Full report

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3 2 NationalAeronautics and SpaceAdministration Lyndon6.JohnsonSpaceCenter Houston,Texas 77058 Reply 10 Atin o! SN3-91-42 February 15, 1991 TO: Distribution FROM: Eric L. Christiansen/SN3 SUBJECT: Shield Sizing and Response Equations REFERENCES: (1) Memorandum SN3-90-131, E.L. Christiansen: "Shield Sizing Equations, October 12, 1990. (2) Memorandum SN3-91-19 ver.2, E.L. Christiansen: "Whipple Shield Sizing Equations," December 18, 1990. (3) Memorandum SN3-91-21, E.L. Christiansen: "Ballistic Limit Equations, December 21, 1990. ( 4 ) Memorandum SN3-91-25, E.L. Christiansen: "Weight Reduction Strategies for Meteoroid/Debris Shielding,Il February 4 , 1991. This memorandum provides a consolidated list of meteoroid/debris shield equations which have been given in the referenced memorandums. In some cases, equations have been updated; thus, this memorandum supersedes Reference 1 (i.e:, SN3-90-131). The equations in this memorandum are presented in two parts: (1) shield sizing equations which are used to produce preliminary estimates of shielding weights, and (2) response equations to describe the impact conditions (projectile size as a function of velocity, density, and impact angle) causing failure of a given shield that are to be used for probability analyses (such as in the modified BUMPER program). Specific equations are given that are applicable for the following types of shields: aluminum Whipple shields, Nextel multi-shock (MS) shields, and mesh double-bumper (MDB) shields. These equations will be updated in the future as warranted by the results of additional tests, analyses, and shield modelling. 1

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Nomenclature C Speed of sound in target (km/sec) d projectile diameter (cm) dc critical projectile diameter (cm) causing failure 6 density (g/cm3) H Brinell hardness of target (BHN) m areal density (g/cm2) M projectile mass (9) P penetration depth (cm) S overall spacing between outer bumper and rear wall (cm) CJ rear wall yield stress (ksi) t thickness (cm) e impact angle (deg) measured from surface normal V projectile velocity (km/sec) vn normal component of proj. velocity (km/sec) = V cos 0 Subscripts: b bumper(s) [all bumpers in Multi-Shock (MS) shield, first & second bumper in Mesh Double-Bumper (MDB) shield] I intermediate layer P projectile W rear wall 1,2,3,4 individual bumpers EQUATIONS FOR PRELIMINARY SHIELDING DESIGN For the WP-2 preliminary design review (PDR), McDonnell Douglas Space Systems Company (MDSSC) selected an aluminum Whipple twosheet shield for meteoroid and debris protection of WP-2 critical equipment. A simplified method was used by MDSSC to size the thicknesses of the bumper and rear wall of the shields and estimate shielding weights. A Ildesign" particle size was calculated for each surface of a critical element from probability of no-failure requirements, environment models, surface area, and orientation considerations. The bumper and rear wall thicknesses for each surface were calculated based on the "designitparticle size, assuming average orbital debris and impact velocity (10 km/sec and 20 km/sec, meteoroid respectively), debris and meteoroid densities of 2.8 g/cc and 0.5 g/cc, and a normal impact angle (i.e., 8 = 0 deg.). This approach is adequate for deriving estimates of shielding weights and for performing quick trade studies, but it is not suitable for verifying design adequacy or for assessing design options to a greater level of detail. However, because MDSSC and JSC organizations are using this simplified method for estimating shielding weights for Whipple and advanced shields, the following equations are provided based on recent hypervelocity impact (HVI) 2

