II

i NSWC/WOL/'r 76-7

0

00 WHITE OAK LABORATORY

THE EFFECT OF MOISTURE ON CARBON FIBER REINFORCED EPOXY COMPOSITESI DIFFUSION

0 BYJoseph M. AugI 27 SEPTEMBER 1976Alan E. BergerNAVAL SURFACE WEAPONS CENTER

WHITE OAK LABORATORY

SILVER SPRING, MARYLAND 20910

* Approved for public release; distribution unlimited

NAVAL SURFACE WEAPONS CENTER DWHITE OAK, SILVER SPRING, MARYLAND 20910 fl

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UNCLASSIFIED ______________________________

ELUtliT'. CLASSIFICATION Of TH4IS PAGE (When Dots EnIWO41)__________________________________________________READ_ INSTRUCTIONS______________

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9SWCIWL/TR-2&fi I'The Effect of Moisture on Carbon Fiber'

Reinorcd EoxyComposites. onZI j , l

Joseph M./Augll- lan E./egr,. E RORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK

PER ARtEA A WORK UNIT7 NUMBERSNaval Surface Weapons Center EIM.53II; WRO 204White Oak Laboratory WR02201401; WrR3911

,iteL.Oak, jilyer spr Mgflrland 20910Q11. CONTROLLING OFFICE NAME AND ADORFS5

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Approved for Public Release; Distribution Unlimitod

17. DISTRIBUTION STATEMENT (of the absttted entered in Block 20. If different host Report)

IS. SUPPLEMENTARY NOTES

It. KEY WORDS (Continue an reverse side it necessar end Ientty~ by block nimber)

CompositesMo~isture effectsDiffusionCarbon fiber composite*

20. A bf AACT (Ceedhlua on rverse side it meosemp &W idmtl' 5 bl eek mmbeet)

Mathematical models are suggested for calculating the reducedmisture diffusivities in unidirectional carbon fiber reinforced

composite* with hexagonal and tetragonal fiber alignment, paralleland perpendicular to the fiber direction, as a function of fiberalum fraction.

DD 1 1473 "Oo O I NOV0 48t OUSOLEY8 UNCLASSIFIEDS/N 010-LF414601 SECUXITY CLASIPICATIO11 OF THIS PAOt (Ma Does # EaOr*

UNCLASSlF1P -__SECUm L ASSI 11 ATION I '.IS PAGE (Wh,,, fl.,. P ,,..,d

The effective diffusion coefficients measured perpendicular

to the fiber direction of 6 carbon fiber composites were deter-mined as a function of temperature and relative humidity.

The knowledge of the diffusion coefficients as a function oftemperature, relative humidity, fiber volume fraction and compositgeometry allow the prediction of the internal moisture distri-bution in a composite if the environment can be specified. Afew simple examples have been illustrated.

UNCLASSIFIED5CURITY CLAWICATION OPVMIS1 PAOQU9MVl. Doaf 3t ,

Ade

NSWC/WOL/TR 76-7 27 September 1976

The Effect of Moisture on Carbon Fiber Reinforced Epoxy Composites.I Diffusion.

The observation by earlier investigators that the flexural andshear strengths carbon fiber reinforced composites may deteriorateat ambient storage condition made it necessary to investigate thesephenomena more closely in order to get a better understanding, andultimately, to be able to predict how these materials would behavein longtime service and storage conditions.

The work described in this report is a part of this investi-gation. It describes the diffusion of moisture in carbon fibercomposites which may serve as a basis for prediction of longtimecomposite changes in various environments.

This program was funded by the Naval &M Systems Command(Task No. A3200000010123) during the periods of 1 July 1974 to1 January 1976.

J. R. DIXONMaterials Division

ACCESSION for

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NSWC/WOL/TR 76-7

TABLE OF CONTENTS

Page

INTRODUCTION.............................5

BACKGROUND INFORMATION ......................... 5

EXPERIM4ENTAL.............................7

DISCUSSION AND RESULTS ......................... 9

APPENDIX A.............................A-i

APPENDIX B...............................B-i

Tables

Table Title

I Carbon Fiber Properties. ................. 82 Properties of Epoxy Resin Candidates .............. 13 Reduced Diffusivities as a Function of Fiber

Volume Fraction.. ........................... 244 Relative Humidities Above Saturated*Salt

Solutions at Various Temperatures. ............. 275 Equilibrium Concentration of Moisture in Epoxy

Resins at Various Temperatures (at 30 and 80% RH) ... 286 Diffusion Coefficients of Varibus Carbon Fiber Epoxy

Composites as a Function of Temperature andRelative Humidity..........................29

7 A comparison of the effectivemoisture diffusioncoefficients (DeAp) in the HMS and T300 carbonfiber composites. ............. ... .. ... 32

Illustrations

Figure Title

1 Geometry of Unidirection Fiber ReinforcedComposites .. .. .. .. .. ... ... .. .. ... 37

2

NSWC/WOL/TR 76-7

ILLUSTRATIONS (Cont.)

Figure Title Page

2 Relation of Percent Fiber Volume to the Ratio ofFiber Distance to Fiber Radius in a HexagonalTwo-Dimensional Latice of Fibers in aUnidirectional Fiber Reinforced Composite ......... .. 38

3 A Comparison of the Reduced Diffusivity Verticalto the Fiber Direction with Thermal and ElectricalAnalogs . ................. . .. . 39

4 Equilibrium Concentration of Moisture in NARMCO 5208Resin as a Function of Temperature and RelativeHumidity. . . ........... 40

5 Concentration of Moisture in Air as Function'ofTemperature .......... . . . . . ..... 41

6 Fractional Water Absorption atVarious Temperatures ofEpon 1031/HMS Composite at 30% RH .... . . . .... 42

7 Fractional Water Absorption at Various Temperaturesof Epon 1031/HMS Composite at 80% RH ............. .43

8 Diffusion Coefficient of Water for Narmco5208/T300 C-Fiber Composite as a Function ofTemperature and Relative Humidity .. .. . . . .... 44

9 Diffusion Coefficient of Water for DER 332/T300C-Fiber Composite as a Function of Temperature andRelative Humidity . . . . . ........... 45

10 Diffusion Coefficient of Water for Epon 1031/T300C-Fiber Composite as a Function of Temperature andRelative Humidity . . .......... ....... 46

11 Diffusion Coefficient of Water for Narmco5208/HMS C-Fiber Composites as a Function ofTemperature and Relative Humidity...... . .. . . . 47

12 Diffusion Coefficient of Water for DER 332/HMSC-Fiber Composite as a Function of Temperatureand Relative Humidity . . . ............... 48

13 Diffusion Coefficient of Water for Epon 1031/HMSComposite as a Function of Temperature andRelative Humidity . . . . . . . . . ......... 49

14 Concentration Distribution (Master Plot) atVarious Times in the Sheet - h < X < h with InitialUniform Concentration CO and Surface ConcentrationCI.. . . * *. . . ...... 50

15 Pot of Fractional ALsorption of Any Materiai with"Fickean Behavior Versus (Dt/h2)l/2 for PlateGeometry. . . . . . . . ............... . 51

16 Distribution of Moisture in an Unidirectional 5208/T300Epoxy Composite: a. At 250C and 80% RH (Thickness1 CM): b. At 250C and 30% RH (Thickness 1 CM): c. At350 and 80% RH; d. At 350C and 80% RH (Thickness0.25 CM). . . . . . . . . ... .............. 52

3

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NSWC/WOL/TR 76-7

ILLUSTRATIONS (Cont.)

Figure Title Page

17 Percent Weight Increase of 5208/T300 Epoxy CompositeAt Various Conditions .................... 53

18 Diffusion of H 0 Into DER 332/DADS-HMS Composite(Vertical to Fiber Direction) at 250C and 80% RH. . . 54

19 Diffusion of HZO Into Epon 1031/NMA-HMS Composite(Vertical to Fiber Direction) at 250C and 80% RH. 55

20 Arrhenius Plot of Moisture Diffusion Into HMS Fiber 5Composites (Determined at 33% RH) ............ 56

21 Rate of Moisture Pick-up xn a Sheet of Narmco5208 Resin at 300C ........ .................. .. 57

4

INTRODUCTION

The use of carbon fiber reinforced composites for primaryand secondary structural components in aircraft constructionpromises not only benefits in weight savings, and with it, maneu-verability and range of the aircraft, but also a considerablesavings in labor cost. This savings in labor cost more thancompensates for the higher cost of the raw materials.

Serious consideration is given today to the replacement ofvarious components in aircraft with carbon fiber composites. Forinstance, the Lockheed Aircraft Corporation has decided to usecarbon fiber-epoxy composites in the future for the verticalstabilizer of their 1011 commercial airliner. It is true thatwhile the demands of commercial aircraft are less severe, thanthose of military aircraft the above use also indicates thatconfidence in these advanced composites has increased over thepast few years. Therefore, it becomes even more necessary tolearn as much as possible about these materials, such as theirbehavior in various environments and the change of propertieswith time.

This report describes part of an investigation to highlightcertain aspects of environmental property changes in carbon fiberreinforced composites. There are a number of mechanisms that canlead to changes of composite properties. In this investigationemphasis was given to the effect of moisture on these composites,since the rate of moisture absorption at ambient conditions isconsiderably higher than the rate of any other mechanism that maylead to property changes in benign environments. Specifically,the subject of this report is the diffusion process of moisturein high performance carbon fiber reinforced composites. Diffusioncoefficients were determined on several composite systems as afunction of the relative humidity and temperature. These dataserve as basis for estimating the moisture distribution insidethe composites as functions of composite thickness, time andtemperature. The concomitant composite property changes will bedescribed in a subsequent technical report.

