of High Temperature Metal Matrix Composite Ply Properties · PDF filePREDICTION OF HIGH...

NASA Technical Memorandum 102490

. Prediction of High TemperatureMetal Matrix CompositePly Properties .....

J.J. Caruso and C.C. Chamis

Lewis Research Center

Cleveland, Ohio

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PresentecVat the

29th Structures, Structural Dynamics, and Materials (SDM) Conference .............cospons-_ed by the A!AA, ASME, ASS, and ASC .....

Williamsburg, Virginia, April I8-20.I988

(NASA-TM-IO?490) PREDICTION _F HIGH N90-17817TEMPERATURE METAL MATRIX COMPOSITE PLY

PROPERTIES (NASA) 19 p CSCL ll_

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https://ntrs.nasa.gov/search.jsp?R=19900008501 2018-04-24T16:58:42+00:00Z

PREDICTION OF HIGH TEMPERATURE METAL MATRIX COMPOSITE PLY PROPERTIES

J.J. Caruso and C.C. Chamls

National Aeronautlcs and Space AdministrationLewis Research Center

Cleveland, Ohio 44135

COC'JLO!

L_

SUMMARY

The application of the finite element method (superelement technique) In

conjunction with basic concepts from mechanics of materials theory Is demon-

strated to predict the thermomechanlca] behavior of hlgh temperature metal

matrix composites (HTMMC). The simulated behavior Is used as a basis to estab-

fish characteristic properties of a unidirectional composite Idealized as an

equivalent homogeneous material. The ply properties predicted include: ther-

mal properties (thermal conductlvltles and thermal expansion coefficients) and

mechanical properties (modulI and Polsson's ratio). These properties are com-

pared wlth those predicted by a simplified, analytical composite mlcromechanlcs

model. This paper illustrates the predictive capabillties of the finite ele-

ment method and the simplified model through the simulation of the thermo-

mechanical behavior of a PlOO-graphlte/copper unidirectional composite at room

temperature and near matrix melting temperature. The advantage of the finite

element analysis approach is its ability to more precisely represent the com-

posite local geometry and hence capture the subtle effects that are dependent

on this. The closed form mlcromechanlcs model does a good Job at representlng

the average behavior of the constltuents to predict composlte behavior.

INTRODUCTION

High temperature metal matrix composites (HTMMC) are emerglng as candi-

date materials offering high potentlal payoffs in hot structures applications

for advanced aerospace propulsion systems. Reallzatlon of these high potential

payoffs depend on the development of" (1) fabrication techniques, (2) experi-

mental techniques for characterizing the complex nonlinear behavior antlclpated

for these appllcatlons, and (3) computational methods for engineering design

that account for this complex behavior.

Recent research at NASA Lewis Research Center has demonstrated two

approaches for predIctlng HTMMC behavior. These approaches consist of:(1) applIcatlon of the finite element method (superelement technlque) in con-

Junctlon with concepts from mechanlcs of materials theory and (2) appllcatlon

of closed-form equations derived from a simplified, analytical mlcromechanlcs

model. The first approach has previously been demonstrated by Caruso (ref. l)

and Caruso and Chamls (ref. 2) to predict equivalent thermal and mechanical

properties of polymer matrix composites. The second approach employs a varla-

tlon of the mIcromechanlcs model developed by Hopkins and Chamls (ref. 3) In a

form more recently implemented by Hopklns and Murthy (ref. 4).

The objectives of this paper are to: (1) descrlbe the appllcatlon of thefinite element method in conjunction with the mechanics of materlals conceptsas an approach to HTMMC mlcromechanlcal modeling and (2) compare the finiteelement results with those predlctlons based on the closed-fprm model Imple-mented In the Me.__t.talMatrix Composlte Analyzer (METCAN computer code) (ref. 4).