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test results. They will be updated in the future as warranted by the results of additional HVI tests, analyses, and shield modelling. Aluminum Whipple Shield Eauations: Where, in equation 2, coefficient c = 0.16 rn-sec/g'/~-km. Bumper thickness, in Equation 1, has been adjusted by the ratio of projectile to bumper density. This change will result in reductions in the MDSSC weight estimate for bumpers on surfaces of critical equipment that are only exposed to the meteoroid flux (because meteoroids are low density). The coefficient in Equation 1 has been increased to 0.25 from the MDSSC PDR approach of using 0.20. This is required to reduce the possibility of underestimating the required rear wall thickness with small standoff distances (i.e., when S/d < 15). If standoff distance is large (i.e., S/d > 30), then the original 0.20 coefficient can be substituted without reduction in accuracy of Equation 2. Equation 2 is a slightly modified version of the Cour-Palais Whipple equation (11non-optimum81)which was used in the Apollo program to extrapolate test data to meteoroid impact conditions (B.G. Cour-Palais: I1MeteoroidProtection by Multiwall Structures,I1A I M Paper No. 69-372, 1 9 6 9 ) . The wall thickness calculated by Equation 2 is for a ballistic limit defined as no perforation or detached spa11 of the rear wall (corresponding to damage categories D1-D2, E1-E2, and F1-F3 as given in Figure 1). The Equation 2 coefficient was derived from HVI testing with aluminum, glass, and nylon projectiles that varied in diameter from 0.04 cm to 1.9 cm. Equation 2 is valid for normal component velocity (V,) of greater than 7 km/sec, S/d ratios of greater than 15, and tb/d ratios of greater than 0.15. Outside of these ranges, the equation potentially will underpredict rear wall thickness. Reference 2 contains more information on the derivation and applicability of these equations. Nextel Multi-Shock (MS) Shield The multi-shock (MS) shield is an advanced, low-weight shielding alternative to the Whipple shield. Sizing equations for two types of MS shield are given in this section: (1) Nextel ceramic fabric MS bumpers with an aluminum rear wall and (2) An allflexible shield consisting of Nextel MS bumpers with a Nextel 3

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.rear wall. The equations are based on four equal areal density Nextel bumpers, all equally spaced. In these equations, the combined areal density of all four Nextel bumpers is given by "mbll,and the overall spacing (from outermost bumper to the rear wall) is given by lrStt. Equations for Nextel bumpers and aluminum wall: mb = 0.19 mp = 0.19 d 6, (3) m, = 43.1 M VJS' ( 4 0 / 0 ) ~ . ~ (4) Equations for Nextel bumDers and Nextel wall: mb = 0.19 mp = 0.19 d 6, m, = 43.6 M V,/S2 These equations are slightly a modified version of the MS Cour-Palais and J.L. Crews: "A equations presented in B.G. Multi-Shock Concept for Spacecraft Shielding,I1 International Journal of Impact Engineering, Vol.10, pp.135-146, 1990. The wall areal density calculated by Equations 4 and 6 is based on the ballistic limit criterion of preventing both perforation and detached spa11 (Damage Category: F1 and F3 in Figure 1). HVI testing with aluminum projectiles up to 1 cm have been performed on the Nextel bumper and aluminum wall MS configuration (Figure 2). The all Nextel MS shield has been demonstrated with aluminum projectiles up to 0.32 cm. These equations can be applied for normal component velocity (V,) of greater than 6 km/sec and S/d ratios of greater than 15. Mesh Double-Bumper (MDB) Shield The Mesh Double-Bumper (MDB) is another advanced shield that provides similar protection benefits as the MS shield. A schematic of the MDB shield is given in Figure 3. It was developed to show how additions of a mesh and high strength fabric to a Whipple shield could provide a large improvement in shielding protection capability. Impact testing at the JSC Hypervelocity Impact Research Laboratory has shown that a double bumper system with a mesh outer bumper exhibits superior performance than the same weight double bumper consisting of two continuous aluminum sheets. The following equations have been modified from those presented in E.L. Christiansen: I'Advanced Meteoroid and Debris Shielding Concepts,11AIAA Paper No. 90-1336, April 1990. 4

