pore collapse on pullback. While complete pore collapse was observed for the soft-recovered 200 μm samples, there are some pores that are only partially collapsed in the 350 and 500 μm samples. The 0.33 mm/μs2 recompression rate could, therefore, be capturing the rate of pore compression, though further studies are required to confirm this.

A summary of the damage modes of LPBF SS316L samples of different pore sizes and porosity levels to impact is provided in Table III. Generally, as the pore size and the porosity volume percent are increased, the main damage mode transitions from the typical spall-centered/tensile-stress dominated failure occurring along the expected plane, or off-planar, i.e., shifted toward the rear-surface, to pore-centered/microstructure-dominated damage with no failure occurring along the expected sample plane. Both the pore size and the volume percent of pores are found to play a role in the observed primary damage mode, as summarized in Table III.

TABLE III.

Summary of material response to uniaxial-strain impact loading for various porosity levels.

1%3%5%
200 μSpall-centered/tensile-stress dominated Spall-centered/tensile-stress dominated Spall-centered/tensile-stress dominated—off planar 
350 μSpall—off planar Mixed Mixed 
500 μMixed pore-centered/microstructure dominated pore-centered/microstructure dominated 
1%3%5%
200 μSpall-centered/tensile-stress dominated Spall-centered/tensile-stress dominated Spall-centered/tensile-stress dominated—off planar 
350 μSpall—off planar Mixed Mixed 
500 μMixed pore-centered/microstructure dominated pore-centered/microstructure dominated 

SEM micrographs shown in Fig. S4 in the supplementary material give examples of each failure mode designation from Table III. Although spall damage is not seen in the pore-centered/microstructure-dominated samples within the interior 9 mm diameter containing intentional pre-existing porosity, the samples do undergo local spallation, at the edges of the disk, away from the local influence of the porous inner diameter.

For the samples with pre-existing porosity, SEM micrographs of impacted specimens reveal varying degrees of pore collapse across the thickness of the sample. Figures 7 and 8 show the cross sections of impacted and soft-recovered 500 μm-5% and 500 μm-1% samples, respectively. The expected spall plane is denoted by the blue dashed lines and pre-existing pores are denoted by yellow squares (500 μm in length and width) to assist in visualization of the degree of pore collapse present. While pre-existing pores in the 500 μm-5% sample are in various states of collapse, there are still several pores that have not fully closed, particularly those toward the back free surface of the sample.

FIG. 7.

(a) Sample 500 μm-5% showing pore collapse in impacted specimen. Samples show full pore collapse near the spall plane and partial pore collapse away from the spall plane. Yellow boxes (500 μm in length and width) illustrate a relative reduction in pore size. The theoretical spall plane and centerline is shown by the dashed blue line. Partially compacted and uncompacted powder is found in partially collapsed pores. (b) Illustrates a pore with minimal compaction. Uncompacted powder is observed as well as cracking at the corners. (c) Highlights a pore at the impact surface of the sample with intermediate compaction and the presence of partially compacted powder. (d) highlights a fully collapsed pore near the spall plane. Pore collapse appears to have occurred normal to the impact face.

FIG. 7.

(a) Sample 500 μm-5% showing pore collapse in impacted specimen. Samples show full pore collapse near the spall plane and partial pore collapse away from the spall plane. Yellow boxes (500 μm in length and width) illustrate a relative reduction in pore size. The theoretical spall plane and centerline is shown by the dashed blue line. Partially compacted and uncompacted powder is found in partially collapsed pores. (b) Illustrates a pore with minimal compaction. Uncompacted powder is observed as well as cracking at the corners. (c) Highlights a pore at the impact surface of the sample with intermediate compaction and the presence of partially compacted powder. (d) highlights a fully collapsed pore near the spall plane. Pore collapse appears to have occurred normal to the impact face.

Close modal
FIG. 8.

(a) Sample 500 μm-1% showing pore collapse in impacted specimen. Samples are fully collapsed near the spall plane and experience partial collapse away from the spall plane. Yellow boxes are 500 μm in length and width to illustrate a relative reduction in pore size. The theoretical spall plane and centerline is shown by the dashed blue line. (b) and (c) highlight areas of suspected pore collapse in the sample both before and after the centerline/spall plane.

FIG. 8.

