Shock recompaction of spall damage

Spall fracture, or dynamic tensile failure, is a terminal process often observed in shock loading experiments.¹ When a compressive shock wave in a material reaches a free surface (or one of a significantly lower impedance), it reflects as a rarefaction wave. These rarefactions, or release waves, reduce the stress in the material by accelerating material in the opposite direction to their propagation. Hence, if two rarefaction waves intersect, they can form a region of intense tension at extremely high rates (typically tens of GPa $μ$s $−1$ or strain rates of $≥$ 10$4s−1$⁠). If the tensile stresses are sufficient, damage will begin to accrue in the material; for a ductile metal, this happens through the process of void nucleation, growth, and coalescence. This process has been extensively studied in a wide range of materials and loading conditions.^2–4 Figure 1(a) shows the spall process for a plate-impact experiment in the form of an $x$–$t$ diagram, where the Eulerian position is on the horizontal axis and time is on the vertical axis. This demonstrates how the target material splits internally as the two rarefaction waves intersect.

The conditions that generate spall in real-world applications are rarely isolated, and secondary loading events can be expected to occur; armor, for example. While a large body of published work exists on examining the factors that influence the failure process, such as loading conditions,⁵ secondary phases,⁶ crystallographic orientation,⁷ and grain size,⁸ there are few studies on what happens when a material that contains spall damage is subjected to a second shock. This situation is demonstrated in Fig. 1(b). Here, the flyer-plate has a second, high-impedance layer a small distance behind the original impactor. When this backing plate arrives at the original flyer-plate and target package, it drives a second compressive shock wave through them both. When this second shock arrives at the spall plane, which is now a free surface inside the target, it rapidly accelerates it toward the other side of the spalled target. In theory, this closes the spall region, but what happens at this closing interface remains unknown. Does this simply push the two damaged halves back together, or is there enough energy to drive some sort of bonding at the interface, whether mechanical or chemical? Would the sample that has undergone such a recompaction event have any strength across this interface? This work aims to answer this question through a series of controlled gas-gun flyer-plate impact experiments, where the microstructure both before and after the recompaction can be studied.

The first example in the literature of possible spall recompaction in metals is by Koller et al.,⁹ where a high-explosive plane wave lens was used to drive copper into spall fracture, with the sample then soft-recovered with the aim being to characterize where damage nucleates in the microstructure. However, in spite of producing stresses in the copper of 22 GPa and 36 GPa, well above the few GPa typically required to observe spall,^10,11 the recovered samples were intact and contained no voids or cracks, and only a thin band of perturbed microstructures where the spall plane would be expected. Since the velocity diagnostics on the rear of the sample suggested that spall had occurred (a sharp pullback in the velocity followed by a ringing consistent with waves trapped in a much thinner spalled layer rather than the full sample thickness), their conclusion was that extreme strain-rate strengthening had occurred, pushing the nucleation stress for damage to occur far higher than that at quasi-static rates. Due to how localized the damage region was, they ruled out the possibility that spall and subsequent recompaction had occurred. It should be noted that the sample was soft-recovered by decelerating it in a tank of water located under the explosive and sample assembly. At the terminal velocities generated by the two different explosive lenses used, the copper impacting the water would be subjected to compressive stresses of 3 GPa or 5 GPa, an order of magnitude greater than the Hugoniot elastic limit (⁠$∼0.3$ GPa¹²)—the stress at which a shock wave begins to do plastic work. As such, one would expect the recovery process to introduce large deformation in the sample.

At around the same time, Becker et al. performed gas-gun experiments with layered flyer-plates and copper targets,¹³ although this technique was developed far earlier to investigate how damaged ceramics respond to a second shock load by Yaziv et al.¹⁴ Briefly, copper was impacted with an aluminum flyer-plate at velocities of 165 m s$−1$ and 220 m s$−1$ to generate incipient spall; that is, the damage remains in the nucleation and growth phase and, therefore, voids are fairly isolated with a few connecting cracks. These experiments were then repeated but with the aluminum flyer-plate now backed with a tantalum one (with a thin layer of polycarbonate between them). This has the effect of driving a second shock through the damaged sample, as in Fig. 1(b). The experiments showed a clear evidence of damage in samples that were driven by the aluminum flyer only. In contrast, the samples with the aluminum–tantalum flyer showed a thin band of perturbed microstructures identical in composition to that seen by Koller et al. Hydrocode simulations were also performed to further support this hypothesis that the band was formed due to the recompaction of the pre-exisiting spall plane. However, while the ringing features in the free-surface velocimetry suggested that a spall plane had opened and recompacted, post-mortem analyses could not resolve the microstructure of the perturbed band, specifically whether a bond with strength had formed or not.