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MDB Equations For the mesh first bumper: m, = c, d 6, (7) Where, in Equation 7, the coefficient, c,, can range from 0.035 to 0.057 without affecting the accuracy of the following equations. The mesh is composed of wires in a square pattern with a wire diameter to projectile diameter ratio of from 0.07 to 0.10. Generally, from 4 to 6 wires are Ircut"by the diameter of the projectile. The first to second bumper spacing is: S, = 4 d. The second bumper is a continuous aluminum sheet that is sized by the following equation: m2 = 0.093 d 6, A high strength fabric intermediate layer (Spectra, Kevlar, etc.) is mounted at a short distance in front of the rear wall (S3 = 4 d). For Spectra or Kevlar, the sizing equation is: m, = 0.064 d 6, (9a) Nextel has also been tested successfully as an intermediate layer. If Nextel is used, the sizing equation is: m, = 0.095 d 6, The rear wall sizing equation is: mu = 34.8 M V,/S2 ( 4 0 / 0 ) ~ ' ~ (9b) (10) HVI testing of the mesh double-bumper (MDB) shield has been performed for 0.32 cm, 0.635 cm and 1 cm projectiles (Figure 2). These equations can be applied for normal component velocity (V,) of greater than 6 km/sec and S/d ratios of more than 15. The wall areal density calculated by Equation 10 is based on the ballistic limit criterion of preventing perforation and detached spa11 (Damage Category: F1 and F3 in Figure 1). Based on limited HVI testing, if no intermediate cloth layer is used with the MDB shield, the rear wall sizing equation is: mu = 2.1 d'.' V/S (40/0)~.' Single Aluminum Sheet The following Cour-Palais cratering equations are recommended for predicting single wall penetration. For projectile density (6,/6, < 1.5), the penetration depth into a semi-infinite target 5

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is: 19/18 H-0.25 P, = 5.24 d ( 6 p / 6 t ) O s 5 (vn/c)2/3 For projectile density ( 6 p / 6 t 2 1.5) : 19/18 H-0.25 P, = 5.24 d ( 6 p / 6,) 2/3 (vn/c)2/3 If there is attached spall, the penetration depth is greater than into a semi-infinite target: P = 1.05 P, (13) If there is detached spall, penetration depth can vary between 1.08 and 1.5 times the semi-infinite target penetration, i.e.: P = 1.08 P, to 1.5 P, ( 1 4 ) The plate thickness to prevent perforation, but not detached spall (Damage category B3) : t = 1.8 P, Plate thickness to prevent perforation and detached spall, but would allow attached spall (Damage category B2): t = 2.2 P, (16) Plate thickness to prevent perforation and incipient spall (Damage category B1) : t = 3 P , EQUATIONS FOR PROBABILITY ANALYSES The velocity and directional distribution of the meteoroid and debris threat must be assessed against shield capabilities before the design process is complete (i.e., to verify that the shielding design meets the specified no-failure requirements). The MDSSC PDR shielding designs must be refined to account for the directional nature of debris and meteoroids, the complex response of the shielding to oblique and low speed impact, and to account for shadowing from nearby equipment. This part of the memorandum provides ballistic limit equations for the Whipple, Multi-Shock (MS), and Mesh Double-Bumper (MDB) shields that can be used in probability analyses. The equations are in a form that relates critical particle diameter to fail a given structure with impact velocity and impact angle. The equations are consistent with the equations given previously, but 6

