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Citation for published version

Wickham-Eade, J.E. and Burchell, M.J. and Price, M.C. and Harriss, K.H. (2018) Hypervelocity

impact fragmentation of basalt and shale projectiles. Icarus, 311 . pp. 52-68. ISSN 0019-1035.

DOI

https://doi.org/10.1016/j.icarus.2018.03.017

Link to record in KAR

http://kar.kent.ac.uk/66613/

Document Version

Publisher pdf

(2)

ContentslistsavailableatScienceDirect

Icarus

journalhomepage:www.elsevier.com/locate/icarus

Hypervelocity

impact

fragmentation

of

basalt

and

shale

projectiles

J.E.

Wickham-Eade,

M.J.

Burchell

,

M.C.

Price,

K.H.

Harriss

CentreforAstronomyandPlanetarySciences,SchoolofPhysicalSciences,IngramBuilding,UniversityofKent,Canterbury,KentCT27NH,UnitedKingdom

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received11July2017 Revised12March2018 Accepted15March2018 Availableonline16March2018 Keywords: Impactprocesses Moon AsteroidCeres AsteroidVesta Pluto

a

b

s

t

r

a

c

t

Resultsarepresentedforthefragmentationofprojectilesinlaboratoryexperiments.1.5mmcubesand spheres ofbasalt and shale wereimpacted ontowater atnormalincidenceand speedsfrom 0.39to 6.13kms−1;correspondingtopeakshockpressures0.7–32GPa.Projectilefragmentswerecollectedand measured(over100,000 fragmentsinsomeimpacts,atsizesdownto10µm).Powerlaws werefitted tothecumulative fragmentsizedistributions andthe evolutionofthe exponentvs.impact speedand peak shock pressure found.The gradient ofeach ofthese power laws increased with increasing im-pactspeed/peak shockpressure.Thepercentageoftheprojectilesrecoveredintheimpactswasfound andusedtoestimateprojectileremnantsurvivalindifferentsolarsystemimpactscenariosatthemean impactspeedappropriatetothatscenario.ForPluto,the Moonand inthe asteroidbelt approximately 55%,40% and 15%, respectively, ofanimpactor could surviveand be recoveredatan impact site. Fi-nally,the catastrophicdisruption energydensitiesofbasaltand shaleweremeasuredandfoundtobe 24×104J kg−1 and 9×104Jkg−1,respectively, afactorof2.5difference.Thesecorrespondedtopeak shock pressuresof1 to1.5GPa(basalt),and0.8GPa(shale). Thisisfornear normal-incidenceimpacts wheretensilestrengthisdominant.Forshallowangleimpactswesuggestsheareffectsdominate, result-inginlowercriticalenergydensitiesandpeakshockpressures.Wealsodetermineamethodtoascertain informationaboutfragmentsizesinsolarsystemimpacteventsusingaknownsizeofimpactor.The re-sultsareusedtopredictprojectilefragmentssizesfortheVeneneiaandRheasilviacraterformingimpacts onVesta,andsimilarimpactsonCeres.

© 2018TheAuthors.PublishedbyElsevierInc. ThisisanopenaccessarticleundertheCCBYlicense.(http://creativecommons.org/licenses/by/4.0/)

1. Introduction

Impacts in excess of a few km s−1 are deemed hypervelocity

impacts, and have long been studied as a major evolution

pro-cessforsolarsystembodiesandsurfaces.HereonEarththemean

impact speed is usually givenas around 20km s−1 (Steel, 1998;

Jefferset al., 2001). However, the mean speed of impacts varies

dependingon their location within the Solar System. For

exam-ple,themean impactspeed inthe asteroid beltis approximately

5kms−1(Bottkeetal.,1994),withtheexactspeeddependingon

theexact conditions,e.g. the meanimpact speed on Vestais

es-timatedas4.75kms−1 (Reddy etal.,2012). Lowerimpactspeeds

(0.5–1km s−1) are expectedfor Kuiper Belt objects in the outer

SolarSystem(Zahnleetal.,2003).However,ifabodyisasatellite

ofaplanet,therewill alsobe acontribution tothemeanimpact

speedfromthegravitationalattractionofthelargernearbyplanet.

Hence thesatellitesof JupiterandSaturn will havemeanimpact

speedsthatincrease theclosertheyaretotheparentplanet(e.g.,

Correspondingauthor.

E-mailaddress:m.j.burchell@kent.ac.uk(M.J. Burchell).

seeZahneetal.,2003;Burchelletal.,2005).Thereareevenmore

specific, niche examples, of impacts, such as that of terrestrial

material ejected after impacts on Earth, which then impacts the

Moon. Such impacts have speed ranges which need to be found

forthatspecificexample(e.g.,seeArmstrong,2010,whogivesthe

mode speed for terrestrialejecta on the Moon asapproximately

2.8kms−1).

Therehasbeensignificantresearchintoimpactcrateringevents

andthe resulting ejecta. Atypical recent summary ofimpact

re-lated research can be found in Osinski and Pierazzo (2013) and

referencestherein.Whatissometimesoverlookedhoweveristhat

projectilematerialitselfmaysurvivetheimpact(albeitinmodified

and/or heavily fragmented form).There haslong been discussion

ofthis, albeit lessthanthat forother aspects of impacts.For

ex-ample,earlyworkbyGaultandHeitowit(1963)lookedtoseehow

thekineticenergyoftheprojectilewaspartitionedduringan

im-pact, andestimatedthat theprojectile internalenergy(the waste

heat)was6% (ofthe projectile’skinetic energy) forsandand

be-tween4%and12%forbasalt.Later,GaultandWedekind(1978)

dis-cussedprojectile ricochet inshallowangleimpacts inthe

labora-tory,as well asthe energydensity(Q

p) neededto fragment

alu-https://doi.org/10.1016/j.icarus.2018.03.017

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minium and basalt projectiles in an impact. Note that this con-cept ofQ

p issimilartothat ofthecriticalenergydensityneeded in an impact to disrupta target (Q). Thus it is theenergy

den-sity(kineticenergydividedbymass)which,onaverage,resultsin thelargestsurvivingfragmentpossessinghalftheoriginalmassof theparentbody(heretheprojectile).Thepresenceofthesubscript

pindicatesthat theprojectilealoneisbeingconsidered,andthus

Q

pv2.ThisapproachisextendedinSchultzandGault(1990a),

who considered indetail the break-up of projectiles insuch

im-pacts. Inthat work,Schultz andGaultreported firingaluminium

and basaltspheres attargets of mostlysteel, butwith examples

of water and aluminium targets as well. The impacts covered a

speedrangeof0.4to5.3kms−1,andwereatveryshallowangles

ofincidence(30°fromthehorizontalorless).Projectiledisruption

wasreported,withsignificantfragmentsoftheimpactorrecovered

post-shot(over50%insome cases).Whereprojectilericochet was

reported,insome casestheincident projectile waseffectively

in-tact afterthe impact.Studies ofshallowangle ricochet havealso

beenreportedforbasalttargetscoveredwithsand(Burchelletal., 2010,2015).Aswellasobservingintactricochet,theyalsoreported

very little reduction in outgoingspeed compared to the incident

speed. Separate studies have also considered projectile

fragmen-tation during penetration of thin plates (e.g. Piekutowski, 1995).

SchultzandGault(1984)alsoconsideredhowprojectile

fragmenta-tioncaninfluencecratermorphology.Theyshowedthatwhenthe

impactinducedshockpressuresexceededthedynamicstrengthof

the projectile, cratering efficiency wasreduced. Since thisoccurs

atmodest impact speeds(less thana few kms−1),extrapolation

of low speed datato higherspeed examples in theSolar System

maynotbeeffective.

Previous workinthe laboratorywhichhasobserved projectile

fragmentation also includes impacts into metal targets atspeeds

of up to 5 or 6km s−1 (which can involve shock pressures of

80 to over 100GPa). Examples of this include Hernandez et al.

