Explosive induced shock damage in copper and recompression of the damaged region

Explosive induced shock damage in copper and recompression of the damaged region Explosive induced shock damage in copper and recompression of the damaged region W D Turley, , G D Stevens, R S Hixson,[.]

Explosive-induced shock damage in copper and recompression of the damaged region , W D Turley , G D Stevens, R S Hixson, E K Cerreta, E P Daykin, O A Graeve, B M La Lone, E Novitskaya, C Perez, P A Rigg, and L R Veeser Citation: J Appl Phys 120, 085904 (2016); doi: 10.1063/1.4962013 View online: http://dx.doi.org/10.1063/1.4962013 View Table of Contents: http://aip.scitation.org/toc/jap/120/8 Published by the American Institute of Physics JOURNAL OF APPLIED PHYSICS 120, 085904 (2016) Explosive-induced shock damage in copper and recompression of the damaged region W D Turley,1,a) G D Stevens,1 R S Hixson,2,3 E K Cerreta,3 E P Daykin,4 O A Graeve,5 B M La Lone,1 E Novitskaya,5 C Perez,4 P A Rigg,6 and L R Veeser1,3 National Security Technologies, LLC, Special Technologies Laboratory, Santa Barbara, California 93111, USA National Security Technologies, LLC, New Mexico Operations, Los Alamos, New Mexico 87544, USA Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA National Security Technologies, LLC, North Las Vegas Operations, North Las Vegas, Nevada 89030, USA University of California, San Diego, La Jolla, California 92093-0411, USA Washington State University, Pullman, Washington 99164, USA (Received 20 May 2016; accepted 19 August 2016; published online 31 August 2016) We have studied the dynamic spall process for copper samples in contact with detonating lowperformance explosives When a triangular shaped shock wave from detonation moves through a sample and reflects from the free surface, tension develops immediately, one or more damaged layers can form, and a spall scab can separate from the sample and move ahead of the remaining target material For dynamic experiments, we used time-resolved velocimetry and x-ray radiography Soft-recovered samples were analyzed using optical imaging and microscopy Computer simulations were used to guide experiment design We observe that for some target thicknesses the spall scab continues to run ahead of the rest of the sample, but for thinner samples, the detonation product gases accelerate the sample enough for it to impact the spall scab several microseconds or more after the initial damage formation Our data also show signatures in the form of a late-time reshock in the time-resolved data, which support this computational prediction A primary goal of this research was to study the wave interactions and damage processes for explosives-loaded copper and to look for evidence of this postulated recompression event We found both experimentally and computationally that we could tailor the magnitude of the initial and recompression shocks by varying the explosive drive and the copper sample thickness; thin samples had a large recompression after spall, whereas thick samples did not recompress at all Samples that did not recompress had spall scabs that completely separated from the sample, whereas samples with recompression remained intact This suggests that the hypothesized recompression process closes voids in the damage layer or otherwise halts the spall formation process This is a somewhat surprising and, in some ways controversial, result, and the one that warrants further research in the shock compresC 2016 Author(s) All article content, except where otherwise noted, is licensed sion community V under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/ 4.0/) [http://dx.doi.org/10.1063/1.4962013] I INTRODUCTION 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 Because spall is a complex phenomenon, dependent upon several variables, it is not surprising that spall resulting a) Author to whom correspondence should be addressed Electronic mail: turleywd@nv.doe.gov 0021-8979/2016/120(8)/085904/11 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 Dislocation densities are correlated to increased shock hardening3–5 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 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 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 120, 085904-1 C Author(s) 2016 V 085904-2 Turley et al In previous studies,6,7 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 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 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 Previously, an apparently anomalous result was reported for direct triangle wave loading of copper with the explosive Baratol.10 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 timeresolved 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 Subsequent experiments10 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 J Appl Phys 120, 085904 (2016) sectioned for metallurgy Recovery techniques are not capable of providing time resolution of the sample loading and unloading history A possible explanation of this behavior was postulated by Becker and LeBlanc.11 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 spallinduced surfaces to “stick” 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 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 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 The fundamental question in this argument arose: Can the spall scab and the remaining sample be recompressed together in such a way as