Much more recently, Turley et al.¹⁵ have revisited the explosively driven experiments of Koller by performing systematic recompaction experiments to understand the discrepancies between the photon Doppler velocimetry (PDV) profile and lack of damage in the recovered targets as observed previously. Their experiments recorded the rear free-surface velocity of a copper target for a longer duration. This revealed that the thinner samples were experiencing a second shock compression event at a late time, similar to the work of Becker. However, while the gas-gun experiments were specifically designed to recompact, in the explosive works of Koller and Turley, it would appear that this unexpected second loading was a result of the detonation products from the explosive lens driving the remaining part of the sample at such a velocity that it caught up with the initial spall scab and recompacted. The samples were recovered and again contained the thin band of perturbed microstructures instead of the expected voids and cracks of a spall experiment. From the extended velocity-time histories and the recovered samples, they concluded that certain geometries, notably thin samples driven explosively, can be subjected to secondary shocks capable of recompacting spall damage. They are in agreement with Becker et al. that the thin band or scar found is an artifact of this recompacted damage. They remain cautious, however, saying that some sort of time resolved radiography would be the ideal tool for responding to the criticism that ex situ or post-mortem diagnostics (surface velocimetry and soft-recovery, respectively) cannot determine whether spall damage was ever present.

To this point, Fig. 2 shows a sequence of images taken by the authors at the proton radiography (pRad) facility at the Los Alamos National Laboratory. This facility has the ability to take short movies of dynamic events, such as a gas-gun flyer-plate impact.¹⁶ A schematic of the experiment is shown at the top of the figure. This was designed to make a density measurement in shocked titanium but also captured the late time spall event. In the second frame, the shock wave in both the flyer and target is visible. By the third frame, some 3.6 $μ$s later, a clear spall plane has opened in the target. It is also clear that the original gap behind the flyer-plate, separating it from the aluminum sabot, has now collapsed. This impact drives a second shock wave through the flyer-target assembly, and it can be observed in the final frame the spall plane has recompacted and is no longer visible. This sequence clearly demonstrates that a second shock event can recompact spall, but as there was no soft-recovery or velocimetry, we cannot make any comments on the properties of the recompacted target, only that it is possible to remove the porosity from the sample.

As mentioned, the main point of contention in the existing work on recompaction of spall damage is determining that there was in fact spall damage (voids, cracks, etc.) in the sample prior to the compaction event. In this study, we separate the previous single experiments of shock-spall-recompaction into a two-stage process damage generation and recompaction. In step one, two identical samples are shock loaded in a way that generates incipient spall damage in the middle of the samples, which are soft-recovered. One of these samples is then sectioned for microscopy to confirm and quantify the internal damage. The second sample, with the assumption that it will contain a statistically similar and representative amount of damage when compared to the sectioned one, is placed in a new target assembly and subjected to a second shock loading event. It is again recovered and sectioned to examine how the recompaction shock has affected the previous spall damage. Electron microscopy techniques are used to determine what microstructural properties are found at the recompaction plane, answering the second question—is there any form of bond formed at this interface?

Oxygen-free high conductivity (OFHC) copper was used for all samples in this study. The copper was given two different heat treatments to produce uniform, equiaxed microstructures with average grain sizes of 60 $μ$m (600 $°$C, 1 h, in vacuum) or 200 $μ$m (900 $°$C, 35 min, in vacuum). Twins have been omitted in the grain size analyses. No strong texture was observed in either sample. This exact copper plate and heat treatments are described in greater detail by Escobedo et al.,⁸ where it was revealed that the grain size was an important factor in determining the morphology of the damage caused by spall. The two grain sizes chosen here were selected to examine if recompaction was affected by the morphology (average void size, void number, etc.) of the damaged region.

Two damage generation (spall) experiments were fielded. Disc-shaped samples of copper were machined, 16 mm diameter by 4 mm thick, from the two different heat treated plates—each experiment then contained two samples of the same grain size. These were fitted into a series of radial rings, also made of OFHC copper, designed to mitigate damage from edge release waves and ensure that any internal damage was only from the single, longitudinal shock and release process. A detailed description of this experimental geometry can be found in Gray (Chap. 6 of Ref. 17) and Bourne.¹⁸ Two of these samples were mounted in a target plate and placed in the target tank of a 100 mm bore single stage light gas-gun. A 2 mm thick copper flyer-plate was affixed to the leading face of a projectile to serve as the impactor. The flyer-plate thickness was half that of the sample to generate a spall plane in the center of the sample thickness. Target alignment was facilitated by shining a laser down the entire length of the barrel and reflecting off a mirror on the target; impact tilt is typically sub-milliradian. Behind each sample, two photon Doppler velocimetry (PDV)¹⁹ probes were mounted in a thin lexan bar. One probe was at the sample center, and the other was 3.81 mm offset to one side. These measured the shock-wave profile, allowing the peak stress in the sample and the spall strength to be calculated. A fifth PDV probe was placed between the two samples, collimated down the gun barrel, to measure the impact velocity. A cross section of the experimental geometry is shown in Fig. 3(a). A list of experiments is provided in Table I, with the initial spall experiments numbered 1 and 3.

