NASA-CR-ZO0969

j/ // ._

Final ReportAttachment 2

CONTRACT NAS8-38856

October 17_ 1995

Structural DamagePrediction and Analysisfor Hypervelocity Impact

AIAA 92-1407

Space Debris Surfaces(Computer Code):Probability of NoPenetration versusImpact Velocity andObliquity.

Prepared for:National Aeronautics and Space AdministrationGeorge C. Marshall Space Flight CenterMarshall Space Flight Center,Alabama 35812

I. OC|IliiO

MAF/MMA 31-100 (3/95)

https://ntrs.nasa.gov/search.jsp?R=19960023925 2018-06-06T17:03:37+00:00Z

i

AIAA 92-1407

Space Debris Surfaces (Computer Code):Probability of No Penetration versus

Impact Velocity and ObliquityN. Elfe "_R Meibau_ and G Olsent

, " 1 "

Martin Marietta,t NASA-Marshall

Huntsville, AL

New Orleans, LASpace Flight Center,

I

L 0.5 to 16 krrVs "-"

AIAA Space Programsa]'_c:i Technologies Conference

March 24-27, 1992 / Huntsville, AL

For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics370 L'Enfant Promenade, S.W., Washington, D.C. 20024

SPACE DEBRIS SURFACES:

PROBABILITY OF NO PENETRATION

VERSUS IMPACT VELOCITY AND OBLIQUITY

N. Elfer*,t, R. Meibaum*, G. Olsen**,t

AbstractA unique collectionofcomputer codes,Space

Debris Surfaces (SD_SURF), have been developed

toassistin the designand analysisofspace debris

protection systems. SD_SURF calculates and

summarizes a vehicle'svulnerabilityto spacedebris

as a functionofimpact velocityand obliquity.

An SD_SURF analysis will show which

velocitiesand obliquitiesare the most probable to

cause a penetration.This determination can help

the analystselecta shielddesignthatisbestsuited

to the predominant penetrationmechanism. The

analysisalsosuggeststhe most suitableparameters

fordevelopment orverificationtesting.

The SD SURF programs offerthe option of

eitherFORTRAN programs or MicrosoftEXCEL

spreadsheetsand macros.The FORTRAN programswork with BUMPERII. The EXCEL spreadsheets

and macros can be used independently or with

selected output from the SD_SURF FORTRAN

programs.Examples willbe presented ofthe interaction

between space vehiclegeometry, the space debris

environment, and the penetration and critical

damage ballisticlimitsurfacesof the shieldunderconsideration.

Space debris probabilitycodes, BUMPERII

and Space Debris Vulnerability(SDV), analyze a

space vehicleas a facetedgeometry.1"4These codes

calculatethe probabilityofno penetrationforeach

facet based on the exposure area and the

penetration resistance (ballisticlimit)to each

* Martin MariettaManned Space Systems,

New Orleans,LA 70189

t AIAA Member

** NASA Marshall Space FlightCenter,

Huntsville, AL 35812

Copyright O 1992 by the American Instituteof Aeronautics and

Astronautics, Inc. No copyright is asserted in the United Stat_

under Title 17, U.S. Code. The U.S. Government has a royalty.

free license to exercise all rights under the copyright claimed

herin for Governmental purposes. All other rights are reserved

by the copyright owner.

threat'simpact velocityand obliquity,as described

in the following sections.The output tellsthe

designerwhich areas are most vulnerable.

.En.zinmm_The space debris environment is defined in

terms of a flux of particles of diameter, d, or larger,dependant on the year of interest (due to assumedgrowth in the environment and solar flux varia-

tions) and the spacecraft altitude. 4 Figure 1 showsa flux versus d curve for typical parameters ofinterest.

Orbital Debris Flux

o.E

.,,--.

X

_=14.

10

0.1

0.001

0.0_01

0.0000001

0.001

SSP 30425

Year = 1998

Altitude = 388 km

Inclination = 28.5 =

Solar Flux - S = 10C

Flux Definition

(W'_hout

Collision

Avoidance)

W'lth10o%Collision

Avoidance

over 10 cm I

i IIIBIII i i Rill I I iK,Inl I I 111121 I I lUtEI

I

0.01 0.1 1 10 100

Minimum Debris Diameter [cm]

Fig. 1. Impact flux versus space debris diameter.