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additional equations are given to cover the full range of onorbit impact velocities and impact angles. Hypervelocity impact testing is currently in progress to better define these ballistic limit equations. An update to these equations will be made after testing results have been analyzed. Aluminum Whipple Shield This shield consists of an aluminum bumper and aluminum rear wall. A set of three ballistic limit equations that covers the three primary penetration regimes is given below. The three penetration regimes are based on normal component velocities with penetration of the rear wall occuring by molten material, vapor, and possibly solid particulates at normal component velocities above 7 km/sec; a fragmenting projectile regime between 3 km/sec and 7 km/sec; and a non-fragmenting projectile ballistic regime below 3 km/sec. For V, 2 7 km/sec: d, tu2/3 -113 6,-1/9 (V cos g )-2/3 s1/3 = 3.918 &P For 3 km/sec < V, < 7 km/sec: ( a / 7 0 ) ’I3 (18/19) * d, = {[(tu (0/40)-+tb)/(1.248 6p0” COS e ) ] 2/3 -1/3 -1/9 s1/3 { [ 1 . 0 7 1 tu 6, ‘b ( 0 / 7 0 ) ’ / ~ ] * ( 1 . 7 5 - (V COS 0)/4)} + ( ( V cos 0)/4 - 0 . 7 5 ) ) For V, I 3 km/sec: (19) 0.5 $/3) 1(18/19) d, = [ (tw ( c ~ / 4 0 ) ~ . ~+tb)/(0.6 (COS (20) Multi-Shock (MS) Shield 6, The following MS shield ballistic limit equations are valid for a shield consisting of 4 Nextel bumpers and an aluminum rear wall, with equal spacing between sheets. In these equations, the overall spacing from the first, outer-most, bumper to the rear wall is given by l*S1l. 7

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For V, 2 6 km/sec: d, t,1/3 -1/3 JW1/3 ( V cos 8 )-1/3 s2/3 = 0.354 6P For 3 km/sec < V, < 6 km/sec: ( a / 4 0 ) 'I6 cos (18/19) * d, = {[(t, ( c T / ~ o ) ' - ~+ 0.37 m b ) / ( 0 . 6 2 4 6p0.' e ) ] t,1/3 -1/3 6,1/3 s 2 / 3 ( a / 4 0 ) 1/61 * (2 - (V COS 8)/3)) + { [ 0 . 1 9 4 8 6, ( ( v COS 8 1 1 3 - 113 For V,, 5 3 km/sec: d, = (t, ( a / 4 0 ) ~ - ~+ 0.37 mb)/(0.3 (22) (cos 6,Om5V2/3) (23) Figure 4 shows the results of applying the above equations for a MS shield consisting of four Nextel AF26 bumpers (each with an areal density of 0.043 g/cm2) and a 0.0208f( 0 . 0 5 0 8 cm) A 1 2024-T3 rear wall, with 1" ( 2 . 5 4 cm) between each sheet, 4" (10.16 cm) overall spacing. This plot shows that a 3.18 mm (1/8") aluminum projectile impacting at 6.5 km/sec and normal impact angle will be on the ballistic limit of the shield, while the shield will stop a 1.25 mm projectile in a normal impact at 3 km/sec. Mesh Double-Bumper The following MDB equations are based on a mesh double-bumper shield using either Kevlar or Spectra cloth as an intermediate layer. For V, 2 6 km/sec: d, = 0.3% 3I:t 6,-'/3 6,113 (V cos e )-1/3 $/3 For 3 km/sec < V, < 6 km/sec: ( a / 4 0 ) 'I6 d, = ([(t, ( C T / ~ O ) ' ' ~+ 0.37 Xm,,+,,>/(0.%36pOm5cos e ) ] (18/191 * (2 - (V COS 8)/3)) + (C0.209 t,1/3 6, -113 6w1/3 $3 ( ( r / 4 0 ) 1 / 6 ] * ( ( V cos 0)/3 - 1)) ( 2 5 ) 8

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For V, 5 3 km/sec: (cos e)5'3 $'3)](18'19) (26) d, = [(t, ( a / 4 0 ) ~ ' ~+ 0.37 Xm,,)/(0.4 Distribution: Ray Nieder/ET13 Burton Cour-Palais/MDSSC-Houston/T7H Dale Haines/KC2 Jeff Fukushima/MDSSC-HB/A95-J849/17-5 Jeanne Crews/SN3 Gregg Edeen/ES2 9

