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JAN 03 19921

*Energy Absorption of UGraphite/Epoxy Plates LUsing Hopkinson Bar ImpactPiyush K. Duffa, David Hui and Magna R. Altamirano October 1991

I,

For conversion of SI metric units to U.S./Britlsh customary unitsof measurement consult ASTM Standard E380, Metric PracticeGuide, published by the American Society for Testing andMaterials, 1916 Race St., Philadelphia, Pa. 19103.

CRREL Report 91-20

U.S. Army Corpsof EngineersCold Regions Research &Engineering Laboratory

Energy Absorption ofGraphite/Epoxy PlatesUsing Hopkinson Bar ImpactPiyush K. Dutta, David Hui and Magna R. Altamirano October 1991

C Accesion For

NTIS CRA 7DTIC TABUi a.nounced

-JuI~tif i cdtiod ... ... .. ...

By ..................... .

Di. t ibtui :

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92-00119Prepared for IIEIIIlhilIOFFICE OF THE CHIEF OF ENGINEERSandU.S. AIR FORCE FLIGHT DYNAMICS LABORATORY

Approved for public release; distribution is unlimited. ,I ..

PREFACE

This report was prepared by Dr. Piyush K. Dutta, Materials Research Engineer of the AppliedRese,.rch Branch, Experimental Engineering Division, U.S. Army Cold Regions Research andEngineering Laboratory (USACRREL); Dr. David Hui, Associate Professorof Mechanical Engineer-ing, University of New Orleans; and Magna R. Altamirano, graduate student, University of NewOrleans. The work has been carried out in the Materials Research Laboratory of CRREL. Funding forthis work was provided partially by DA Project 4A762784AT42, Cold Regions Technology, Task SS,Work Unit 019, Behavior of Materials at Low Temperatures. and partially by Department of the AirForce Flight Dynamics Laboratory at Wright Patterson AFB, Ohio, under MIPR FY 1456-90-N0066of July 1990.

The authors express their appreciation to Dr. Arnold H. Mayer, Assistant for Research andTechnology, AFWAL Flight Dynamics Laboratory, for his support, ideas, suggestions, and ballisticimpact data analysis results. The authors are especially indebted to Gregory Czarnecki, Scientist,AFWAL Flight Dynamics Laboratory, for supplying the specimens and closely working with theauthors to support the experimental tasks. John Kalafut of the Engineering and Measurement ServicesOffice of CRREL provided much-needed support and participated in the experimental measurementprogram. Capt. Karen Faran of CRREL did the arduous task of numerical analysis of the data. Specialthanks are given to Frederick Gemhard of the CRREL machine shop who built the test fixture.

The contents of this report are not to be used for advertising or promotional purposes. Citation ofbrand names does not constitute an official endorsement or approval of the use of such commercialproducts.

ii

CONTENTSPage

Preface .................................................................................................................................. iiIntroduction .......................................................................................................................... 1M echanics of wave propagation ........................................................................................... 1Discussion of results ............................................................................................................ 5Conclusions .......................................................................................................................... 9Literature cited ..................................................................................................................... 9Appendix A: W ave propagation in a Hopkinson bar apparatus ........................................... I1Abstract ................................................................................................................................ 13

ILLUSTRATIONS

Figure1. Schematic of the Hopkinson bar test setup ................................................................. 22. Photograph of the setup showing the hemispherical indentor ..................................... 33. Stress pulse reflections and transmissions through the interface ................................. 54. Interface velocity and force ........................................................................................ 55. Im pact energy absorption results ................................................................................. 56. Results of force, velocity, and strain history measurements ........................................ 67. Bar stresses and energy absorption history ..................... t ........................................... 78. Influence of temperature and velocity on energy absorption ..................................... 79. Effect of tem perature on Hertzian contact energy ....................................................... 8