The space debrisenvironment may be modeledas a seriesofthreatsfrom discretedirections.For

low earth orbit (LEO), space debris may be

assumed toexistin circularorbits.This assumption

fixesthe orbitalvelocity.Debris cannot intercepta

spacecraftfrom more than approximately 10°above

orbelow a plane tangenttothe localEarth normal.Otherwise the debris would enter the Earth's

atmosphere and be removed as a threat.Therefore,

the relativeimpact velocityin LEO isdetermined

by the orbitalvelocity,Vo, and the intersection

angle,_, ofthe two orbits.The impact velocity,Vi,is:

.180°-0,Vi = 2 Vo- cost_J

Figure2 shows the fractionofthe totalfluxcoming

from angles relativeto the directionofflight.The

relativeimpact velocityforthe intersectionof 388

km orbitsisalsoshown on the plot.

150__ 4

__) VIIOCII 7 |bROIl]

lao .o.ol-p...p.01.0.o20.oo.o.o4-'I" o' s

Dt_n e_

Pilghl

210 330

Fr,¢Ucm et Total FhCll

2?0

Fig. 2. Angular and velocity distribution of flux.

BallisticLimitSurface

The spectrum of debrissizes,velocities,and

obliquitiesthat may impact a shield lead to a

varietyofpenetrationmechanisms. Figure 3 illus-

tratesa ballisticlimit surface for hypervelocity

impact on a multiwallshield.A projectilediameter

at a velocityand obliquityabove the surfacewill

penetratethe shield.A diameter below the surface

willnot penetrate the shield.There are several

penetrationmechanisms which are describedin

Fig.3. Changes in shieldparameters affecteach

penetrationmechanism differently.Therefore,itis

important for the designer to know what

penetrationmechanism has the greatesteffecton

the overallprobabilityofno penetration.

Itisnecessarytounderstand the consequences

of a penetration.A small penetration should beavoided because ofpotentialdifficultiesin finding

and repairinga leak.However, a smallpenetration

EO

O

Eelo

1.00,

0.00.

0.54

Velocity [km/s]

7.511

I - Singleparticlepenetration.2 - Fragmentpenetration.

90°

45°

0o14.5

Obliquity[degrees]

3 - Momentumfailureby bulgeorspell.4 - Ricochet,bumperfragmentspenetrate.

Fig. 3. Ballistic Limit Surface with multiplepenetration mechanisms.

does not resultin an immediate fatality.Critical

damage willbe definedas penetrationsresultingin

rapiddepressurizationas wellas catastrophiccrack

growth. There is a theoreticalthreat of bodilyinjurydue tofragments,but thisismuch lesslikely

and willnotbe treatedinthispaper.

For Space StationFreedom, the criticalhole

size for too rapid depressurization has been

estimated as 10 cm in diameter. To get this

diameter,eithera largeprojectileorpetallingofthe

hole isnecessary.Conservativefractureanalyses

predictthatlargepetalsmay lead to catastrophic

Eo

Q

EQ

o

0.54

Velocity [kzn/s]

1114.5

90°

45°

0•Obliquity

[degrees]

Fig. 4. Critical Damage Surfaces.

2

rupture rather than simple

depressurization.

A criticaldamage limitsurfacesis

presented in Fig. 4. At high velocitythereissufficientintermediatethermal

blanket/shieldto prevent crateringor

spall, and the rear wall fails by

momentum induced bulging and

petalling.This can open a hole or

propagatea cracktoa much largersizethan the initialdamage area. The

projectilediameter to cause critical

damage was estimatedtobe 50% larger

than the projectilediameter to cause

penetration. For low velocity

penetrationthe projectedarea of the

projectile,plus a damage zone, is Iassumed to control criticaldamage. IThis is a very rough assumptionbecause thereisinsufficientdata about

the momentum deposited in the rearwall.The estimate of the size of the

damage zone willnot have a stronginfluenceon the

overallprobabilitybecause ofthe large projectilesize.

An alternative high-velocity penetrationmechanism may be wide area spall.A larger

particlewould then be necessaryto drivepetalling

and crackgrowth inthe rearwall,because much ofthe momentum willbe transferredto the spall

fragment.To estimate the influenceofthisfailure

mechanism, the projectilediameter was assumed tobe 225% of the ballisticlimit diameter for the

followingcalculations.

