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International Journal of Impact Engineering 38 (2011) 892e899

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International Journal of Impact Engineering

journal homepage: www.elsevier .com/locate/ i j impeng

Penetration response of silicon carbide as a function of impact velocity

Charles E. Anderson Jr. a,*, Thilo Behner b, Timothy J. Holmquist c, Dennis L. Orphal d

a Engineering Dynamics Department, Southwest Research Institute, P.O. Drawer 28510, San Antonio, TX 78228-0510, USAb Fraunhofer Institut fur Kurzzeitdynamik, Eckerstr. 4, 29104 Freiburg, Germanyc Southwest Research Institute, 5353 Wayzata Blve, Minneapolis, MN 55416, USAd International Research Associates, 4450 Pleasanton, CA 94566, USA

a r t i c l e i n f o

Article history:Received 19 April 2011Received in revised form6 June 2011Accepted 8 June 2011Available online 21 June 2011

Keywords:Silicon carbidePenetration velocityDamageSteady-state penetration

* Corresponding author. Tel.: þ1 210 522 2313.E-mail address: canderson@swri.edu (C.E. Anderso

1 According to Dr. R. Palika, President of BAE Systesion, the composition of SiC-B and SiC-N is the sammanufacturing process was changed for SiC-N, whiballistic performance.

0734-743X/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.ijimpeng.2011.06.002

a b s t r a c t

Reverse ballistic experiments were used to investigate confinement, pre-damaged and intact, and rodsize effects on penetration of long, gold rods into silicon carbide (SiC-N). Rod diameters were 1.0 mm and0.75 mm, and lengths were 70 mm and 50 mm, respectively. Within data scatter, penetration velocitywas the same for intact (bare or sleeved), pre-damaged (thermally shocked with non-contiguous cracks),and in situ comminuted SiC-N. Penetration velocity was independent of rod diameter within the datascatter. An expression for the penetration velocity versus impact velocity is found using linear regression.It is proposed that the reason there is no difference in the penetration rate between intact and pre-damaged (failed) SiC is because, after the first few microseconds following impact, the rod penetratesfailed material in both cases.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Orphal and Franzen [1] conducted an experimental study con-cerning the penetration behavior of silicon carbide (SiC-B) usinga tungsten rod at impact velocities between 1.5 and 4.6 km/s. Theexperiments were conducted in the reverse ballistic mode wherethe SiC target was launched at the penetrator, which was sus-pended in the flight path. More recently, another experimentalstudy was conducted, similar to that of Ref. [1], but the velocityrange was 2.0e6.2 km/s, and a gold (Au) rod was used for thepenetrator [2]. Additionally, in the newer study, SiC-N was usedinstead of SiC-B, although no differences were observed in thepenetration of the two types of SiC1 at these high impact velocities[2]. Another difference between the two sets of experiments wasthat the SiC-B was confined within a titanium sleeve in Ref. [1],whereas the ceramic specimenwas bare in Ref. [2]. The objective ofthese latter experiments was to investigate whether or not a failurewave or failure front exists that could be detected by a change inpenetration resistance. No effect of a failure front was detectedwithin the penetrationetime results.

n).ms Advanced Ceramics Divi-e; however, the proprietarych has resulted in improved

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It has been very difficult to obtain independent laboratorymeasurements of the constitutive parameters for failed ceramicsbecause they are so strong (e.g., loading platens fail before theconfined specimen; confining sleeves yield and limit confiningpressures, etc.). It was decided that a series of experiments tomeasure the penetration performance of a ceramic material withinitially different strengths [3] would be of value for the study anddevelopment of computational ceramic constitutive models.Therefore, to assist in the determination of the strength of failedceramic, ballistic experiments were performed on cylindrical SiC-Ntargetswith threedifferent grades ordegrees of pre-impact damage,described in Section 3.1. These variously damaged ceramics, con-tained in an Al-sleeve, were launched in the reverse ballistic modeagainst stationary gold rods. Impact velocities ranged from 1 to3 km/s.