(a) Sample 500 μm-1% showing pore collapse in impacted specimen. Samples are fully collapsed near the spall plane and experience partial collapse away from the spall plane. Yellow boxes are 500 μm in length and width to illustrate a relative reduction in pore size. The theoretical spall plane and centerline is shown by the dashed blue line. (b) and (c) highlight areas of suspected pore collapse in the sample both before and after the centerline/spall plane.

Close modal

Conversely, nearly all pre-existing pores in the 500 μm-1% sample have fully collapsed, suggesting that the strain accommodation due to the presence of pre-existing pores has been fully exhausted. The presence of pre-existing pores and their locations is difficult to fully observe post-mortem, particularly close to the impact face of the specimen where pores are fully collapsed [see Fig. 8(b)].

A selection of slices from the nano-CT scan performed on the post-impact 500 μm-1% and 500 μm-5% samples is presented in Fig. 9. These scans support 2D micrograph data obtained through SEM which suggest a mixed failure mode and pore-centered microstructure-dominated mode for the 500 μm-1% and 500 μm-5% samples, respectively. While local spalling is observed in the 500 μm-1% sample (circled in yellow in Fig. 9), no spall failure is detected in the 500 μm-5% sample. Spall generated voids are captured by flecks of color in the spall region of the scan, while pre-existing pores are represented by large colored boxes.

FIG. 9.

CT scan selections of impact face, spall region, and back face for 500 μm-1% and 500 μm-5% samples. Red circles in the back face of the sample highlight PDV probe placement locations for each sample. Circular depressions can be found on the back face where the PDV probe impacted the instrumented sample during gas gun experiments. Otsu thresholding was used in conjunction with connected component analysis to identify multi-regions of interest (MROI). Those larger MROI are assumed to be individual pores (colored boxes in the spall region for both samples). Smaller pores and cracks resulting from dynamic tensile failure were also identified in the MROI and are shown as colored flecks in the 500 μm-1% sample and circled in yellow.

FIG. 9.

CT scan selections of impact face, spall region, and back face for 500 μm-1% and 500 μm-5% samples. Red circles in the back face of the sample highlight PDV probe placement locations for each sample. Circular depressions can be found on the back face where the PDV probe impacted the instrumented sample during gas gun experiments. Otsu thresholding was used in conjunction with connected component analysis to identify multi-regions of interest (MROI). Those larger MROI are assumed to be individual pores (colored boxes in the spall region for both samples). Smaller pores and cracks resulting from dynamic tensile failure were also identified in the MROI and are shown as colored flecks in the 500 μm-1% sample and circled in yellow.

Close modal

Post-mortem EBSD analysis of soft-recovered specimens reveals the presence of shear banding, twinning, extensive deformation, and cracking in the vicinity of the pre-existing pores even in the case where scans are taken far from the spall plane (Fig. 10). Micrographs taken from different samples with 350- and 500-μm sized pores show similar mixed and pore-centered/microstructure-dominated failure responses. It is hypothesized that the pre-existing pores slow the plastic wave front and cause local accommodation and dissipation of impact stresses. The observed damage and deformation local to the pores and away from the theoretical (expected) spall plane support the hypothesis.

FIG. 10.

Inverse Pole Figure-Image Quality (IPF-IQ) overlay maps reveal (a) shear banding and twinning near pores and away from expected spall regions in a recovered 500 μm-5% sample. (b) Shear banding, twinning, and cracking near a pore and away from the spall plane in a recovered 500 μm-1% sample. (c) Damage observed near pores in a recovered 350 μm-3% sample highlighting the localized nature of strain accommodation near the pore. (d) Crack propagation radiating from a pore in a recovered 350 μm-5% sample. Scans were taken with a step size of 0.1 μm for micrographs in (a), (b), and (d) and a step size of 0.3 μm was used for the micrograph in (c). Pore corners are observed in the top right corner in micrographs [(b)–(d)], while the crack propagation direction is highlighted by yellow arrows.

FIG. 10.

Inverse Pole Figure-Image Quality (IPF-IQ) overlay maps reveal (a) shear banding and twinning near pores and away from expected spall regions in a recovered 500 μm-5% sample. (b) Shear banding, twinning, and cracking near a pore and away from the spall plane in a recovered 500 μm-1% sample. (c) Damage observed near pores in a recovered 350 μm-3% sample highlighting the localized nature of strain accommodation near the pore. (d) Crack propagation radiating from a pore in a recovered 350 μm-5% sample. Scans were taken with a step size of 0.1 μm for micrographs in (a), (b), and (d) and a step size of 0.3 μm was used for the micrograph in (c). Pore corners are observed in the top right corner in micrographs [(b)–(d)], while the crack propagation direction is highlighted by yellow arrows.