(2006) for metal projectiles, and Burchell et al. (2008) for

min-eralic impactors.Despite theextremeshocks, inthe latter

exam-ple,post-impactfragmentsofthemineralprojectilesretained

suf-ficientinternal structure tohaverecognisable Raman spectra.

Re-cently,studies ofRamanspectrafromolivinegrainsafterimpacts

atspeedsupto 6kms−1,dohowevershowsome subtlechanges

inpeakpositions.Thissuggeststhatsomefinechangesinstructure

may be occurringdue to the shock during impact (Foster et al.,

2013;HarrissandBurchell,2016).

In addition, Nagaokaet al.(2014) fired millimetre-sized

pyro-phylliteandbasaltprojectilesontoregolith-likesandtargetsat ve-locitiesupto960ms−1.TheydeterminedQ

ptobe(4.5±1.1)×104 for pyrophyllite and (9.0±1.9)×104J kg−1 for basalt projectiles

(Nagaoka et al., 2014). They also found that destruction of rock

projectiles occurred when the peak pressure was approximately

tentimesthe tensilestrengthofthe rocks(Nagaokaetal., 2014). Recently, Avdellidou et al.(2016) firedforsterite olivine and syn-thetic basalt projectiles onto low porosity (<10%) pure water–

ice targets at speeds between 0.38 and 3.50km s−1. From this,

the estimated implantedmass on the target body was found to

be a fewpercent oftheinitial projectile mass.Furthermore,they

foundanorderofmagnitudedifferenceforQ

p,betweentheolivine (Q

p=7.07×105J kg−1) and basalt (Qp=2.31×106J kg−1). How-ever,theyfoundthatthetwoprojectilematerialshadverysimilar fragmentsizefrequencydistributions(Avdellidouetal.,2016).

As well aslaboratoryexperiments,there isextensiveevidence

for projectile survival in Solar System impact events. For

exam-ple,projectilefragmentshavebeenrecoveredat13terrestrial

im-pact sites including Barringer, Morokweng and Chicxulub craters

(see Table 15.1,Goderis etal., 2013,and referencestherein).

Fur-thermore,analysisofApolloeralunarsamplesshowsthat

projec-tile fragments from impacts early in the Moon’s history can be

found within the lunar regolith (e.g. Joy et al., 2012, and

refer-ences therein). Schultz andCrawford (2016) have suggested that

the high meteoritic component found in samples returned from

theApollo16landing sitemayarise fromejectafromthe impact

which formed the Imbrium basin on the Moon. As well as

pro-jectilematerial being mixedwithin the lunar regolith,Yue etal.

(2013)usednumericalmodelstoshowthatforverticalimpact ve-locities below12km s−1,projectile material maysurvive the

im-pact andbe found in the central peak of the final crater. There

arealsosuggestionsby Reddyetal.(2012)that thedarkmaterial

on Asteroid (4) Vesta could be of exogenic origin. This is based

on the observation that the majority of spectra of the dark

ma-terialaresimilarto carbonaceouschondritemeteorites,indicating

mixingofsuchimpactorswithmaterials indigenoustoVesta.

Re-lating to this observation, Daly and Schultz (2013, 2014, 2015a,

2015b,2016)haveconductedhypervelocityimpactexperimentsin

ordertoexplain the implantationof an impactorontoVestan

re-golith, and also the surface of Ceres. They fired basalt and

alu-miniumsphericalprojectiles, approximately6.35mmin diameter,

ontopumiceandhighlyporousicetargetsatspeedsbetween4.5

and5.0kms−1.Survivingprojectilefragmentsrangedfrom

approx-imately<105µmto 5mm. Basedon their results, itwas inferred

that both Vesta and Ceres should have significant levels of

exo-genicmaterialdeliveredviaimpacts.

In parallel to this, renewed interest in the distribution of or-ganic(andpossiblyevenbiologicalmaterial)aroundtheSolar

Sys-tem as contents of small rocky bodies etc., has led to a steady

increase in the number of laboratory studies into the survival

of projectiles. For example, the survival of biomarkers in

pro-jectile fragments in hypervelocity experiments has been studied

(e.g.,seeBowdenetal., 2008;Parnell etal., 2010;Burchelletal., 2014a).Furthermore,eventhesurvivalofdiatomfossilsin

projec-tile fragments has been demonstrated in laboratory experiments

(Burchelletal.,2014b,2017).Thisindicates thatnotonlycan pro-jectilefragmentssurviveafterimpact,theycandeliverawide va-rietyofmaterialstothetargetbodies.

The subsurface regions at man-made impact sites should

also contain impactor material. For example, consider the crater

on comet 9P/Tempel-1 arising from the Deep Impact Mission

(Schultz etal.,2013).Thismission consistedofa363kgimpactor

(ofwhich49%wasporouscopper)impactingthecometnucleusat

10.3kms−1 (A’Hearnetal.,2005;Veverkaetal.,2013).In

labora-tory impacts onto icetargets at speeds up to 6.3kms−1, it has

been shown that fragments of copper projectiles can survive at

theimpactsite(McDermottetal.,2016).ExtrapolatingtotheDeep

Impact case, McDermott et al.(2016) predict the survival of

be-tween 8% and15%of thecopper projectile atthe impact site. In

that study, McDermott et al. (2016) also reported extensively on

theprogressive stagesofdisruption undergone by copper

projec-tilesforimpactsinvolvingshockpressuresupto50GPa,including

providingsize distributions ofthefragments.Using highporosity

targets, Avdellidou et al.(2017), haveshown that whilst, in gen-eral,projectile fragment survival increases with increasing target

porosity,this is not the casewhen target mineral grain size

ex-ceedsprojectilesize.

Given the growing interest in emplacement of projectile

ma-terial onto targets after impact we have conducted a series of

impacts inthe laboratory, recoveringthe projectile material after

impact. Here we look at the fragmentation of basalt and shale

projectiles in normal incidence impacts at speeds from 0.39 to

6.13kms−1.Thetargetswerewater,ahomogeneoustarget which

iseasilymodelledandfromwhichtheprojectilefragmentscanbe

readilyrecovered.WefindQ

pandfragment sizedistributions,and

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foran impactoronVesta usingthecumulativefragment size dis-tribution.

2. Method

2.1.Projectiles

The projectile materials used in this study were basalt and

shale, mostly in the form of cubes, 1.5mm along each edge,

al-thoughinsomeshotsbasaltspheres (1.5mmdiameter)were also

used.Basalt was used as a projectile type asit is often used as

ananalogueforchondritemeteorites(e.g.DalyandSchultz,2016).

Shalewaschosenasacomparisonmaterialwhichhasbeenusedin

previousimpactstudies(e.g.Parnelletal.,2010).Thebasaltcubes werecutfromblockscollectedfromtheIsleofSkye,Scotland,and

werefinegrainedwithsmallvesicles(mmsized).Thecomposition

of the basalt, as measured by SEM-EDX was: Olivine (Fa80Fo20),

Clinopyroxene (En10Fs46Wo43) and Feldspar (An57Ab32Or11). The

shalewasalso collectedfromScotland. Inboth cases,the

projec-tiles were cut by hand, and measured and weighed before use.

Thebasaltglassspheresusedwereacquiredfrom‘Whitehouse

Sci-entific’(http://www.whitehousescientific.com/)andhave atypical composition of SiO2 (43%), Al2O3 (14%), CaO (13%), Fe2O3 (14%),

MgO (8.5%),Na2O/K2O(3.5%) andothers (4%). These spheres are

thesameasthoseusedinAvdellidouetal.(2016).

2.2.Thelight-gasgunandtheshotprocedure

The projectiles were shot using the University of Kent’s two

stagelight-gasgun(Burchelletal.,1999).The speedwasselected

ineach shotby varyingthe pre-pressureof thelight gasused in

thegun’sfirststage.Toachievespeedsbelow1kms−1,the

burst-ingdisk,whichseparatedthetwostagesinthegun,wascalibrated toburstatspecificpressurestoensureslowprojectilespeeds.The

speedoftheprojectilewasmeasuredin-flightbypassagethrough

two laser screens with a known spatial separation, providing a

speed determination to better than±1% (Burchell et al., 1999).