Additional experiments were conducted to extend the experi-mental database for one of the types of pre-damaged ceramic tolower impact velocities [4]. Some of the impact velocities over-lapped with the previous data so that direct comparisons could bemade between the new and older data. The results of theseexperiments are shown in Section 3.1. Additionally, experimentswere conducted with intact ceramic inserted into the aluminumsleeve. A major conclusion resulting from analysis of the combineddata sets of Refs. [3e6] was that, within data scatter, there is nodifference in the penetration rate of intact (sleeved) SiC ceramic versuspre-damaged (sleeved) SiC ceramic.

C.E. Anderson Jr. et al. / International Journal of Impact Engineering 38 (2011) 892e899 893

The penetration rate of the intact bare SiC-N specimens reportedin Ref. [2] is consistently lower than for the intact sleeved SiC-Ntargets reported in Ref. [4]. Besides the absence or presence of analuminum sleeve (with a cover plate), the diameters of the Au rodswere different. In Ref. [2], the rod diameter was 0.75 mm (50-mmlong). In the subsequent work [3,4], the rod diameter wasincreased by 33% to 1.0 mm (70-mm long) to facilitate handling ofthe Au rod.

It was decided to investigate if a scaling effect of the roddiameter could be the reason for differences in the penetrationrates of the two intact SiC-N data sets. A test series using the twodifferent rod diameters against bare (not sleeved) SiC-N was con-ducted. The test set-up was similar to the earlier experiments. Allspecimens were launched in the reverse ballistic mode againststationary Au rods. Penetration of the gold rod was monitored withfive flash X-ray tubes. Impact velocities ranged from 2 km/s to3 km/s. Results of these eleven experiments are presented here andcompared with the other data. It will be shown that the penetrationrate into SiC-N is independent of the initial condition of the ceramic(intact or pre-damaged), and independent of bare or confined in analuminum sleeve. A possible explanation is proposed for thisobservation. An expression for the penetration velocity as a func-tion of impact velocity is found using linear regression analysis.

2. Experimental procedures

2.1. SiC-N targets

The ceramic samples were SiC-N cylinders from BAE SystemsAdvanced Ceramics Division (formerly Cercom), with a 18 or 20-mm diameter and a length of 35 mm. The measured properties ofthe SiC-N are: density¼ 3.21 g/cm3; longitudinal veloc-ity¼ 12.27 km/s; shear wave velocity¼ 7.74 km/s; Poisson’sratio¼ 0.17; Young’s modulus¼ 450 GPa; and shear mod-ulus¼ 192 GPa. These properties were measured/provided by BAESystems, and agree within measurement accuracy the properties ofother lots of SiC-N that have been produced by BAE Systems used inprevious studies [2e6].

2.2. Projectiles

The pure gold rods had a diameter of either 0.75 mm or 1.0 mm,and a length of either 50 mm or 70 mm. Properties of the Au rodare: density, rp¼ 19.3 g/cm3; hardness¼ 65 HV5; UTS¼ 220 MPawith an elongation of 30%. The 0.75-mm diameter rods were fromthe original 2004, Ref. [2], tests. The 1.0-mm rods were from the2006/7, Refs. [3e5], tests. Au was used for the rod material toreduce the effect of rod strength while maintaining a high density[7]. Fig. 1 shows the rod and target dimensions at the same scale.

Fig. 1. Dimensions of rod and target to scale.

2.3. Reverse ballistic test methodology

The reverse ballistic method was used in conducting theexperiments; the test set-up was similar to the experiments donein Refs. [2e6]. The arrangement for the impact tank is shown inFig. 2. Depending upon the impact velocity, the SiC targets werelaunched either from a powder gun or two-stage light-gas gun. Theexperiments used a single piece sabot.

The Au rod was aligned in the trajectory by laser light reflectionfrom the blunt nose of the rod with yaw angles <�0.1�. The rear ofthe rod was inserted in a Styrofoam holder which allowed adjust-ment in three dimensions. The rod was positioned about 2 m fromthe gun muzzle.