Close modal

While partially collapsed pre-existing pores are clearly observed for all 500 μm samples, those in the 200 and 350 μm pore size samples were fully collapsed, making detection difficult. EBSD micrographs near the expected spall planes in the 200 and 350 μm samples reveal some clues as to how the pre-existing pores contribute to spall and crack propagation in the region of dynamic tension within the sample. The dark (black) regions within the Image Quality/Inverse Pole Figure (IQ/IPF) map correspond to pores, cracks, and areas in the sample which are too damaged to be identified. Areas presumed to correspond to collapsed pores rather than traditional cracking and void damage from spall in the bulk material were identified by their size. For example, in Fig. 11(a), a straight crack measuring 200 μm in length is observed in the right corner of the micrograph, followed by an almost perpendicular turn at the “corners” of the pore, which are hypothesized to correspond to areas of severe shear from edge effects and jetting. Conversely, material that failed in the bulk is expected to display a failure signature like that observed in the left corner of the micrograph in Fig. 11(c), with rounded ductile voids (typical of spall failure) that have begun to grow and coalesce. This pattern of pre-existing pore collapse with observed deformation nearly perpendicular to the corners of the pore is seen at all levels of volume percent of porosity for the 200 and 350 μm samples [see Figs. 11(a)11(f)].

FIG. 11.

(a) Sample 200 μm-5% shows pore collapse in the right corner of the micrograph. Jetting from the collapsed corners of the square pore is noted at each edge of the collapsed region and is designated by yellow arrows. (b) This IPF-IQ micrograph shows an additional example of pore collapse in the 200 μm-5% sample. (c) Sample 200 μm-3% shows pore collapse with jetting designated by yellow arrows. (d) Sample 200 μm-1% shows pore collapse with potential jetting at a collapsed corner observed in the lower left corner of the micrograph. (e) Sample 350 μm-5% includes suspected pore collapse and jetting at the corners of the collapsed pore. In all instances, severe material deformation is found in the area surrounding the collapsed pore and surrounding jetting at the corners of the collapsed pore. (f) Sample 350 μm-5% includes suspected pore collapse, which again takes a tortuous path through grain boundaries. The impact direction proceeds from left to right for all figures.

FIG. 11.

(a) Sample 200 μm-5% shows pore collapse in the right corner of the micrograph. Jetting from the collapsed corners of the square pore is noted at each edge of the collapsed region and is designated by yellow arrows. (b) This IPF-IQ micrograph shows an additional example of pore collapse in the 200 μm-5% sample. (c) Sample 200 μm-3% shows pore collapse with jetting designated by yellow arrows. (d) Sample 200 μm-1% shows pore collapse with potential jetting at a collapsed corner observed in the lower left corner of the micrograph. (e) Sample 350 μm-5% includes suspected pore collapse and jetting at the corners of the collapsed pore. In all instances, severe material deformation is found in the area surrounding the collapsed pore and surrounding jetting at the corners of the collapsed pore. (f) Sample 350 μm-5% includes suspected pore collapse, which again takes a tortuous path through grain boundaries. The impact direction proceeds from left to right for all figures.

Close modal

The effect of rise time on the resultant spall strength of the material is considered for further discussion. Figure 12 plots the measured spall strength and corresponding 50%–90% shock wave rise time for all samples with pre-existing pores of three different sizes and their volume percent, revealing linear correlations for each mode of failure (designated in Table III). Different failure mechanisms are indicated by the varying dependences of rise time on spall strength. In the case of spall-centered tensile stress dominated failure mode, the spall strength appears to be independent of the rise time (two blue data points). Even with the spall plane being offset (orange trend line in Fig. 12), the effects of pore collapse on rise time influencing the spall strength are seen to play a minor role. In the case of mixed failure modes, with some local spall (gray trend line in Fig. 12), there is a strong dependence of the spall strength on the shock rise time and failure. However, once the spall mechanism is effectively shut down through dampening of the shock wave as it travels through the sample with pre-existing pores, the spall strength essentially remains constant with rise time indicating no obvious trend which is indicated by the pore-centered microstructure-dominated failure mode (yellow trend line in Fig. 12).

