Characterizing the response of metals to direct high explosive (HE) shock loading is a research problem that has been pursued since the earliest days of dynamic material properties research. Early interest was focused on, for the most part, the understanding how energy output from the detonating HE could be best coupled into moving metals in a well characterized way for a broad range of applications. However, as has been clearly shown in the past, spall in the metal is also of concern when loading metals with a detonation wave (which is generally triangular in shape), a shock followed immediately by a more gradual release. Damage or spall occurs because reflection of a triangular wave at a free surface causes the immediate development of tension.1<\/sup><\/a><\/span> Because spall is a complex phenomenon, dependent upon several variables, it is not surprising that spall resulting from triangular wave forms can yield different results than research done using flat top shocks. Flat top shock waves are commonly produced using flyer-plate impacts, for example. The time under stress may be important because work hardening in a ductile metal depends upon the time available for plastic processes, such as dislocation multiplication and glide.2<\/sup><\/a><\/span> Dislocation densities are correlated to increased shock hardening3\u20135<\/sup><\/a><\/span> via increased work hardening, which has been linked to lower spall strengths in some materials. For triangular wave shapes, relatively less time is spent at peak stress, reducing the time for nucleation and growth of damage and possibly leading to a higher spall strength.6,7<\/sup><\/a><\/span> The degree of spall and damage formation is also thought to depend on the peak stress, tensile strain rate, material microstructure, and locations of impurities.8,9<\/sup><\/a><\/span> Of these effects, tensile strain rate is known to have a relatively large effect, and reported variations of spall strength with stress amplitude may actually be a manifestation of changing the tensile strain rate.<\/p>\n In previous studies,6,7<\/sup><\/a><\/span> it was reported that copper targets subjected to compressive and tensile loading from flyer-plate impacts producing flat top and triangular shocks can exhibit free surface velocity profiles indicative of spall, depending on the details of the exact stress-time history applied. When there is a complete spall or a very extensive and continuous plane of damage in a sample, an acoustic wave is trapped in the spall scab and reflects back and forth, leading to a sample free surface velocity profile with oscillations (ringing). The oscillation period is twice the thickness of the spall scab divided by the sound speed. Having such a single-frequency trapped wave is strong evidence of either complete spall or a significant number of voids. For samples that do not spall or damage extensively, there can be a similar ringing, but in this case, the period is often consistent with the full sample thickness. In experiments where the velocimetry indicates spall scab ringing, the metallurgical analysis of the recovered copper samples for various experimental stresses and release rates reveals a variety of conditions, ranging from plastic strain without damage to complete spall. However, the location of the damage plane, whatever be the extent of the damage, is consistent with the ringing period.6,7<\/sup><\/a><\/span> These observations suggest that a free surface velocity measurement is a good indicator of the location of the damage plane, but is not always a reliable indicator of complete spall separation.<\/p>\n Previously, an apparently anomalous result was reported for direct triangle wave loading of copper with the explosive Baratol.10<\/sup><\/a><\/span> No ductile voids or evidence of void or crack coalescence were observed in the cross section of the recovered copper samples, in spite of the fact that the measured wave profiles showed a ringing signature indicative of a spall plane (either complete or with a large population of voids). Instead, the recovered sample showed a metallurgical feature that was at the time interpreted to be localized plastic strain features and high dislocation densities with no evidence for voids. This feature was at the location in the sample where spall damage was expected based upon ringing in the time-resolved free surface data. This data set has raised many questions concerning HE-driven spall damage; the overarching issue is reconciling the time-resolved data, which show strong evidence for considerable spall damage, with the microstructural evidence from the recovered sample.<\/p>\n Subsequent experiments10<\/sup><\/a><\/span> with PBX-9501, a more energetic HE, showed multiple spall and damage layers consistent with the velocity profile. It was postulated that different release rates and\/or local plastic deformation can alter the local impedance of the material enough for acoustic wave reflection without void formation. However, this has not been experimentally verified, and a change in local impedance (a damaged layer) almost certainly could not have caused the kind of ringing observed in the wave profiles. Such a layer would allow for both reflected and transmitted waves, which would alter the nature of the ringing signature. A spall plane would allow for only a reflected wave with a single ringing frequency observed. It is worth noting here that the recovered samples exhibit features from the entire process that the sample was subjected to, from the moment the shock enters the sample until it is recovered and sectioned for metallurgy. Recovery techniques are not capable of providing time resolution of the sample loading and unloading history.