10. Energy loss as a function of impact energy ................................................................. 811. Energy loss as a function of impact velocity ............................................................... 9

iii

Energy Absorption of Graphite/Epoxy PlatesUsing Hopkinson Bar Impact

PIYUSH K. DUTi A, DAVID HUI AND MAGNA R. ALTAMIRANO

INTRODUCTION duration of impact produced by the striker bar on theHopkinson bar apparatus persists for a few hundred

Most literature dealing with energy absorption in microseconds, and it takes a small but finite time for thelaminated composites describes the use of a dropweight effects of the impact force (stress wave) to enter theor pendulum impact test apparatus. In these techniques, graphite epoxy test laminate at the opposite end of theenergy absorption is determined by subtracting the re- bar. Upon enteringthe laminate, aportion of the incidentsidual kinetic energy from the initial energy. Thus the stress wave is propagated into the transmitter bar andeffects of stress wave propagation, which is a source of another portion is reflected back into the incideit bar.damage initiation, cannot be examined using these test- Incident, reflected, and transmitted stress waves areing techniques. Further, the laminate's energy absorp- measured by strain gauge instruments described else-tion during the penetration process and the projectile's where (Dutta et al 1987).velocity, contact force, and duration of impact are diffi- In the current study, the laminate specimens con-cult to measure. Hopkinson bar testing eliminates these sisted of 30 plies of AS4/3502 graphite epoxy with therestrictions and allows a thorough examination of the following stacking sequence:projectile impact process.

The effort described in this report involved an ana- [(+ 45/02)21901± 45/02/± 45]slytical and experimental study of energy absorptionwithin graphite/epoxy plates impacted by a hemispheri- The indentor was driven into the laminate by the forcecal-nosed impactor attached to a split Hopkinson bar test of the incident bar's stress wave. Figure 1 shows aapparatus. The work is novel in that the plate's energy schematic of the Hopkinson bar, the impactor, and theabsorption was accurately measured using the recorded laminate panel clamping assembly. Figure 2 is a photo-incident, reflected, and transmitted stress waves. The graph of the setup. The transmitter bar is free to slideHopkinson bar test apparatus allowed accurate determi- forward or backward. As the striker hits the incident barnation of velocity, force, and energy absorption informa- and drives the indentor into the laminate plate, the platetion during the entire impact duration. Thus the setup bends and behaves like a spring-mass system. Plateallowed "controlled" testing, capable of determining the bending was recorded from strain gauges mounted onenergy absorption of impacted composite specimens. the rear face of the laminate.The only limitation was that the impactor was forced into The wave mechanics within this system was analyzedthe laminate at relatively !ow velocities, to determine the force-displacement relationship be-

tween the impactor and the composite laminate. Energyabsorbed during the process was also determined as a

MECHANICS OF function of time. The velocity, force, and energy ab-WAVE PROPAGATION sorbed were calculated from incident, reflected, and

transmitted waveforms.The theoretical wave mechanics involved in the im- An impact of bar I (the striker bar) into bar 2 (the

pact process are discussed based on elementary prin- incident bar) produces a compressive force at interfaceciples of unidirectional stress wave propagation. The A. According to elementary stress wave propagation

Striker Test Ptate

Bar - Incident Bar Transmitter Bar Free End

,'f 8 ft --7t -8 ft

Gr • Ep Test Plate

Bat Bar 3

IFigure 1. Schematic of the Hopkinson bar test setup.

theory (Kolsky 1963, Dutta et al. 1987), stress Y and The force of penetration at any time t can be calcu-force P generated by the impact are lated more directly by considering the particle velocity

in the following equation:

= (p/g)CV (1)V =dulpt- (4)

and (98) cP = (A) (pig) (cV) (2) where u is the axial displacement of the bar and is given

where p is the density of the incident bar, g is the byacceleration due to gravity, c is the speed of sound in the

bar, V is the particle velocity in bar 2, and A is the cross-sectional area. T '! stress wave propagates along bar 2 to u = 1L a(t)dt (5)the opposite end where it encounters a discontinuity of P_ cits impedance (a product of density and stress wave(g) t=ovelocity, pc) at interface B. In the experimental setup,the impactor and leminate respond to this incoming Under the incident stress wave ai(t), the penetratorstress pulse. As a result of the discontinuity, a portion of end of bar 2 will be subjected to a displacement ui giventhe stress pulse energy (E,) is reflected (ER) and a portion byis transmitted (ET) through the spring-mass system.Most of the remaining energy goes into the formation ofplastic deformation of the plate. Some energy is also lost 1 Yi (t) dt (6)in overcoming frictional forces in various joints and uf = -- (through noise and vibration of the entire system. Nett= 0energy lost in the impact can be calculated by subtractingthe energy of the transmitted and reflected waves from Due to the change of impedance, a portion of the stressthat of the incident wave: wave is reflected, which produces a corresponding dis-

placement of the indentor in the opposite direction; thisEA = El - ER - ET (3) displacement ur is

The procedure for computing energy from the stress vstime waveform is given in Appendix A.

2

Figure 2. Photograph ofdie setup showingthe hemispherical indemtor.

material in the in-plane radial direction. Since the deflec-tion was measured to be less than 20% of the laminate

14 r f or (t) dt (7) thickness, the membrane energy (Em) was neglected.( )Cg o Although Hertzian contact law was established for

local static indentation of two elastic bodies, it is com-monly applied to impact situations where permanent

The resultant displacement ut is given by plastic deformations occur (Goldsmith 1960). The Hert-zian contact energy of a spherical indentor with radius Rimpacting a flat plate is (Greszczuk 1982)

ut(t) = 1 ft (t) - (y, (t)] Lit (8)(t c I Ec (p 5/3)(4/5) (31t / 16) 2/ 3

t=0

Force on the penetrator [F(t)] is the algebraic sum of [(k, + k2)/(R/2)112] 21 3 (12)the incident force Aci(t) and the reflected force Aar(t):

where

F(t) = A [i (t)+ Or(t) dt (9) k I =(1v)/(tEs) (13)

t=0 k2 rV1 v2) 1(nEz) (14)

From eq 8 and 9, the force-displacement curve for theindentation can be plotted. The area under the curve will where Es and v, are the Young's modulus and Poisson'syield the energy absorbed as a function of time through- ratioof the steel indentor, respectively,E z is the laminate'sout the impact. modulus in the thickness direction, andvris the laminate's

Energy absorbed by the graphite epoxy plate can be Poisson's ratio.computed from the following energy balance equation Assuming point contact between the indentor and(Greszczuk 1982, Shivakumar et al. 1984): plate, the deflection can be computed from the in-plane

stress a (Roark and Young 1975):EA =Ec+ Eb+ Em+ Ed+ Ef (10)

where EC = the energy expended in Hertzian contact oh2 /6 = [P/(4 n)] (I + v)

indentation,Eb = the energy due to plate bending, (ln [a/(.325h)]} (15)Em = the energy due to the stretching of the

middle plate surface, Further, deflection y at the center of the circular plate dueEd = the energy due to permanent plate damage, to a concentrated load P is

andEf = the energy due to friction, heating, etc. y- (Pa'ln~) (3/4) [ (I -V2) /(Eh 3)] (16)

All of these energies are recoverable, except thedamage and frictional energy. Plate damage may include Measured strain can be converted to stress by multi-any or all of the following modes of failure: matrix plying the strain by the in-plane Young's modulus, so acracking, delamination, fiber breakage, and spalling. is a known quantity. Eliminating the applied loadP from

The bending energy of a circular plate clamped along the above two equations, the deflection can be obtainedits edge under a concentrated load P is (Roark and Young in the form1975, Greszczuk 1982)

a 2a (-v)Eb = (p 2 ) (3a2/2) (i v) (4n Erh2)- (11) (2hE) In [a,(O.325h)]

where a is the radius of the circular plate, h is the Upon stress wave arrival, the indentor acceleratesthickness of the plate, and Er and Vr are the Young's into the plate and creates a compressive stress wave thatmodulus and Poisson's ratio, respectively, of the plate propagates through the thickness. Stress wave velocity