BACKGROUND INFORMATION

The effect of moisture on high temperature properties ofcarbon fiber epoxy composites was discovered jointly by investi-gators of the Fiberite and Aerospace Corporation and is well

5

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NSWC/WOL/TR 76-7

documented in a summary report by J. Hertz[l]. C. C. Browning [2]at the Air Force Materials Laboratory (AFML) compared compositeswith different fiber orientations and showed that the propertieswhich are most strongly affected by moisture are the matrixcontrolled properties.

In earlier repots, R. Simon et al. [3] at the Naval SurfaceWeapons Center had investigated the effect of water on variouscarbon fiber composites and concluded that mechanical propertychanges are affected by both the nature of the carbon fiber andthe type of resin used.

The longterm degradation effects on fiber reinforced compositescan be caused by various mechanisms. Which mechanisms predominatedepends, of course, on the type of materials that constitute thecomposite. In fiber reinforced composites a degradation of theresin, the fiber or the interfacial bonding will have a pronouncedeffect on various composite properties.

There are a number of mechanisms that can lead to compositeproperty changes which may be differentiated as reversible andirreversible changes.

Chemical and mechanical matrix degradation such as photo-oxidation, thermal degradation (in the presence or absence ofair), hydrolytic polymer chain cleavage, high energy radiaiton,stress cracking, microbial degradation, and thermal [4] andmechanical cycling may lead to irreversible property changes offiber reinforced composites.

We define reversible property changes as those changes thatcan be reversed to the original properties (at least within thelimitations of the sensitivity of the measurements).

A trivial case of a reversible property change is a change dueto temperature, as long as the temperature change is not too highwhich could lead to an irreversible degradation.

Another reversible change in composite properties is observedwhen small molecules such as moisture or organic molecules penetratethe matrix and plasticize it. The effect of such a plasticization

1] J. Hertz, Final Report NASA8-27435, June 1973 (NASA Contract).2 C. E. Browning, 28th Annual Conference of the Society of the

Plastic Industry, Feb 1973 (Washington, D.C.); Proceedings 15A.[3] R. A. Simon and S. P. Prosen, NOLTR 68-132, Oct 1968;

M. L. Santelli and R. A. Simon, NOLTR 70-258, Feb 1971.[4] E. L. McKagne, Jr., J. E. Halkias and J. D. Reynolds, "Moisture

in Composites: "Effects of Supersonic Service on Diffusion,"J. Comp. Materials, 9, 2, (1975).

6

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NSWC/WOL/TR 76-7

is a reduction in the glass-transition temperature (T ) of thematrix and also a reduction in the matrix modulus ove a widetemperature range. By heating and/or evacuating of such materialsone can remove the moisture again and the original strengthproperties may be regained.

The fact that this reaction is reversible is of little practical,value, since the strength properties of a large structure cannot beeasily restored. On the other hand, the composite strength isexpected to deteriorate only to a certain level depending on theequilibrium conditions, which are governed by the environment,especially by the relative humidity.

The Experimental section will briefly describe the materialswe have investigated and the techniques for measuring the diffusioncoefficients. The following Discussion section will focus on themoisture diffusion in composite materials, while the resultingchanges in mechanical properties will be described in a subsequentreport.

EXPERIMENTAL

Materials

A. Resins

1. Narmco 5208. This resin was obtained from the WhittakerCorporation, Narmco Division. It is a one-component system :resinplus curing agent).

2. DER 332/DADS. The resin system consists of 100 parts ofDER 332 (a diglycidyl ether of bisphenol A) and 36 parts of DAS(4,4' diaminodiphenyl sulfone).

3. Epon 1031/NMA. This resin consists of 100 parts of Epon1031 [l,l,2,2-tetra(p-glycidyloxyphenyl) ethane ], 77 parts ofNadic methyl anhydride, and 1 part of BDMA (benzyldimethyl amine).

B. Fibers

1. Thornel 300. This material was obtained from UnionCarbide Corporation and consists of a continuous strand of 3,000filaments which have an epoxy sizing for better handleability.(For properties reported by the manufacturer see Table 1.)

2. HMS fibers. This material is a tow with 10,000 continuousfilaments manufactured by the Hercules Corporation. The fibershad no sizing. (For properties reported by the manufacturer seeTable 1.)

7

NSWC/WOL/TR 76-7

C. Composites

The composites were made from 8 plies of 9-inch wide prepregs,which were layed up unidirectionally and molded (in a vacuum bag)under 100 psi pressure. The details of the prepregging operationand the composite curing conditions will be described in a forth-coming technical report that will deal with the moisture andtemperature effects on the mechanical properties of these composites.

Table 1: Carbon Fiber Properties

Properties Hercules HMS Thornel 800

Strand Modulus, psi x 106 50 - 55 33 - 34.5(G Pasc.) (345 - 379) (227 - 238)

Strand Break Strength, psi x 103 340 (2.34) 361 (2.49)

(G Pasc.)

Density, g/cc (lot average) 1.85 - 1.90 1.74 - 1.78

Filament Diameter, microns 7.2 - 7.5 8

Number of Filaments 10,000 3,000

a

8.

N' U

NSWC/WOL/TR 76-7

Measurements

A. Equilibrium Concentrations. To determined the moistureequilibrium concentrations of the resins and composites finemachine shavings were obtained and dried for 48 hours at 120°C invacuum. The dried shaving samples were stored over magnesiumperchlorate desiccant before use. One gram samples were preparedin individual crucibles. The sample exposure during the weighingoperation was kept below 3 minutes. The samples were then exposedto 30% and 80% RH, at 30*, 450, 600, and 75*C.

The equilibrium concentration was defined as the concentrationwhen the weight increase vs. time curve leveled out, whichgenerally occurred within a few days. The percent weight gainafter two weeks was designated the equilibrium concentration.

B. Fractional Weight Increase. 5 x 5 cm square samples weremachined from the composite panels and sealed around the edges witha strip of aluminum foil (adhesively bonded). These specimens weredried for 72 hours at 125*C before exposure in the humiditychambers (30% and 80% RH, at 300, 450, 600 and 750C). The platesamples were removed after various time intervals and the fractionalweight increase [Mt(%)/M (%)] was plotted vs. square root oftime, where Mt is the percent weight increase after the time(t)and M. is the equilibrium value.

Humidity Chambers

The samples were put into a sample holder and placed in awide-mouth screw cup container (23.5 cm high, 11.5 cm diameter).Various salt solutions (2 cm high, with undissolved solute) servedto keep the relative humidity constant. The exposure chamberswere closed and submerged into 4 water baths held at 30° , 450,600, and 75C (+.2*C).

DISCUSSION AND RESULTS

A. Materials

Considerations of aerodynamic heating which predicted that partsof the aircraft may reach 350OF (177C) during supersonic flightmade it mandatory that the composite materials to be used for theseaircraft be stable at this temperature. Composites with 1770Cperformance capability require resin matrices with a glass transitiontemperature, Tg' > 177*C, i.e., resins that have no considerableloss of modulus below this temperature. Because absorption ofmoisture leads to a plasticization of the matrix it was expectedthat resins with low moisture affinity would show a better strengthretention than those with high moisture saturation values.

This work was restricted to the investigation of six compositesystems made from two different carbon fibers and three resins.

9

NSWC/WOL/TR 76-7

The resins were: Narmco 5208, DER 332/DADS and Epon 1031/NMA.The fibers were Thornel 300 and HMS fiber.

During the original screening of resins by torsional braidanalysis for their thermomechanical behavior, we found that severalother resins also fulfilled the temperature requirements. Some ofthe properties of these resins are listed in Table 2.

Two of these resins, Fiberite 904 and X-801, are no longercommercially available. The choice of resins for this investigationwas somewhat arbitrary. For purposes of scientific understandingthose resins whose chemical composition was known were preferred.Nevertheless, Narmco 5208, a proprietary commercial material wasalso included because of its attractive properties. (Hercules 3501appeared similarly attractive; we intend to investigate thismaterial at a later time.)

The choice of carbon fibers was based mainly on the similarityin tensile properties and on their dissimilarity in modulus (themanufactures' data are given in Table 1).

B. Effect of Moisture on Composite Strength

The change of composite strength as a function of temperatureand moisture will be the subjects of two forthcoming technicalreports. It will suffice here to summarize what might be expectedif a composite is exposed to humidity.

At ambient temperature the rate of degradation of compositestrength due to oxidation or hydrolysis is very small compared tothat of moisture absorption. Thus it should be possible to predictthe ultimate strength and modulus changes which are reached whenthe moisture content in the composite is in equilibrium with itssurrounding. This equilibrium, of course, is a function of thetemperature and of the relative humidity. The degradation ofcomposite properties is expected to be a function of the absorbedmoisture:

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NSWC/WOL/TR 76-7

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Thus, in order to estimate the strength degradation of composites asa result of long term exposure to the environment, specifically tohumidity, at least two things must be determined:

1. The strength (or modulus) retention as a function oftemperature and the amount of moisture absorbed.

2. The rate of moisture absorption (diffusion) as a functionof temperature and relative humidity. Knowing the rate should allowone to predict how long it takes to reach a certain change instrength.

Of course, different strength parameters such as tensilestrength, flexural strength, shear strength, compressive strengthand their corresponding moduli are affected differently for the samechange in moisture concentration. Also, it is assumed that acertain moisture content in the composite corresponds always to onlyone strength (modulus) value independent of the way the moisture wasallowed to be absorbed in the sample. There is experimentalevidence that the strength changes with moisture pick-up are thesame whether the sample was moisture loaded by a water boil test orby water soak at ambient temperature [5]. This fact might beexpected as long as the moisture concentration distribution is thesame in the interior of the composite. The same overall moistureconcentration might also correspond to different interior distri-butions, in which case there may or may not be only one strengthvalue for a given value of percent moisture.