When the gun was fired, the target chamber was evacuated to

50mbartoavoiddeceleration oftheprojectileinflight.The shot regimeusedherewasfrom0.51to6.02kms−1forbasalt,and0.39

to6.13kms−1forshale(seeTable1).

The target in each shot wasa thin plastic bag ofwater held

inametal frame,see Fig.1a.The plasticwaswaterrichandhad

a thicknessof lessthan 50µm, andin effect,acts asthe surface

layerofthe watertarget intermsoftheprojectileimpacts.There

was approximately 250ml of water in the target in each shot,

andin the line-of-flight ofthe projectile there was a water

col-umndepthof typically 3cm.Previous experimentswiththis

tar-gethaveshownthat thisissufficienttocontain theimpactevent

withoutcausingcratering inthe rearsurfaceofthe target holder

(Baldwin etal.,2007). Duringa shotthetarget holder stoodina

metal tray with a metal cover over it (Fig. 1b). This design was

toensuremaximum collectionofthewaterafterimpact (asmall

apertureinthecoverpermittedentranceoftheprojectile).

After asuccessfulshotthetargetwasremovedfromthe

cham-ber and the water collected. The collected water, containingthe

fragmentedprojectile,wasthenfilteredthrougha0.1µmDurapore

membranefilterusingavacuumpump.

2.3.Fragmentmeasuring

Aftereachshot,theresultingDuraporefilterpaperwasmapped

inthe University ofKent’sHitachi3400-H Scanning Electron

Mi-croscope(SEM).The SEM wasrun at20kV, withamagnification

ofx95andinvariable pressuremode (90–110Pa) toavoid

charg-ingasthesampleswereuncoated.Theresultingmaptypically

in-Fig.1. (a)Theoceantargetframeinitsbasetray.Thebagwhichcontainsthe wa-terisheldbetweenthetwoverticalplateswhoseseparationcanbeadjusted.The impactdirectionisshownwith theredarrow.(b)Thecoverwhichfitsoverthe framein(a).Theprojectileentersthecoverintheholeseenintheface.Theruler is30cmlong.(Forinterpretationofthereferencestocolourinthisfigurelegend, thereaderisreferredtothewebversionofthisarticle.)

cludedatleast800individual fieldsofview.Eachimage wasthen

analysed using ImageJ software. ImageJ is a public domain, Java

based script, designed to help computer analysis of images,and

wasdevelopedattheNIH(https://imagej.nih.gov/ij/index.html,site

accessed July 2017). This software draws an ellipse over the

sil-houette of each fragment (see examples in Fig. 2) and produces

theareaandsemi-major(a)andsemi-minor(b)axisofeach

indi-vidualellipse(fragment).ThisprocedurewasusedbyDurdaetal.

(2015)forexample,toaccuratelymeasuretheaandbvaluesofthe

36largestfragmentsfromcatastrophic disruptioneventsof

irreg-ularandregulartargets.Fragmentvolumesareobtainedassuming

an ellipsoid shape withsemi-major axis,a, andsemi-minor axes

b.Here we isolateandidentify fragmentsdown toaround 10µm

insize, andcanfindover 100,000fragmentsinthe higherspeed

shots.Toaccountforcontaminationfrommaterial whichwasnot

the projectile, i.e.anyfine bursting diskor sabotmaterial which

mayaccompany the projectile ina shot, a control shotwas

con-ducted. This control involved firing the gun in the same wayas

usual, butinto ice(instead ofwater) andwithout a projectile in

the sabot. Icewasused becauseany smallgun debriswould not

be ableto piercethebag, meaningit could notbe collected. The

meltedicewasanalysedasusual andthesize distributionofthe

resultingfragmentsmeasured.Aninsignificantamountofmaterial

above10µmwasmeasured.Asmallcorrectionwasthenmadeto

thesize distribution ineach trueshot, butasthe datapresented

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ef-Table1

Shotandprojectilesummary.Thepeakshockpressuresweredeterminedusingtheplanarimpactapproximation(PIA,Melosh,2013).Tocalculate pres-sureinthePIA,alinearwavespeedrelationoftheformU=c+Suisused,whereuandUaretheparticlespeedandshockspeed(bothinkms−1),with

separatevaluesforCandSforprojectileandtargetmaterials.ForbasaltandwatervaluesofC=2.60kms−1,S=1.62andadensityof2860kgm−3,

andC=2.39kms−1,S=1.33and997.9kmm−3wereused,respectively,(Melosh,2013).ForshaleweusedC=2.30kms−1,S=1.61andadensityof 2545kgm−3(AhrensandJohnson,1995).Anyblankentriesforthemeanfragmentdiameterareduetotheprojectilenotfragmenting;insuchcases

theoriginalprojectilewasrecoveredwithminordamage.Fortheinclinedangleshotsthefragmentdistributionwasnotmeasuredhencethereareno valuesgivenformeanfragmentdiameter.Thecontrolshothadnoprojectilethereforehasnomassandpeakshockpressure.Theerroronthemean fragmentdiameteristheFWHM.

ShotID Projectilematerial Mass[mg] Speed[kms−1] Peakshockpressure(PIA)[GPa] Meanfragmentdiameter[µm] m L,p/Mp S290715#1 Basalt 7.291 0.51 1.09 – 0.996 S100615#1 Basalt 8.141 0.64 1.41 – 0.996 S240615#1 Basalt 8.708 0.70 1.57 23.8±21.9 0.177 S050815#1 Basalt 7.270 0.84 1.95 18.5±14.0 0.003 S050315#1 Basalt 11.021 0.96 2.30 18.0±10.9 0.009 G261115#1 Basalt 8.806 1.95 5.80 16.8±8.2 0.003 G010515#2 Basalt 8.003 3.04 10.9 15.3±6.5 0.004 G141015#1 Basalt 7.008 4.05 16.9 15.6±7.0 0.001 G101215#1 Basalt 7.684 4.71 21.4 14.0±5.3 0.002 G041115#1 Basalt 7.889 4.92 23.0 15.4±6.6 0.001 G271114#1 Basalt 7.809 5.31 26.0 14.2±5.7 0.001 G211015#2 Basalt 7.753 6.02 31.9 14.6±5.8 0.002 G110516#1 Basalta 5.143 1.98 5.93 18.0±10.7 0.011 S270416#1 Basaltb 7.253 0.59 0.29 – 0.998 S110316#1 Basaltb 7.494 0.98 0.50 0.234 G200416#3 Basaltb 7.424 2.01 1.12 0.032 S280116#1 Shale 7.518 0.39 0.74 – 0.998 S030216#1 Shale 7.106 0.59 1.20 29.5±36.8 0.291 S181115#1 Shale 7.136 0.95 2.12 22.7±27.5 0.413 G130116#2 Shale 7.403 1.93 5.34 15.5±7.7 0.038 G041115#1 Shale 6.465 3.12 10.3 15.5±7.2 0.013 G031215#2 Shale 7.487 4.64 19.7 15.5±6.6 0.006 G211015#2 Shale 8.083 6.13 30.9 16.0±7.6 0.002 G250315#1 Control – 5.36 – 14.6±6.4 –

a Glassbasaltsphere.

bBasaltcubeshotat15°angleofimpact.

Fig.2. SEMfieldofviewforfragmentsat0.70kms−1(left)andtheellipsesfittedbytheImageJsoftware(right).

fect ontheresults.Asacheck ontheImageJprocess,one sample

wasmeasureddirectlybyeyeontheSEMtoconfirmtheaccuracy

ofthe softwaremethod.Goodcorrespondencewasfound inboth

totalnumberandsizedistribution.