4

V1 u. V 2

Forcel I Velocity

A,,Pll O. R, , -'OT'UT A2,P2 C2 Z5 \<Vl ' "

OR, U R

: Time\ /

I I

1 I Force

Figure 3. Stress pulse reflections and trans-missions through the interface. Figure 4. Interface velocity and force.

in the thickness direction of the plate is approximately at velocity V1 while the indentor continues to move into(McMaster 1963) the plate with a velocity V1 (see Fig. 3).

During the duration of the stress wave, three condi-cz = [EzI(plg) 12f (v)] (18) tions are possible. First, when V2<Vl,the indentoraccel-

erates into the plate (positive contact force) with a forcevs time relationship as shown in Figure 4. Second, when

f(v)= (l-v)/[(l + v)(I -2v)]) 1 2 (19) V2 _ V1 , both the indentor and the plate move in theincident direction with no change in contact force. Third,

where Ez is Young's modulus in the thickness direction when V2 > V , loss of contact occurs between the in-and v is Poisson's ratio (for n = 0.31,ftv) = 1.17732). dentor and plate, and a tensile force develops in the

For a quasi-isotropic graphite epoxy laminate, where incident bar. Both the indentor and the plate move for-Er = 51.16 GPa (7.42 Msi), Ez = 11.86 GPa (1.72 Msi), ward monotonically even though loss of contact occurs.and p = 1522.4 kg m- 3 (0.055 lb-mass in.- 3), wave speedCz = 3.043 km s- (0.1198 x 106 in. s- 1). This wave willpropagate with speed cz as a compressive wave and will DISCUSSION OF RESULTSeventually reflect off the rear (free) surface as a tensilewave with the same velocity. When the wave arrives at Figure 5 is a graph of energy absorption vs displace-the rear surface, the plate moves away from the indentor ment. The energy absorption of the plate (curve A) is

Energy(Joule) (in - lbf)9.04 80

- Z B (System)

6.78 60- 6.78 -- 60 A (Plate) --

4.52 40-

2.26 -- 20-

0 4 8 12 16 20 24 28 32x 10 - (in-)

I I I I I I I I I I I I I I I I0 0.1 0.2 0.3 0.41 0.51 0.61 0.71 0.81 (mm) Figure 5. Impact energy absorp-

Displacement tion results.

5

(N) (Ib) (in. s-1) (m s")30 x 10

.3 _ 133.45 x 10 30 x 10 I 300'- 7.62

20 89.0 20 D (Velocity) 200- 5.08 >,

-- - oStrain Gauge 1u.C (Farce) . i >

1. Gauge10 44.5 - 102 Failure 100 2.54

0 0 0 0 _J 0ti t 2 t3V 4 ts

-10 I I I I, j0 100 200 300 400

Time (gs)

Figure 6. Results offorce, velocity, and strain history measurements.

computed from the force vs displacement of the indentor. minish but, because of the gap between theEnergy absorbed in the system, consisting of the plate plate and the indentor, the indentor experi-and clamping fixture shown in curve B, is computed ences a tensile force. (Note a reversal of thefrom the incident, reflected, and transmitted waves, force direction.)Appropriate formulae are given in Appendix A. The • The final stage (t4 < t < t5 ) is the vibrationsmall difference between these two energy absorptions stage, during which the plate exerts an oscil-is the energy loss in the fixture (Ep). lating force on the indentor where contact

Indentor force vs time (curve Cof Figure 6) follows may be lost and regained many times.the model of Figure 4. There are five stages involved in Figure 7 shows the cumulative energy absorption vsthe penetration process: time. Energy absorbed increases rapidly with time in the