LIST OFSYMBOLS

A area

dT change In temperature

E Young's modulus

F force

G shear modulus

K thermal conductivity

L length

qt flux

u displacement

¢ thermal expansion coefflclent

v Polsson's ratio

Subscripts

x,y,z denotes the components of the global structural Cartesian coordinatesystem

1,2,3 denotes the components of the composlte material Cartesian coordinate

system

MODEL DESCRIPTION

In the analytical mlcromechanlcs model, the representation of the funda-

mental unldlrectlona] composite unlt cell Is a square array. The unlt cell

contains a single circular fiber surrounded by matrix to form a square array.In the finite element model, the representation Is also a unit cell. The unit

cell subsequently becomes the "superelement" that can be "Imaged" to form the

complete nlne-cell model (fig. l). The impetus for adapting the super-

element technique is derived from: (1) the abillty to represent a singlesquare array (flber/matrix unlt cell) that could be easily modified, (2) the

consistency with which the slngIe unlt cell can serve as the building block toform a multlcell model wlth the ability thereby provided to create a stiffness

matrlx of the multlcell model wlth much fewer total degrees of freedom comparedto the full dlscretlzatlon, and (3) the capabillty to simulate multIcell models

substantially larger than conventional fln|te element analysis would allow.

The superelement model (flg. I) consists of one primary superelement (center

cell) containlng 192 three-dlmenslonal solid (hexahedron and pentahedron) iso-

parametric elements and eight secondary or "Image" superelements, comprlslng a

total of 1133 grld points. The MSC/NASTRAN (ref. 5) general purpose finite

element analysis software was used for the slmulatlon. The load and boundary

conditions are applled to the model as enforced grid point dlsplacements and/ortemperatures.

The single cell Is modeled in such a manner so as to allow the fiber

volume ratio (FVR) to be varied to any one of the four values: 7, 22, 47, or

62 percent, rather routinely. This is achieved by changing the elements along

the circumference of the fiber to matrix elements thereby decreasing the diam-

eter of the fiber. As previously mentioned, the particular composite system

chosen for the study consists of PlOO-graphlte fiber (an orthotroplc material)

and a pure copper matrix (an Isotroplc material). Values of constituent pro-pertles at room (70 °F) and elevated (1500 °F) temperature assumed for the

study are summarized In table I.

ANALYSIS PROCEDURE

The following sections describe the analysls procedures to determine the

mechanical and thermal properties, which involves the choice of appropriate

boundary and loading conditions together with the relevant equations from

mechanics of materlals concepts. Composite modull are determined by obtaining

forces from the finite element stress analysis resulting from prescribed dls-

placements and calculating the property using the associated mechanics of mate-

r|als equations. Likewise, composite Polsson's ratlos and thermal expanslons

coefficients are calculated by obtalnlng the displacements from the finite

element stress analysls whlch results from prescribed mechanlcaI and thermal

loading, respectively, again calculating the property uslng the associated

mechanics of materials equations. The composite thermal conductivity is

determlned by obtalnlng the flux and free surface temperature from the finite

element heat conduction analysis and calculatlng the composite property from

thermodynamics concepts. The composlte properties at elevated temperatures

are predicted assuming steady state equilibr|um condltlons. Under these condi-

tlons, temperature dependent properties and llnear analysis are consldered to

be adequate.

MECHANICAL PROPERTIES

The mechanical properties simulated from finite element analysis and the

predIctlons of METCAN methods are described below. The properties are for

room temperature (70 °F) and high temperature (1500 °F) condltlons.

Longltudlnal Modulus and Polsson's Ratio (E_I 1 and vC12)

The boundary and load conditions for the flnlte element simulation are

applied to the composite through enforced displacements (including prescribed

zero dlsplacements). The boundary conditions are as follows:

(I) Constrain the degrees of freedom on the front YZ-plane in theX-dlrectlon (flg. 2).

(2) Constrain the degrees of freedom on the centerllne parallel to the

X-axls on the top and bottom XY-planes In the Y-dlrectlon.

(3) Constrain the degrees of freedom on the centerllne parallel to theX-axls on the right and left XZ-planes In the Z-dlrectlon.

The composite Is loaded wlth a prescribed uniform displacement on the backYZ-plane In the X-dlrectlon.

The composite longitudinal modulus Is calculated from the followingequation"

where a_l 1 Is the applied stress due to an enforced dlsplacement on the YZ

face and _C11 Is the 1ongltudlnal strain.

The 1ongltudlnal modulus slmulated by the finite element analysis Is plot-

ted as a function of flber volume ratio (FVR) for the room and hlgh temperature

conditions In figure 3. The METCAN predictions are plotted for comparison pur-

poses In figure 3. The comparison between the two results Is, as expected,very good.