2.4. Estimatingtheshockpressure

ThePlanarImpactApproximation(PIA) wasusedtodetermine

the peak shock pressure upon impact. This provides an

estima-tion of maximum pressures computed from the Hugoniot

equa-tions andthe equationsof state (Melosh, 2013). The PIA is valid

solong asthelateraldimensionsoftheprojectile aresmall

com-pared with the distance the shock has propagated. It requires a

linearshockwave speed relationintheformU=C+Su, whereU

is the shockspeed andu isthe particle speed (bothinkm s−1).

Separate values are required for C and S for both the projectile

and target materials. From Melosh (2013) we take the values for

basaltof C=2.60km s−1, S=1.62and a density of2860kg m−3,

andC=2.39kms−1,S=1.33 anddensityof997.9kg m−3 for

wa-ter.For shale we used C=2.30km s−1, S=1.61 anda densityof

2545kg m−3 (Ahrens and Johnson, 1995). Values for the peak

shockpressureestimatedusingthePIA,foreachshotaregivenin

Table2.

Tocompare to thepeak shock pressure fromthe PIA we also

usedtheANSYSAutodyn3D hydrocodetomodeltheimpacts(see

HayhurstandClegg,1997).Thisusedboththeprojectileandtarget

materialequation ofstate (EOS) anda VonMisesstrength model

fortheprojectile. We useda shockEOSwiththe samevaluesas

that usedin thePIA. The values usedforthe strength modelfor

basaltwere a shearmodulus of8.0GPa(Christensenet al.,1980)

and yield stress of 200MPa (Rocchi et al., 2002). For shale we

usedashearmodulusof1.6GPa(Foxetal.,2013)andyieldstress of 62MPa (Koncagül and Santi, 1998). The shape of the projec-tile(cubicorspherical)wasallowedforintheappropriate

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simula-Table2

Comparisonofpeakshockpressuresdeterminedfromtheplanarimpact ap-proximation(PIA)(seeTable1)andtheresultsfromrunsofAutodynas de-scribedinthemaintext. FortheAutodyn results,wegivethreeresultsper simulation.The‘Highest’and‘Lowest’arethelargestandsmallestvaluesfor thepressureintheprojectile.Thehighestvaluewastypicallyclosetothe im-pactpoint,andthelowestistothereartrailingportionoftheprojectile.The ‘median’valueisthattowhich50%oftheprojectilewassubject.

Speed[kms−1] Material PIA[GPa] AUTODYN-3D[GPa]

Highest Median Lowest 0.51 Basalt 1.09 2.14 0.44 0.05 0.64 Basalt 1.41 2.71 0.60 0.05 0.70 Basalt 1.57 3.00 0.68 0.06 0.84 Basalt 1.95 3.63 0.85 0.07 0.96 Basalt 2.30 4.20 1.05 0.07 1.95 Basalt 5.80 8.96 3.07 0.23 3.04 Basalt 10.9 14.6 6.07 0.84 4.05 Basalt 16.9 20.2 9.79 1.34 4.71 Basalt 21.4 24.0 12.1 1.79 4.92 Basalt 23.0 31.0 12.6 1.66 5.31 Basalt 26.0 30.5 13.9 2.07 6.02 Basalt 31.9 48.3 21.5 3.50 0.39 Shale 0.74 1.18 0.28 0.01 0.59 Shale 1.20 1.87 0.47 0.02 0.95 Shale 2.12 3.07 0.93 0.06 1.93 Shale 5.34 6.66 2.78 0.36 3.12 Shale 10.3 11.4 5.72 0.91 4.64 Shale 19.7 33.2 9.88 1.73 6.13 Shale 30.9 53.3 20.6 4.95

tion.Thisallowedustoseethedistributionofpeakshockpressure throughoutthebulkoftheprojectileandnotjustnearthecontact

phase asin the caseof the PIA. In particular, corners can be an

issuefornon-sphericalimpactors,so byusing 3Dsimulations we

tryto take thisexplicitly intoaccount. Peak pressures acrossthe projectilecalculatedusingAutodyn,aregiveninTable2.

3. Resultsanddiscussion

There were a totalof24shots inthiswork (16 withbasalt, 7

withshaleand1control).Table1summariseseachshotandgives

the mass of each projectile, the peak shock pressure, the mean

fragment diameterandthe ratio ofthe largest fragment massto

the projectile mass (mL,p/Mp). Table 2 gives the shock pressures

determinedbythePIAandtheAutodynhydrocodesimulationfor

eachshot.InAutodyn,thepeakshockpressuresweredetermined

at250pointsevenlyspacedoverthewholevolumeofthe

projec-tile.This allowed forthe peak pressure not beinga singlevalue

acrossthebody,andpermitsreasonableidentificationoftheboth

themaximum andminimumpressures in theprojectile. In

addi-tion,we also give in Table 2the median peak shockpressure in

thesamples,whichprovidesamorecompletepictureoftheshock

pressure inside the projectile. From Table 2, it can be seen that

thepeakshockpressurecalculatedusingthePIAliesbetweenthe

maximumandmedian valuesfound by Autodyn,and istypically

some50% ofthemaximumvalue atlowspeeds(0.5kms−1),

ris-ingto 75%at intermediatespeeds(4kms−1), andfinally back to

60%at6kms−1.Itisthereforeareasonableindicator ofthepeak

shockin a finite volume ofthe sample (and not justat a single

point),sowe useitasthemeasure ofshockpressureinthe

sub-sequentanalysis.However, itshouldalwaysbe recalledthatthere

aremorelightlyshockedregions ineach impactorandthatwhen

cubesareusedtherecanbeparticulareffectsincornerregions.

Fig.3showshowthepressuremeasuredbyattwopoints(#234

atthefront and#9atthe backof theprojectile)inthe Autodyn

simulationchanged with time forthe 6.02kms−1 basalt impact.

Position 234 wasa computational cell inthe leading half of the

projectile and which was numerically eroded in the simulation,

Fig.3. PressurereadingsfortwopositionsintheAutodynsimulation,atthefront (#234)and backface(#9) ofa1.5 mmcubeshapedbasaltprojectileimpacting waterat6.02kms−1.

hencethesuddenfalltozeroGPa.Position9waspositionedinthe latterhalfoftheprojectileandthereforetheshockwavereachedit later.Aftertheinitialcompression(increaseinpressure)therewas

anexpansionofthematerial(representedbyanegativepressure).

Thispatternofbehaviourrepeatedforapproximately6µs.The

dif-ferenceinpeakshockpressurebetweenthetwopointsshowsthat

materialattherearoftheprojectilereceivedaconsiderablylesser

shock than that at the front. Note that these positions did not

recordthehighestorlowestpeakshockpressuresintheevent.The

positions which recorded the highestpressure (peak shock

pres-sure)werepositionedjustbehindthefrontimpactingface,andthe lowestwereattherearoftheprojectile.

3.1. Morphologyofprojectilefragments

Fig.4showsexampleSEMfields-of-viewforthreetypicalbasalt

shots (0.96, 3.04 and 5.31km s−1). These show the average size

ofthefragmentsaregettingsmallerwithincreasing impactspeed

(sizesaregiveninTable1).

Fig.5showstheratioofthesemi-minor(b)tosemi-major (a)

for all fragments measured in typical shots, where a ratio of 1

referstoacircleand0.1toabarshape.Atthelowerspeeds,both basaltandshalehadahighmeanvalueofb/a.However,forbasalt this rapidlyreduced to b/a ∼0.55by speeds of 1kms−1 andis

then stable. Forshale, the value of b/a of ∼0.55is only reached

for impact speeds of approximately 4.5km s−1 and above. This

suggeststhatinitiallywhentheprojectile hasbeendisrupted,the

fragments appear to be more spherical on average, but with

in-creasingimpact speed/pressurethey are moreelliptical, and that

thisismaterialdependent.

In Fig. 6 we show the mean value of each b/a plotand how

it changeswithimpact speed (alsosee Table3). When excluding

the partially disrupted shots (shots<1km s−1), the averages are

0.58±0.16(basalt)and0.59±0.14(shale)asrepresentedinFig.6.