Model Generation

* SupertabNASTRANtranslator

I GEOMETRY• Space Debris• Meteoroids

ProbabilityAnalysis

The probabilityofno penetration(PNP) fromeach directionand foreach element isbased on the

Poissondistributionforzeroevents:

( nthreats

PNPel = exp[- Z(Ni.Ai)'tI

\ i=l l

where (withconsistentunits)

Ni = flux that penetrates from each threat

direction,i,

= 4-fi.Nr(di).

Nr = flux on a randomly tumbling plate

(specificationdefinition)of diameter d or

larger,di isthe diameter to penetrateat

the velocity and obliquity of the ith

threat.

fi = fractionoffluxfrom threatdirection.

RESPONSE I

• Space Debris• Meteoroids

I+ I

SHIELD I,e Space DebrisMeteoroid8

Fig. 5. BUMPERII Modules, Input and Output.

A i = projected area of the facet in the fluxdirection.

t = exposuretime.

The totalPNP isdetermined by the productof

the PNP foreach element.

nelements

PNPtotal = I'_PNPj

j=l

Figure 5 shows the BIYMPERII modules and

their input and output as they calculatePNP.

BUMPERII startswith a SuperTab output file

finiteelement model ofthe spacecraR.The GEOMETRY module of BUMPERII

calculatesthe projected area of the elements

exposed toeach threatdirection.A significantpart

of thiscalculationis intercomponent shadowing.

This can be a very time consuming processfor a

largemodel.The RESPONSE module creates a ballistic

limit surface from a menu of user selected

penetrationequations.The ballisticlimitforeach

shieldofinterestisstoredin a matrix forevery0.25

km/s and 5° obliquity.This isalsostoredinbinaryform in the computer. Another BUMPERII code,

RPLOT, reads the binary fileand puts out a

formattedfilewith the ballisticlimitat 0°,15°,30°,

45°,and °60 obliquityfor2D plots.The SHIELD module calculatesthe PNP for

any range of element numbers requested by the

analyst.SHIELD alsohas an option to create a

SuperTab fileto plotprobabilitycontours on the

originalgeometry model.

3

SD SURF Analysis Annroach

To design the most effective shield, theanalyst must know which penetration or damagemechanism is predominant. It is the goal of theSD_SURF computer programs to provide thisinformation.

The flux associated with each point on the

ballistic limit surface can be weighted by the prob-ability of an impact at that particular velocity andobliquity.

PNP(V,6) = exp[-N(d).A(V,6).t]

where A(V,6)isthe totalarea ofthe spacecraftthat

willbe impacted at an obliquity,6,from a debris

particle at velocity,V, and N(d) is the fluxassociatedwith the diameter d thatjustpenetrates

atV and 6.There isa differencein the PNP calculatedfor

a unitarea ata singlevelocityand obliquityversus

distributingthe area overtwo bracketingvelocities

and two bracketingobliquities.This is due .tothe

non-linearrelationshipbetween fluxand diameter.

On the other hand, the analysis of a curved surfacein BUMPERII is more accurate only if the size ofthe facets is smaller than the five-degree incre-ments used on the RESPONSE and AREASURFACE tables.

SD SURF - FORTRAN Version

The interrelationship of the FORTRANmodules of SD_SURF is shown in Fig. 6. SD_SURFacts as a post-processor of BUMPERII-RESPONSEand GEOMETRY output. It provides additionalinformation not readily obtainable fromBUMPERII.

The A_SURF module reads the BLrMPERII-

GEOMETRY binary output to create the exposedarea matrix as a function of velocity and obliquity.Rather than lump the area of one facet at thenearest velocity and obliquity, A_SURF uses thelever rule to distribute the projected area, for onefacet and one threat, over the four nearestvelocities and obliquities. The sum of the exposedareas is equal to the area reported by BUMPERII.

The A_SURF module puts out both anunformatted file and a formatted file. The unfor-

matted binary file can be read by the P_SURFmodule. The formatted text file can be used to

check the output manually, or it can be read by theEXCEL modules as described in the next section.