• In the initial loading stage (0 < t < t,), the first two stages and very slowly in the third stage. Duringindentor accelerates into the plate, as can be the plate separation stage, a portion of the energy returnsseen from the increasing slope of the velocity to the incident bar as the indentor accelerates into the freetrace (curve D). space in front of it. This energy is subtracted from the

• The second stage (ti< t < t2 ) is the initial cumulativeenergy, so the energy curve dips at this stage.unloading stage where the indentor force de- Energy absorbed in the final stage is constant and is thecreases rapidly and the corresponding veloc- energy required to cause plate damage.ity increases at a slower rate. The drop in the Figure 6 also shows data from two strain gaugesindentor force is attributed to damage either in mounted at two positions on th,; rear surface. Strainthe contact region or near the rear surface due gauge I is mounted at the plate center and gauge 2 nearto a reflected tensile wave. The latter may the comer. The strain gauge data show that plate bendingcause the plate tomove away fromthe indentor, continually increases but remains small during the firstthus reducing the contact force (which will be four stages of impact. The increase becomes more pro-more evident in the next stage). nounced in the final vibration stage and results in strain

* The third stage is the constant velocity stage gauge failure near t = t5 .(t2 < t < t3) in which there is very little contact Figure 8 shows the laminate's energy absorption EAforce. Referring to eq 9, note that at this stage vs the maximum velocity of the indentor. The data01(t) = OR(t), indicating that there is no inter- follow the relationshipfacial contact force.

" In the fourth stage (t3 < t < 4 ), the effects of EA= n Vm (20)stage 3 become more pronounced, and sepa-ration between the indentor and plate is pos- wi.ere exponent m is found to be 2.55 for room tempera-sible. Similar loss of contact behavior has ture (21 C) and 4.53 for low temperature (-30"C). Thebeen reported by Wu and Springer(1988)and value of the constant n for 21°C is 3.75 x 10-5 and forSun and Chen (1985). At this stage, the ap- -30 0 C is 1.01 x 10--9.

plied incident stress amplitude begins to di- These data are currently considered a precursor to a

6

Energy Stress(Joule) (in. - Ibf) (lb in.- 2 ) (MPa)

9.04 80 1 1 1 I I 80x103 - 0.55

6.78 60 Energy Absorbed 60 0.41

4.52 40 40 0.28

2.26 20 Incident Stress Wave 20 0.14

0 0 tlt 2 t t"0 0

Reflected Stress Wave-20 -0.14

0 100 200 300

Time (lis)

Figure 7. Bar stresses and energy absorption history.

Energy

(Joule) (in. - lbf)

9.04 80 1

* 21 0C Datao -30C Data o

4.52 40 2

/ (70*Fl

2.26 20 -

foo/-30oc0 .. (-22°F)

0 -- 0 -' o ''S I I I

100 140 180 220 260 (in. s - 1)

I I I I I I I 1 12.54 3.55 4.57 5.58 6.60 (m s- 1 )

Particle Velocity

Figure 8. Influence of temperature and velocity on energy absorption.

detailed analysis oftemperature's influence on the dam- impact velocity more damage occurs at lower tempera-age mechanisms associated with composite plate im- tures and more energy is absorbed. The experimentalpact. It is well known that low temperature reduces the data in Figure 8 clearly show this trend after a transitionfracture toughness of most materials, but no extensive velocity of about 4.8 m s-I (190 in. s-1). Above thisdata are available for composites. In research performed velocity, more energy is absorbed by specimens held atby Nishijima and Okada (1982), cloth-reinforced ep- low temperature. Below this transition velocity, the lowoxide resin composites were subjected toCharpy impact temperature has an opposite effect, as discussed next.tests at room and liquid nitrogen temperatures. These Greszczuk (1982) and Shivakumar et al. (1985) havetests demonstrated that a reduction in temperature causes shown that in the low velocity range, among non-a reduction in impact strength. Therefore, for a given recoverable energies, the Hertzian contact force is the

7

6.0 x 10-

5.8

5.6

5.4

5.2+

. 5.0

4.8

4.6

4.4

4.2450 -40 -30 -20 -10 0 10 20 Figure 9. Effect of temperature on HertzianTemperature (°C) contact energy.