Thereforebothbasaltandshaleprojectilesappeartohavesimilar

morphologies upon disruption, butshalerequires a higher speed

andagreatershockpressuretoachievethislevelofdisruption.

3.2. Cumulativefragmentsizedistributions(CFSD)

InFig.7,wepresentsometypicalcumulativefragmentsize dis-tributions (normalised to the original projectile diameter) forsix

typical shots (3 basalt and 3 shale) at a range of speeds. Each

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Fig.4. ExampleSEMfieldofviewsofbasaltfragmentsforimpactspeedsof0.96,3.04and5.31kms−1.Imagesarefrombackscatteredelectrons,invariablepressuremode

(100Pa),withacceleratingvoltage20kV.Somelongthinfibresarepresentintheimagesandtheseareexcludedfromtheanalysisastheyarenotmineralinnature.

Fig.5. Histogramoftheratioofthesemi-minor(b)tosemi-major(a)forallfragmentsmeasuredintheseshots.Aratioof1impliesacircleshape,and0.1abar-likeshape.

Fig.6. Meanb/avaluesforeachshot.Thetwolinesrefertothemeanvaluesfor basalt(solidline)andshale(dottedline),excludingtheslowerspeedshotdata.

lawsintheformN(>S)=aSb,whereNisthenumberoffragments

greater than a givensize S.A singlepower b did not fit the

en-tire size range forany shot, so we havedivided each size range

intothree. Theserefer to thelarge sized fragments,intermediate

sized fragmentsand smallsized fragments ineach shot. The

ap-proximatenormalisedsizerangesare<0.05,0.05–0.1and>0.1for

small,intermediate andlargerespectively. Thepowerbvaluesfor

basaltandshalearegiveninTable4.

In Fig. 8 we show how the power b changes withincreasing

impactspeed.It wouldappearthat forslowershots (partial

frag-mentationdomain)thegradientofthelargefragmentsisshallower

than the intermediate or small size ranges. This is because the

largeprojectilefragmentsintheseshotshavenotbeenbrokenup

intomultiplesmallersimilarlysizedfragments.Asspeedincreases

above 1kms−1 for basalt, there isa sudden large changein the

slope for the large fragments fromapproximately −2 to

approx-imately −5 or −6. This jump does not occur for shale until the

speed exceeds approximately 3kms−1. Thisparallels the change

inb/aratiosinthetwomaterialsvs.speed.

Overall,eachsizesectionappearstogetsteeper(largerb)with

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frag-Fig.7. Cumulativefragmentsizedistributions(normalisedtotheoriginalprojectilediameter)forsixtypicalshots.Theleftplotsarebasaltandtherightshale.Thelines arefitsineachsizeregion(greenforsmallsizes,blueforintermediate,andredatlargestsizes).TheslopeofeachfitlineisgiveninTable4.(Forinterpretationofthe referencestocolourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)

ments.Thisisexplainedbytheincreasingshockpressurebreaking

largerfragments into multiple similar sized fragments. Hence, at

thehighestimpactspeed(greatestshockpressure)therearefewer

largerfragments.

3.3.Survival/retainedprojectilepercentage

Assuming thateach fragment’smassisapproximatelyequalto

the mass of an ellipsoid calculated, as stated above, using the

semi-major (a, xi) andminor (b, yi) axis, and knowing the

den-sity(

ρ)

of the material,we can deduce an approximation of the

massofeachfragment. Fromthiswe candetermineapercentage

ofprojectilesurvivalbasedontherecoveredfragments:

Total Sur

v

i

v

edMass=

N i=0 4 3

ρπ

xiy 2 i. (1)

Thisassumesthethirdaxis,notseeninthe2DSEMimages,is

equalinsizetothesmallerofthetwomeasuredaxes.

In Fig.9 the estimated surviving masspercentage against the

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Table3

Summaryofthemeanratioofthesemi-majorandsemi-minoraxes(b/a) valuesforbasaltandshalecubesfiredateachspeed.Thestandarderror onthemeanisgivenineachcase,alongwithσ,thestandarddeviationof thedistributionaboutthemean.

Impactspeed[kms−1] Meanb/a Standarderror(×10−4) σ

Basalt 0.51 1.00 – – 0.64 1.00 – – 0.70 0.69 6.45 0.12 0.84 0.62 5.33 0.16 0.96 0.58 2.53 0.16 1.95 0.57 2.86 0.16 3.04 0.57 2.60 0.16 4.05 0.61 4.03 0.16 4.71 0.56 2.83 0.16 4.92 0.60 3.86 0.17 5.31 0.57 2.88 0.16 6.02 0.59 3.75 0.16 Shale 0.39 1.00 – – 0.59 0.77 10.0 0.09 0.95 0.74 11.0 0.11 1.93 0.59 3.28 0.16 3.12 0.62 3.42 0.16 4.64 0.56 2.50 0.16 6.13 0.61 3.02 0.16

goodpowerlawfit:

Sur

v

i

v

ing%= 115P−0.49, (2)

wherePisthepeakshockpressureinGPa.Thegoodnessoffitfor

thisisr2=0.9449.

Thesamepowerlawfitfortheshaledatagives:

Sur

v

i

v

ing%= 100P−0.33. (3)

Thegoodnessoffitforthepowerlawfittoshaleisr2=0.8444.

Shale appears to have a higher surviving mass percentage at

the higher shockpressure. We considered ifthis wasan artefact

of Eq. (1), whereby the third axis of each fragment (the depth)

is not measured andis assumed to be equal to the semi-minor

axis.However,upon furtherinvestigationofthefields-of-viewthe fragmentsofshaledonot appeartobeparticularlyflat(or ‘plate’

shaped)comparedto thebasalt. Looking atFig.7, atagiven

im-pactspeed thelargestfragmentofshaleislarger thanthelargest

fragmentinthebasaltshots.Giventhatmostmassresidesinthe

largerfragments,thismayexplainwhyshalegivesmorecomplete

massrecovery than basaltintheseimpacts. Masscan be lostvia

tworoutes.The firstisduetothemasspresentinfragmentsofa

sizebelowtheexperimentalresolution.Asecondmechanismis

re-movalofprojectilefragmentsfromtheimpactsitemixedwith

tar-getmaterialejectaduringthe impactprocess.Themixingof

pro-jectilematerial withtarget ejectahasbeenshownexperimentally

by,forexample,Burchelletal.(2012).

4. Discussion

4.1. Largefragments

InFig. 10 we display thebehaviour of fragment size

distribu-tions at the very largest sizes, which depend sharply on impact

speed. At slower speeds the fragment size distributions have a

concave shape. At intermediate speeds (approximately 3km s−1)

thisflattensout.Finally,athigherspeedsthereisaconvexshape. Thisbehaviourisseeninthelargestfragmentsofdisruptedtargets (Durdaetal.,2007;Leliwa-Kopystynskietal.,2009)andisrelated tothe objecttransitioningfroma partially disruptedto aheavily catastrophicallydisruptedregime.Astheenergydensityincreases,

thelarger fragments(which appearinthe slowerspeed impacts)

are replaced by multiple smaller fragments. Thus the behaviour

normallyassociatedwithdisruptionoftargets,appearsalsotohold forfragmentationofprojectiles.

4.2.SurvivalestimatesforimpactsontheMoon,Mars,Asteroidsand Pluto

We use the fit (Eq. (2), Fig. 9) to deduce an estimation of

theimpactorsurvival percentageindifferentimpact scenarios. In

Table4

Summaryofallfittingvaluesforeachpowerlawandsizesectionofthecumulativefragmentsizedistributions(examples ofwhichareshowninFig.7).ThepowerlawisintheformofN(>S)=aSb,whereNisthenumberoffragmentsgreater

thanagivensizeratioS.Wherenoentriesaregiventheprojectilewasrecoveredvirtuallyintact.Alsogivenisthesquare oftheregressioncoefficientforeachfit(R2).