Penetration (and dwell) was observed with five 180-kV flashX-rays. The X-ray film was placed 200 mm from the trajectoryinside the tank and had the shape of a circular segment. The timemeasurements for the flash X-ray pictures are very accurate (betterthan �5 ns). Thus, the error for the velocities determined from theX-ray pictures rests in the accuracy of the position measurement,which is on the order of �0.1 to 0.15 mm. For some experiments,a high-speed video camera (Shimadzu HPV-1) was used to monitorthe impact process optically. That camera took a video sequencewith an interframe time of 2 ms and an exposure time per frame of0.5 ms.

3. Investigation of rod size effect on penetration velocity

3.1. Previous work

Pre-damaged SiC-N specimensdwith a diameter of 18 mm anda lengthof 35 mmdwereplaced inside (slipfit) a7075-T6aluminumsleeve of 31.5-mm outer diameter and 45-mm length (Fig. 3). The7075-T6 base plate was machined with a 45-deg bevel, and thenwelded to the cylindrical sleeve. After the specimen was insertedinto the Al-sleeve, a 7075-T6 cover plate was press-fit into placeusing superglue. Three specimen typeswere prepared.1) Thermallyshocked (TS): pre-damage, in the form of non-contiguous cracks,was induced by 3 cycles of heating the specimen for one hour at750 �Cwitha subsequent icewaterquench; thereafter, placing in theAl-sleeve. Although cracked, the specimens had integrity andstrength. 2) Thermally shocked/cyclic loaded (TS/CL or in situcomminuted): specimens were thermally shocked as above andthen subjected to six MTS machine loading/unloading cycles to1.7 GPa while in the aluminum sleeve. After the cyclic loading, theloading anvils were removed and the cover and base plates wereapplied. The specimen, if removed from the aluminum sleeve, hadinterlocked comminuted pieces, and crumbled easily under a very

Fig. 2. Test set-up.

Fig. 3. Test specimen with aluminum sleeve and cover plates (dimensions in mm).

2 The compacted powder results and the hydrodynamic lines are deleted fromFig. 5 for clarity.

C.E. Anderson Jr. et al. / International Journal of Impact Engineering 38 (2011) 892e899894

smalld“finger-pressure”dapplied load. 3) Compacted powder(CP): SiC-N powderwas placed into the Al-sleeve through a series ofincremental pours and compaction using an MTS machine,achieving 72e73% of the theoretical density of SiC-N (rcomp.

powderz 2.35 g/cm3). (Compacted powder is not a pre-damagedceramic; it is the raw material from which the intact SiC is fabri-cated. But for purposes of this article,wewill use theword “damage”to describe all three specimen types.)

For these experiments, the ceramic specimen was launched ata suspended gold rod with a diameter of 1.0 mm and length of70 mm. The slope of the penetrationetime (Pet) least-squareslinear regression gives the penetration velocity, u. Additionaldetails on the experiments can be found in Ref. [3]. The thermallyshocked targets were launched at high velocities (>2.2 km/s); all ofthese had steady-state penetration. Steady-state penetration wasobserved for impact velocities above 1.8 km/s for the in situcomminuted (TS/CL) ceramic, and above 1.5 km/s for the com-pacted powder specimens. The penetration velocities versusimpact velocities for these experiments are shown in Fig. 4.

Open symbols denote results where the Pet response wasnonlinear over some or most of the penetration event (i.e., non-steady-state penetration). The penetration velocities of only theearly or linear portion of penetration are plotted for these opensymbols. Also included in the figure are the data for intact (bare)SiC-N specimens from Ref. [2]. The data for the intact SiC extends toimpact velocities of w6 km/s; only the three lowest velocity datapoints are shown here.

The test series with intact SiC-N in [2] provided a linear (least-squares) relationship between penetration velocity u of the goldrod in the ceramic and impact velocity vp:

Ref : ½2� u ¼ �0:5844þ 0:7547vp: (1)

For Eq. (1), the velocities have units of km/s. The velocity range forthe regression analysis was 2.0< vp< 6.3 km/s.

This regression line for intact SiC has been extrapolated in Fig. 4to lower impact velocities, as indicated by the dashed line. Weknow that the u versus vp response of intact SiC-N cannot be

linearly extrapolated to the very low impact velocities shown inFig. 4, because at some impact velocity the projectile begins todwell at the target interface (for example, see [5,6]), but the linearextrapolation serves as a “trend” line.