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Ctass IMPACT - I DlRECTlON CATEGORY A: SINGLE CXATEF1 PATTERN LOW VELOCITY PROJECTILE REMAINS INTACT I AI * NO PERFORATlON OR REAR SURFACE DEFORMATION CRATE3 DIAMETEA APPROXIMATE SIZE OF PROJECTILE A;! * NO PENEfRATlON * CRACKS OR SPLITTING MAY 9E PRESENT * R k R SURFACE DEFORMATION A3 *PENETRATION * HOLE DIAMETER APPROXlMATE SIZE OF PROJECTILE CATEGORY B: SINGLE CRATER PATTERN - HYBERVELOCfTY PROJECTILE REMAINS INTACT 81 * NO PERFORATION OR REAR SPALL SINGLE ROUNDED CRATER FRONT SURFACE LIP OR SPALLATION 82 NO PERFORATION, BUT WITH ATTACHED REAR SPALL * SINGLE ROUNDED CRATER FRONT SURFACE LIP OR SPALLATION E3 * NO PERFORATION, BUT WITH DETACHED REAR SPALL SiNGLE ROUNDED CRATER FRONT SURFACE LIP OR SPALLATION LIGHT TIGHT I I 84 * PERFORATION DUE TO CRATER AND REAR SPALL MEETING (HOLE DIAMETER c 2 rnm) * FRONT SURFACE LIP OR SPALLATION * NOT LIGHTTIGHT 85 0 PENmATION HOLE FORMED BY CRATER AND DETACHED SPALL (HOLE DIAMETER 2 2 rnrn) FRONT AND REAR SURFACE LlPS OR SPALLATION FIGURE 1 barnage Classificationfor Shielded Metallic Targets REF. Dah1 and Cour-Palais: ltStandardizationof Ispa Damage Classification and Measurements fcr iiletzllic Tarqers", 1990

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IMPACT Cfass DIRECTlON CATEGORY C: MULTIPLE CRATER PATTERN PROJECTILE BREAKS UP I M O COARSE AND FINE FRAGMENTS CI NO PE3FORATION. REAR SURFACE DEFORMATION OR SPALL = RANDOM SURFACE CRATERS. PR77NG OR EROSION C2 NO PERFORATION, BUT WITH ATACHED SPALL(S)OR HEAR SURFACE DEFORMATION * RANDOM SURFACE CRATE3S, PITTING, OR ESOSION C3 * NO PERFORATION, BUT WITH DETACHED SPALLE) * RANDOM SURFACE CRATERS, PllTNG OR EROSION LlGHT TIGHT c3 PERFORATION CRACKS OR SMALL HOLE@) (ALL HOLE DIAMRERS c 2 mm) * NOT LIGHTTIGHT C5 PENETFIATION LARGE HOLE@) (APPLICABLE IF ANY HOLE D l A M t E R 1 2 rnrn) CATEGORY D: CENTRAL CRATER PATTERN PROJECTILE BREAKS UP INTO FINE PARTICLES D1 NO PERFORATION OR REAR SPALL * CENTRAL SURFACE CRATER, PITTING OR EROSION 02 NO PERFORATION, BUT WITH ATTACHED SPALL CENTRAL SURFACE CRATER, PITTING, OR EROSION D3 * NO PERFORATION, BUT WITH DETACHED SPALL * CENTRAL SURFACE CRATER, PITTING OR EROSION .LIGHT TIGHT 04 * PERFORATION CRACKS OR SMALL HOLE(S) DUE TO CRATER AND SPALL MEETlNG (ALL HOLE DlAMtfERS e 2 rnrn) * NOT LlGHT TIGHT 05 * PENETRATION 0 LARGE HOLE@) FORMED BY CRATER AND DETACHED SPALL (APPLICABLE IF ANY HOLE DIAMETER 1 2 mm) - FIGURE 1 . Damage Classification for Shielded Metallic Targets (Cant.) t REF. Dah1 and Cour-Palais: "Standardization of Irnuact Damage Classification and Measurements for Xetallie Tarqets" , 1990