FIG. 12.

Shock wave rise time vs spall strength demonstrates a dependence of observed failure mode on spall for each velocity profile.

FIG. 12.

Shock wave rise time vs spall strength demonstrates a dependence of observed failure mode on spall for each velocity profile.

Close modal

The data presented allows for an understanding of the response of LPBF SS316L to varying pre-existing low-volume fraction porosity materials in the weak shock regime. Porosity is found to affect the initial rise time to peak pressure by way of pore collapse, with the degree of strain accommodation through pore collapse directly influencing the measured spall strength, spall plane, and observed final failure modes. When full pore collapse is observed, the excess stress in the material may result in a symmetric spall response as dictated by the sample and flyer plate geometries, whereas if excess porosity is present the stress input may be insufficient to cause full collapse of the pores, leading to dampening or complete shutdown of the spall failure.

The direct effects of pore size and volume percent on the spall strength measured from PDV interferometry measurements of the free surface velocity profiles are depicted in the bar chart in Fig. 13. The spall strength generally tends to decrease with increasing volume percent of porosity for each pore size grouping. Although, the difference in the spall strength for the 3% and 5% loadings for the 200 μm pores is not statistically different. The effect of pore size was also found to be less pronounced as the overall pore volume percentage increased. For example, the drop in spall strength when comparing 200 μm-1% pore samples to 500 μm-1% pore samples is much more pronounced than in the case with the 200 μm-5% and 500 μm-5% samples as shown in Fig. 13. This suggests that the effect of pore size on spall strength decreases as pore volume increases.

FIG. 13.

Spall strength plotted vs pore size and pore volume. As the pore volume percentage increases, the influence of pore size is minimized. Error bars capture the minimum and maximum calculated spall strength for a given pore size and volume percent porosity and highlight the heterogeneous response present between velocity profiles from the same impact experiment. Note only one velocity profile was captured for the IP control sample.

FIG. 13.

Spall strength plotted vs pore size and pore volume. As the pore volume percentage increases, the influence of pore size is minimized. Error bars capture the minimum and maximum calculated spall strength for a given pore size and volume percent porosity and highlight the heterogeneous response present between velocity profiles from the same impact experiment. Note only one velocity profile was captured for the IP control sample.

Close modal

The effects of the number of pores as well as the center-to-center average distance between pores do not appear to have a direct influence on the HEL or the spall strength values, as shown in Fig. 14, which plots the spall strength and HEL values as a function of the pore characteristics. This suggests that while the size of pores is important to the overall failure response, the dynamic spall strength of the material is not simply dependent on the number and spacing between pores in the sample. To provoke a change in failure mode and the resulting change in the observed spall behavior in the material, samples must have sufficient porosity to allow for interaction of the wave in the bulk and the pores must be large enough to allow for significant slowing of the propagating shock wave prior to it exiting the sample thickness.

FIG. 14.

(a) Spall strength vs center-to-center pore distance for samples reveals no significant trends. (b) Spall strength does not appear to be dependent on the number of pores present in the material. (c) and (d) HEL is also not dependent on inter-pore distance and the number of pores present. Error bars capture the minimum and maximum calculated HEL and spall strength for all collected velocity profiles at a given pore size and volume percent porosity.

FIG. 14.

(a) Spall strength vs center-to-center pore distance for samples reveals no significant trends. (b) Spall strength does not appear to be dependent on the number of pores present in the material. (c) and (d) HEL is also not dependent on inter-pore distance and the number of pores present. Error bars capture the minimum and maximum calculated HEL and spall strength for all collected velocity profiles at a given pore size and volume percent porosity.

Close modal

The results of this work also suggest that the slowing of the initial rise time to peak pressure is not necessarily a bulk cumulative response, though the material is affected by the segmentation of time spent in the bulk or in the pores. From this assertion, we can speculate that the shock wave velocity through the pores is not linearly dampened. Rather, acceleration and deceleration of the shock wave through the material as it enters and exits the pore must occur to allow for different material responses with the same low-volume percent porosity.

Given the scatter observed in the collected data for spall, initial rise times, and HEL, it is important to consider the various sources of uncertainty that might influence the conclusions presented in this work. These sources include errors in the measurement of the free surface velocity, density, and sound speed introduced through experimental error, graphical determination of the uHEL and ΔUfs, and heterogeneities in the bulk microstructure affecting porosity and grain anisotropy in the 3D printed material.