The hydrodynamic lines are calculated from

uhydro ¼ vp

1þffiffiffiffiffiffiffiffiffiffiffiffirt=rp

q ; (2)

where rt and rp are the target (SiC) and projectile (Au) densities,respectively. The density for intact SiC-N is 3.21 g/cm3, whereas thedensity for the compacted powder is 2.35 g/cm3. The density of theAu rod is 19.3 g/cm3.

Linear regression analyses were performed on the experimentaldata shown in Fig. 4, and it was found that the slopes for TS, TS/CL,and CP were very similar to that for the intact SiC. Therefore,additional linear regression analyses were conducted to determinethe intercepts for the TS, TS/CL, and CP data, with the slope con-strained to be 0.7547, the value determined for the intact SiC data.These are the parallel regression lines shown in Fig. 4. For theregression to the TS data, the data point at vp¼ 2.4 km/s wasomitted since it deviates more than 6.5 standard deviations froma regression fitted without the point. Examining Fig. 4, it wasconcluded that:

uintact < upre�damaged < uin situ comminuted < upowder

< uhydrodynamic (3)

corresponding to reductions in strength or resistance to penetra-tion in the reverse order; i.e., uintact has the highest penetrationresistance, etc.

Additional experiments were conducted approximately oneyear later [4] to verify that the TS datum at 2.4 km/s was really anoutlier, and to extend the TS data to lower impact velocities.Additionally, it was decided to compare the penetration response ofintact SiC-N encased in the aluminum sleeve to the response of thebare SiC-N. Two target sets were constructed: 1) six thermallyshocked (TS) SiC-N specimens, denoted as TS-2, were prepared byheating for one hour at 750 �C with a subsequent ice water quench(3 cycles), thereafter placing them in an Al-sleeve (Fig. 3); and 2) sixintact SiC-N specimens, 18-mm diameter and 35-mm long, andinserted into an Al-sleeve (Fig. 3).

The results are summarized in Table 1. For each test, the yawangle of the projectile and the off-center distance of the impactpoint (oc) were also measured and are listed, along with the impactvelocity, penetration velocity, and consumption velocity, vc. Testresults are sorted by increasing impact velocity vp. The results forthese two sets of experiments are displayed in Fig. 5 as the openinverted triangles (TS-2) and the solid hexagons (sleeved intact).2

With these additional data, it is no longer true that the TS data(TS combined with the TS-2 data) consistently lie below the in situcomminuted (TS/CL) results (the solid circles) for impact velocitiesabove 1.5 km/s. At impact velocities less than w1.5 km/s, someportion of the penetration of the TS-2 experiments is nonlinear intime; only the nominally linear Pet data were used to estimate thepenetration velocity, similar to what was done previously for thelow velocity TS/CL data (open circles in Fig. 4, but now shown assolid circles in Fig. 5). At these lower impact velocities, the new TS-2data are also indistinguishable, within data scatter, from the TS/CLresults.

Fig. 4. u versus vp for different types of SiC-N specimens, from Ref. [3].

C.E. Anderson Jr. et al. / International Journal of Impact Engineering 38 (2011) 892e899 895

The results for the intact SiC-N specimens encased in the Al-sleeve are shown as the solid hexagons in Fig. 5. It was expectedthat the presence of the cover plate would affect the lowest velocityexperiment by allowing dwell [5,6], and the lowest impact velocityof 1.234 km/s showed dwell-like behavior and very little penetra-tion. However, the results at the higher impact velocities wereclearly surprising. Within data scatter, the penetration response ofthese intact (but confined within the aluminum cylinder) SiC-Ncylinders cannot be distinguished from the penetration response ofthe pre-damaged SiC-N specimens (circles and inverted triangles).Linear regression analysis, with the slope constrained to be 0.7547,was redone with all data points with u> 400 m/s (the regressiondid not include the three (Ref. [2]) datum). The result is shown inFig. 5 as the long dashed line.