100 I I I I I

80 Ti-

60 -0,

4-AS4/3502 16 Ply

20 - (m - 2.5 kg)

0 2 4 6 8 10 12 14 Figure 10. Energy loss as a function ofImpact Energy (Joule) impact energy (after Sjoblom et al. 1988).

most dominating energy absorption mechanism. From Ez Ef Em (T) (23)eq 12thisenergy isafunctionof(k +k2)2 /3 . Substituting v f(T) Em (T) + vm Efvs = 0.3 and Es = 206.9 GPa (30 x 166 psi) for a steelindentorintoeq 13,k I =0.9.67x 10-9 . Referring toeq 14, where vm and vf are the matrix and fiber volume ratios,k2 contains the term Es (the Young's modulus of the and Em and Ef are the matrix and fiber modulus ofcomposite plate in the thickness direction), which is elasticity. (7) indicates the prevailing temperature of theinfluenced at low temperature by the change in elastic matrix. Solving for Ez and setting vr = 0.31, k2 is de-modulus Em of the resin matrix. The empirical relation termined via eq 14. Figure 9 shows a plot of (k, + k2) 2/3

established by Dutta (1989) for matrix stiffening with vs temperature. It is clear from this graph that as thelower temperature is temperature is reduced the value of Ec (the Hertzian

contact energy, which is a direct function of (k I + k2)2 3)Em (T)=Em(TO)- 2.9 103 (T - To) (21) decreases. The experimental results in Figure 8 confirm

this.where To is the room temperature and T is the low In a separate ballistic experiment involving the pen-temperature in 'C. Applying the above relationship to etration of identically configured 30-ply graphite epoxythe rule-of-mixtures equation (Tsai and Hahn 1980) laminates by 12.7 mm (0.5 in.) spheres, Mayer and

Altamirano* observed energy absorption Ea in the form

E = E Em (22)Vf Em + Vm Ef

* Personal communication (1990) from A. Mayer, Air Forceyields Wright Laboratories, Dayton, Ohio.

8

80 I I I I I I

60

0-J

0

20

Figure I]. Energy loss as a function of impactvelocity as obtained from Sjoblom et al. (1988) 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2

data. (q1 Impact Enegy ) = f (V) (J

Ea = C0 V 1.489 (24) Low temperatures influence the energy absorptioncharacteristics and control the damage mechanisms.

where V is the impact velocity and C0 is a constant. Existence of a transition velocity was observed; aboveExperimental velocities ranged from 500 to 1500 m s~i this velocity energy absorption from an impact is higher(1600-4900 ft s-1). Comparing the exponents of V from than at room temperature. At low temperature, reducedthe three series of experiments-1.489 from the ballistic impact strength causes a larger volume of damage.tests, 2.55 from the Hopkinson bar room-temperature Below the transition velocity (at low temperatures) thetests, and 4.53 from the Hopkinson bar low-temperature laminate absorbs less energy, which can be approxi-tests-it is clear that the damage mechanisms and energy mated by Hertzian contact theory.partitioning are different at higher velocities than under When comparing data generated via the HopkinsonHopkinson bar low-velocity impact. The lower value of bar apparatus to data obtained via high velocity ballisticthe exponent suggests a failure mechanism that progres- impact, the failure mechanism is seen to be a function ofsively requires less energy as the velocity is increased. impact velocity. As the impact velocity increases, theThis trend was also validated by Sjoblom et al. (1988) fracture requires less energy.(Fig. 10). The solid line in this figure shows that energyloss is a function of V2 A reconstruction of the energyloss vs velocity (Fig. 11) clearly shows a decrease in the LITERATURE CITEDenergy absorption rate at higher velocities.