When assessing sources of error in the recorded free surface velocity, the experimental error was assumed to be random with assessed accuracy limits and uncertainties from both the chosen data collection26 and data analysis27 method propagated throughout observed velocities and calculated strengths (both HEL and Spall). Error in the Archimedes density measurements was similarly propagated through the calculated strengths and elasticity values. Methods for graphical analysis of the uHEL, ΔUfs, and slope changes were kept consistent between velocity profiles and are not felt to be a serious contributor to the heterogeneous responses observed in the collected data.

The relatively low uncertainty and error present in individually recorded free surface velocity profiles supports the hypothesis put forward by the authors that the scatter observed between profiles is due to heterogeneities (porosity) in the samples themselves rather than from uncertainty in the measurement or analysis technique.

The progression of damage in low-volume pre-existing intentional porosity LPBF SS316L samples from traditional tensile stress spall failure to pore-centered microstructure-dominated effects and strain accommodation generating twins, shear bands, etc., is a function of both overall pore volume percent and pore size. The extent and type of damage can be correlated to the rise time of the plastic wave, characterized in this work from 50% to 90% of the overall rise time.

The spall strength of samples correlates with the 50%–90% Us rise time when specific failure modes defined as spall-centered tensile stress dominated, mixed, or pore-centered microstructure dominated are considered. A steeper rise time slope is associated with samples experiencing at least some spall (mixed, offset, and spall failure modes), compared to those samples which exhibit pore-centered response and show no spall. Post-mortem analysis supports the notion that strain is accommodated through microstructural deformation and damage at pore locations away from the spall plane, and at areas of local spall (both centered and offset). Highly heterogeneous deformation and damage mechanisms are observed at both the vicinity of pre-existing pores and expected spall failure sites. The deformation processes include twinning, shear banding, and grain rotation, in addition to cracking both near those damaged pores and along the spall plane. Areas of complete and partial pore collapse are also observed at all pore levels. CT scans of select samples confirm that observed 2D patterns from SEM are applicable to the bulk of the material.

Further investigations should aim to understand the local area of damage for pores of differing sizes as well as how pore interactions in both the build direction (stacked) and the X–Y plane (parallel) effect wave propagation and spall failure in the material. Experiments that examine the effects of two interacting pores in differing release conditions (i.e., two pores located in the region of tension or two pores located some distance apart near the rear free surface or the impacted surface) would also help understand the local pore–pore interaction during shock wave release and initial pullback. Time-resolved measurement techniques such as using in situ x-ray phase contrast imaging may be particularly beneficial in determining the deformation processes and causes of slope changes at ∼140 m/s observed in some of the velocity profiles on initial shock loading, as seen in the present work. These investigations should help inform models which seek to understand strain accommodation through pore collapse in low-volume porosity solids for delayed spall failure.

See the supplementary material for tabulated velocity and ultrasound measurements for the studied AM SS316L, and figures depicting the impact experiment setup and cross-sectioned samples post-impact.

This research was supported in part by funding from the Steel Founders Society of America, Award No. AWD-002255. K.K. was supported by a NASA Space Technology Research Fellowship which also provided funding for the materials, supplies, and characterization performed in the present work. T.S. was supported by the Department of Energy through a cooperative agreement with the DOE NNSA Lab Residency Graduate Fellowship under Contract No. DE-NA000396. K.L. was supported by Consolidated Nuclear Security, LLC (CNS) as accounts of work sponsored by an agency of the United States Government under Contract No. DE-NA-0001942. The characterization work was conducted at the Georgia Tech Institute for Electronics and Nanotechnology or Joint School of Nanoscience and Nanotechnology, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the National Science Foundation (Grant No. ECCS-2025462). Analyses/x-ray CT were performed at MIMIC, CU Boulder (RRID: SCR_019307).

This work of authorship and those incorporated herein were prepared by Consolidated Nuclear Security, LLC (CNS) as accounts of work sponsored by an agency of the United States Government under Contract No. DE-NA-0001942. 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. This manuscript has been authored under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (https://www.energy.gov/downloads/doe-public-access-plan).

The authors have no conflicts to disclose.