There are also data from an additional eight experiments thatwere performed earlier that can be considered. These experimentswere designed to investigate interface defeat and the transitionfrom dwell to penetration [5,6]. In these 8 experiments, the targetswere bare, 20-mm diameter SiC-N cylinders (no aluminum sleevewas used for these experiments). The Au rods were all 1.00-mm indiameter. Because the interest was in dwell and interface defeat,the impact velocities were relatively low, all below w1.6 km/s. Theopen squares in Fig. 5 denote the penetration velocity as a functionof impact velocity for these 8 experiments. Interface defeat on

Table 1Experimental results for sleeved pre-damaged and intact SiC-N.

Exp Target yaw [�] oc [mm] vp [km/s] u [km/s] vc [km/s]

11349 TS13 2.2 2.1 1.248� 0.005 0.332� 0.034 0.941� 0.03411351 TS14 0.7 1.5 1.280� 0.005 0.533� 0.008 0.734� 0.00711341 TS9 1.5 0.8 1.517� 0.004 0.737� 0.024 0.786� 0.02311343 TS10 4.3 3.5 2.122� 0.008 1.222� 0.021 0.903� 0.02211345 TS11 3.1 2.1 2.358� 0.011 1.344� 0.011 1.002� 0.03711346 TS12 3.1 2.3 2.543� 0.013 1.482� 0.008 1.087� 0.010

11350 IT6 7.1 3.0 1.234� 0.006 0.115� 0.010 1.142� 0.01311340 IT1 7.5 2.3 1.497� 0.006 0.587� 0.039 0.912� 0.05711342 IT2 5.9 3.2 2.170� 0.008 1.149� 0.058 1.028� 0.05311348 IT5 1.6 1.4 2.511� 0.004 1.424� 0.004 1.076� 0.01511344 IT3 2.0 0.0 2.564� 0.008 1.533� 0.028 1.043� 0.02011347 IT4 1.6 1.5 3.051� 0.017 1.881� 0.039 1.187� 0.058

a bare ceramic was seen at an impact velocity of 0.776 km/s.Otherwise, the penetration response is similar to the other 1.00-mm diameter Au rod data. As these experiments did not have thealuminum sleeve or cover plate, and since there is no difference inthe penetration response of the intact and pre-damaged targets, itseems unlikely that the disagreement between the original intactdata [2] and these newer data can be explained by differences inconfinement.

3.2. New experiments on bare, intact SiC-N

The results displayed in Fig. 5 raised the question: Why is therea discrepancy between the penetration velocities of the initialexperiments of Ref. [2] and the newer intact SiC experiments shownin Fig. 5? One difference was that the intact experiments of Ref. [2]used a 0.75-mm diameter Au rod, whereas all the other experi-ments in Fig. 5 had a diameter of 1.0 mm. Recently, Andersson et al.[8], suggested aprojectile size effect for the dwell transition velocity,but made no predictions concerning the penetration velocity.Therefore, to provide insight into the surprising results of Fig. 5,

ig. 5. Comparison of results of additional experiments to original data set: u versusp.

Fv

ig. 7. Positionetime and rod length versus time for Exp. 11549, along with lineargression results.

Table 2Experimental results for investigation of rod size effects.

Exp. Rod [mm] yaw [�] oc [mm] vp [km/s] u [km/s] vc [km/s]

11547 0.75� 50 3.7 5.0 2.082� 0.014 1.191� 0.021 0.851� 0.01811546 1.00� 70 2.6 2.8 2.086� 0.015 1.162� 0.023 0.913� 0.04111550 0.75� 50 2.6 1.1 2.334� 0.012 1.345� 0.025 0.991� 0.01511549 1.00� 70 1.2 0.5 2.360� 0.019 1.282� 0.028 1.053� 0.01611558 0.75� 50 1.8 3.1 2.510� 0.021 1.572� 0.044 0.918� 0.00811551 1.00� 70 1.5 3.1 2.576� 0.017 1.457� 0.014 1.091� 0.04011552 1.00� 50 0.9 2.3 2.594� 0.025 1.517� 0.008 1.064� 0.04211555 1.00� 50 0.7 0.8 2.800� 0.019 1.482� 0.022 1.288� 0.02311554 0.75� 50 0.9 2.3 2.815� 0.018 1.656� 0.013 1.153� 0.01811557 1.00� 50 0.8 5.0 3.003� 0.020 1.869� 0.011 1.112� 0.01911556 0.75� 50 0.5 1.7 3.020� 0.014 1.888� 0.005 1.141� 0.008

Exp. 11558: ceramic sample with 15 mm diameter and 40 mm length (originalRef. [2] specimen).