<\/p>\n A possible explanation of this behavior was postulated by Becker and LeBlanc.11<\/sup><\/a><\/span> They suggested that the damaged zone could be recompressed after void formation using a shock wave of sufficiently high stress. Specifically, they proposed that if a sufficiently strong recompression wave follows tension, the recompression can drive the damaged layer back together, causing the voids to collapse and the spall-induced surfaces to \u201cstick\u201d back together. They further postulated that collapsed voids might not be readily apparent in subsequent metallurgical analysis of the recovered sample. They conducted gas gun experiments with a layered flyer plate to drive a recompression shock into the spalled target and determined that their experimental results support their hypothesis. They found highly strained material where the spall plane was expected, but there were no remaining voids in the optical images of the recovered samples. More detailed analysis using electron backscatter diffraction revealed highly localized plastic deformation and the remnants of what were interpreted to be collapsed voids. Others have also used layered flyer plates to produce spall and recompression.12<\/sup><\/a><\/span><\/p>\n For HE drive, spall may occur while the sample is still being accelerated by the detonation product gases. Tension from release at the free surface can pull the spall scab away from the sample, and it can coast at a constant velocity for a while. If the HE product gases continue to accelerate the remaining sample sufficiently, it may impact the scab and cause recompression and acceleration of the scab. Details of this recompression will depend upon the thickness (or mass) of the remaining target and the explosives used. Fig. 1<\/a><\/span> is a notional time versus position diagram for an HE-driven experiment with spall and recompression. The initial shock front (a) is reflected at the free surface (b) as a release wave and interacts with the still oncoming Taylor wave release, creating tension and spall at (c) and perhaps also later at (d). A trapped wave (e) in the spall scab (f) causes the characteristic ringing in free surface velocity profiles, but on average, the scab travels with a constant speed. A trapped wave (g) rings in the remainder of the sample, which continues to accelerate because the HE product gases are still under pressure. Eventually, the sample can catch up to and impact (h) the spall scab and recompress the spall plane. After recompression, both waves (e) and (g) may be able to pass through the spall plane.<\/p>\n Click to view<\/p>\n<\/div>\n The fundamental question in this argument arose: Can the spall scab and the remaining sample be recompressed together in such a way as to \u201cweld\u201d them back together and leave the metallurgical \u201cscar\u201d observed in the recovered sample? Answering this question was the primary motivation for this research. Detailed simulations using the CTH hydrodynamics code13<\/sup><\/a><\/span> were done to see if the fundamental governing equations, as solved numerically, support this possibility. Results support the hypothesis that, depending upon sample thickness, a sample could be spalled, and then, the pieces pushed back together by continued drive from the HE product gases. The details were somewhat different, but the overall features were captured. We plan to document these results in a future publication.<\/p>\n In the Baratol experiment,10<\/sup><\/a><\/span> the velocimetry data also showed an increase in particle velocity (usually indicative of a wave arrival) at late times, but the published data were truncated because it was believed that the increase was caused by edge releases. These data might also be interpreted to mean that the copper sample spalled, but later push by HE products caused a recompression event that essentially welded the sample back together. However, we note that in Ref. 10<\/a><\/span> the authors state that the post-recovery metallurgical analysis yields no evidence supporting such a recompression event. This discrepancy indicates a strong need to do further experimentation.<\/p>\n Click to view<\/p>\n<\/div>\n The experimental configuration is shown schematically in Fig. 2<\/a><\/span>. We used a 5- or 6-layer stack of 25\u2009mm diameter by 1.7\u2009mm thick sheets of Detasheet to produce a peak shock stress very close to that of Baratol, which is no longer readily available. This was done to allow comparison with the previous experiments10<\/sup><\/a><\/span> that used Baratol drive. The HE is axially detonated with an RP-1 detonator. This yields a slightly divergent, nearly 1-D shock wave in the sample.<\/p>\n Click to view<\/p>\n<\/div>\n To minimize the effects of wave releases from the edge of the 25\u2009mm diameter HE drive, we used only the center 10\u2009mm of the target for our analysis. The copper target was a 10\u2009mm diameter disk press fit into a guard ring14<\/sup><\/a><\/span> (40\u2009mm outer diameter and 10\u2009mm inner diameter) of similar copper with an interference fit and no measureable gap. After assembly, the target was polished flat to the final thickness of 0.6 to 4.3\u2009mm. The guard ring formed a momentum trap for edge releases, allowing planar compression but no significant radial tension in the central sample, thereby minimizing 2-D perturbations. Often, momentum-trapping rings used on gas gun experiments require several components.15<\/sup><\/a><\/span> Since our HE drive has a slightly curved shock front, we are able to use 2-D hydrocode simulations to design a single guard ring that quickly pulls away from the sample, leaving a gap between the sample and ring while the sample remains relatively flat. All targets were prepared from 99.99% pure oxygen-free, high-conductivity (OFHC) copper (c10100 specification). The center 10\u2009mm portion was from a sample annealed under vacuum at 600\u2009\u00b0C for 1 h, resulting in an average grain size of 40\u2009\u03bc<\/span>m.