Dutta, PXK (1989) A theory of strength degradation ofunidirectional fiber composites at low temperature. Pro-

CONCLUSIONS ceedings of the Industry- UniversiyAdvan4 edMaterialsConference, Advanced Materials Institute, Colorado

The energy absorption of laminated plates under School of Mines, March 6-9 (F.W. Smith, Ed.), p. 647-normal impact generated by a Hopkinson bar apparatus 662.was examined. Using wave propagation theory, the Dutta, P.K., D. Farrell and J. Kalafut (1987) The CRRELenergy absorption agrees with theoretical predictions. Hopkinson bar apparatus. USA Cold Regions ResearchThe force, velocity, and energy were recorded through- and Engineering Laboratory, CRREL Special Reportout the impact event, which encompassed several hun- 87-24.dred microseconds. The experimental procedure pro- Goldsmith, W. (1960) Impact. London: Edward Arnoldvided a controlled condition enabling the full analysis of (Publishers), Ltd., p. 82-144.events during this period. Loss of contact between the Greszczuk, L.B. (1982) Damage in composite materialsimpactor and laminate occurred frequently during the due to low velocity impact. Chapter 3 in Impact Dynam-impact process due to stress waves in the plate reflecting ics (J.A. Zukas et al., Ed.). New York: John Wiley andback and forth through the thickness. The energy bal- Sons, p. 55-94.ance equation provides a powerful tool for analyzing the Koisky, H. (1963) Stress Waves in Solids. New York:energy available to cause laminate damage. Dover Publications.

9

McMaster, R.C. (1963) Nondestructive Testing Hand- Sjoblom, P.O., TJ. Hartness and T.M. Cordell (1988) Onbook. New York: Ronald Press Co., p. 43.9-10. low-velocity impacttesting of composite materials. Jour-Nishijima, S. and T. Okada (1982) Charpy impact test of nal of Composite Materials, 22: 30-52.cloth reinforced epoxide resin at low temperature. In Sun, C.T. and J.K. Chen (1985) On the impact of initiallyNonmetallic Materials and Composites at Low Tern- stressed composite laminates. Journal of Compositeperatures (G. Hartwig and D. Evans, Ed.). New York: Materials, 19: 490-504.Plenum Press, p. 259-275. Tsai, S.W. and H.T. Hahn (1980) Introduction to Com-Roark, R.J. and W.C. Young (1975) Formulas for Stress posite Materials. Lancaster, Pennsylvania: Technomicand Strain. New York: McGraw-Hill Book Co., p. 332- Publishing Co., p. 389.367. Wu, H.Y.T. and G.S. Springer (1988) Impact inducedShivakumar, K.N., W. Elber and W. Ilig (1985) Prediction stresses, strains and delaminations in composite plates.of impact force and duration due to low-velocity impact Journa! of Composite Materials, 22: 533-560.on circular composite laminates. ASME Journal of Ap-plied Mechanics, 55: 674-680.

10

APPENDIX A: WAVE PROPAGATION IN A HOPKINSON BAR APPARATUS

The incident, reflected, and transmitted energy are denoted by El, ER, and ET respectively. Thegoverning equations for stress o(t), velocity V(t), and displacement u(t) are

O(t) =(p) (cig) V (t) (Al)

V (t) = duld, (A2)t

u(t)=(c/E) f a(t)dt (A3)[=0

where E = Young's modulus,t = time,

p = density,V(t) = velocity,

c = the wave speed in the material, andg = the acceleration due to gravity.