C.E. Anderson Jr. et al. / International Journal of Impact Engineering 38 (2011) 892e899896

additional experimentswere conductedusing 20-mmdiameter SiC-N cylinders (from the same production lot). No aluminum confine-ment was used, i.e., these were bare, intact ceramic specimens. Thecylinderswere launched at suspendedAu rods 0.75 mmand 1.0 mmin diameter, over a velocity range of 2.1e3.0 km/s.

3.2.1. Experimental dataA total of 11 experiments were performed. An example of the

flash X-ray results is shown in Fig. 6. The depths of penetration androd lengths were measured from the X-ray shadowgraphs andplotted as a function of time (time zero is impact on the ceramic

Fig. 6. Flash radiographs for Exp. 11549; vp¼ 2.36 km/s.

Fre

front surface); an example is shown in Fig. 7. The penetrationetimedata are extremely nonlinear for approximately the first 5 ms [9].But starting about 5 ms, the data are highly linear (time zero is notincluded in the regression analysis), so linear regression was usedto fit the data, typically with the regression coefficient (r2) greaterthan 0.99. A squared correlation coefficient of greater than 0.99indicates that over 99% of the variation in the observed measure-ment can be explained by the linear predictor variable (r2¼1.0corresponds to a perfect correlation). The slopes of the linearregressions provide the penetration velocity, u, and the consump-tion velocity, vc, which are summarized in Table 2. Again, testresults are sorted by increasing impact velocity vp.

3.2.2. Comparison with sleeved experimentsThe data for the two different rod diameters (open and solid

diamond symbols) are shown in Fig. 8. For the new test series, thereare no differences, within data scatter, in penetration velocity u asa function of impact velocity vp when compared to the sleevedintact, pre-damaged, and in situ damaged ceramic. Occasionally,apparently randomly, there is an outlier (e.g., a solid diamondlocated at 2.8 km/s). For these new tests, there is no rod scalingeffect detectable with the data scatter. Linear regression includingthe 8 new data points, again with the slope constrained to be0.7547, changed the intercept by only 1%.

Clearly, the penetration data do not match the data from theRef. [2] test series. This is somewhat surprising as test set-up andmaterials used are practically the same, and the possibility of rodscaling was eliminated. This resulted in an examination of the dataanalysis procedures used in the different test series, which isdescribed in the following section.

3.3. Change in data analysis

All velocities derived from the experiments are calculated bya linear regression analysis of the Pet data. The impact velocity isdetermined from independent instrumentation. As the first triggerevent is always before impact, e.g., see Fig. 6, the time of impact, t0,is calculated. With that calculated t0, penetration velocity u can bedetermined from the penetration depth P versus penetration timetP¼ t� t0, again using linear regression:

P ¼ cþ utP: (4)

In the ideal case, axis intercept cwould be zero as penetration startsat the time of impact and would be steady state, i.e., linear withtime.

For the Ref. [2] original test series completed in 2004, this“ideal-case thinking” influenced the procedure for determining the

ig. 8. Penetration velocity versus impact velocity for sleeved and bare SiC-N, andifferent rod diameters.

Fig. 9. Updated regression fit for u versus vp for all SiC-N data, expanded scales.

C.E. Anderson Jr. et al. / International Journal of Impact Engineering 38 (2011) 892e899 897

penetration velocity u. In addition to themaximum four data pointsafter impact, the origin 0/0 was taken as a fifth data point and theregression was forced through 0/0; that is, the x-axis intercept was bydefinition zero, i.e., ch 0 in Eq. (4).