The time to reach a certain moisture concentration (or better,moisture distribution) is, of course, dependent on the compositegeometry and the temperature and humidity profile, but can becalculated in principle if the diffusion coefficients (and theirtemperature and concentration dependences) are known.

Thus, one of the very important parameters to be measuredfor the prediction of property changes in composites is theireffective diffusion coefficients of moisture along the principalaxes of diffusion. Of special interest is the diffusion coefficientacross the fiber direction because of the sheet geometry of mostcomposites.

C. Methods For Determining Diffusion Coefficients in Polymers

The two most widely applicable methods for measuring diffusioncoefficients (D) are based on either steady state flow rate

[5] Personal communication with N. Judd Royal Aircraft Establishment,Farnborough, England, and Hercules, Inc.

13

NSWC/WOL/TR 76-7

determinations through a membrane or on the analysis of sorptiondata [6 to 8].

The flux (J) through a membrane is described by equations laand lb.

J= -D dc (la)c dx

J Jdx = D dc (lb)f fC c

0 X.

where Dc = the diffusion coefficient (which may depend onconcentration), c = concentration, x = distance through the membrane.

In a steady state condition the flux is independent of x andequation (2) follows.

j f Ddc (2)

C£Z

The dependence of D on concentration can be determined bymeasuring the flux St different concentrations on one side of themembrane while the other side is kept essentially at zeroconcentration.

The other method for determining D is based on absorption ordesorption measurement of the diffusant in plate, sphere or rodsamples.

The solution of Fick's second equation of diffusion (3)

r 2c a2c 2c]

t I ax a

[6] J. Crank, "The Mathematics of Diffusion", Oxford Univ. Press.1956.

[7] J. Crank and G. S. Parks, "Diffusion in Polymers" Acad. Press(1968).

[8] G. J. Van Amerongen, "Diffusion in Elastomers," Rubber Chem.and Techn. 37, 1065, (1964).

14

NSWC/WOL/TR 76-7

for a two-dimensional plate with infinite extension and exposure toconstant concentration C1 and C2 of the diffusant on either sidesand with constant initial internal concentration Co can be expressedby the series solution (4) [6].

_ _8 1 exp [-D(2m + 1)2112t/k2 ] (4)

- 1 m =0 (2m + 1)

where

Mt = Weight increase after time t, M, = Weight increase atsaturation level, £ = thickness of plate.

For Fickean behavior of diffusion the plot of Mt/Mm vs.

t is practically a straight line up to a value of 0.6 of Mt/M.Thus, the initial absorption or desorption curves of uniformlyloaded plate specimens can be used to determine D by eitherexpression (5) (p. 241 of [6]) or (6).

D = 0.049/(t/i2 (5)

where the subscript indicates that t is taken as the time forMt/M,. to reach the value 0.5.

Mt _ 4 i (6)

If the initial gradient, G d(Mt/M)/d(t/£2) is observed ina sorption experiment in which D isconcentration-dependent, thenthe average diffusion coefficient, D, deduced from (6) is

1-G (7)

We have used this expression to calculate the diffusioncoefficients from the sorption measurements.

D. Diffusion of Moisture in Fiber Reinforced Composites

Since composites are anisotropic media Fick's second law ofdiffusion takes a more complicated form (8) than for isotropicmedia (3). The diffusion coefficient Dnm has a tensor form.

15

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NSWC/WOL/TR 76-7

cc D D c + 2 c D 32 y a211 _77 22 _ D33 =_ C23 32--7ax y az

2 2(D + c + (D2 + D 2 c(8

(D31 3D T) i 12 D2 1 F (8)

where x, y and z are Cartesian coordinates.

Equation (8) can be transformed into one with three principal axesof diffusion, with principal diffusion coefficients Dl, D2 ,and D3 and (8) can be expressed by (9)

c + D 2c D2c acat 1 2 2 2 3 + D 77 (9)

where C, , , are the principal axes. Various symmetry consi-derations such as found in crystallographic systems may lead to stillsimpler expressions.

In a system with more than one solid component, such as afilled plastic or a fiber reinforced composite, the overall diffu-sion is obviously dependent on the diffusion in both substances, onthe equilibrium distribution of diffusant in substance A and B asexpressed by the distribution coefficient k = CA/CB, and on thespatial arrangement of A and B in the solid phase.

E. Effective Diffusion Coefficient in Unidirectional CarbonFiber Composites

From the symmetry of unidirectional carbon fiber compositestwo of the three principal diffusion coefficients are shown to beequal (see Figure la). The question to be answered is, how do therates of diffusion change with respect to the unfilled matrix as wechange the fiber content and the fiber direction.

If the diffusion of moisture in the carbon fiber is negligiblecompared with that in the resin, the problem is simplified. Afurther assumption is that there are no voids in the resin orbetween resin and fiber and that there is no significant masstransport along the resin/fiber interface.

In compacting fibers in a resin under pressure there is ahigher probability for the fibers to assume a hexagonal packing(Figure lb) than a tetragonal arrangement (Figure 1c), although ina real composite a mixed geometry due to many latice defectsprobably exists.

16

Adl

NSWC/WOL/TR 76-7

The reduced diffusivity parallel to the fiber direction in acarbon fiber epoxy composite with hexagonal fiber arrangement is theratio of the effective diffusion coefficient to the diffusivity ofthe unobstructed resin.

DeN h = 1 -V (14)

D rfr

For a tetragonal fiber arrangement one can arrive at similarrelations (from Figure lc) as indicated below

v f r 2 (15)(2r + d)

2r + (16)

(d = 1.7724 2 (17)

t Vf

Detv = 1- V (18)

Dr

The fiber volume fraction for the highest packing density

(d=O) for composites with hexagonal fiber arrangement is ITrv/6and with tetragonal arrangement it is n/4.

The ratios of d/r for the hexagonal and tetragonal fiberarrangements as a function of percent fiber volume is shown inFigure 2.

Effective diffusion coefficients for diffusion of water vaporacross the fiber direction in a composite material with a hexagonalor tetragonal arrangement of fibers may be determined numericallyby solving a Poisson equation (with appropriate boundary conditions)on a unit cell of the material (a detailed demonstration that it

17

. . . . . . . . . . - - - - -r m mm m m m o

NSWC/WOL/TR 76-7

To simplify the discussion, we consider a two-dimensionalplate through which moisture diffuses under steady state condi-tions. If there are no fibers in the matrix the amount of materialdiffusing through the plate is given by Fick's first law

J = -D (10)r r 9z

where J = flux in g/cm 2 sec through the surface vertical to theflow difection, Dr = average diffusion coefficient of the resin,LC = difference in concentration of the diffusant on both matrixsurfaces, 9 = thickness of the sheet.

If fibers are introduced into the matrix parallel to the flowdirection, the effective cross section for the diffusion is reducedproportionally to the cross sectional area of the introduced fibers,i.e., proportionally to the fiber volume fraction, Vf.

The cross sectional area of the fibers with respect to a unitr2

cell of a hexagonal fiber arrangement is 4 fh = /2 (where

r = radius of fiber). The total cross sectional area of the unit2

cell is tot h = (2r + d) (sin 60)/2. The fiber volume fraction istherefore

2 2sV n 60 x r 3.6276 (11)

2sin 60 (2r + d)

The volume fraction of the resin matrix is Vr = 1 - Vf. Thesubscripts h or t refer to hexagonal or tetragonal fiber arrange-ments, and the subscript f and r refer to fiber and resinrespectively.

From (11) follows

r2r 52503 4 Vf (12)

and

( )h = 1.9046 2 (13)

where d = shortest distance from fiber to fiber surface.

18

NSWC/WOL/TR 76-7

is sufficient to solve only within a unit cell is given inAppendix A). Unit cells for computing the effective diffusioncoefficient of water vapor perpendicular to the fibers in a hexa-gonal and in a tetragonal array are shown in Figure 1.

To determine the effective diffusion coefficient de (in the ydirection) with either a hexagonal or tetragonal arrangement of thefibers, we consider the following. Allow no diffusion across thevertical sides of the unit cell. Let the bottom and top faces ofthe unit cell be exposed to uniform concentrations of water vaporso that the water vapor concentration in the matrix along thebottom face is a constant C2 and so that the water vapor concen-tration in the matrix along the top face is a constant CI . Asteady state concentration water vapor, C(x,y), will then becomeestablished in the unit cell. The effective diffusion coefficientde is given by

de = -q • y/(C 1 - C 2 (r + d/2) (19)

where y is the height of the unit cell, and q is the flux throughany y=constant surface in the unit cell (q being independent of yin the steady state). Letting d (x,y) = Df (the diffusioncoefficient of the fiber) if (x,y) is a point lying in the fiber,and letting d (x,y) E Dr (the diffusion coefficient of the resin)if (x,y) is a point in the resin, one has that q is given by

r + d/2

q = jo - (x,y) c (x,y)dx for any yc [o,y]. (20)

The specific differential equation and boundary conditionssatisfied by c(x,y) will now be given. There is a constant k(the distribution coefficient, which depends on the particularmaterials in the resin and in the fiber) so that at any point plying on an interface separating the resin and fiber regions, onehas

cf(p)/cr (P) = k,

where Cf(p) (C (p)) denotes the limit at p of the concentrationas one approaches from within the fiber (resin). Let the function

u(x,y) be given by

u01,Y) c(x,y), for points (x,y) in the resin (21)c(x,y)/k for points (x,y) in the fiber

19

...................................................