Further, the energy of the wave in a one-dimensional bar is

E = Ac oa2(t)dt (A4)Ef

t=0

where A is the cross-sectional area of the circular Hopkinson bar. Displacement of the indentor u,(t)can be obtained from the incident, reflected, and transmitted stresses (al(t), OR(t), and OT(t),respectively):

Ul (t) = (cIE) f [1 1(t) - OR (t) - OT(t)] dt (A5)

t=0

The force on the indentor is

F(t) = (A) [a,(t) + OR (t)] (A6)

Energy produced by the indentor (E ) can be computed from an integration of the product of force anddisplacement over the duration of the wave:

t

Ep = (AcIE) f ([Of (t) + CR (t)] - [01 (t) - OR (t) - OT(t)]) dt (A7)

t=0

The energy of the incident, reflected, and transmitted waves can then be computed from

I

(E 1 ,ER , ET) = (AcIE) f [o 1 (t)2 , OR(t)2 ' OT(t)2] dt (A8)

1=0

11

The total energy absorbed within the system (i.e. that absorbed during damage generation and minor

losses within the fixture) is

EA = E, - (ER., ET). (M9)

which can be rewritten as

EA =(Ac JE) J, (aI (t) 2 - [C;R (t) 2 + OT (t)2] cit (AlO)

The H-opkinson bars used in this test series were steel with the following parameters:

A = 1140MM2 (1.7675 in.2 )c =5017 m s-' (197531 in. s-1 )E = 193.05 GPa (28 x 106 psi)

so that Ac/E 0.02963 m3 GPa-1 s-I (0.012467 in.5 lb'- S-1).

12

REPORT DForm ApprovedREPORTDOCUMENTATION PAGE OMB No. 0704-0188Public repottlig burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources gathenng andmeinfaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information,including suggestion for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports. 1215 Jefferson Davis Highway. Suite 1204, Arlington.VA 22202-4302, and to the Office of Management and Budget. Paperwork Reduction Project (0704-0188), Washington, DC 20503.

1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVEREDI October 1991

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Energy Absorption of Graphite/Epoxy Plates Using Hopkinson Bar Impact PE: 6.27.84APR: 4A762784AT42

6. AUTHORS TA: SSWU: 019

Piyush K. Dutta, David Hui and Magna R. Altamirano andMIPR FY1 456-90-N0066

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATIONREPORT NUMBER

U.S. Army Cold Regions Research and Engineering Laboratory72 Lyme Road CRREL Report 91-20Hanover, New Hampshire 03755-1290

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORINGAGENCY REPORT NUMBER

Office of the Chief of Engineers U.S. Air Force Flight Dynamics LaboratoryWashington, D.C. 20314-1000 Wright Patterson AFB, Ohio

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Approved for public release; distribution is unlimited.

Available from NTIS, Springfield, Virginia 22161

13. ABSTRACT (Maximum 200 words)

This work summarizes the analytical and experimental study on the energy absorption of quasi-isotropic graphite/epoxycomposite plates due to the impacting hemispherical penetrator in a Hopkinson bar apparatus. The mechanics of stress wavepropagation through the bar and the composite laminate plate are discussed to predict the phenomenological process involved.The experimental data provided the results in terms of force, velocity, and energy of impact at all times during the penetrationprocess occurring in microseconds. It has been concluded that loss of contact occurs frequently during the penetration processdue to the stress wave reflections back and forth in the thickness direction. The damage process seemed to be both velocityand temperature dependent. Below a certain transition velocity the laminate absorbs less energy at low temperature than athigh temperature. The reverse is truc above this transition velocity. The mechanism of failure tends to change with impactvelocity in such a way that progressively less energy is absorbed at higher velocities.

14. SUBJECT TERMS 15. NUMBER OF PAGES

18Advdnced composites Composites Fiber composites Impact Stress wave 16. PRICE CODECold Damage Graphite/epoxy Low temperature

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACTOF REPORT OF THIS PAGE OF ABSTRACT

UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL

NSN 7540-01-280-550C Standard Form 298 (Rev. 2-89)U.S. GOVERNMENT PRINTING OFFICE: 1 9gi-6OO-063/42-39 PEGICN i Preecrbed byANSlStd. Z39-18

298-102