The 1ongltudlnal Polsson's ratio Is calculated from the followlngequation:

where C_l I Is the longltudinal straln In the load direction and _22 Is

the transverse strain In the unloaded dlrection.

Polsson's ratio as predlcted by the flnlte element slmulatlon shows 11tile

effect to temperature (flg. 4). Polsson's ratio Is affected by neighboringflbers and the multIcell flnlte element results show thls when compared to theMETCAN predicted result which does not take thls affect Into account. The

affect of other fibers on Polsson's ratlo represents a displacement compatibll-Ity (due to Polsson effects) between the cells which Is not considered for the

slngle cell model or METCAN. The METCAN prediction becomes worse as the FVR

Increases. Thls Is because as the FVR Increases the dlsplacement Incompatlbll-Ity becomes more predomlnant; however, the trend Is In the same direction.

Transverse Moduius and Polsson's Ratio (E_22 and v_23)

The boundary and load condltlons for the flnlte element simulation are

applied through enforced displacements (Inc1udlng prescribed zero displace-ments). The boundary conditions are as follows"

(1) Constrain the degrees of freedom In the center YZ-plane In theX-dlrectlon (flg. 2).

(2) Constraln the degrees of freedom In the bottom XY-plane In theZ-dlrectIon.

(3) Constrain the degrees of freedom on the centerline parallel to the

X-axls on the top and bottom XY-plane In the Y-dlrection.

The composite Is loaded wlth a prescribed displacement on the top XY-plane Inthe Z-dlrectlon.

The transverse modulus is calculated from the followlng equation:

where _33 Is the applied stress due to an enforced displacement on the YZ

face and _£33 Is the longitudinal strain,

As shown In figure 5, the modulus decreases with Increaslng FVR. Thls Is

expected because the transverse modulus of the matrix Is larger than that of

the flber. The METCAN predictions (the continuous curves) are practically

Identical wlth the finite element simulations at both temperatures but deviate

sllghtly wlth decreasing FVR.

The transverse Polsson's ratlo Is calculated from the followlng equation"

where a£33 Is the transverse strain In the load dlrection and c£22 Is the

transverse strain In the unloaded dlrectlon.

Polsson's ratio as predicted by the flnlte element slmulatlon shows llttle

effect to temperature (flg. 6). The Poisson's ratlo (v_23) Is greatly affected

by the neighboring fibers and the multlcell finite element results show thlswhen compared to the METCAN results whlch do not take thls affect Into account.

Values for v£23 are plotted assuming transverse Isotropy (curves labeled

Isotroplc) for comparison to the two methods described here. That Is the trans-

E£22 - l) mayversely Isotroplc relation between v£23, G£23, and E£22 v_23 - 2G£23not be justified on the constituent level.

Shear Modulus G£12

The boundary and load conditions for the flnlte element simulation are

applled through enforced dlsplacements (Includlng prescribed zero dlsplace-

ments). The boundary conditions are as follows:

(I) Constrain the degrees of freedom in the left XZ-plane In theX-dlrectlon (flg. 2).

(2) Constraln the degrees of freedom for all nodes In the Y- andZ-dlrectlon.

The composite has a prescribed dlsplacement on the right XZ-plane In theX-dlrectlon.

The modulus Is calculated from the following equation"

where _12 Is the applled stress due to an enforced displacement on the XZ

face and Y_12 Is the transverse strain.

The finite element predictions (flg. 7) show the high temperature propertyIs smaller than the room temperature property. This Is expected since at hlgh

temperature PIO0 and copper have lower shear modull than at room temperature.The METCAN predictions (contlnuous curve) compare well wlth the flnlte element

prediction at both temperatures through the full range of FVR. These results

further Indicate that adjacent fibers have negllglble Influence on the shearmodulus.

Shear Modulus GE23

The boundary and load conditions for the finite element analysis are

applied through enforced displacements (Including prescribed zero displace-ments). The boundary conditions are as follows:

(I) Constrain the degrees of freedom in the left XZ-plane In the

Z-dlrectlon (flg. 2).