to “weld” them back together and leave the metallurgical “scar” observed in the recovered sample? Answering this question was the primary motivation for this research Detailed simulations using the CTH hydrodynamics code13 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 085904-3 Turley et al J Appl Phys 120, 085904 (2016) FIG Notional time (t) versus position (x) diagram for a metal driven by HE Metal-vacuum and HE-metal boundaries are solid blue lines and metalspall layer boundaries are dashed blue lines Shocks are shown as solid black or red arrows and rarefaction fronts are dotted (a) Detonation wave from HE; (b) free surface; (c) initial spall; (d) possible second spall; (e) ringing in spall scab; (f) spall scab; (g) ringing in sample; and (h) shock wave in sample (which begins to recompress damage region) the overall features were captured We plan to document these results in a future publication In the Baratol experiment,10 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 the authors state that the post-recovery metallurgical analysis yields no evidence supporting such a recompression event This discrepancy indicates a strong need to further experimentation II EXPERIMENT A Description To test the recompression hypothesis, we executed a set of HE experiments in which we varied the details of recompression to look for a sudden late-time increase in the surface velocity after spall formation We used the computer simulations to help guide this process The goal was to determine whether recompression can close the voids formed during spallation (or recompress a full spall plane back together) in a manner similar to the layered flyer plate experiments done by Becker et al.11 The dynamic processes caused by the direct HE drive were studied using free surface optical velocimetry and pulsed x-ray radiography After soft recovery, the samples were analyzed using optical imaging and microscopy We fielded five experiments shocked by Detasheet explosive, and we varied the sample thickness to tailor the amplitude of the recompression pulse In addition, we fielded a shot driven by a 25 mm diameter by 14 mm thick sample of nitromethane (NM) sensitized with 0.2% diethylenetriamine Its Chapman-Jouguet (CJ) stress is less than for Detasheet In the NM experiment, the objective was to use a relatively thin sample to be able to match the observed free surface velocity of a Detasheet experiment done with a thicker sample Table I shows the copper sample thicknesses and shock parameters The experimental configuration is shown schematically in Fig We used a 5- or 6-layer stack of 25 mm diameter by 1.7 mm 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 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 To minimize the effects of wave releases from the edge of the 25 mm diameter HE drive, we used only the center 10 mm of the target for our analysis The copper target was a 10 mm diameter disk press fit into a guard ring14 (40 mm outer diameter and 10 mm 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 mm 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 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 mm portion was from a sample TABLE I Experimental shot parameters Experiment (Shot No.) (141107) (141120) (140522) (141119) (140523) (140424) a Sample thickness (mm) HE drive Peak stress (GPa)a Spall stress (GPa) Recompression amplitude (m/s) 0.6 1.0 1.9 3.0 4.3 2.2 Detasheet Detasheet Detasheet Detasheet Detasheet Nitromethane 27.1 25.1 22.4 19.5 16.7 15.7 3.1 2.7 2.5 2.5 2.2 2.0 336 241 91 None None 90 Peak stress near the rear free surface of the sample prior to the shock wave breakout 085904-4 Turley et al J Appl Phys 120, 085904 (2016) FIG Schematic diagram of the experimental setup The sample thickness, Dx, varies from 0.6 to 4.3 mm annealed under vacuum at 600  C for h, resulting in an average grain size of 40 lm A steel stripper (a steel plate with a hole that allows only the center 10 mm 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 ls after detonation to verify the shape and trajectory of the 10 mm 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 to GPa because of the relatively high velocity imparted to the sample by the HE drive These are significant reshocks B Velocimetry We used photonic Doppler velocimetry16 (PDV) to measure the free surface velocity profiles of the shocked samples for 30 ls or longer after detonation The velocities of the surfaces are shown in Fig All velocities show a sudden shock wave followed by Taylor wave-like development of dynamic tension with oscillations consistent with the formation of a damage layer within the sample in the early portion of the experiment 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 GPa for the 0.6 mm sample and decreased to about 17 GPa for the 4.3 mm sample The release rate immediately after the shock breakout also decreases with sample thickness, from 2100 m s1 ls1 at 0.6 mm to 630 m s1 ls1 for mm 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 mm for a sample thickness of 0.6 mm and at 0.43 mm for a sample thickness of 4.3 mm 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 GPa (Table I) This approximate value was calculated using the momentum shock jump condition rspall ¼ q0 Cb Duf s ; (1) where q0 is the initial density, Cb is the bulk sound velocity, and Dufs is the change in the free surface velocity from the peak value to the first minimum The velocity oscillations