The experiments described in Refs. [3,4] used an aluminumsleeve and aluminum cover. Because of the aluminum cover, onlythe penetration datawithin the ceramicwas used for the regressioncalculations since the penetration rate through the cover/buffermaterial is different than that in the ceramic, which prevents theuse of 0/0 as an additional point. Subsequently, it was found thatthe penetration rate is very low for the first few microseconds afterimpact [9]. After a fewmicroseconds, the penetration rate increasessignificantly. This can actually be seen in the data plotted in Fig. 7.Because of this high penetration resistance immediately afterimpact, the data point 0/0 should not be used in the regressionanalyses to determine the penetration velocity (and erosion rate)for penetration times greater than w5 ms.

Therefore, the 2004 data were reanalyzed two ways [9]. 1) Achange from forced 0/0 regression to regression with 0/0 as anadditional point had little effect; the small difference of theresulting regression fit was within a very small error. 2) Recalcu-lated the penetration velocities without the 0/0 point. The majoreffect of not forcing the regression fit through 0/0 is for impactvelocities below w3.0 km/s, as will be shown shortly.

The three u< 3-km/s data points from the 2004 test series,reanalyzed without the 0/0 point, are replotted in Fig. 9 as the opencircles. The open circles fall within the scatter of all the other data.Therefore, it can be concluded that the 2004 data and all the newerdata are consistent with the observation that the penetrationvelocitydwithin data scatterdis independent of whether theceramic is intact, pre-damaged (TS and TS-2) or in situ comminuted(TS/CL), or sleeved or not sleeved, for impact velocities greater thanw1.3 km/s. Also, there does not appear to be any effect of roddiameter on the penetration velocity. The apparent differences inthe penetration velocities shown in Fig. 4 were the result ofinsufficient experimental data to quantify data scatter, and differ-ences in the analysis techniques for determining the penetrationvelocities.

3.4. Re-evaluation of u versus vp regression analysis

It was decided to re-do the linear least-squares regressionanalysis of u versus vp for SiC-N, using all the experimental dataover the entire velocity range.3 All penetration data were analyzedwithout a 0/0 data point. No data with a penetration velocity lessthan 400 m/s were included in the linear regression fit. A total of 63data points, ranging in impact velocity from 1.21 km/s to 6.24 km/s,were used for the linear regression of u versus vp. An initialregression was conducted, and points greater than 2s (a total of 3points) were eliminated and the regression was recalculated,giving:

u ¼ �0:3662þ 0:7165vp; w1:2 km=s < vp < 6:25 km=s (5)

The linear regression has an r2 value of 0.996, with a standarddeviation (s) of 65.1 m/s. The resulting regression line is plottedin Fig. 10, showing all the experimental data. The regression lineis also plotted in Fig. 9. The slope changes only 5% from thatreported in Ref. [2], and shown in Figs. 4, 5 and 8. However, the

3 There were three SiC-B data points included in the original regression analysisof Ref. [2]. These 3 data points had impact velocities at approximately 3.5 km/s. TheSiC-B data were not included in the revised analysis reported here.

Fd

intercept changed 37%, which greatly affected the three lowvelocity points in Figs. 4 and 5.

Eq. (5) is applicable for Au rods penetrating SiC-N, with therestriction that it applies to predicting a linear penetration rate.Belowapproximately 1.2 km/s, the penetration rate is nonlinear; thedegree of nonlinearity depending upon the specific geometry and

Fig. 10. Updated regression fit for u versus vp for all SiC-N data.

4 The accuracy and precision of the data are too good for the scatter to beprimarily the result of errors or uncertainties in the measurements.

C.E. Anderson Jr. et al. / International Journal of Impact Engineering 38 (2011) 892e899898

initial condition of the ceramic (confined/unconfined, intact/pre-damaged). Different penetrator materials will have different pene-tration rates as a function of projectile density and projectilestrength.At thehigher impact velocities, projectile strengthdoesnotgreatly affect the overall penetration rate; rather, the penetrationrate is controlled largely by thedensity (inertial effects). The effect ofprojectile strength is illustrated in Ref. [2] where the penetrationrates for W and Au rods were compared. A very large difference instrength, but essentially the same density, results in only a relativelysmall change in penetration velocity. At lower impact velocities,projectile strength not only affects the penetration rate, but also thedeceleration rate of the projectile. At higher velocities, decelerationof the projectile is a minor effect until near termination [10,11].These dependencies were not investigated in this study.