Speed[kms−1] Small Intermediate Large

a(×10−3) b R2 a(×10−3) b R2 a(×10−3) b R2 Basaltcube 0.51 – – – – – – – – – 0.64 – – – – – – – – – 0.70 139.6 −2.64 0.9986 12.1 −3.54 0.9911 497.7 −1.66 0.9495 0.84 62.8 −2.36 0.9964 31.4 −3.25 0.9960 582.4 −1.63 0.9880 0.96 1623.6 −2.40 0.9972 24.0 −3.46 0.9982 0.2 −5.51 0.9845 1.95 10.8 −3.49 0.9995 0.6 −4.24 0.9944 0.04 −5.17 0.9876 3.04 36.2 −3.17 0.9948 0.4 −4.22 0.9992 0.3 −4.41 0.9833 4.05 60.3 −2.91 0.9990 2.3 −3.68 0.9998 0.01 −5.28 0.9769 4.71 21.0 −3.13 0.9940 0.1 −4.70 0.9979 0.01 −5.02 0.9370 4.92 2.8 −3.62 0.9984 0.3 −4.18 0.9981 0.02 −5.06 0.9293 5.31 3.8 −3.58 0.9990 1.3 −3.81 0.9969 0.001 −6.05 0.9923 6.02 2.1 −3.69 0.9965 0.2 −4.19 0.9973 0.0001 −6.88 0.9891 Basaltsphere 1.98 1900 −2.41 0.9791 16.7 −3.66 0.9966 0.14 −6.25 0.9351 Shale 0.39 – – – – – – – – – 0.59 14,165.2 −1.19 0.9893 114.0 −2.42 0.9987 1595.1 −1.17 0.9466 0.95 1612.1 −1.72 0.9897 11.0 −2.94 0.9881 2772.8 −0.79 0.9216 1.93 52.3 −3.00 0.9992 1.6 −3.83 0.9998 150.5 −2.26 0.9927 3.12 269.2 −2.66 0.9973 1.7 −3.82 0.9990 73.5 −2.15 0.9317 4.64 5.9 −3.63 0.9992 0.3 −4.33 0.9961 0.0002 −7.63 0.8260 6.13 11.2 −3.40 0.9984 0.4 −4.35 0.9987 0.001 −6.53 0.9250

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Fig.8. Thegradientsofthecumulativefragmentsizedistribution(seeFig.7)vs(a)impactspeedand(b)bysizeregimeforbasalt,andsimilarly(c)and(d)areforshale. Thefitlinesin(a)aregradient=−0.144x−2.72,0.138x−3.48 and0.628x−2.63forthesmall,mediumandlargefitsrespectively.In(c)thefitsaregradient=0.381x−1.45,

−0.319x−2.69and−1.21x−0.08forthesmall,mediumandlargefits,respectively.

Table5

Estimateofthepercentageofimpactorsurvivalindifferentsolarsystemimpactscenarios.Thepeakshockpressurewasdeterminedusingthe PIAandthepercentagesurvivalwasobtainedfromtheequationshownonFig.10.

Body Speed[kms−1] ShockPressure[GPa] PercentageSurvival Referenceforimpactspeed

Pluto 1.9 4.6 54 Zahnleetal.(2003)

TheMoon 2.3 8.9 39 Burchelletal.(2014a)

MeancollisionSpeedintheAsteroidBelt 5.0 48 17 Bottkeetal.(1994)

Mars 9.3 135 10 Steel(1998)

Fig.9. ProjectilesurvivingmassatpeakshockpressuresdeterminedusingthePIA. Thesolidlineisafittothebasaltdata.Thesolidanddashedlineisthefitforthe basaltandshaledata,respectively.

Table5 we take theaverage impactspeed on differentsolar

sys-tem bodies, and, use the planar impact approximation to

deter-mine a peak shock pressure for that impact. The impactors are

taken as basalt, and the target bodies are either regolith (sand),

watericeorbasalt(fortheMoon,PlutoandbothMarsand

Aster-oidbelt, respectively).TheappropriateC,S anddensityvaluesfor thetargetmaterials are1.70kms−1,1.31and1600kgm−3 for

re-golith(dry sand),1.32kms−1,1.53and915kg m−3 forwaterice,

and2.60kms−1,1.62and2860kgm−3 forbasalt(Melosh,2013).

Using the results for the PIA, combined withEq. (2) we find an

approximate surviving percentage of the projectile (see Table 5).

Whenextrapolatingtootherbodieshowever,thesesurviving

frac-tions shouldbe consideredupperlimits. Thisisbecauseother

is-suesthanfragmentationmayinfluenceretentionattheimpactsite.

Forexample,onsmallbodies,duetothelowescapevelocitymore

material maybelost asejectafromacrater andnot retained

lo-cally.Asalreadypointedout(seeabove),ejectacancarryimpactor materialmixedwithit.

Thesepredictedvaluesprovideonlyaveryrough guideowing

to a lackof detailedknowledge relatingto theeffects of,for ex-ample, scaling to different projectile sizes, porosity in both pro-jectile and target, differing local gravity influencing retention of ejecta,theinfluenceofsurfacecurvatureontheimpactevents,etc.

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Fig.10. Cumulativefragmentsizedistribution(inlog–logspace)forthe10largest fragmentsfor(a)basaltand(b)shaleatthreetypicalimpactspeeds.Atlowspeeds (right-mostdatasetineachpanel),thecumulativesizedistributionforthevery largestfragmentsdisplaysaconcavebehaviour(dottedline).Atintermediatespeeds thishasflattenedtoastraightlineandatthehigherspeeds(left-mostdatasetin eachpanel)hasbecomeconvex.

However they do suggest that Pluto and the Moon should have

large amounts of impactor remnantson their surface (or in the

sub-surfacebeneathimpactcraters).Furthermore,althoughitisa

slightextrapolationfromthedata,itdoessuggestthat17%of ma-terialinanasteroidimpactshouldsurvive.Additionally,theresults inTable5suggestthatoforder10% oftheimpactorcouldsurvive

an impactonMars. Thisishoweveramajorextrapolationbeyond

theshockpressureregimeinwhichthedataweretakenhere.The

curve inFig. 9doesnotvary greatlywithshockpressure athigh

pressures,however,thisresultshouldbetakenasapproximate.

4.3. Onsetofprojectiledisruption

Theprojectileenergydensityisdeterminedbytheequation

be-low (Eq.(4))(see SchultzandGault,1990a;Nagaoka etal., 2014).

Qp

(

θ

)

0.5Mp

v

i2sin2

θ

Mp

=0.5

v

i2sin2

θ

, (4)

whereMpisthemassoftheprojectile,viisthevelocityofimpact

and ϴis the angle ofimpact from the target surface(where for

normal incident impacts this givessin2

θ

=1). It isassumed that

energylostinfragmentationgreatlyexceedsotherinternalenergy

lossessuchasdeformation.Thefragmentationlimit,Q

p,isdefined

astheminimumspecificenergyrequiredtodisrupttheprojectile

sothatthemassofthelargestfragmentequals50%oftheoriginal projectiles’mass(mL/Mp=0.5).

InFig.11thedataformL/Mpvs.Qpareshownforallimpactsof

thecubeshapedprojectilesatnormalincidence.Wefitonetrend

line to the shale data. By contrast the basalt appears to display

two trend lines,as thereare severaldistinct regions apparent in

thedatainthisprojectileenergydensityrange.

Theequationsofthelinesare;forshale(r2=0.9278): mL

mp

=1.05×105Q−1.07

p , (5)

andforbasaltwhereQp<106Jkg−1(r2=0.9967):

mL mp =4.58×1022Q−4.27 p , (6) andwhereQp>106 Jkg−1 (r2=0.9852): mL mp =2.50Q−0.46 p , (7)

where Qp is in J kg−1. From Eqs. (5) and (6) we deduce the

catastrophic disruption energy densities to be 9×104J kg−1 and

24×104Jkg−1,forshaleandbasaltrespectively.Thisisafactorof

∼2.5differencebetweenthetwomaterials.