The P_SURF module reads in the A_SURFand RESPONSE output files, and uses the sameflux routines in BUMPERII-SHIELD to calculate

the flux.area.time (NAT) array. A text based con-

tour map is generated, which should be compatible

with any FORTRAN platform, and also a text filethat may be used with sophisticated graphics pack-

ages. Examples of the contour plots will be shownin the examples in the next section of this paper.

The final FORTRAN module is R_PLOTS. It is

used to translate BUMPERII-RESPONSE outputfiles to text formatted files. The text formatted file

is set up at 0.5 km/s and five-degree incrementsrather than the 0.25 km/s and five-degree incre-

ments used by RESPONSE. Commas are used asdelimiters to ease import by the EXCEL modules.

SD SURF - EXCEL 3.0 Version

The EXCEL version can be used both as an

alternative or a complement to the FORTRANversion. The EXCEL version is not as fast or as

"turnkef' as a FORTRAN application. However, ithas the advantages of a spreadsheet: customized

calculations and analyses are simple to generate;error checking is very easy; there is quick access tographing.

The structure of the EXCEL version is shown

in Fig. 7. The backbone of the PNP calculation isthe PNP_Template. There are several differentareas on the worksheet:

• Ballistic Limit surface, diameter to penetratein increments of 0.5 km/s and five degrees ofobliquity. (It is created on a Ballistic LimitTemplate or imported from RESPONSE viaR_PLOT 5.)

• Environment definition including year, solarflux level (explicit or calculated), and altitude.

• Flux calculation for each diameter in the

ballistic limit surface. (This is a function macrothat is defined on the function macroworksheet.)

• Area Surface, A(V,6), created usingArea_Maker Macro, or imported fromA_SURF.

• Flux • Area • Time, N.A.T, for each V and 6.(The summation of these cells is used to

calculate the PNP.)

Function macros operate as subroutines andare used to calculate ballistic limits or flux for

appropiate input values. Command macros provide

control of files and the pasting of named arraysfrom ballistic limit and area templates to the PNP_Template.Any ofthe templatesmay be customized

and saved by any name forlateruse.Hardcoding

the names would make iteasierfora new user,but

the flexibilityprovidedby usinggeneralnames was

deemed tobe more important.

4

Model Generation• Supertab• NASTRAN

translator

I GEOM II Space Debn_ i[ • Meteoroids J ,

A_SURFArea Fraction Table• Space Debris

by vel. and obl.[binary]

by vel. and obl.

SURF(FORTRAN vers.)• Space debris only• BUMPERII flux

subroutines

PNP by range• Flux.Area.time

by vel.and obl.[formatod]

RESPONSE• SpaceDebris• Meteoroids

Y:i BUMPERII ]

Program

Fig. 6. SD_SURF - FORTRAN and BUMPERII Modules, Input and Output.

Optional Input fromFORTRAN programs:

R PLOT5 Output

A_SURF Output

by vel.and obl.formated]

SD_Surf EXCEL vers. (o_5 km/s by 5 degree increments)Command Macros Function Macros• Create Pull Down Menus • Ballistic Limit calculations• Dialog boxes and messages * Flux calculations• Open/Save files and templates Templates• Control order of calculation • Prodofined areas, calculations• Cut and paste from templates and formats

I BI_Macro Template P_NP/Flux Templa_

• Function Macro

• Paste truing SD_SURF Obliquit 7 .

V Ballistic Limit iBL-RPLOT Template •• Open and Pasteusing I

SD_SURF Macro

AREA Template

Area_Ma fills in template 0Vel. Distrib. function

Direct from text file i

uJing Aroa_Maker j

0

¢

it

;Y

Flux (d, environment t

• Function macro I

Fig. 7. SD_SURF - EXCEL and SD_SURF - FORTRAN Modules, Input and Output.

The Area Surface maybe created on the

Area_Template using the Area_Maker Macro. The

analyst selectsthe geometry desiredfrom a pull-

down menu. The standard geometriesare shown in

Fig. 8. The specificgeometry is entered in cus-

tomized dialogboxes.Each facetisanalyzedateach

velocityincrement.This iseffectively64 threats(at

equally spaced velocities),compared to the 45threatdefaultinBUMPERII.