from the trapped acoustic wave damp out within 1 ls after the shock wave breakout, and the velocity then reaches a quasi-steady value (labeled as the spall scab coast velocity in Fig 3(a)) The existence of a constant velocity shows that there is little to no stress acting on the spall layer during the time of coasting of the scab Consequently, this layer of the material (between the free surface and the damage region) is not strongly attached to the bulk sample, which continues to undergo acceleration from the high-pressure HE product gases that have not yet dissipated This behavior strongly suggests that this layer is a nearly free spall scab for some time After a period of coasting, samples that were 2.2 mm and thinner undergo an apparent recompression, postulated to be from the bulk sample catching up and impacting the spall scab The thinnest samples were accelerated to the highest asymptotic velocities by 085904-5 Turley et al J Appl Phys 120, 085904 (2016) FIG Measured spall scab coast velocity (open green circles) and asymptotic bulk velocity (filled blue circles) as a function of copper sample thickness The solid lines are a guide for the eye FIG Velocity records of each of the Detasheet-driven copper experiments (a) Spall ringing and recompression in the first ls after breakout (b) The entire record, including the asymptotic velocities of the samples (except the 4.3 mm sample, in which the spall scab completely detached from the bulk) the HE product gases Therefore, the recompression pulses occurred earlier and were larger for thinner samples Following the reshock signal, longer-period velocity oscillations are present; these ringing periods are consistent with the full sample thickness, indicating that the scab layer is no longer detached from the bulk sample and the acoustic waves are free to transverse the damaged region If the scab had never detached, these long period oscillations would have been present throughout the coasting part of the record Our hypothesis is that this recompression shock causes the damage to be recompacted and modified We further postulate that upon recompression, the damaged surface is compressed sufficiently to allow the trapped acoustic waves to pass through it at late times without a significant change, causing the ringing period to be consistent with the full sample thickness The 3.0 mm and 4.3 mm samples, shots 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 E, show a spall scab that was nearly detached from the sample for shot and a scab that was completely detached for shot The measured spall scab coast velocities and asymptotic bulk sample velocities are plotted as a function of sample thickness in Fig In the case of the 4.3 mm 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 mm, 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 mm, recompression cannot occur and complete spallation is expected, as shown in Fig 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 It is interesting to compare shots and 6, which were a 4.3 mm thick copper sample driven by a Detasheet shock and a 2.2 mm thick sample driven by NM, respectively The velocimetry from these shots is plotted in Fig As can be FIG Velocimetry measurements for shots and The velocity for shot remained roughly constant or decreased during the entire 25 ls of recorded data Although the two experiments have nearly the same release rates and peak free surface velocities (and stresses), only shot 5, too thick to have a recompression signal, produced a separate spall scab 085904-6 Turley et al J Appl Phys 120, 085904 (2016) 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 The recovered sample from shot shows a separate spall scab, while the sample from shot does not (This will also be evident in the x-rays, Section II D.) The principal difference is that only shot had a recompression wave As described above, the thicker sample does not accelerate enough to overtake its spall scab C Maximum distension before recompression It is instructive to consider the amount of distension that occurs during spallation prior to recompression of the damage layer for metallurgical analysis Using the velocity data, we constructed a simple model to estimate the maximum separation distance between the spall scab and the underlying material before it is recompressed (see the Appendix) We calculated the maximum distension of the center of the damage zone for experiments with recompression to be 30 lm for the 0.6 mm sample, 60 lm for the 1.0 mm sample, and 430 lm for the 1.9 mm sample We therefore not expect any voids to have grown larger than these values prior to recompression D X-ray images X-ray images of the copper samples from the Detasheet experiments are shown in Fig These images were taken approximately 100 ls after detonation, which is later than the PDV can track the velocity but before the samples enter the ballistic gel for soft recovery The 0.6 mm, 1.0 mm, and 1.9 mm samples, as well as the NM sample, were intact with no indication of spallation The center portion of the 0.6 mm sample was, however, somewhat curved For the 4.3 mm thick sample, the spall layer was completely separated from the bulk sample The 3.0 mm sample shows a spall scab that was still somewhat attached, at least at the edges, but the center portion was separated or distended 2 mm from the bulk sample The faint white line between the spall layer and the bulk sample indicates that the damage layer is