K. D. Koube: Conceptualization (supporting); Data curation (lead); Formal analysis (lead); Funding acquisition (supporting); Writing – original draft (lead). T. Sloop: Data curation (supporting); Writing – review & editing (supporting). K. Lamb: Conceptualization (supporting); Data curation (supporting); Methodology (supporting); Writing – review & editing (supporting). J. Kacher: Conceptualization (equal); Funding acquisition (equal); Resources (equal); Supervision (equal); Writing – review & editing (lead). S. S. Babu: Conceptualization (supporting); Funding acquisition (equal); Supervision (supporting). N. N. Thadhani: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (lead); Resources (lead); Supervision (lead); Writing – review & editing (lead).

The data that support the findings of this study are openly available in Mendeley at http://doi.org/10.17632/tw4cyxmtr4.2, Ref. 30.

1.
V. A.
Lubarda
,
M. S.
Schneider
,
D. H.
Kalantar
,
B. A.
Remington
, and
M. A.
Meyers
, “
Void growth by dislocation emission
,”
Acta Mater.
52
,
1397
1408
(
2004
).
2.
L. P.
Dávila
,
P.
Erhart
,
E. M.
Bringa
,
M. A.
Meyers
,
V. A.
Lubarda
,
R.
Becker
, and
M.
Kumar
, “
Atomistic modeling of shock-induced void collapse in copper
,”
Appl. Phys. Lett.
86
,
161902
(
2005
).
3.
T.
Hatano
, “
Dislocation nucleation in shocked fcc solids: Effects of temperature and preexisting voids
,”
Phys. Rev. Lett.
93
,
085501
(
2004
).
4.
T.
Hatano
, “
Spatiotemporal behavior of void collapse in shocked solids
,”
Phys. Rev. Lett.
92
,
015503
(
2004
).
5.
J. W.
Mintmire
,
D. H.
Robertson
, and
C. T.
White
, “
Molecular-dynamics simulations of void collapse in shocked model-molecular solids
,”
Phys. Rev. B
49
,
14859
14864
(
1994
).
6.
B.
Branch
,
A.
Ionita
,
B. E.
Clements
,
D. S.
Montgomery
,
B. J.
Jensen
,
B.
Patterson
,
A.
Schmalzer
,
A.
Mueller
, and
D. M.
Dattelbaum
, “
Controlling shockwave dynamics using architecture in periodic porous materials
,”
J. Appl. Phys.
121
,
135102
(
2017
).
7.
S.
Gangireddy
,
E. J.
Faierson
, and
R. S.
Mishra
, “
Influences of post-processing, location, orientation, and induced porosity on the dynamic compression behavior of Ti-6Al-4V alloy built through additive manufacturing
,”
J. Dyn. Behav. Mater.
4
,
441
451
(
2018
).
8.
M.
Calvo
,
A. E.
Jakus
,
R. N.
Shah
,
R.
Spolenak
, and
D. C.
Dunand
, “
Microstructure and processing of 3D printed tungsten microlattices and infiltrated W–Cu composites
,”
Adv. Eng. Mater.
20
,
1800354
(
2018
).
9.
D. R.
Jones
,
S. J.
Fensin
,
B. G.
Ndefru
,
D. T.
Martinez
,
C. P.
Trujillo
, and
G. T.
Gray
III
, “
Spall fracture in additive manufactured tantalum
,”
J. Appl. Phys.
124
,
225902
(
2018
).
10.
Y.
Cui
,
J.
Cai
,
Z.
Li
,
Z.
Jiao
,
L.
Hu
, and
J.
Hu
, “
Effect of porosity on dynamic response of additive manufacturing Ti-6Al-4V alloys
,”
Micromachines
13
,
408
(
2022
).
11.
R.
Fadida
,
A.
Shirizly
, and
D.
Rittel
, “
Dynamic tensile response of additively manufactured Ti6Al4V with embedded spherical pores
,”
J. Appl. Mech.
85
,
041004
(
2018
).
12.
R.
Fadida
,
D.
Rittel
, and
A.
Shirizly
, “
Dynamic mechanical behavior of additively manufactured Ti6Al4V with controlled voids
,”
J. Appl. Mech.
82
,
041004
(
2015
).
13.
D. M.
Dattelbaum
and
J. D.
Coe
, “