4. Conclusions

The experiments with scaled gold rods impacting sleeved andbare SiC-N cylinders, with impact velocities between 2 km/s and3 km/s, provided several interesting results and helped to resolvesomeopenquestions concerningearlier test seriesdonewithsleevedSiC-N ceramics. Themost important findings are as follow. A scalingeffect of the penetration velocity for different rod diameters, withindata scatter, is not observed. A thorough examination of the analysisprocess used to determine the penetration (and rod consumption)rate after impact revealed that the first test series done in 2004 [2]used a different method of regression analysis than all subsequenttest series. The, Ref. [2], regression analysis forced the regression togo through the 0/0 point.When the 2004 data are analyzed similarlyto the more recent data, the “old” data are consistent with the morerecent data. They align the different findings of earlier work andcombine them into a coherent picture. There are no differences,withindata scatter, for the penetration velocity of intact (bare or sleeved)ceramic, pre-damaged (thermally shocked, TS) ceramic, or in situcomminuted (thermally shockwith load/reloadcycles, TS/CL) ceramic.Aregression analysis was performed on the complete set of data togenerate an updated u versus vp relationship for the penetrationvelocity of Au rods into SiC-N, which is given in Eq. (5).

A fundamental question is why there is no difference in thepenetration rate into intact and pre-damaged ceramic, and why isthere considerable scatter (compared tometallic targets) in the data.The penetration response of glass provides insight. It has beenobserved inglass [12e15] that a damage front propagates faster thanthe rod penetration front; and therefore, the projectile penetratesdamaged material. It was shown for glass that the speed of thedamage front is a function of the impact velocity, but for the range ofvelocities investigated, the damage front travels from one-third(vp¼w1.0 km/s) to two-thirds (vp¼w2.5 km/s) the shear wavespeed. For SiC-N, two-thirds the shear wave speed is approximately5.2 km/s, much faster than the rod is penetrating. This idea that therod penetrated damage material was first proposed in computa-tional modeling of tungsten alloy long rods into glass [16], prior toany experimental evidence. This conceptdassuming that theprojectile penetrates failed ceramicdwas carried further byWalkerwhen he showed good agreement between an analytic model andpenetration of thick ceramic by long rods [17,18]. Thus, it is proposedthat a damage front propagates away from the projectile and thisdamage front propagates faster than the rod penetrates. Then, afterat most a few microseconds, the rod penetrates failed (probablycomminuted) ceramic. This hypothesis is consistent with the highpenetration resistance observed at very early times after impact [9],which would be due to the transition of initially intact ceramic todamaged (comminuted) ceramic.

The data scatter is likely due to variation in detailed failuredynamics of a brittle material during penetration, i.e., it is inherent

to the material4; for example, see the compilation of data by Orphalfor three different ceramics [19], and the nonlinear penetrationvelocity observed by Holmquist et al. [6]. It is noted that the failurefront in glass can be quite irregular, particularly at lower impactvelocities [12e14]. It is conjectured that the dynamics of theprogression from intact to cracked and then highly comminutedceramic can be quite variable, particularly if the penetrationstresses are comparable to the strength of the ceramic. X-rays oftenshow a penetration channel with small disturbances and side-channelsdparticularly at the lower impact velocitiesdwhich canhave a strong influence on the measured penetration depths. It hasalso been demonstrated, using numerical simulations, that thepenetration velocity through comminuted ceramic surrounded byintact (elastic) ceramic is influenced by the radial extent of thecomminuted material [20]. Thus, it seems reasonable to concludethat the variability observed in the penetration velocity of SiC-N asa function of impact velocity is the result of variability in the failuredynamics as the ceramic transitions from intact to failed material.

Acknowledgments

The authors would like to thank Dr. Douglas Templeton and Mr.Rick Rickert of RDECOM-TARDEC for their technical, administrativeand financial support of this research effort.

References

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