SD_SURF for EXCEL lacks some of the

featuresof BUMPERII. BUMPERII must be used

for shadowing analysisin GEOMETRY, multiyear

flux averaging in SHIELD, or the extensive itera-tions required to run PEN4 in RESPONSE.However, the GEOMETRY and RESPONSE outputmay be imported via the FORTRAN A_SURF and

R_PLOT5 programs. Multiyear flux calculationscan be programmed into the EXCEL macros with a

corresponding increase in analysis time.

Probability Studies

The A_SURF program and the Area-Template

calculatethe effectiveexposed area at each velocity

and obliquity.Figure 9 illustratesthe analysisofa

fiatplatethatisorientededge on tothe directionof

flight (90 degrees yaw in Fig. 8). The first part ofthe analysis is the calculation of the projected area

relative to each impact velocity direction. Figure 9(b) shows the probability associated with each

impact velocity. Figure 9(c) shows the final resultafter multiplying the projected areas by the relativeprobability.

A_SURF reveals the coarseness, or granular-ity, in the spacecraft model and debris threat in theGEOMETRY analysis. The default of 45 threat

directions in BUMPER gives only 22 velocities due

to symmetry. This will produce gaps along thevelocity axis. _Waves" on the surface are an artifact

of the coarseness of the modelling. The sphere is aneasy shape to analyze since it looks the same from

any direction. (That is why it is a separate option inthe AREA_Maker macro.) The projected area fromany direction is shown in Fig. 10. Also shown is itsappearance if it were modelled using facets thatcover15 degreesof curvature.The granularity,orwavinessisobvious.

The sphereisalsoa good representationofthe

surfacearea of any spacecraftthat is not Earth

oriented.Itwillappear tobe randomly tumbling to

the debrisflux and average out to the obliqueimpactson a spherewiththe same surfacearea.

AXE5 ROTATION RECTANGLE DI5K

II P_¢h "r_w I L'I Radius = L1

or I1¥ I\x T x I x

11CYLINDER SPHERE CONE

1Note: 5tart and stop angles are shown positive starting from zero (heavy line).

Negative numbers may be used. (Eg. -90 to 90 for *y Side Of cylinder.)

Cone anti cylinder are not symmetric. O" to 5" does not also generate 175" to 180".

The difference in the start 2nd stop angles must De evenly divisible by the tncremenL

Fig. 8 AREA_MAKER Available Geometries

E

E4(

O.S

0,4

0.3

0.2-

0.1

0

O _

Velocity [knVs]

a) Projected areas in each threat direction.

: 0.04.q:

o.03.0.02 •

_= 0.01

12

voloc [knVs]

b) Probability distribution (as In Fig. 2.)

_' 1.5E-2.

=r1.E-2.

9(5.E-3 -

¢%1

ObliquityId,,g,_sI

c) Effective area at each velocity and obliquity.

Fig. 9 AREA_MAKER analysis of a plate edgeon to the direction of flight. (The surfacenormal Is in the y axis In Fig. 8.)

Since the distributionsare not smooth, the

analystmust recognizethatadjacentcellsallwith

moderately high impact ratescan be more signifi-

cant than a singlecellwith the maximum impact

rate.

penetrationAna]vsis

Figure 11 shows the P_SURF analysisofthe

effectivearea in Fig.9.This isan example ofthe

text-basedcontourplot.The ballisticlimitwas the

RESPONSE output fora 0.050 inch bumper, four

inch standoff, MLI, and a 0.125 inch 2219

aluminum rear wall, using the BUMPERII

regression equation and default analysis ofWilkinsonmomentum failure.

Figure 12 is an illustrationof the velocities

and obliquitiesforwhich most penetratingimpacts

couldoccuron one earlyconceptfora spacestationmodule. (The same RESPONSE ballisticlimitsur-

faceisused as in the previousexample.)Itcan be

noted thatBUMPER analyzedthe PNP forone year

as 99.88305%, while P_SURF calculated it as99.88475%.The effectiveareawas identical.But,as

mentioned previously,partitioningthe area to

discretevelocitiesand obliquitieswillaffectthe

result,justas assuming a curved surfaceisrepre-

sentedby a fiatfacet.The probabilityofpenetration(POP : 1 - PNP) was 0.11695% for BUMPERII to

0.11525% forP_SURF. The percentchange betweenthe two is1.5% ofthe POP.