(2) Constrain the degrees of freedom for all nodes in the X- andY-dlrectlon,

The composite has a prescribed displacement on the right XZ-plane In theZ-dlrectlon.

The modulus Is calculated from the following equatlon:

where _23 Is the applled stress due to an enforced dlsplacement on the XZ

face and YC23 Is the transverse straln.

The flnlte element predictions for G_23 are similar to those for G_l 2

(flg. 8). The METCAN predictions (continuous curve) are in good agreement wlththose from the flnlte element method at both temperatures through all FVR.

6

THERMALPROPERTIES

The thermal properties synthesized from the finite element simulation and

those predicted by the simplified mlcromechanlcs model implemented in METCAN

are described below. The properties are for both room temperature (70 °F) and

high temperature (1500 °F) conditions. The thermal properties of interestinclude expansion coefficients and conductivities.

Longitudinal and Transverse Thermal Expansion Coefflcient

The boundary and load conditions for the finite element analysis are

applled through enforced displacements (Inc1udlng prescribed zero dlsplace-

ments) and temperatures. The boundary conditions are as follows:

(I) Constrain the degrees of freedom on the center YZ-plane in theX-dlrection (fig. 2).

(2) Constraln the degrees of freedom on the centerllne parallel to theX-axis on the top and bottom XY-plane In the Y-dlrectlon.

(3) Constrain the degrees of freedom on the centerllne parallel to theX-axis on the right and left XZ-plane in the Z-dlrectlon.

The composite is subject to a uniform temperature applied to the entirestructure.

The thermal expansion coefficients are calculated from the followingequations:

where c_i I is the longitudinal strain, cC22 is the transverse strain and ?T

is the temperature change.

The 1ongitudlnal expanslon as shown in flgure 9 decreases rapidly with

increasing FVR. This large decrease is due prlmarlly to the negative expansion

coefflclent of the PlO0. The METCAN predictions (contlnuous curve) are in good

agreement with and follow the same trend as the finite element predlctlonsthrough all FVR.

The flnlte element predictions for the transverse expansion (fig. lO) areaffected by the nelghborlng fibers. The expansion coefficient increases

sllghtly with increasing FVR up to about 0.4 and then the decrease slightly

with increasing FVR greater than 0.4. This occurs at high temperature and room

temperature. The METCAN predictlons follow the same general trend as the super-

element predictions at room and high temperature for all FVR. The room temper-

ature METCAN prediction (continuous curve) is in better agreement than the hlghtemperature prediction although both are considered reasonable based on thesimplifled assumptions In METCAN.

Longitudinal Thermal Conductivity

The boundary and load condltlons for the finite element analysis areapplied through enforced temperatures. The boundary conditions are as follows:

(l) Constrain the temperature of the atmosphere (fig. 2) on the cold face(front YZ-plane) to 0 °F.

(2) Insulate the structure on the four sides paralle1 to the heat flow.

(3) Constrain the back YZ-plane to conduct heat to the atmosphere.

The composite Is subject to an Increase In temperature to the front YZ-plane.

The longitudinal therma] conductivity Is calculated from the followingequations:

qt " Lx

K_11 - A • VT

where, qt Is the flux through the composite, Lx Is the X length, A is the

cross-sectlonal area, and VT Is the temperature change.

The finite element and METCAN predictions of the longitudinal conductlvltyare shown In figure II. The room and high temperature predlctlons Increase

wlth Increaslng FVR. The room temperature METCAN predIctlons are slightly

lower than the flnlte element prediction whlle the hlgh temperature METCAN pre-dictions are slightly higher than the superelement predictions.

Transverse Thermal Conductlvlty

The boundary and load conditions for the finite element analysls areapplied through enforced temperatures. The boundary condltlons are as follows:

(l) Constrain the temperature of the atmosphere (flg. 2) on the cold face(right XZ-plane) to 0 °F.

(2) Insulate the structure on the four sides parallel to the heat flow.

(3) Constrain the left XZ-plane to conduct heat to the atmosphere.

The composite Is subject to an increase in temperature to the right YZ-plane.

The transverse thermal conductivity Is calculated from the followlngequatlons:

qt " LyK_22 " A • VT

where, qt Is the flux through the composite, Ly Is the Y width, A Is the

cross-sectlonal area, and VT Is the temperature change.