Schultz andGault(1990a) suggest that the energy partitioned intotheprojectilefragmentation,

EPF,canbesplitintotheenergy

partitionedinto fragmentationafter impact,

EF, andthe energy

wastedingettingtothefragmentationlimit,

EoEq.(8).

EPF mp

=

EF mp

+

Eo mp

. (8)

ItwassuggestedbySchultz andGault(1990a)thatEq.(8)can

be rewritten by introducing the largestfragment mass,mL,p,and

rearrangingterms:

mL mp

=

mL mp

CD

EF

EPF

+

mL mp

PD

Eo

EPF

, (9a) =a

EF

EPF

CD +b

Eo

EPF

PD , (9b)

where a and b represent fractions of the original projectile

massthat define partialand catastrophic disruption,respectively, (Schultz and Gault, 1990a). The first term can be shown to

be equivalent to the projectile strength S (given by the tensile

strength ofthe material), divided by thepeak vertical stress

σ

θ, or,equivalently,whencatastrophicdisruptiondominatesfailure:

mL mp

σθ S

−1 ∼

ρpQ S

−1 ∼

Q

ctρt cpρp sin 2

θ

S ρ

ε

˙1/4

−1

−1 =[Qc

(

θ

)

]−1 (10)

where

ǫ

˙ isthestrainrate,crefers tospeedofsoundand

ρ

refers

tothedensity.Whenpartialdisruptionoccurs,thesecondtermin

Eq.(9b)dominates.Itcanbeshownthat:

mL mp

Qsin6

θ

S

ρ

ǫ

˙ 1/4 −1 =[Qo

(

θ)

] −1 . (11)

Combiningtheseequationsgives:

mL mp =

a Qc

(

θ)

+ b Qo

(

θ)

, (12)

whereQcistheenergydensitywhencatastrophicdisruption

dom-inatesfailure,Qoistheenergydensitywhenpartialdisruption

oc-cursandthe valuesofa andb can be derived empirically.a and

bare notderived forthedatainthiswork.However, Schultzand

Gault(1990a)doderiveaandbfortheirdata.

InFig.12weshow resultsformL/mpvs. Qpfromfourseparate studies;Schultz andGault(1990a),Nagaokaetal.(2014), Avdelli-douetal.(2016)andtheresultsforbasaltprojectilesinthispaper.

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Fig.11. Massratiooflargestsurvivingfragmentofprojectileversustheprojectileenergydensity,Qp.Thehorizontaldottedlinereferstothecatastrophicdisruption

thresh-old,mL/mp=0.5.Thedashedandthesolidlinesarethefitstotheshaleandbasalt,respectively.Thefitsweremadeinlog–logspace.

Allthesestudies usedbasaltprojectiles.Herewe alsoincludethe

datafor the basaltsphere and non-normal incident impact from

Table 1. As stated before, Schultz and Gault (1990a) fired basalt projectiles(diameter5mm)atinclinationanglesbetween7.5°and

15°intosandandoneshotintowater;Nagaokaetal.(2014)fired

basaltcylinders(5mmindiameterand5mminlength)intosand;

andAvdellidouetal.(2016)firedsyntheticbasaltspheres (diame-ter2.0–2.4mm)intoice.

The data in Fig. 12a follows two trends – Trend 1 (basalt

impacts at normal incidence from this work) and Trend 2

(shots at non-normal incident, this work, and from Schultz and

Gault (1990a) involving basalt onto sand at 7.5°). Trend 1 has

almost intact projectiles recovered after the impact, until Q

∼105Jkg−1. The survivingfraction then fallsoff rapidly between

105 and5×105Jkg−1 asdisruption occurs. Above 5×105J kg−1,

theprojectile isfullydisruptedandthe gradientofthe slope de-creases.

The shots in Schultz and Gault (1990a) that were into sand

were all fired at an angle of 7.5°. This means that the

projec-tileenergy density is considerably lower than that in thiswork,

i.e. Qp is lower due to the sin2

θ

term in Eq. (4). Schultz and

Gault(1990a)showthattheprojectileusuallyfragmentsatamuch

lowerQp value thaninourworkatnormalincidence;thisisdue

totheshallowimpactangle.Theimplicationisthat,althoughthe

non-normalincidence at a given impact speed should, according

toEq.(4), reduce theenergy densityin theprojectile, it is actu-allyleadingtodisruptionatasignificantlylowerQpvalue.A

plau-sibleexplanation, is that in shallow angle impacts, shear effects

are important (i.e. so called “impact decapitation”, Schultz and

Gault,1990b),unlikeinmoreverticalimpactswhereitisthe ten-silestrengththatiscritical.

In Fig. 12b we compareour work withthat of Nagaoka etal.

(2014).Thedatacould(mostly)be takenasfromasingledataset withthe same trendvs. Qp,namely an initial step fall in mL/mp until Qp ∼106 J kg−1 (or mL/mp ∼0.01), and then a shallower

dependenceonQpemerges. Thissuggeststhat thereisno

signifi-cantdifferencebetweenimpactsonsand(porosity45%)andwater.

Targetporosity is known to play a part inimpact cratering

pro-cess (see Love et al., 1993; Love and Ahrens, 1996), but it does

not appear to have significantly influenced projectile disruption

here.

Finally, in Fig. 12c we compare our results to those of

Avdellidouetal.(2016)whousedthesamelightgasgunfacilityas here,andsimilarsizedprojectilesofthesamesyntheticbasalt,but firedontosolid icetarget (porosity<10%).Herethechoiceof

tar-gethas clearlyinfluencedthe outcome oftheevent. Catastrophic

disruption on ice occursat an increased Qp∗ (by a factor of 10). Weshotabasaltsphereintoourwatertargetatasimilarspeedto

Avdellidouetal.(2016)toseeiftheshapeoftheprojectilewas sig-nificant(Avdellidouetal.,2016)usedspheresratherthancubesas

here).Theresultwasclosertowhatwefoundfromourotherdata

withcubeprojectiles, ratherthantothatforthebasaltspheresin

Avdellidouetal.(2016).Itthereforeappearsprojectileshapeisnot asignificantissue.Itshouldbenotedhoweverthatthespheresare asynthetic,glassy,basalt.Sothereissomestructuraldifference

be-tweenourcubeshapednaturalbasaltprojectilesandthesynthetic

sphereswhichmayexplainwhythecubeandsphericaldatainour

workdonotfullycoincide– but thisobservationisbasedonone

impact.

Next,wecalculatethepeak shockpressure atthecatastrophic

disruptionthresholdQ

p,forNagaokaetal.(2014),Avdellidouetal.

(2016)andthis work.InTable6 wetake theQ

p valuesfor basalt of24×104Jkg−1,9.00×104Jkg−1and2.31×106Jkg−1fromthis

work, Nagaoka etal. (2014) and Avdellidou etal. (2016),

respec-tively.From Eq.(4) we can deducethe associated impact

veloci-ties to be, 693m s−1, 424m s−1 and2149m s−1. Using the PIA,

withtheappropriate targetvaluesforC andS, anddensitytaken

fromMelosh(2013),theseimpactspeedscorrespondtopeakshock

pressures of 1.55GPa (our work), and 1.00GPa (Nagaoka’s work).

Avdellidouetal.(2016)haveestimatedthepeakshockpressurein

their impacts using Autodynas 1.32GPa at 2.14kms−1. We thus

findthatdisruptionoccursat1.55, 1.00and1.32GPa,verysimilar

values in all three experiments on a variety of target types. The

yieldstrengthofbasaltrocksisveryvariableandsamplespecific. However,theyieldstrengthofbasalt(atlowstrainrate)is

approx-imately 250MPa (Schultz, 1993). Therefore the peak shock

pres-sureatthecatastrophicdisruptionthresholdforthesethreeworks

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Fig.12. Massratiooflargestsurvivingfragmentofprojectileversustheprojectileenergydensity,Qp.ForallthebasaltimpactslistedinTable1,comparedtodatafrom(a)

SchultzandGault(1990a),(b)Nagaokaetal.(2014)and(c)Avdellidouetal.(2016).Thehorizontaldottedlinereferstothecatastrophicdisruptionthreshold,mL/mp=0.5.