Shock-driven decomposition of polymers and polymeric foams
,”
Polymers
11
,
493
(
2019
).
14.
S.-N.
Luo
,
L.-B.
Han
,
Y.
Xie
,
Q.
An
,
L.
Zheng
, and
K.
Xia
, “
The relation between shock-state particle velocity and free surface velocity: A molecular dynamics study on single crystal Cu and silica glass
,”
J. Appl. Phys.
103
,
093530
(
2008
).
15.
T.
Wang
,
Z.
Li
,
L.
Wang
,
Z.
Ma
, and
G. M.
Hulbert
, “
Dynamic crushing analysis of a three-dimensional Re-entrant auxetic cellular structure
,”
Materials
12
,
460
(
2019
).
16.
D. B.
Reisman
,
W. G.
Wolfer
,
A.
Elsholz
, and
M. D.
Furnish
, “
Isentropic compression of irradiated stainless steel on the Z accelerator
,”
J. Appl. Phys.
93
,
8952
8957
(
2003
).
17.
W.
Herrmann
, “
Constitutive equation for the dynamic compaction of ductile porous materials
,”
J. Appl. Phys.
40
,
2490
2499
(
1969
).
18.
M. M.
Carroll
and
A. C.
Holt
, “
Steady waves in ductile porous solids
,”
J. Appl. Phys.
44
,
4388
4392
(
1973
).
19.
D. C.
Ahn
,
P.
Sofronis
,
M.
Kumar
,
J.
Belak
, and
R.
Minich
, “
Void growth by dislocation-loop emission
,”
J. Appl. Phys.
101
,
063514
(
2007
).
20.
C.
Czarnota
,
A.
Molinari
, and
S.
Mercier
, “
The structure of steady shock waves in porous metals
,”
J. Mech. Phys. Solids
107
,
204
228
(
2017
).
21.
T.
Cohen
and
D.
Durban
, “
Steady shock waves in porous plastic solids
,”
Int. J. Solids Struct.
71
,
70
78
(
2015
).
22.
K. D.
Koube
,
G.
Kennedy
,
K.
Bertsch
,
J.
Kacher
,
D. J.
Thoma
, and
N. N.
Thadhani
, “
Spall damage mechanisms in laser powder bed fabricated stainless steel 316L
,”
Mater. Sci. Eng. A
851
,
143622
(
2022
).
23.
G. T.
Gray
,
V.
Livescu
,
P. A.
Rigg
,
C. P.
Trujillo
,
C. M.
Cady
,
S. R.
Chen
,
J. S.
Carpenter
,
T. J.
Lienert
, and
S. J.
Fensin
, “
Structure/property (constitutive and spallation response) of additively manufactured 316L stainless steel
,”
Acta Mater.
138
,
140
149
(
2017
).
24.
J. G.
Callanan
,
A. N.
Black
,
S. K.
Lawrence
,
D. R.
Jones
,
D. T.
Martinez
,
R. M.
Martinez
, and
S. J.
Fensin
, “
Dynamic properties of 316L stainless steel repaired using electron beam additive manufacturing
,”
Acta Mater.
246
,
118636
(
2023
).
25.
M. A.
Meyers
,
Dynamic Behavior of Materials
(
John Wiley & Sons
,
1994
).
26.
B. J.
Jensen
,
D. B.
Holtkamp
,
P. A.
Rigg
, and
D. H.
Dolan
, “
Accuracy limits and window corrections for photon Doppler velocimetry
,”
J. Appl. Phys.
101
,
013523
(
2007
).
27.
T. J.
Voorhees
, “
High-precision measurements and modeling of how brittle granular materials behave under shock compression
,”
Doctoral dissertation
(
Georgia Institute of Technology
,
2020
).
28.
V.
Voort
,
G.
Lucas
,
G. M.
& Manilova
, and
E.
P
, “
Metallography and microstructures of stainless steels and maraging steels
,” in
ASM Handbook
(ASM International,
2004
), Vol. 9, pp.
670
700
.
29.
See http://www.theobjects.com/dragonfly for Dragonfly 2020.2 (computer software), Object Research Systems (ORS) Inc., Montreal, Canada, 2020.
30.
K. D.
Koube
,
T.
Sloop
,
K.
Lamb
,
J.
Kacher
,
S.
Babu
, and
N. N.
Thadhani
(
2023
). “An assessment of spall failure modes in laser powder bed fusion fabricated stainless steel 316L with low-volume intentional porosity,” Mendeley Data. https://doi.org/10.17632/tw4cyxmtr4.2

Supplementary Material