NSWC/WOL/TR 76-7

so then u(x,y) will be continuous across any interface betweenmatrix and fiber. If p is a point on an interface between resinand fiber, let n denote a unit normal to the interface curve at p.Then the condition of continuity of flux at p is

-D k ufu(p) -D ur (p) (22a)fD • n(P =-r n

where u f(p) denotes the normal derivative of u at p calcu-n

lated from within the fiber (resin). In the case Df = 0 the leftside of (22a) is defined to be 0. The differential equation andother boundary conditions satisfied in the unit cell by u are;

0 = Dr Au Dr (Uxx + u yy) in the resin, (22b)

0 = Df * kAu in the fiber (22c)

with the understanding that when D - 0 conditions on u holdingin the fiber region are to be omitted,

u(x,o) = C2 and u(x,y) = C 1 for 0<x<r+d/2, (22d)

ux (o,y) = 0 and ux (r+d/2,y) = 0 for 0 y y (22e)

Note that (20) in terms of u is

r+d/2

q=f -d(x,y) Uy (x,y)dx for any ye [o,y], (23)

0

where d(x,y) = Dr in the resin and d(x,y) = k • Df in the

fiber.

Numerical approximation of (19), (22), and (23) was done asfollows (a completely detailed discussion is given in Appendix 1).Rather than solve the interface problem (22) directly, which wouldinvolve dealing directly with the geometry of the curved interfacebetween matrix and fiber, a variable diffusion coefficientproblem (24-26) approximating (22) was solved on the rectangularunit cell;

u(x,o) = C2 and u(x,7 ) = c for 0Ox<r+d/2 (24)

ux (o,y) = 0 and uX (r+d/2,y) = 0 for O<y<y (25)

20

NSWC/WOL/TR 76-7

V'd (x,y)Vu = 0 on O<x<r+d/2, 0<y<y (26)

where away from the interface, d = Dr in the resin and d = k.Dfin the fiber, while in a narrow zone near the interface d changesLontinuously from Dr to k.Df. In the situation Df = 0,

was defined to be k/1000 in the fiber, and varied from Dr to k/1000near the interface.

The Equations (24-26) were solved using the D'Yakonov ADI(alternating direction implicit) finite difference method on a gridwith uniform mesh spacings Ax and Ay in the x and y directions,respectively. The flux q given by (23) (with d(x,y)) replaced byd(x,y)) was evaluated by differencing u to obtain u and by usingthe trapezoidal quadrature rule to evaluate the imt~gral.

F. Thermal and Electrical Analogs to Diffusion Processes

A thermal analogue to the diffusion of moisture through amedium with cylindrical obstacles perpendicular to the flow direc-tion has been treated by G. S. Springer and S. W. Tsai [9]. Theseauthors have calculated the thermal conductivity of a system withtetragonal arrangement of cylindrical rods embedded in a matrixwith different thermal conductivity. They obtained the followingequation

km 41 B2f/g ta , 2Vf/11

_/m_ 1 +27B

B = 2 Mfl (27)

k2 2 = thermal conductivity perpendicular to the axes of thecy inders,k = thermal conductivity of the matrix, Vf = volumefraction omthe cylindrical rods.

If k becomes zero (or for the analog in diffusion, the diffusioncoefficient of the fiber becomes zero), the second term goes tozero.

At equilibrium the difference in concentration of diffusantin phase (f) and phase (r) can be expressed by the ratio

[9] G. S. Springer and S. W. Tsai, "Thermal Conductivity ofUnidirectional Materials" J. Comp. Mat. 1, 166 (1967).

21

NSWC/WOL/TR 76-7

k = c /cr,(the distribution coefficient between resin andfiber. If Henry's law applied, the analog kDf/Dr can besubstituted for kf/kr so that the Springer-Tsa equationbecomes

Det i 24 - - B2Vf/11(D1~ + [B I -2 -l ___r1 1 - 2Vf/Hj 1 +;2Vfr]

B 2 1 (28)

Another analog has been calculated for an electrical conductivityproblem by Lord Rayleigh [10] and Runge [11]. Again the system wascomposed of tetragonaily arranged cylinders in a matrix with differentconductivity. An equation was derived which gave the overall conduc-tivity in terms of the conductivities of the cylinder and matrixmaterials

K 2Vf-=1 K K (29)K+ - 1- -

K KmKf + f f x 0.3058--f f+--K Km. m

which reduces to equation (30) when the conductivity of the cylindersbecome zero

K 2VfK-1- (30)Km 1 + Vf -. 3058 Vf ...

The conductivity in the Rayleigh equation does not become zero asit should for the highest packing density of tetragonal cylinderarrangement (see Figure 3). No explanation was given by the author.

There is a considerable difference at the lower fiber volumefractions between the Rayleigh curve and that of Springer-Tsai forzero thermal conductivity of the cylinders.

[10]Lord Rayleigh, Philosoph. May. 34, 481 (1892).[ll]I. Runge, Z. Tech. Phys. 6, 61 (1925).

22

NSWC/WOL/TR 76-7

The curve we obtained from the finite difference approachwas in excellent agreement to that of Rayleigh (for the tetragonalfiber arrangement) up to about .70 fiber fraction. Above thisdensity the Rayleigh equation fails. The reason why the Springer-Tsai model gives lower values of reduced diffusivities over thewhole range is, that it is based on a simple thermal model wherethe composite elements are connected in series [9]. This meansthat a single fiber running through the matrix (vertical to theflow direction) has the same effect as a whole sheet of graphitewith the same thickness as the fiber being placed in the flowdirection.

That there is a difference can be shown by the same finitedifference method if the following boundary value problems aresolved:

a) for the unobstructedN region dx(2r+d)

N A- b) for the region withinA (r+d) x (2r+d)

If this simple thermal model would be applied for the hexagonalfiber arrangement it would fail already at r/8 V3 fiber volumefraction because this model does not take into account that thediffusant can flow around the fibers. The difference of variousmodels is given in Table 3 and Figure 3.

G. Diffusion Coefficient in an Arbitrary Angle to the FiberDirection of a Unidirectional Carbon Fiber Composite

The principal axes of diffusion are parallel and perpendicularto the fiber direction. De, therefore, constitutes a rotationalellipsoid with two principal diffusion coefficients being equal.For the general case one can state that the diffusion coefficient,D, at right angles to surfaces whose normals have the directioncosines k, m, n relative to the principal axes of diffusion is givenby

D =Z 2D + m2D + n2D (31)x y z

23

-J ,

'44 -4

0)CD 0 N r-4 .-4 a'N (N m~ C1 %D m. ~LI ON C) 0 > 0 ) ON C> 0 O U, -4 U, '.

4-) a- C0 0 1 m' M' -W r. '.0 m. N O 4(4-Ja) = . * *

44 1 1 ; ;

0-'-4 44' -44.i 4-4 4.)U -4 0 0 Ch ON (4 0O .- l 0 o '. 4 co(a ax in U N Ch 0 0 ('-) (Ni a% 00 .0W

4j 4- ' -4 CD 0D -4 q. U - OD -4 '.0

S -4

'-4 FL40

-44

44 j - C4 IT m M 1-4 a) ~ (n 00(D r N m U, -4 %.D (N U, U, (4

tN tr -*, Cw C 0 0 0 0N 1 , (N 4o - N'0 r- r-) (N vN '-4 0, 0,

-4i 41i*

0H CL a4-i

~L4 4

%D C14 '.n % 0 U, M r' o CO - N O N0)4 -0W (N fn '' m1 C) C) On U, 01,

(n r-4 -4 r-i w' wO '.0 U, '' c4 ( 4 -' 0- 0>

-4

> 0-4 u 4 en) Oh 4 .0 0) %p0 %D0 w U, -;r

(fl 00 U, r- N NJ '.4 '.0 (N w0' N0) N0 .-4 W. n (N (N m~ 00 m~ a% I

4-4 w. -4 -4 ON O %D0 U, 0' rn C14 -4 1-4 044 0) 4J)**

0 44 0 1

-4 cr

0) a)2 aw ON ~ ON 1- O 4 %.0 m~ 0D N- -4 (c100~0C U, CO OD U, a, '-4 -4 N- (N %D

-4 1. 00 %D t.o m' (N4 (N 1- -I N a 0CD

cr ON 00 r o0)-

--4 , ,U U '

.4 N r-4 C1 n *W n %D r- *- *o 0

'24

.A)

NSWC/WOL/TR 76-7

and the corresponding fluxes are

= -D J = -DDJ=x x ax y y y z z 3z

Thus, knowledge of Dell and Del is all that is required todescribe diffusion in a unidirectional carbon fiber composite.

For instance, the reduced diffusivity in a unidirectionalcarbon fiber composite, which is rotationally symmetric in thefiber direction, can be expressed as follows.

Dcr Dell Cos2 + D sin 2 (32)

D Deli

H. Effective Diffusion Coefficients in Cross-Plied LaminarComposites

If a composite is made of several layers of the same prepregbut with the layers laid up such that the fiber directions aredifferent for each layer, there is basically no difference in theeffective diffusion coefficient perpendicular to the fiber directionif the average fiber volume fraction is known. The reason is thata laminar ply consists usually of many layers of fibers in the samedirection. The effective diffusion coefficients in various direc-tions in the plane of the sheet is a superposition of all thesingle plies and their respective fiber directions. Each ply canbe treated as a unidirectional composite for which Del andDe are known as a function of their fiber volume fraction. Ofcourse, the angular dependence of the diffusion rates in eachply is not independent of the other plies since there is anadditional requirement. In order to maintain equilibrium, theconcentrations at the bounaries between plies (m and n) must becontinuous. For instance, if the flow is parallel to plym (=0°), then the flow in ply n (# 00) is increased because thereis an outflow from m into n which has a slower rate of diffusionin this particular direction. Thus, for the same reason, theeffective diffusion rate in ply m (in the 00 direction) is retardedas compared to the original rate of diffusion parallel to thefibers without neighboring plies (with different fiber directions).