Two recompaction experiments were fielded (numbers 2 and 4 in Table I), each containing one of the samples from the initial spall experiments. Each pre-damaged sample was carefully machined and placed into another recovery assembly, removing as little material as possible. Contemporary work on recompaction is all based on a single experiment approach, where there is essentially zero time (a few 100 ns) between the spall and the recompaction. As such, the sample would be at an elevated temperature for the recompaction phase, due to the heating from the shock and spall events. It was decided to emulate this by heating the sample just prior to the recompaction experiment, i.e., while the sample is in the gas-gun target chamber. Calculations based on the principal Hugoniot for copper suggest that the bulk temperature increase at a shock stress of 2 GPa would be approximately 50 K.²⁰ Simulations were also performed in CTH,²¹ a hydrocode package, to estimate the sample temperature after the full shock, release, and spall process. Based on the results of these, it was decided to heat the sample to a bulk temperature of approximately 475 K. It is important to note that there would have been intense localized heating around the voids in the spall experiments and that this bulk heating approach has not been able to replicate that. Each sample was placed in a recessed slot in a copper heating block, which contained four cartridge heaters (Omega Engineering, Inc., model HDC00011). This is visible in Fig. 3(b). Thermocouples were located in the heating block and in contact with the rear of the sample. A typical heating cycle was a ramp to 475 K over 90 s and then a hold at a temperature for 120 s prior to impact. At this relatively low temperature and a short timescale, no grain growth would be expected. As before, PDV was used to measure the sample rear free-surface velocity and the projectile velocity.

The wave profiles for the initial spall experiments (No. 1: 60 $μ$m grain size and No. 3: 200 $μ$m grain size) are shown in Fig. 4. These were extracted from the raw PDV data with contemporary sliding short time Fourier transform techniques.²² Both experiments had an impact velocity of $107±2$ m s$−1$⁠. Each experiment contained two identical samples, and the wave profiles were indistinguishable within uncertainties. The wave profiles for the two grain sizes both demonstrate a classic flyer-plate impact response, with a small elastic precursor wave, a sharp rise to a steady shock state, and then a pullback and ringing associated with spall fracture.

The magnitude of the elastic precursor marks the point at which plastic deformation begins. Using Eq. (1), this stress, the Hugoniot elastic limit (⁠$σHEL$⁠), is²³ 

where $ρ0$ is the initial density, $CL$ is the longitudinal sound speed, and $uHEL$ is the free-surface velocity at the elastic limit. The HEL was calculated as 0.17 GPa and 0.08 GPa for the 60 $μ$m and 200 $μ$m grain sizes, respectively. This is in good agreement with the literature data for a similar pedigree copper.¹¹ 

After the elastic precursor, the wave profiles rise to a steady shock state for approximately 0.75 $μ$s at a stress of 1.9 GPa. As the rarefaction fan from the flyer-plate reaches the sample rear surface, a deceleration occurs. At this time, tension increases in the sample interior until damage occurs through void nucleation and growth. The rapid expansion of the damaged region launches a compressive wave to the sample rear surface, breaking out at just after 2 $μ$s. The magnitude of this deceleration pullback was used to calculate the spall strength, or resistance to dynamic tensile damage, with Eq. (2),

where $σsp$ is the spall strength, $CB$ is the bulk sound speed, and $Δufs$ is the pullback (the difference between the peak free-surface velocity and the first minimum). The spall strength for both grain size samples was found to be approximately 1.5 GPa. This is in agreement with the work of Escobedo et al.,⁸ where the grain size was not observed to have an effect on spall strength. It has been shown that free-surface based spall strength measurements are not accurate indicators of the amount of internal damage, especially when the damage remains incipient (i.e., there is no spall scab formed).⁵ To examine the internal damage, and demonstrate that there were voids in the samples that would be subjected to recompaction, one of the samples from each spall experiment was sectioned for microscopy. They were cut diametrically, mounted in epoxy, and then ground and polished such that micrographs could be taken normal to the impact direction. These are shown in Fig. 5. A region 14 mm wide by 1.2 mm high, centered around the spall plane, was subjected to a particle size analysis in the ImageJ software package to characterize the void distribution. Table II lists the number of voids, the average void diameter, and the void percentage in the analyzed area, for the two grain sizes.