8

The flnlte element and METCAN predlctlons are shown In figure 12 for thetransverse thermal conductlvlty. The predlctions decrease wlth increasing FVRfor room and high temperature. The METCAN results are lower than the finiteelement predlctlons for both room and high temperature. Since the finite ele-ment predlctlons are higher at low FVR and approach the METCAN results as theFVR is increased, it may be concluded that denser whiskers may be required forsmaller diameter fibers.

SUMMARYOF RESULTS

The important results of adaptlng mechanics of materials concepts with

finite element analysis, or alternatively the slmpllfied analytical models such

as Is implemented In METCAN, to HTMMC mlcromechanIcs are as follows:

(I) The mechanlcs of materials concepts and the finite element (super-element) method provides an independent method of predicting the thermomechanl-cal properties of MMC at room and high temperature.

(2) The mechanical properties include modull and Polsson's ratlo. Compar-

isons with the simplified mIcromechanIcs equations (METCAN) are in good agree-

ment. Polsson's ratio (v_23) does not satisfy the assumption of transverseIsotropy.

(3) The thermal propertles Include thermal expansion coefficlents and

thermal heat conductlvltles. The longitudinal thermal expansion coefficlent

predicted by METCAN is In good agreement wlth the flnite element results. Thetransverse thermal expansion coefficlent predicted by METCAN deviates slightly

from the flnlte element results. The thermal conductlvltles predicted from

METCAN are In good agreement with the flnite element simulations.

CONCLUSION

The important concluslons of adapting the superelement method to thermo-mechanical behavior of HTMMC are as follows:

I. The finite element technlque used in conjunctlon wlth mechanics ofmaterlals concepts provides the ability to analyze ordinary composlte struc-tures well and offers an alternative for predlctlng composite propertles.Because of its utility this method can be extended to analyze more complexcomposite Interactlons. These may Include flber fracture, flber/matrIx dls-bonding, hybrid composltes, etc.

2. The superelement method can provlde detalled Information about local

composlte behavior that cannot be obtalned through experiments.

REFERENCES

I. Caruso, J.J., "Appllcatlon of Finite Element Substructurlng to CompositeMicromechanlcs," NASA TM-83729, 1984.

2. Caruso, J.3. and Chamls, C.C., "Assessment of Slmp|Ifled Composite

Mlcromechanlcs Using Three-Dlmenslonal Flnlte-Element Analysis," Journal

of Composites Technoloqy and Research, Vol. 2, No. 3, Fall 1986, pp. 77-83.

3. Hopkins, D.A. and Chamls, C.C., "Simplified Composite Mlcromechanlcs

Equations for HygraI, Thermal and Mechanlcal Properties," NASA TM-83320,1983.

4. Hopkins, D.A. and Murthy, P.L.N., "METCAN - the Meta] Matrix Composite

Analyzer," Lewis Structures Technology 1988, Vol. 2,.Structural Mechanics,NASA CP-3OO3-VOL-2, 1988, pp. 141-156.

5. Schaeffer H.G., HSC/NASTRAN: Primer Static and Normal Modes Analysis,Schaeffer Analysis, Inc., 1979.

TABLE I. - FIBER AND MATRIX PROPERTIES

Property symbol

Longitudinalmodulus

Transverse modulus

Longitudinal shearmosulus

Transverse shearmodulus

LongitudinalPoisson's ratio

TransversePoisson's ratio

Longitudinal heatconduction

Transverse heat

conduction

Longitudinalthermal expansion

Transverse thermalexpansion

Units

E11 Mpsi

22 Mpsi12 Mpsi

G23 Mpsl

_12

_23

Btu in.

K11 hr °F in. 2

Btu in.K22 hr °F in.2

_II xlO-6 in.in. °F

_22 xlO-6 in.in. °F

Temperature,°F

70 1500

PIO0 Copper

]05.0

.gol.lO

.70

.200

.250

I.74

-.90

5.6

25.