radiographically thin, so it must contain, at a minimum, a high percentage of voids, or it may even be completely detached When recovered, the mm thick sample was back in one piece, with a thickness slightly smaller than the preexperiment thickness As discussed above, there can be a FIG Samples recovered from shots (left) and (right) For shot 5, the spall scab flew ahead of the sample and was found in the recovery gel in roughly the position shown The sample for shot is shown with its free surface side up and has a circumferential defect near the top that is consistent with the spall layer thickness as determined from the post-spall ringing in the velocimetry FIG X-ray images of the samples in-flight about 100 ls after the explosive detonations The samples are moving from bottom to top in the images A radiographically thin white line is labeled in the 3.0 mm Cu image The 4.3 mm image shows that the spall scab is completely detached from the sample The scab is rotated in this image, probably due to striking the pellicle mirror significant reshock when the sample impacts the ballistic gel used for soft recovery It is worth considering the possibility that this process caused the sample to be recovered in one piece despite the clear evidence from the x-ray image that it spalled This will be looked at in more detail in future research The x-ray images are consistent with the spall and recompression hypothesis as discussed above III METALLURGICAL ANALYSES OF RECOVERED SAMPLES In the Baratol-based experiments,10 a metallurgical “scar” was observed at the approximate distance from the free surface as predicted for spall to have occurred (based upon the ringing period in the velocimetry data) Nevertheless, the authors rule out the possibility that their sample was recompressed because there was no evidence of ductile failure, such as void formation or coalescence Although there was evidence for localized plastic strain, the grain structure surrounding the metallurgical feature remained largely undisturbed It is worth noting that a recent reexamination of the velocimetry results for times beyond where the velocity waveform was truncated in Ref 10 showed a recompression wave very similar to that observed in our Detasheet experiments In Fig 8, we show data from that experiment as reanalyzed over a longer time frame Early times show a typical triangular-wave spall signature with associated ringing, and late times show a 085904-7 Turley et al J Appl Phys 120, 085904 (2016) reported by both Becker11 and Koller10 in their results This band is very close to the location predicted from the period of ringing in the velocimetry from this experiment Before shock deformation, the copper metal used in our experiments contained grains of sizes that ranged from 10 lm to greater than 100 lm, as shown in the optical micrographs of Figs 10(a) and 10(b) They also had some texture to them, as observed in the scanning electron micrograph (SEM) of Fig 10(c) The texturing is more clearly observed on the grains of darker contrast, which happen to be optimally oriented for best texture imaging The lighter grains exhibit a homogeneous surface that is lightly etched After impact, the samples show significant deformation, depending upon the sample thickness SEM pictures of the FIG Data from P022 (Baratol) lens on OFHC copper, LANL shot 8872.10 In that paper, the record is truncated around ls after shock breakout recompression pulse The late-time (5 ls) increase in particle velocity was ignored at that time, believed to be caused by edge release waves We also note that micrographs made using optical imaging and orientation imaging microscopy (Fig of Ref 10) show a metallurgical feature about mm from the free surface, which is similar to the distance calculated from the ringing structure in the time-resolved data (Table I of Ref 10) The authors concluded that these features were not evidence for spall having occurred This brings into focus the fundamental issue: the time-resolved data showed clear evidence for spall damage, but the microstructural analysis did not We have looked at some of our recovered samples using optical imaging The analysis of the complete set of recovered samples is an ongoing process and will continue into the future as resources allow We show here early results from our 1.9 mm sample driven by Detasheet explosive Fig is a photograph, made with an optical microscope, of a cross section of the center part of this sample The sample was cut through a radius and then polished and etched We see evidence for a band of perturbed microstructure similar to that FIG Cross section of the center portion (3 mm wide) of the recovered 1.9 mm copper sample driven at the bottom by Detasheet explosive The damaged layer is about 0.43 mm from the free surface at the top of the sample FIG 10 (a) and (b) Optical micrographs and (c) SEM image of the unshocked copper sample microstructure 085904-8 Turley et al J Appl Phys 120, 085904 (2016) 1.9 mm specimen (Fig 11) were found to be completely different in morphology when compared to the pristine copper specimens This sample shows definite inhomogeneities reminiscent of highly deformed and recrystallized copper in the presumed spall region, not surprising if one assumes a significant increase in temperature17,18 during the tensile strain process Note that the shock that initially compresses the target carries a stress that is estimated to cause a relatively minor (