It is clear that while the PDV data and calculated spall strengths were essentially identical for the two grain sizes, the distribution of damage was markedly different. The overall amount of damage was very similar, with only a 0.1% difference between the two samples. However, this damage amount in the 60 $μ$m sample was made up of a far higher number of smaller size voids when compared to the 200 $μ$m sample. It is well established that spall is a weak-link driven phenomenon, with microstructural features such as grain boundaries,²⁴ impurities,²⁵ and secondary phases,⁶ having important roles as void nucleation sites. This is observed here, with most voids tending to originate at grain boundaries in the 60 $μ$m sample. In the larger 200 $μ$m sample, fewer voids nucleate, due to the reduced number of grain boundaries in the region of maximum tension. However, to accommodate the plastic work, these fewer voids must then grow to a larger size than in the smaller grained sample, hence the relationship between an increased number of voids and a lower average void size.

As described earlier, the samples from each spall experiment that were not sectioned for microscopy were remachined into new target assemblies. For the first recompaction experiment (No. 2), to avoid any spall damage from interacting release waves, the copper flyer-plate was made the same thickness as the sample (3.7 mm). This symmetric impact should have had the rarefactions collide at the flyer–sample interface, avoiding any further damage nucleation in the target. However, it was found that the pre-existing spall damage retarded the initial compressive shock and subsequent rarefaction, shifting the interaction point back into the sample and generating a second spall plane. For this reason, the second recompaction experiment used a thicker (5 mm) copper flyer plate to ensure that rarefactions intersected in the flyer and not the sample. The wave profiles for the two recompaction experiments are shown in Fig. 6.

Using the impedance matching technique, the impacts should have generated peak compressive stresses in the samples of 2.7 GPa and 2.2 GPa in the 60 $μ$m and 200 $μ$m samples, respectively. This is based on the existing Hugoniot data for copper and will only be valid in the sample between the impact face and the pre-existing damage region, where the porosity will mean that conditions are off of the principal Hugoniot. Although the impact velocities were different, both wave profiles share the same overall features and shape. There is a clear elastic wave, with a Hugoniot elastic limit of approximately 0.3 GPa for both samples. While this is still a low value, it is a substantial increase over the values calculated from the first time these samples were shocked and consistent with an increase in the dislocation density from the work introduced by the damage generation experiments.²⁶ 

The time between the elastic precursor and the main shock breakout is far longer than in the initial damage generation experiments. This is consistent with the samples containing damage since porosity reduces the shock velocity in the material.²⁷ The crush-up of the voids and cracks in the damaged sample is the reason for the long rise time of the plastic wave, $∼500$ ns compared with $∼50$ ns in the pristine copper. The dashed horizontal lines indicate the expected peak free-surface velocity for a copper on the pristine copper (without pre-existing damage) impact at the flyer velocities produced. However, both profiles have an initial “shoulder” at this velocity, followed by a spike or overshoot of some 11%, followed by a return to the expected value before rarefaction waves arrive. While it is not certain what is producing this feature, experiments on instabilities such as ejecta—where perturbation features are intentionally placed on the rear free surface of a sample subjected to a planar shock load—have demonstrated jets of material moving at velocities far higher than that of the bulk surface.²⁸ If a high-velocity jet is formed inside these voids, when it impacts the other side of the void, it will generate a second shock in the sample, increasing the stress and, therefore, the particle velocity. Many of these events occurring simultaneously could present as the overshoot feature in the free-surface velocity data. Further efforts modeling this process are needed to confirm this hypothesis.

Figure 7 shows optical micrographs of the recompacted samples, taken at the location of the expected spall plane. It is important to note that these images are taken after chemically etching the surface with an acid-based solution—this preferentially attacks high energy features such as dislocation rich regions and grain boundaries, revealing them under reflected light microscopy. In the as-polished condition (before etching), the samples appeared solid and smooth, with no visible damage or cracks, demonstrating that the voids and cracks generated in the damage experiments were fully recompacted by the second shock experiments, such that after recompaction, there was essentially zero porosity in the samples.