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Table6

Summaryoftheprojectileenergydensityatcatastrophicdisruptionandthecorrespondingimpactspeedforshaleand basaltfromthiswork,andbasaltfromNagaokaetal.(2014)andAvdellidouetal.(2016).

Impactor Qp∗[Jkg−1] Impactspeedatthe

Qp∗value[ms−1]

Peakshockpressure (PIA)[GPa]

Reference

Shale 9.42×104 434 0.84 Thiswork

Basalt 24×104 693 1.55 Thiswork

Basalt 9.00×104 424 1.00 Nagaokaetal.(2014)

Basalt 2.31×106 2149 1.32 Avdellidouetal.(2016)

(atlowstrainrates)ofbasalt.Forshalehowever,wefindthepeak

shockpressure at Q

p was 0.84GPa, which is some 14 times the

yieldstrength.

4.4.Comparisontotargetfragmentation

The resultshere forprojectile fragmentation(Table 6) can be

comparedtothatforlaboratoryexperimentsconcerningdisruption

oftargets(seeRyan,2000,forareview).Forexample,Takagietal. (1984) disrupted targets of basalt at impact speeds from 70 to 990m s−1. (i.e. low speed impacts). Theyfound Qfor basalt of

473J/kg,or362J/kgwhenthey combinewithother,similar data

sets.Thesevaluesaremuchlessthanthosefoundherefor

projec-tilefragmentation. Holsapple etal. (2002) summarise a range of

experimentallaboratory resultsfor target disruption,andfor sili-catetargets againsuggest a typical Qofa few hundred J kg−1.

However,thesearecmscaletargets,i.e.atadifferentscaletothe projectilesusedhere.

Recently, Durda etal. (2015) reported on impact experiments

oncm scale basalttargets atspeedsof 4–6kms−1. All their

ex-perimentswere above thecatastrophic disruption limit, withthe

largestsurviving mass fragment rangingfrom 0.24 to 0.02 times

theoriginaltargetmass.Takingtheleastdisruptiveoftheseas set-tinganupperlimit,weobtainQ<2240Jkg−1.Apowerlawfitto

their data suggests Q=1321J kg−1, but thisis based on only 6

datapoints. Thisis greaterthan inthe lower speed experiments,

butstill belowwhat wefind hereforbasaltprojectiles. However,

theirtargetsizeiscmscalecomparedtommscaleforthe

projec-tileshere,andscalerelatedstrain effectschangeQwithsize.For

exampleHousenandHolsapple(1999)suggestthatforgranite,Q

wouldincreasebyafactorofjustoverfiveforeachdecreaseofan orderofmagnitudeinsize.Thispointisreturnedtobelow.

Durdaetal.(2015)alsoreportedontargetfragmentshape.They

found a mean b/a ratio of 0.72±0.13, greater than the value of

0.58±0.16 wefindhereforbasalt. Theyalsoreportedonthe

cu-mulativemassdistributionoftargetfragments,Asusual,theyfind apowerlawbehaviour,andgivethepowerof−0.75to−1.2inthe

fragment mass rangecomparable to our intermediate size range.

Sincemassdependsonsizecubed,thisisequivalenttoaslopein

sizeof−2.25to−3.6,slightlysmallerthanwhatwefind,whichis

−3.2to−4.7.

Michikamietal.(2016),havealsocarriedout impactsinto(5– 15cmsized)basalttargetsatspeedsof1.6–7.1kms−1.Theyagree

withtheearlierresultsofFujiwaraetal.(1978),thatb/aisroughly

constantaround0.7.Michikamietal.(2016) alsoreport on

cumu-lativemassdistributions. Theyfindapowerlawbehaviour,where

the power increases with Q (i.e. with increasing fragmentation).

Forlow massfragmentstheyfindthepowerranges from−0.4to

−1.1. The lower values of −0.4 correspond to Q values of a few

hundredJ kg−1. Forthe higher Q valuestheir resultsare similar

toDurda et al.(2015). Although they make no attempts toscale theirresultswithsize,Michikamietal.(2016)notethattheshape

ratios they find are similar to those of m sized boulders on

as-teroid 25143 Itokawa suggesting a catastrophic disruption origin

for that body. This direct comparison of boulders (m scale) on

Itokawawiththeresultsoflaboratoryimpactfragmentation

exper-iments(cmscale)followsonfromthatofNakamuraetal.(2008)

who alsonotedthesimilaritiesin shape.Michikamietal.(2018),

revisit target fragmentation, looking at fragments sizes ranging

from<120µmto>4mm.Atsmalltomedium sizes, theyfindb/a

isconstantataround0.7independentofthedegreeof

fragmenta-tion.Theygoontonotethatb/aforItokawaparticlesreturnedby

theHayabusamission(seeTsuchiyamaetal.,2014)haveameanof

0.67,andsuggestthattheyarefragmentsfromanimpactedtarget.

InTsuchiyamaetal.(2014),thecumulativesizedistributionofthe Itokawaparticleswasfoundtobe−2.0.

Wecan alsocomparetopredictionsfrommodelling.Benzand

Asphaug (1999) model the disruption of basalt bodies at speeds of 3kms−1, andtheir resultssuggest that at the mm size scale

here,Qshouldbeapproximately2.3×104Jkg−1.Wenotethatat

cmsize scales, we havepreviously reportedQ=1447±90Jkg−1

forcementtargetsinourgun(MorrisandBurchell, 2016), within afactorof2–3forsimilartargetsreportedelsewhere(Daviesand Ryan,1990;Fujiwaraetal., 1989).Moregenerally,Holsappleetal. (2002)summarisearangeofpredictionsforQvstargetbodysize

forrockytargets.Extrapolating thepredictionsinHolsappleetal. (2002), to the mm size scale here, suggests a range of val-ues of Qfrom 5×103 – 5×104J kg−1. More recently,

Leliwa-Kopysty´nskiet al.(2016) use an analytic model fordisruption of

rocky bodies which produces similar results. So there is a range

forQfortarget bodiesintheliterature,butthevaluefoundhere

fortheshaleprojectilesistwicetheuppervalueinthisrange,and

thatforbasaltissome 5timeslargerthantheuppervalueinthe

modelling.

4.5. Solarsystemimplications

From the results herewe can, assuming no size effects, scale

to impacts onrealbodies inthe SolarSystem. Cautionisneeded

however,strengthiswell knowntobesizedependent.For

exam-ple, in catastrophic disruption of bodies, the energy density

re-quiredto justdisrupta body,fallsasbody size increases.Thisis

duetogrowthofcracksetc.beingscaledependent,meaning that

largerbodiesareineffectweaker(seeforexampleHolsappleetal., 2002). Similarlythere areparticular straindependent effects that

show up at small sizes. This is illustrated for example by Price

etal.(2010,2012,2013)wherethestrengthofseveralmaterialsis showntobehighlynon-linearabovestrainratesof105s−1,rising

byoveran orderofmagnitudeasstrain ratesincreaseto108 s−1.

This regime is entered when projectile ortarget bodies are very

small(less than say10µm). Whilstthesesmall sizesare not

rel-evant here, itdoesillustrate thedifficulties ofextrapolatingfrom onesizescaletoanother.

Afullextrapolationoftheresultsheretodifferentsizescalesis thus difficult.No appropriate modelis readilyavailable which,at

all size scales,produces forexample size andshape distributions

offragmentsbasedonmineralogyoftheimpactors.Wetherefore

follow the approach of Daly andSchultz (2015b, 2016), who

at-tempt to identify key properties of laboratory scale experiments

andcompare tosolarsystem scaleexamples. Forexample,if

im-pactorfragmentswereidentified,andthemeanb/aratioobtained

References

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