17.0

17.06.54

6.45

.300

.300

19.3

19.3

9.8

9.8

PIO0 Copper

93.8 8.87

.804 8.87,982 3.41

.625 3.41

.179 .300

.223 .300

24.4 16.8

1.70 16.8

-I.01 19.6

6.27 19.6

10

:-J-i\\

FIGURE 1, - 9-CELL FINITE ELEMENTMODEL,

11

F CENTER LINEZ I OF TOP

i, _ XY-PLANECENTER

YZ-PLANE _ ,_, ¢

CENTERLINE yOF LEFT

XZ-PLANE

"-CENTERLINE

"//] / \"- CENTERLINEXZ-PLANEOFRIGHT

/ OF BOTTOM

XY-PLANE

FIGURE 2. - GENERAL BOUNDARY CONDITIONS FOR THE 3-B SUPER-

ELEMENT MODEL.

75

60

_.4s

30

15

P]OO-GRAPHIIE FIBER/COPPER MATRIX

METHOD TEMPERATURE,

oF

Z_ 3-D FINITE ELEMENT 1500

METCAN ISO0

[] 3-D FINITE ELEMENT 70

..... METCAN 70

$s/SO

s$$ $/_

d'" "//

.," / ,,97 o / _olo o/1

/ MULTI-_ ,.,l,-, _ " /I

t .... IioiooF,,,,,'-_,/

I I I.2 .4 .6

FIBER VOLUME RATIO

FIGURE 3. - LONGITUDINAL MODULUS OF UNIDIRECTIONAL

COMPOSITES.

I.B

12

PIOO-GRAPHITE FIBER/COPPER MATRIX

METHOD TEMPERATURE,

oF

Z% 3-D FINITE ELEMENT 1500

-- METCAN 1500IG0 3-D FINITE ELEMENT 70

-, METCAN 70

14

.30 -- _ I_ _ 12

? J3,

oJ ///4 _ooo/]

.,0 o o o/J_.._ '_ooo/

MULTItjCELL -il

l/

1 I 1. 1,2 .4 ,G ,8

FIBER VOLUME RATIO

FIGURE 4. - POISSONS RATIO OF UNIDIRECTIONAL COMPOSITES.


METHOD TEMPERATURE,

oF

Z% 3-D FINITE ELEMENT 1500

-- METCAN 1500


METCAN 70

--D 3

.%,,

I I 1 I.2 ,4 .G .8

FIBER VOLUME RATIO

FIGURE 5. - TRANSVERSE MODULUS OF UNIDIRECTIONAL COM-

POSITES.

13

o


.40

•30

.20

.10

Z_

w

[3

METHOD TEMPERATURE,

oF

3-D FINITE ELEMENT 1500

METCAN 1500

3-D FINITE ELEMENT, 1500

ISOTROPIC


METCAN 70

3-D FINITE ELEMENT, 70

ISOTROPlC

/

___. s-,_

/

_ I -'_----

-- MULTI- i_O_C_LL>p_ 2

1 1 1 I.2 .4 .6 .8

FIBER VOLUME RATIO

FIGURE 6. - POISSONS RATIO OF UNIDIRECTIONAL COMPOSITES.

@._4

2

PlOD-GRAPHITE FIBER/COPPER MATRIX

METHOD TEMPERATURE,

OF

A 3-D FINITE ELEMENT 1500

METCAN 1500


METCAN 70

3

t

!I°°oCELL )I0 0 0

-_, (Io o o%

-,,[3

1 k I t.2 .4 .6 .8

FIBER VOLUME RATIO

FIGURE 7, - SHEAR MODULUS OF UNIDIRECTIONAL COMPOSITES.

14

G

3 2

A

[]


METHOD TEMPERATURE,

OF


METCAN 1500


METCAN 70

iiOoOon°-- [] MULTI- I 6

• CELL ! v"',. 0 0 I0 2-7.

_", [] i_ .z

-.,_ 4

.2 .4 .6 .8 0

FIBER VOLUME RATIO

FIGURE 8, - SHEAR MODULUS OF UNIDIRECTIONAL COMPOSITES.


METHOD TEMPERATURE,

oF


METCAN 1500


METCAN 70

0 0 !01/IMULTI-__ _ r

\ CELL_i o oyj_._\ o__o__o/

_J

J.2 .4 .6 .8

FIBER VOLUME RATIO

FIGURE 9. - LONGITUDINAL THERMAL EXPANSION OF UNIDIRECT-

IONAL COMPOSITES.