I. Measurements of the Diffusion Coefficients (Dej) of Carbon Fiber

Reinforced Composites

The effective diffusion coefficients (DeL) of 6 carbon fibercomposite systems (made of 3 resins: Narmco 5208, DER 332/DADSand Epon 1031/NMA were determined as a function of temperature andrelative humidity.

25

, | . -

NSWC/WOL/TR 76-7

a. Equilibrium Concentration of the Composites as a functionof temperature and relative humidity.

Calculations show that it would take more than 100 years forthe composite plate of 1 cm thickness to reach equilibrium at roomtemperature; therefore, the equilibrium concentration was measuredon thin composite shavings. The results thus obtained comparedwell with calculated values from resin equilibrium measurements,also obtained from shavings or films. The calculations were madewith the assumption that only the resin absorbs moisture. Theconstant humidity exposures of 30% and 80%RH were carried out byadjusting the humidity with various saturated salt solutions(Table 4) for different temperatures. The results are shown inTable 5. Figure 4 shows the equilibrium concentration profile ofNarmco 5208 as a function of temperature and relative humidity.

The equilibrium concentration in the samples increase withincreasing RH as is expected from Henry's law, which states thatthe saturation point is proportional to the vapor pressure. However,in some cases the equilibrium concentration seems to decreaseslightly with increasing temperature at constant relative humidityin spite of the fact that at constant RH the absolute concentrationof moisture in the surrounding air increases with increasingtemperature (see Figure 5). The reason for the lower equilibriumconcentration at higher temperature may be due to the fact thatthe surface adsorption is lower at higher temperature. Thus, theequilibrium concentration of the interior seems to be governedby the surface adsorption. Water submersion may show differentresults.

b. Fractional Weight Absorption of Carbon Fiber Composites.2

5 x 5 cm composite plate samples, sealed around the edges withaluminum foil to prevent diffusion parallel to the fiber direction,were exposed at various constant temperatures and constant RHvalues. The fractional weight increases, Mt/MD, (where Mtis the percent weight increase after the exposure time t and M.is the percent equilibrium concentration as determined under [a]),were plotted vs. t for the composite samples Epon 1031/HMS,at 30% and 80% RH at 30 ° , 450, 600 and 75°C (See Figures 6 and 7).

c. Effective Diffusion Coefficients (De±) of Carbon FiberComposites as a Function of RH and Temperature.

From the slope of the sorption curves the diffusioncoefficients, DeL were calculated according to equation 7. Theresults are given in Table 6 and as three-dimensional projectionsin Figures 8 through 13.

Since the composites, made from the T300 and HMS fibers, onlydiffer about 4 percent in fiber volume concentration, the differencein diffusion coefficients between the two sets of composites is

26

NSWC/WOL/TR 76-7

Table 4: Relative Humidities Above Saturated SaltSolutions At Various Temperatures

Approx.Temp. RH < ', 33 < %55 < %80(0C)

30 MgCZ 2 (33) Na 2Cr 2 0 7 * 2H 20 (57) NH4C£. (81)

45 MgCi2 (32) Na2 Cr207 2H20 (54) NH4C. (79)

60 MgC£ 2 (30) Na2Cr207 ' 2H20 (55) KCL (80)

-5 MgC£2 (29) Na2CrO 4 (56) KCk (80)

(a) The numbers in parentheses are the RH values reported in theliterature for the respective temperatures.

27

NSWC/WOL/TR 76-7

Table 5

Equilibrium Concentration of Moisture in EpoxyResins at Various Temperatures (at 30 and 80% RH)

Exposure Exposure EquilibriumResin to (% RH) at (OC) Concentration (%)

5208 80 30 4.645208 80 45 4.575208 80 60 4.505208 80 75 4.50332 80 30 2.84332 80 45 2.61332 80 60 2.48332 80 75 2.071031 80 30 1.671031 80 45 1.441031 80 60 1.231031 80 75 0.905208 30 30 1.935208 30 45 1.835208 30 60 1.805208 30 75 1.75332 30 30 1.31332 30 45 1.27332 30 60 1.04332 30 75 0.821031 30 30 0.601031 30 45 0.581031 30 60 0.521031 30 75 0.445208 100 30 5.935208 100 75 6.105208 100 100 5.98

The equilibrium concentrations have been determined on resin

shavings, or resin films.

28

NSWC/WOL/TR 76-7

4- ) .. 0 4 - -r f -U) G) - - r- r- r - N t -fr -- owwwwwwD0%D0wwwD1- r- r -

to .o- . . . . . . .40 2.4

U) > D

U) ~ U)

-1 050r-0a e4aCD0l N r-4 - 4 4C C n 4 0 0 0

>i 4J tn E-4

OraS -40C)0 00C)0 0 D00C)00 000 0a

0 iA -4 g- ON r- A I a D- 4- - 4- %O hC DH 4 4a

40) 044 mN.xxxxxxxxxxxxx_-4> 44 4)e C4 % D- n wr -wmovmr noooHHwor4W- H' 0

0-.00) -rd a) 0

%0 u V 4

W) U)' tv 1to -4 w a0)

E- 4 0)w

004

6 U)(A 0) 0 dP nmmr nmMmM ntnr m m 0 a00 0a 0

4JE 04 Mnr ~c9 x 0

.-4 0

440 .4r-~~44-4 0) 0000 ~m~mmmo aamm mo o

0 ) oofoooooQ oo ooo oo0 0 0 0Jr'01 C) oo o

141

:34 E4E- - E4E- - E4E- - E-4 P E4~~ 3WW M MWWE- - - -4.44-4

A4,z

29

NSWC/WOL/TR 76-7

0

*.4 0 W 000000 C Cr~> 1&4

UU U C4r 4C 4 4 4C 4 C14 ( C 44 q4C 4( m e e m01-4

.,4 ~

144 44

-r4 0 J - 0C en 04ffnMC e 1 DDo4 Mf N( 0 -0Vin Dr

0u

1 0'.4

E-4 :4

42

x- 0

0.A04P - 4wwwwr4o4r4

m m400~' m r- I4 I- r- i oLmmmm qfA 4noino i

30

NSWC/WOL/TR 76-7

expected to be smaller than the experimental error of the measure-ment. However, if the ratios of the Dej'S of the HMS/T300composites (see Table 7) are listed, then a consistently higherDe is observed for the HMS composites of the same resins andthe same exposure conditions. The diffusion coefficients forNarmco 5208, DER 332/DADS and Epon 1031/MNA HMS composites are onthe average about 40%, 60% and 20%, respectively, higher than thecorresponding T300 composites. The T300 fiber had an epoxy sizingfor better handleability while the HMS fiber had none. Thistreatment of the T300 fibers with an epoxy surface coating appearsto lead to a better wetting of the fibers by the resin, therefore,to a reduction of interfacial void formation. Obviously, thediffusion rates through the voids would be very much larger thanif the same volume were filled with resin. The measurement ofvoid content by the resin digestion method, however, is not sensi-tive enough (if differences are due to voids).

Very little is known about the interface in carbon fibercomposites. The questions of whether there is a significantdiffusion along the interface has, to our knowledge, not beendetermined. This interface may play a role similar to the grainboundaries in metals and ceramics. Low temperature diffusion ofHe, H2 or argon might give some insight as to the microporosity,particularly along the resin-fiber interface.

d. Distribution of Moisture in Composites as a Function ofThickness, Time, Relative Humidity and Temperature.

The solution of Fick's second diffusion equation for a sheetgeometry is shown in Figure 14. The solution is given in dimension-less parameters: Dt/h 2 , the coordinates are given asC-Co/CI-C. and X/h, where D = diffusion constant, t = timeh = is ha~f the thickness of sheet, C = initial uniform concen-tration, C1 = concentration kept consiant at the surface. Thisgraph applies, therefore, for all substances following Fickeandiffusion behavior.

Figure 15 allows very quickly, without the use of a computer,the determination of the moisture distribution inside a solidmaterial, once the diffusion coefficient of moisture has beendetermined.

2After integrating the Dt/h curves of Figure 15, a plot of

Mt/Mm vs. [Dt/h2]l/ 2 (again of dimensionless parameters) canbe derived. This plot, shown in Figure 15, permits the deter-mination of the internal distribution of the diffusant by simplymeasuring the sample's fractional weight increase, Mt/M,assuming D has been previously determined. The measured M /M.,corresponds to a certain (Dt/h2 ]i/2 in Figure 15 from whicADt/h 2 is determined and interpolated on Figure 14 to give theinternal distribution.

31

A0

NSWC/WOL/TR 76-7

Table 7

A comparison of the effective moisture diffusion coefficients (De.)in the HMS and T300 carbon fiber composites.

Exposure Temp. RH Ratio of D (HMS)/D e. (T300)0C % Narmco 5208 DER 332/DADS Epon 1031/NMA

30 30 1.88 1.10 1.0545 30 1.60 1.51 1.3660 30 1.56 2.08 1.2975 30 .98 1.61 .9230 80 1.50 1.42 1.1145 80 1.12 1.48 1.3660 80 1.27 2.16 1.1275 80 1.16 1.50 1.51

Average 1.38 1.61 1.21Coeff. Var 7.70 7.69 5.72

Stand. Deviation .1063 .1238 .0693of the Mean

32

NSWC/WOL/TR 76-7

Of course, a finite difference method for calculating thedistributions by means of a computer can always be employed. Thereis, for instance, the Crank-Nicolson method described inreference [6].