<\/p>\n A steel stripper (a steel plate with a hole that allows only the center 10\u2009mm sample to pass) kept the guard ring fragments from impacting the target during soft recovery in a ballistic gel. After the sample passed the steel stripper and pellicle turning mirror, a single-pulse flash x-ray system provided a radiographic image of the target before it entered the ballistic gel and was captured. These images were taken about 100\u2009\u03bc<\/span>s after detonation to verify the shape and trajectory of the 10\u2009mm center of the target. After an HE experiment, the sample was recovered from the ballistic gel. The shock stress generated in the samples when striking the gel ranged from 2 to 4\u2009GPa because of the relatively high velocity imparted to the sample by the HE drive. These are significant reshocks.<\/p>\n<\/div>\n Click to view<\/p>\n<\/div>\n The shock breakout velocity decreases with increasing sample thickness, as expected for decaying shock waves, because the releasing wave overtakes the leading shock as it propagates. Peak shock stresses near the free surface just prior to the shock breakout were about 27\u2009GPa for the 0.6\u2009mm sample and decreased to about 17\u2009GPa for the 4.3\u2009mm sample. The release rate immediately after the shock breakout also decreases with sample thickness, from 2100\u2009m s\u22121\u2009<\/sup>\u03bc<\/span>s\u22121<\/sup> at 0.6\u2009mm to 630\u2009m s\u22121\u2009<\/sup>\u03bc<\/span>s\u22121<\/sup> for 4\u2009mm thickness. Consequently, the damage layer is expected to form deeper into the sample for thicker samples. The ringing period shows that the putative damage layer forms at 0.17\u2009mm for a sample thickness of 0.6\u2009mm and at 0.43\u2009mm for a sample thickness of 4.3\u2009mm. The depth of the spall signature from each experiment is used to estimate the spall strength, which shows some dependence on the sample thickness and has values around 3.5\u2009GPa (Table I<\/a><\/span>). This approximate value was calculated using the momentum shock jump condition<\/p>\n where \u03c1<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n The 3.0\u2009mm and 4.3\u2009mm samples, shots 4 and 5, did not show any late-time reshock in the velocimetry records, suggesting that these heavier bulk samples never caught up to the spall scabs. X-ray images, described below in Section II\u2009E, show a spall scab that was nearly detached from the sample for shot 4 and a scab that was completely detached for shot 5.<\/p>\n The measured spall scab coast velocities and asymptotic bulk sample velocities are plotted as a function of sample thickness in Fig. 4<\/a><\/span>. In the case of the 4.3\u2009mm sample, the spall scab completely detached from the bulk sample, so we estimated the bulk sample velocity from the timing information obtained from the x-ray image of this experiment. For samples thinner than 2.2\u2009mm, the asymptotic velocity was higher than the spall scab coast velocity, and the bulk sample impacted the spall scab and recompressed the sample. For samples thicker than 2.2\u2009mm, recompression cannot occur and complete spallation is expected, as shown in Fig. 4<\/a><\/span>. It is important to note that the details of the coast and asymptotic velocities are dependent on the geometry of the HE package and are specific to our experiments. Experiments done with different kinds of HE would differ in detail. However, similar qualitative trends are expected for a wide variety of HE experiments.<\/p>\n Click to view<\/p>\n<\/div>\n It is interesting to compare shots 5 and 6, which were a 4.3\u2009mm thick copper sample driven by a Detasheet shock and a 2.2\u2009mm thick sample driven by NM, respectively. The velocimetry from these shots is plotted in Fig. 5<\/a><\/span>. As can be readily observed, the peak shock stresses and the release rates were similar. Consequently, we expect the initial damage should be similar as well. The recovered samples are shown in Fig. 6<\/a><\/span>. The recovered sample from shot 5 shows a separate spall scab, while the sample from shot 6 does not. (This will also be evident in the x-rays, Section II\u2009D<\/a><\/span>.) The principal difference is that only shot 6 had a recompression wave. As described above, the thicker sample does not accelerate enough to overtake its spall scab.<\/p>\n![\"\"](\"http:\/\/scitation.aip.org\/docserver\/ahah\/fulltext\/aip\/journal\/jap\/120\/8\/1.4962013.figures.online.f1_thmb.gif\")
<\/a><\/p>\n![\"TABLE](\"http:\/\/scitation.aip.org\/images\/jp\/table_thmb.gif\")
<\/a>TABLE I.<\/span><\/p>\n![\"\"](\"http:\/\/scitation.aip.org\/docserver\/ahah\/fulltext\/aip\/journal\/jap\/120\/8\/1.4962013.figures.online.f2_thmb.gif\")
<\/a><\/p>\n![\"\"](\"http:\/\/scitation.aip.org\/docserver\/ahah\/fulltext\/aip\/journal\/jap\/120\/8\/1.4962013.figures.online.f3_thmb.gif\")
<\/a><\/p>\n![\"\"](\"http:\/\/scitation.aip.org\/docserver\/ahah\/fulltext\/aip\/journal\/jap\/120\/8\/1.4962013.figures.online.f4_thmb.gif\")
<\/a><\/p>\n
![\"\"](\"http:\/\/scitation.aip.org\/docserver\/ahah\/fulltext\/aip\/journal\/jap\/120\/8\/1.4962013.figures.online.f5_thmb.gif\")
<\/a><\/p>\n