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IMPACT ? n 7 E 3 N 0IRECTEN cIass CATEGORY E: RING CTiLTZ? PROJECTILE 3REAKS UP INTO VERY FINE PARTlCLES 1 El * NO PERFORATION OR REAR SPALL * RING CXATERS SURROUND CENTRAL SURFACE CRATES, PTTTING, OR EROSION E2 NO PERFORATlON * RING CXATERS WITH SPALL PlMPLES A7TACHED AND/OR CENTRAL SPAU ATTACHED CENTRAL SURFACE CXATER, PIlTNG, OR EROSiON * NO PERFORATlON RING CRATERS WITH Si'ALL PIMPLES DETACHED AND/OR CENTRAL SPAU DETACHED CENTRAL SURFACE CFIAER, PTllNG, OR EROSlON * LIGHTTIGHT E4 PERFORATION HOLE(S) DUE TO CXATER(S) AND SPALL(S) MEEflNG NOT LGHT TiGHT E *PENETRATION * LARGE HOLE PUNCHED OUT DUE TO RING PERFORATIONS ZZZa m AND IMPULSIVE LOAD CATEGORY F: NON-PARTICULATE IMPULSIVE LOADING PROJECTILE BECOMES MOLTEN UQUlD OR VAPOR F1 * NO PERFORATION OR REAR SPALL SURFACEPITTING OR MOLTEN SPLASH F2 NO PERFORATION SPALL PRESENT, ATACHED OF?DETACHED SURFACE PilTlNG OR MOLTEN SPLASH NO PERFORATION DENTED, BUT INTACT * SURFACE P m l N G OR MOLTENSPLASH LIGHTTiGKT F4 PERFORATION * DENTED AND SPLIT SURFACE PITTING OR MOLTEN SPLASH NOT LIGHT TIGHT ~5 PENETRATION BY IMPULSIVE LOAD FAILURE * PETALLED HOLE * SURFACE PITTING OR MOLTEN SPLASH FIGURE t . Damage Classification for Shielded Metallic Targets (Cant.) . REF. Dah1 and Cour-Palais: "Standardization of Impact Damage Classification and Measurements for iJP-calli=:Targets", 1990

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. - Mesh Double-Burnper Shieid A Iumlnum -T* P r o j e c t i l e I t S1-3d to 4d S ovorall 2 3 0 d (Ootlmum) f =-3d to 4d ~ Aluminum Mesh: filuminum flesh 1 Disrupt ~ r o j r c t t i a I ( f r a g m a n t / v a o o r i z r Second Bumper e n a l t / v s p o r t t e Int e r m e d t e t e FQbrtc 0 S l o w Dobrlc Cloud S t O D Rorldual Frogmanic J Rarttl ImPuIrlva -Mass efficient method to disrupt projectile. -Greater spread of debris cloud results form impacts on mesh -reduces performance degradahon at s d e r spacings. -Fine mesh used. Small projectiles passing unhindered through mesh easily defeated by remaining shield elements. -Improvement over equal-weight aluminum double-bumpers. * Second bumper used to deliver second shock to remaining fragments. * Intermediate layer of high-strength fabric (Spectra, Kevlar, Nextel, etc.) used to slow debris cloud and decrease impulsive loading on back sheet. Development status: spacing/areal densities optimized, preliminary sizing relationships formulated, scale-up tests perfomed, alternative materials and oblique impacts studied. Future development: ballistic lirmt investigations and additional material optimization (A1 fabric, flexible second bumper, alternative intermediate and backwall materials). Augmentation for protection fmm high-density particles: consider steel mesh or fabric. EL. ChnstiansedSN3

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Lo * m @4 - 0 co co 'i Ta! ". t i d 0 0 0 0 ? 0 d o