For illustrative purposes a Narmco 5208/T300 composite isconsidered. The samples of 1 cm thickness are exposed toa) 80% RH at 250C, b) 30% RH and 25*C, c) 80% RH and 35C,and also, d) a plate of 0.25 cm thickness is exposed to 35*C and80% RH.

The moisture equilibrium concentrations at 250C are 1.26% for80% RH and .582% for 30% RH, and at 350C and 80% RH the equilibriumconcentration is 1.25%. The diffusio coefficients (see Figure 8)

at 250C and 30% and 80% RH are 1 x i0- cm2 /sec and 6 x 0-

cm2/sec respectively and & 35*C and 80% RH the diffusioncoefficient is -2.5 x 10 cm2 /sec.

Using Figure 14 the isochronal distribution of moisture insidethe composite can be obtained for various times; these distributionsare shown in Figure 16. From these graphs it is apparent that thetime required for 98% saturation differs widely. Saturation timesdepend on the square of the thickness of the composite and on thetemperature, which roughly doubles the rate for every 10C increasein temperature.

The percent weight increase with time for these 4 conditionscan be easily obtained from Figure 15 by using the relation ofMt/M. vs. [Dt/h 2]i/ 2 . The results are shown in Figure 17.For varying boundary conditions with changing temperatures andhumidities the problem is more complicated but can be solved witha computer. Details of how to predict the effect of real outdoorweather conditions with constantly varying boundary conditions willbe the subject of a forthcoming NSWC/TR.

Two more distributions for the DER 332/DADS-HMS and Epon 1031/NMA-HMS composites are shown in Figures 18 and 19. Both moisturedistributions were calculated for a 1 cm thick plate exposed at25*C at 80% RH.

e. Temperature Coefficients of Diffusion

The temperature coefficient of moisture diffusion for thethree HMS fiber composites at 30% RH was obtained from Figure 20where the logarithms of the diffusion coefficients were plotted vs.I/T (OK). Since the equilibrium concentration is only slightlydependent on temperature (at least below 60C), the slopes ofthese straight lines might be considered as overall activationenergies of diffusion of moisture across the fiber direction. Thevalues range from about 8 to 10 kcal/mole. Although the slopesare about the same, there is a difference of an order of magnitude

33

NSWC/WOL/TR 76-7

between the Epon 1031 and the Narmco 5208 composites. The diffusionrate of the Epon 1031 composite is about 10 times higher than theNarmco 5208 resin, in spite of the fact that the moisture equili-brium concentration in the 1031 composite is only 1/3 of theequilibrium concentration of Narmco 5208. Therefore equilibriummoisture absorption is not necessarily an indication of the rate ofdiffusion. Thus one ought to be careful in judging resins simply bytheir equilibrium moisture absorption.

Furthermore, as will be reported in a subsequent technicalreport on the mechanical property changes on these composites, alow moisture equilibrium concentration does not necessarily meanthat the mechanical properties changes will be proportionally small.

f. Sample Preparation.

Since the sample's final equilibrium concentration of moisture(M.) depends on the relative humidity of the surrounding environ-ment, the relative humidity at which the samples have beenprepared makes a difference. At the surface of the sheet of resin(or composite) the saturation level is reached within a very shorttime. This is governed by the surface adsorption. This may be thereason why the rate of absorption at a given temperature is differentfor different relative humidities (see Figure 21). Thus, sampleswith the same percentage of moisture content may have differentdistributions. For instance from Figure 21 one can see that (fora sample of 0.370 cm thickness of Narmco 5208, at 300C, a 0.4%moisture pick-up is reached in water after 4.8 days, at 80% RHafter 6.6 days, and at 30% RH after 15.5 days. Obviously, sincethe boundary conditions are different, so is the internal moisturedistribution.

It is not yet known how the mechanical properties of compositesvary, if at all, when they are prepared in different RH's but havingthe same total moisture concentration. Such differences in prepa-ration will have to be considered for sample testing designed topredict the property changes in various climatic environments.

The ultimate equilibrium concentration of moisture insidethe composite will correspond to the longtime average humidity inthe environment. The perturbation due to short-time (daily) humi-dity fluctuations is restricted only to a thin surface layer onthe order of x = 2(nD t ) , where x is the depth in changeof moisture concentratign due to the environmental humidityfluctuation, D is the average effective diffusion coefficient andto is the length of the cycle. For Narmco 5208/T300 compositethis distance would be 0.005 cm at ambient temperature and ahumidity fluctuation around 80% RH over a 24-hour cycle.

J. Comparison With Experimental Data

There are not many numerical data published in the literaturethat would permit the verification of the calculated data with

34

NSWC/WOL/TR 76-7

experiments. Hertz [i] has measured the diffusion coefficientsDell and DeL in a carbon fiber reinforced epoxy composite(Vf = 58.8%, and 2.3% voids). The measured data were Dell= 6.34 x 10-8 cm2/sec and Del = 1.56 x 10-8 cm2/sec.Unfortunately he did not give the diffusion coefficient of theneat resin. The ratio of Dell /Dei should be between 1.6 -1.7 (see Table 3). The experimental ratio is 4.06, indicatingDell is larger than should be probably because of elongated voidsin the fiber direction (perhaps debonding along the fibers).

Also, the measured values of Dell and De. are surpris-ingly high. From DeL = 1.56 x 10- 8 cm2 /sec, according toTable 3 the resin should have a diffusion coefficient of about6.5 x 10-8 cm2/sec, which is rather high for epoxy resins.Thus, even low void contents seem to have a pronounced effect onthe diffusion coefficient. On the other hand the diffusioncoefficients we measured on the Narmco 5208 composites (seeTable 6) are all lower than the values calculated from the finitedifference method. The }IMS fiber composites are 17-20% lower andthe T300 composites between 36-53% lower than the values calcu-lated for a tetragonal fiber arrangement. One reason could be thatthe resin samples were cast from a different resin batch than theresin used for the composite preparation. We have previouslyobserved on a different epoxy resin that within the same resinbatch, a difference in thermal history (for instance differentgelation temperatures but same cure and post cure) give a differenceof 22% in resin diffusion coefficients. Another reason could bethat the composite equilibrium values was determined on powdersamples. Since these fine powders can equilibriate very rapidlythere is the possibility of a weighing error due to the timerequired for removing the samples from the exposure chambers andweighing them.

Conclusions and Recommendations

A finite difference method was used to estimate the reduceddiffusivities in unidirectional carbon fiber composites with hexa-gonal and tetragonal fiber arrangement. For the tetragonal arrange-ment of cylindrical rods these derivations were compared with twomodels, derived by other investigators for the analogous electricaland thermal conductivities. While the Rayleigh model gives almostidentical results with ours at fiber concentrations below60 percent, the Springer-Tsai model deviates considerably over thewhole range of fiber volume fractions.

The effective diffusion coefficients of 6 carbon fiber/epoxycomposites were determined (perpendicular to the fiber direction)as a function of.temperature and relative humidity. There is areasonable agreement with the calculated reduced diffusivity forthe .7 fiber volume fraction of these composites.

35

NSWC/WOL/TR 76-7

The effective diffusion constants for the composites followthe order D(10 31

> D(3 2)> D(5 2 08 ) while the saturation valuesfollow the inverse order C,(5 2 08 )>C, (332)> C-(1031). This

reversal of order indicates that measurement of moisture pickupalone is not sufficient for determining the effect of moisture onresins or composites.

Diffusion processes should be further investigated sincediffusion measurements seem to be quite sensitive to compositechanges (that can generate micro cracks) and which might not bereadily detected by mechanical testing. Furthermore, diffusionmecsurements should be combined with mechanical and thermal cyclingexperiments.

In addition to moisture diffusivities, we expect that lowtemperature He, Ar, or 112 diffusivities may give gome additionalinformation about the resin-fiber interface.

A mathematical model should also be derived to include surfacecoatings on composites to determine any potential benefit of thesecoatings.

Acknowledgement

The authors acknowledge the excellent work done byMr. H. E. Mathews, Jr. in preparing the composite specimens usedin this investigation.

36

NSWC/WOL/TR 76-7

FLOW (J ) PERPENDICULAR TOFIBER DIRECTION

FLOW (Ji! PARALLEL TO

FIBER DIRECTION

000 0800 600d

b. (HEXAGONAL FIBERARRANGEMENT) c. (TETRAGONAL FIBER

ARRANGEMENT)

d/2

RESIN j

RESIN

d/2 r

d. (TETRAGONAL UNIT CELL)d

e. (HEXAGONAL UNIT CELL)

FIG. 1 GEOMETRY OF UNIDIRECTIONAL FIBER REINFORCED COMPOSITES.

37

NSWC/WOL/TR 7S7

10

(dJ UJ

UOw 2

Z <1B;4

ui

o o~

U. 0 Z0 0

(r 0 5! 0cvi >

UA

I~~dfllOU LJ9UII3

3C-i8

NSWCMWOL/TR 76-7

u I 0

/ C

U..

LA. />O // >

-j U.

/ 0 , -z Q ,os LLI L/

/ Wo

4 U.~

0- w

Lj 02

0~~ a: ":

.9.

c; L.9

d d ca:(Al~aoGNO IVIU1313aNVwU3l

All~im a Maa:

39w

NSWCIWOL/TR 76-7

U-0

z

0

z

LU

U.