After the etching, as shown in Fig. 7, there was a clear band of perturbed microstructures as seen in the works of Koller, Becker, and Turley described in Sec. I A. This suggests that the recompaction process has brought the damaged material back together and that there is a large amount of plastic work stored in this region. To further investigate the microstructure, electron backscatter diffraction (EBSD) techniques were used. In short, by recording the diffraction patterns made by the backscattered electrons in a scanning electron microscope, the crystallographic orientation at that point can be determined. Rastering this process over a sample surface allows two-dimensional orientation maps to be produced. Figure 8 shows these data plotted two different ways for the same high-magnification region of the recompacted zone in the 200 $μ$m sample (note that the same features were observed in the 60 $μ$m sample). In Fig. 8(a), the data are plotted as an inverse pole figure (IPF) map, showing the crystallographic orientation relative normal to the shock direction. In contrast, Fig. 8(b) shows the same region but now color coded to show the grain reference orientation deviation (GROD). Here, for each grain, the average orientation is calculated, and then for each point in that grain, the color represents the deviation from that average. Hence, a grain containing little to no residual work or damage appears solid blue, with other colors indicating that there is a high amount of rotation and an increased dislocation density present. In both the IPF and GROD maps, black areas are points that could not be indexed confidently and do not represent cracks or voids.

From the IPF map in Fig. 8(a), it is clear that the perturbed band visible in the etched optical micrographs actually consists of very small grains on the order of 100 nm to 10 $μ$m in size. Many of these grains contain twins, while the GROD map also reveals these grains to be almost entirely free of stored work or damage. Either side of this thin band is the original grain that was spalled to contain a void. Both mapping techniques demonstrate that there is a large amount of misorientation and rotation in this material close to the band, which decreases as a function of the distance from the band.

The structure observed at the recompaction interface—small grains, with no stored work, and containing annealing twins—are consistent with the recrystallization of a severely deformed cubic-structured material (as copper is).²⁹ While the temperature required to drive recrystallization depends on the amount of stored work in the material,³⁰ in general, it is around 40% of the melting point, thus approximately 700 K for copper. This temperature is above that expected by the bulk heating of the shock wave, but the additional plastic work and deformation of the jetting and subsequent jet impacts during recompaction could reach temperatures far higher than that. Recovery of jet fragments from copper shaped-charge liners (explosively driven devices designed to generate high-velocity jets of ductile metals) has been found to contain large amounts of a dynamically recrystallized material.³¹ This hypothesis of jetting and the resulting localized heating is also supported by how narrow the recrystallized band is, only 30 $μ$m or so. At distances farther than this from the recompaction interface, the microstructure was observed to still contain a large amount of stored work, suggesting temperatures remained below the recrystallization temperature in the sample bulk during the second shock loading experiments.

The original aims of this study were to confirm that a second shock loading event could recompact existing spall damage and, if so, characterize the resulting microstructure to determine whether the compacted region has any form of bond. We have presented conclusive results, in copper targets confirmed to contain spall damage, that relatively modest shock stresses of 2–3 GPa can fully recompact the damage back to a state of zero porosity.

Where the original spall was present, a thin band of perturbed microstructures was found. This was the case for both the 60 $μ$m and 200 $μ$m grain size samples. The bands had an identical appearance to those observed in the studies of Koller et al.,⁹ Becker et al.,¹³ and Turley et al.,¹⁵ suggesting that recompaction due to a secondary acceleration of the sample by detonation products was responsible for the lack of spall damage observed in the recovered samples by Koller et al.

The overshoot feature observed in both PDV traces for the recompaction experiments is consistent with the sort of jetting or ejecta occurring when the shock wave reaches the existing spall damage. As the shock arrives at one “end” of a roughly spherical void, it will begin to form a high-velocity jet due to the high surrounding stresses being concentrated toward the center of the void.³² When the jet impacts the solid material at the other side of the void, this will launch a second shock wave in the copper, increasing the bulk particle velocity. This could explain the overshoot feature, and efforts to model this in a hydrocode are ongoing.

High-magnification imaging of the recompaction band with electron microscopy techniques revealed that where the initial spall voids have compacted, a combination of stored work and high temperatures has allowed recrystallization to occur (again, the same microstructure was found in both the 60 $μ$m and 200 $μ$m grain size samples). As such, the damaged copper is now both free of voids and has formed new bonds across this damage as opposed to simply pushing the free surfaces together. One would expect that this interface has considerable mechanical strength, and future works will involve carefully sectioning small tensile-test samples from the recompaction band to test this hypothesis. Materials with a far higher melting point (and, therefore, recrystallization temperature) are also being studied.

R. A. Beal and A. Samuel are thanked for their assistance in preparing samples for microscopy. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy (DOE) under Contract No. 89233218CNA000001. The authors are grateful for funding through the U.S. Department of Energy Science Campaign 2; unlimited release: No. LA-UR-20-22889.

The data that support the findings of this study are available from the corresponding author upon reasonable request.