CHticalDnma_e AnalysisMathematically the calculations for the

probabilityof no criticaldamage (PNCD) are nodifferentfrom the PNP calculationsexcept that a

criticaldamage surface is used instead of the

ballisticlimitsurface forpenetration.Use of the

previouslydescribedcriticaldamage limitsgivesa

tlm4mmwl_m

1 mmll_

_1_1 wal i_um4 aN

'0

5

/_ea

imP216

4

2

0

0 "0 20 _ 40 50 _ 70 80 90

O_)lt_Jl:)' Angle [Oegree

Fig. 10. Armlysis of a sphere.

7

O

E

k

a14.

Obllqulty

[degrees]

Fig. 11. P_SURF analysis of flat plate In Fig. 9.

PNCD of 99.965 and 99.985, for momentum tearingand spall failure mechanisms respectively.Comparison of the probability of critical damage tothe probability of penetration (POCD/POP) showsthe chance of a critical failure if penetration shouldoccur. This ranges between 10% and 25%, depend-ing on the critical damage limit that is used.

It may be noted that the environment defini-tion does not include collision avoidance for track-

able debris (> 10cm). This may not be significant for

O

E

i===

,T

tO

¢q

Velocity [kin/s]

a) EXCEL Graph

P

Obliquity

[degrees]

Fig. 12. P_SURF analysis of a SSF module.

penetration of the baseline design, but collisionavoidance can affect the flux of particles capable of

causing critical damage.

The SD_SURF collection of computer codes

provides valuable design information:

• The most likely velocities and obliquities tocause a penetration are displayed. This isuseful in shield selection and verification.

= Granularity in the model facets and assumedthreat environment is displayed. Plots alsoprovide an overall "sanity check" on themodel.

An additional benefit of the structure of thecode is that the intermediate results are contained

in fairly small matrices. This allows the followinguses:

° Computations may be made in easily

modifiedspreadsheets.

• Fast recalculation is possible for opti-mizationstudies.

Acknowledgements

Two of the authors (Elfer and Meibaum) grate-fully acknowledge support for this work undercontract NAS8-38856. The authors also wish to

acknowledge the support and guidance of severalpeople in particular: Joel Williamsen, JenniferRobinson, Scott Hill and Sherman Avans.

_J_: 11 _ r_z: 30_050HB_S._

A _ F'JZ: M_I7-ALL.AS8

mUm(t)- 99.884"75 _ _ x _ x ¢_e rm#1 - 0.11532E-02

.12.345 at. e¢luaJ. _ _ 0 ¢,o mfx _ - 0.26100K-04

IMPA(_ _ km/s

CI_ 1 2 3 4 5 6 7 8 9 10 1.I 12 1.3 "t4 15 16

.Oeg I 1 Z 1 1 1 I I I I I Z I I T I

90 ................................................................

75 .............................. 1 ...... i..1 ..... l..I.i ............

i i

65 ........................................ 1..1..2..2.!.212 ........

60 ...................... l...2...!..i...i ..... !..2..2.51/2 .........

55 .......................... 1 ............. i..11.3._ ............

I • .50 .................................. i..3..2..21.51.3 .............

45 .......................... 1...2..1 ...... 31.41.1 .................

40 ..................................... 5..3 .......... ! ............

35 .............................. 2..!i..i ........... i ..............

30 ................................................................

2_ ..................................... l ..........................

20 .................. i ..................... ! .......................

1.5 ........................................... 4..4 ................

I0 _ .I ..............

5 ................................................ I

0 ................................................................

b) FORTRAN Text Plot

(1995 exposure environmem).

I. Coronado, A_ et al.:"Space StationIntegrated

Wall Design and PenetrationDamage Control,"

Contract NAS 8-36426,NASA-Marshall Space

FlightCenter,1987.

2. Graves,Russel:BumperlI User'sManual.

3. Elfer,N.; et al.Martin Marietta IR&D M-01S,

unpublishedresearch,1987.

4. "Space StationProgram Natural Environment

DefinitionforDesign,"NASA SSP 30425.

5. Elfer,N.;and Rajendran, A. M.: "Space Debris

Protection,n in T. Wierzbicki,N. Jones Eds.

StructuralFailure,John Wiley & Sons, New

York, p.41-78,1989.

9