400

zL4U~A4~.

id _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

NSWC/WOL/TR 76-7

400-

360-

320-

280- E

z240- - RH 100%

0

20

12-

40

200 20 3806 0%8TEPRTR 0

16041

NSWC/WOL/TR 76.7

1.0 I

.9 0300 C

13 450 C

A 6o0 c

750C

.7

-J

50.

/z

0

I-

0.0

.5

wI-

2 4A 0 12 1 6 i

-J .4

I-

2 4 6 8 10 12 14 16 18

TIME 1 /2(HOURS)FIG. 6 FRACTIONAL WATER ABSORPTION AT VARIOUS TEMPERATURES

OF EPON 1031/HMS COMPOSITE AT 30% RH

42

-OW

NSWC/VVOL/TR 76-7

1.0

o 300 C

450 CA

A600 C.8 'Z'750 C

-l-

5

z .

2

00

44

... ... .

NSCWOL/TR 76.7

aa0~FE

wA

i~cc I!CC

IL

CcI

2

U -L U -

(~3S/b~J)±N3IOdd3O ddI

NSWC/WOL/TR 76-7

cc -

I t:

Izcc

LL-0

-0

45

U. u

A'

NSWCIWOL/TR 7-7

U

02

0I

(~~39/~~nr) LN IId 3 O u

46.

.~~~~-U U-J- - __ _

w I-

NSWCIWOLITR 76-7

U. -

C4 jLOw

Iz

0C2o U-

-0

2Z

0 U *~q 4~ N U *flq ~ N0a, b b

(~~3s/~~b~o) UNIU3Oii

47

NSWC/WOL/TR 76-7

N N

13-

z

00.0

U

-o0

- -. 0

NSWC/WOL/TR 76-7

a U.0z0

z

au

U.

C,

Q <

La~U.0 C

0

. C

U-

U.

140,

(:D3S/zW3) 1N~I31D1A3O3 J:iIO

Po oPO - 0 VMa or

49

NSWCIWOL/TR 76-7

-10C-Co

C-. C0

0.30

0 ..

NSWC/WOL/TR 767

1. = T- T - T . . [ - T I T T T T

.8-

.7 --

8

.5t-

.3

1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.3

(Dt/h2 )

FIG. 15 PLOT OF FRACTIONAL ABSORPTION OF ANY MATERIALWITH FICKEAN BEHAVIOR VERSUS (Dt/h 2 ) FOR PLATE GEOMETRY

51

A.

NSWC/WOL/TR 76-7

C -CL

ii

0 0

- 0 0 0 0i 0

o Q038HOSOV 3uiiow IN 3DIH3d cc =

8N

Uc 0

0<

0x 0

0l

\\\\ \\Z

OR

0.0

0~ (0I!! 0

C;C

C p EU IA q N 39&OS9V 3Ikifisiow LN3:3W3d

O3RH0SOV 3uflisiow~ iN33H3d

52

NSWCIWOL/TR 76-7

E III E l

Li z

E & 2

004

CD

I.- -zo Z

OU

w 0UJ wc

w 2

LU cz

2 2-wU. CO)

(0 w

N CC Z Nin C- :r0

~SW3~I IHD3M 1N3~Ii

w53

NSWC/WOL/TR 76-7

0

cow

00

2 00

co. N

w m

544

cca '. . .0.Y . y .

*u> cc _ _ _ __ _ _ _ _ __ _ _ _ _

NSWCMIOL/TR 76-7

0

0

0.

0

0 0

cZ< I

> LjO

cc 0 0-

1- oc)

04

*" 0 LL0 1- ! 2

U,. CC

LOu~ ini

Mn NOIEIN3O O-

55

NSWCIWOL/TR 76-7

10-

8-7-6-

5

4-o NARMCO 5208-HMS (8.4k CAL)

3-0 DER 332/DADS-HMS (9.9 k CAL)

2 - EPON 1031/NMA-HMS (9.1 k CAL)

10-89-

w

S6-

-U

wj 3-0

2-

U-'g

9-8-7-6-

5-

4-

3

2-

75 60 4530O

10.10 2.8 2.19 3.10 3.111 3.2 3.3

TX03 (OK)FIG. 20 ARRHENIUS PLOT OF MOISTURE DIFFUSION INTO HMS FIBER

COMPOSITES (DETERMINED AT 33% RH

NSWC/WOL/TR 76-7

CN

00

UJ M

z cz

0

4zU.

- 0I-

0 L)

w coCL,

c.

(0

U.0LlU

cc

3S3HN IH13 I p W

57

1m....

NSWC/WOL/TR 76-7

APPENDIX A

ALGORITHM FOR THE NUMERICAL CALCULATION OFEFFECTIVE DIFFUSION COEFFICIENTS

In this appendix a complete description will be given for thenumerical method used to calculate effective diffusion coefficientsperpendicular to the fiber direction in a carbon fiber composite.As described in Section E. of Discussion and Results, the geometryunder consideration is either hexagonal or tetragonal arrangementof the fibers (Figure 1).

We first demonstrate that it suffices to solve the diffusionproblem within a unit cell, and then we give a detailed descriptionof the finite difference method used in solving (24-26).

Al. Sufficiency of Solving within the Unit Cell

It suffices to show that the solution on the full infiniteplate region of the problem can be generated from the solution onthe unit cell, and that (as will be obvious from the construction)the effective diffusion coefficient calculated from the unit cellis identical with that obtained from the entire domain of theproblem.

The "weak" formulation of (22) is (G E unit cell);

f (d(x,y)u v + d(x,y)u v )dxdy = 0 (33)xx y y

for all square integrable test functions v having square integrablefirst derivative in G (such functions v are said to be in H' (G)) andwhich vanish on the line segments y=O and y=y for 0<x< r + d/2. Thesolution u of (33) is to lie in H' (G) and satisfy (72il). Becausethe interface is smooth and meets the boundary of G at right angles,the (unique) solution u of (33) has square integrable second deri-vatives within the resin and within the fiber and is continuous onG and its boundary [12], [13]. By using Green's formula on (33)to shift derivatives from v onto u, one has (b-r+d/2,

[12]R. B. KellTgg, "On the Poisson Equation with IntersectingInterfaces, "Applied Analysis, 4, 101, (1975).

(13] D. P. Squire, "On the Existence and Uniqueness ofSolutions of the Poisson Interface Problem, "Am. J. Math.85, 241, (1963).

A-i

'a ' . . . . .. .. . . ....

NSWC/WOL/TR 76-7

I interface curve, n = unit normal to I pointing into theresin);

fd(x,y)Auv + (d(O,y)ux (O,y)v(O,y)G-Iy=o

(34)

+ f n r n )d(b,y)ux(b,y)v(b,y)) kDf u n -Du v=

I

and by varying v over H' (G) (with v=0 when y=O and when y=y) onerecovers (22).

Using the weak formulation, one verifies that the solutionmay be extended horizontally (i.e. parallel to the x-axis) byreflection (as is intuitively obvious from the symmetry conditions(22e)). To extend vertically, we use the Schwarz reflectionprinciple [14). By addition of a constant, we may take C2=0in (22d) , and define

u(x, -y) = -u(x,y) for O<y<y, all x (35)

Similarly one may continue the solution an arbitrary number of cellheights along the y-axis.

A2. The D'Yakonov ADI Method

Equations (24-26) have the form

V.AVu - (A(xy)ux) x + (A(x,y)uy) = 0 (36a)

on the rectangle R = (O<x<b, O<y<y

u(x,o)=C2 and u(x,y) = C1 for 0<x<b (36b)

u (o,y) = ux (b,y) = 0 for 0<y<y (36c)

[141 P. R. Garabedian, "Partial Differential Equations,"

John Wiley and Sons, Inc. 1964.

A-2

NSWC/WOL/TR 76-7

where for (24-26) A=d and b=r+d/2. Following [15), we now describethe D'Yakonov ADI (alternating direction implicit) finite differencemethod as it applies to (36) (i.e. (24-26)).

We consider (36) to be the steady state of the time dependentproblem

ut = V.AVu in R (37a)

u(x,o,t) = C2 and u(x,y,t) = C1 for O<x<b, t> 0 (37b)

Ux (0,y,t) = ux (b,y,t) = 0 for 0<y<y, t>O (37c)

u(x,y,t) = U0 (x,y) in R (37d)

where uo is given initial data. By choosing uo and solving (37)one may approach the steady state solution u(x,y) of (36).

To solve (37), a time step At and positive integers J and Kare chosen; the spatial mesh lengths are then defined to eix = b/(J-l) and Ay = y/(K-1). An approximate solution U.,k of 37

is then obtained (n=l,2 ... ) where Un refers to the value of U

at time n-At0 at the spatial mesh point ((j-l)Ax,(k-l)Ay . Bydefinition U. = U ((j-l)Ax,(k-l)Ay). Let r. t Ax,

ry At/Ay and use the notation (for any variable H defined

at the mesh points)

6 xA 6x 11 jk A Aj+l/2 k ( Hj+l,k H j,k) A j-1/2,k (H j,kH"j-l,k)

6 A 6 1 Hjk Ajk+1/2 ( H jk+l- R jk) YA j,k-l/2 (H jk Hj k-1)

where A j+/2,k = A ((j+l/2) Ax,kAy) etc.

The D'Yakonov formula (i.e. system of linear equations) forUn+l n which involves intermediate values Vn+ l is;oj,k f j,k j,k

1 - r xZ6xA6x j k = ,k for 1<j<J 2<k<K-1 (38a)

[15] A. R. Mitchell, "Computational Methods in Partial DifferentialEquations," John Wiley Sons Ltd., 1969.