15

25

_- 20u_

z

z

::L

g_- 5


METHOD TEMPERATURE,

oF


METCAN 1500

0 3-D FINITE ELEMENT ZO

..... METCAN 70

AA A

Z_

[] [] [] D

3

MULTI- i 0 !0 !0

CELL /,_.0_0O 0 /J

I J I I.2 .4 .6 .8

FIBER VOLUME RATIO

FIGURE IO. - TRANSVERSE THERMAL EXPANSION OF UNIDIRECT-

IONAL COMPOSITES.

40

32

245

.c

v

_>

8


METHOD TEMPERATURE.

OF


METCAN 1500


..... METCAN 70

[][] _ _°°

[]0

oolo MULTI-0 010 I/'1CELL 0 010 _ _

tf

I 1 I 1.2 .4 .6 .B

FIBER VOLUME RATIO

FIGURE 11. - LONGITUDINAL THERMAL CONDUCTIVITY OF UNI-

DIRECTIONAL COMPOSITES.

16

40

32

24

16

§ B

PIO0 GRAPHITE FIBER/COPPER MATRIX

METHOD TEMPERATURE,

OF


-- METCAN 1500


..... METCAN 70

ooo

\,, ,ooo/ "

%%

I I I,2 .4 ,G

FIBER VOLUME RATIO

FIGURE 12. - TRANSVERSE THERMAL CONDUCTIVITY OF UNI-

DIRECTIONAL COMPOSITES.

I.8

17

National Aeronautics andSpace Administration

1. Report No,

NASA TM-102490

4. Title and Subtitle

Report Documentation Page

2. Government Accession No.

i

Prediction of High Temperature Metal Matrix Composite

Ply Properties

7. Author(s)

J.J. Caruso and C.C. Chamis

9. Performing Organization Name and Address

National Aeronautics and Space AdministrationLewis Research Center

Cleveland, Ohio 44135-3191

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, D.C. 20546-0001

3. Recipient's Catalog No.

5. Report Date

6. Performing Organization Code

8. Performing Organization Report No.

E-5280

10. Work Unit No.

505-63-11

11. Contract or Grant No.

13. Type of Report and Period Covered

Technical Memorandum

14. Sponsoring Agency Code

15. Supplementary Notes

Presented at the 29th Structures, Structural Dynamics, and Materials (SDM) Conference cosponsored by the

AIAA, ASME, AHS, and ASC, Williamsburg, Virginia, April 18-20, 1988.

16. Abstract

The application of the finite element method (superelement technique) in conjunction with basic concepts frommechanics of materials theory is demonstrated to predict the thermomechanical behavior of high temperature

metal matrix composites (HTMMC). The simulated behavior is used as a basis to establish characteristic

properties of a unidirectional composite idealized as an equivalent homogeneous material. The ply properties

predicted include: thermal properties (thermal conductivities and thermal expansion coefficients) and mechanical

properties (moduli and Poisson's ratio). These properties are compared with those predicted by a simplified,

analytical composite micromechanics model. This paper illustrates the predictive capabilities of the finite element

method and the simplified model through the simulation of the thermomechanical behavior of a P100-graphite/

copper unidirectional composite at room temperature and near matrix melting temperature. The advantage of the

finite element analysis approach is its ability to more precisely represent the composite local geometry and hence

capture the subtle effects that are dependent on this. The closed form micromechanics model does a good job at

representing the average behavior of the constituents to predict composite behavior.

17. Key Words (Suggested by Author(s))

Composite properties; Metal matrix composites; High

temperature metal matrix composites; Compositesmicromechanics; Finite element methods; Square array;

Composite modulus; Composite Poisson's ratio; Compositethermal expansion; Composite thermal conductivity;

P- 100--graphite/copper

18. Distribution Statement

Unclassified - Unlimited

Subject Category 24

19. Security Classif. (of this report) I 20. Security Classif. (of this page) 21. No. of pages

Unclassified l Unclassified 1:2=T

ASAFORM1628OCT86 *For sale by the National Technical Information Service, Springfield, Virginia 22161

22. Price*

A03

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