A-3

1 6 A > Un l = n+lr 6 A5 YAS = Vjk for l<j<J, 2<k<k-i (38b)2 y,~ j~k

where

zn (I + r6A6 H1 1 r 6 A6 )U for l<j<J, 2<k<K-i (39),k 2 xxAx 2 y y y j,k

By making use of the boundary conditions (37b,c) we define

Un n,1 = 2' UK = C1 for 0<j<J+l, n=0,1,2, (40a)

n n n n

Uo,k 2,k, j+,k U ,k for 1<k<K, n=0,1,2, .. (40b)

and (also by symmetry)

A =A 3 A = A 1 for l<k<K (40c)'fk, J 2' k J k

and from (38b)

o,k 2,k, J+l,k J-l,k for 2<k<K-l,n=l,2, ... (40d)

which completes the Equations (38). The point of the ADI methodis that (38a) involves K-2 separate tridiagonal linear systems ofJ equations, rather than a total system of J(K-2) linear equations(and similarly with (38b)) which results in a drastic decrease inthe work necessary to solve the equations.

A3. Comments on Implementation

Concerning actual computer implementation of the D'Yakonovmethod, the following observations are useful. Since the coeffi-cient A and the boundary conditions in (37) are independent oftime, the decomposition of the K-2 tridiagonal linear systemsfrom (38a) (and the J systems from (38b)) can be done once andthen stored. Letting

1oQ. (1 + 1 r 6 A 6 ) U for O<j<J+l, 2<k<K-l

jk2 y y y jk

A-4

NSWC/WOL/TR 76-7

so

zk (1 + 1 r 6 A6 )Q for l<j<J, 2<k<k-l

i~~ , k x j,k

one notes by using the boundary conditions (37b,c) which gave (40)that

Qo,k = Q2,k, QJ+l,k = QJ-l,k for 2<k<K-l. (41)

It is also very useful to note the following method forcalculating Zn (n=l,2,...) [161, [17). Suppose we have just

calculated U n We then have available (assuming proper strategy, k' n n n-1

in the computer code). Ujk , Vn and Z We observe thati ' i, k' j,k"from (38b) (and dropping the subscripts j,k)

Un Vn = r 6 A6 Un

2 y y y

from which

(1 + r 6 A6y)Un = 2 Un

so

Z = (1 + 1 r 6xA6 )(2Un _ Vn)

but by (38a)

(1 rx6 A6x)Vn = zn-

from which

_ rx6 A6 Vn = z n-lv n

2 x x

[16] S. Leventhal, personal communication[17] M. Ciment and S. Leventhal, "Higher Order Compact

Implicit Schemes for the Wave Equation," Math. Comp., 29,985, (1975).

A-5

NSWC/WOL/TR 76-7

and so

z n = 2U n - v n + 2rxA6 2Un + Zn - I - Vn, and2 x x x

Zn =2Un -2Vn + zn-i + rx6x A6 Un (42)

which greatly simplifies the computation of Zn at each step.

A4. Calculation of Diffusion Coefficients

The D'Yakonov ADI scheme was used to solve (24-26) by relaxingthe corresponding time dependent problem toward the steady state.Then de was obtained using (19) and

r+d/2

q =f - d(x,y) U (x,y)dx for any yc [o,y]. (43)

0

Since actually it is the ratio d e/Dr that is of interest, we may

scale distance so that b=l and time so that Dr=l. For conveniencewe also set CI=0 and C2 =y so that (from (19)) d /D = q.

e r

The explicit definition of d(x,y) for the tetragonal unit cellis as follows. A parameter z>0 is given (in general we tookz = .02 with J=K=21). Given (x,y), let p = ((x-b) 2 + y2)1/2and define Df = max(.0 l, Df). _If p > r + z, then d(x,y) = Dr;while if _ r-z, then d(x,y) = Dfr k. For r-z<p<r+z,

d(x,y) = Df*k + (o-(r-z)) (Dr - Df k)/(2z).

For the hexagonal unit cell one also similarly deals with the fibercentered at (O,y). In the hexagonal case we generally choosez=.02 with J=21 and K=41.

The calculation of (43) was done at several different ymvalues (ym - (m - i/2)Ay) using the trapezoidal rule;

n J- x n ,nm m --x ((i-l)AX'Ym HU -l, m+l i-l,m)

i=l1

+d(iAxy)(u m - Uim)]/2Ay (44)

A-6

NSWC/WOL/TP 76-7

n

Comparing q for several values of m provided a cood indAcation of

when n was sufficiently large; once uniformity of the qm values

was obtained (for several m), further increases in n producedlittle charnqe in the flux values.

The choice for initial values was Uo(x,y) = y-y. Other choicesof U. attempting to better approximate u(x,y) produced some

instances of erratic and slow convergence of U n toward the steadyilk

state. The program was written so that a sequence of severaldifferent time steps could be run during the course of a singleproblem in order to obtain faster approach toward steady statevalues. With Df = 0, k=2, tetragonal geometry, J=K=21, z=.02 andfiber volume fraction in the range 0 - .7, an appropriate sequenceof time steps was found to be 40 steps with At = .05, followedby 20 steps with At=20.0, followed by 40 steps with At=.5.With DF=O, k=2, hexagonal geometry, J=21, K=41, z=.02, and fibervolume fraction in the range 0-.85, an appropriate sequence oftime steps was found to be 60 steps with At=.02, followed by60 steps with At=20.0. Convergence tended to be more rapidwith positive values of Df in (0,1). These choices of J,K, At, zwere found by observing the effects of varying these parameters onthe values of de thus obtained.

A5. A Numerical Example

We give results obtained from Df = 0, k=2, hexagonal fibergeometry, J=21, K=41, z=.02, fiber volume fraction =.4, and thechoices of tt stated above. Fluxes were calculated acrossYm = (x-l/)y for m=l, 4, 10, 20, 40. The corresponding fluxvalues at t=o (i.e. for u ) were .3341, .3554, .4802, 1.0, .3341.After 60 steps with At=.0D the flux values were .4279, .4280,.4292, .4321, .4279. After 60 more steps with At=20.0 all fiveflux values were .4289.

A-7

APPENDIX B

Glossary

Symbols

C,c Indicating concentrations (at the boundaiy nd at theinterior respectively).

d shortest distance from fiber to fiber surface

D,d diffusion coefficient

D diffusion coefficient of the resinr

Df diffusion coefficient of the fiber

D average diffusion coefficient

De d effective diffusion coefficiente'1

h - times the thickness of the composite plate

J flux of diffusant

k distribution coefficient

km thermal conductivity of the matrix

kf thermal conductivity of the fiber

K electrical conductivity of the matrixm

k. thickness of the composite plate

q flux (general)

Mt amount absorbed at time t

M amount absorbed after equilibrium

has been reached

r fiber radius

RH relative humidity

B-I

NSWC/WOL/TR 76-7

t time

II parallel

Iperpendicular

Subscripts

Symbols Indicating

e effective

f fiber

h hexagonal

m matrix

r resin

t tetragonal

II parallel

.perpendicular

x first derivative of the variable x

xx second derivative of the variable x

y first deriva ve of the variable y

yy second derivative of the variable y

B-2

NSWC/WOL/TR 76-7

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NSWC/WOL/TR 76-7

DISTRIBUTION

Lockheed-Georgia CompanyDept. 72-26 Zone 28Marietta, Georgia 30060

Attn: Walter S. Cremens 1

Los Alamos Scientific LaboratoryLos Alamos, New Mexico 87544

Attn: Dr. J. Taylor

Prototype Development Associates, Inc.1740 Garry Avenue, Suite 201Santa Ana, California 92705

Attn: Dr. John Slaughter

R & D AssociatesP.O. Box 3580Santa Monica, California 90403

Attn: Dr. R. A. Field

Southern Research Institute2000 Ninth Avenue, SouthBirmingham, Alabama 35205

Attn: Mr. C. D. Pears 1Mr. James R. Brown 1

Systems, Science, and SoftwareP.O. Box 1620La Jolla, California 92037

Attn: Dr. G. A. Gurtman

United Research CenterEast Hartford, Connecticut 06601

Attn: D. A. Scola

Materials Science CorporationBlue Bell, Pennsylvania 19422

Attn: B. W. Rosen 1

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W"$WSWC(W).mS/I (Rwv. 1-75)

TO AID IN UPDATING THE DISTRIBUTION LISTFOR NAVAL SURFACE WEAPONS CENTER, WHITEOAK LABORATORY TECHNICAL REPORTS PLEASECOMPLETE THE FORM BELOW:

TO ALL HOLDERS OF NSWC/WOL/TR 76-7by Joseph M. Augl, Code WR-31

DO NOT RETURN THIS FORM IF ALL INFORMATION IS CURRENT

A. FACILITY NAME AND ADDRESS (OLD) (Show Zip Ccde)

NEW ADDRESS (Show Zip Code)

U. ATTENTION LINE ADDRESSES:

C.

[] REMOVE THIS FACILITY FROM THE 13ISTRIBUTION LIST FOR TECHNICAL REPORTS ON THIS SUBJECT.

0.NUNER OF COPIES DESIRED

eo-C

DEPARTMENT OF THE NAVYNAVAL SURFACE WEAPONS CENTER

WHITE OAK, SILVER SPRING, MD. 20910 POSTAGE AND FEES PAIDDEPARTMENT OF THE NAVY

DOD 316OFFICIAL BUSINESS

PENALTY FOR PRIVATE USE, $300

COMMANDERNAVAL SURFACE WEAPONS CENTERWHITE OAK, SILVER SPRING, MARYLAND 20910

ATTENTIONs CODE WR-31

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