NASA Technical Memorandum 102565 ........ _...... "......

Fiber Pushout Test: A ThreeDimensional Finite Element

CompUtad0na! Simulation ............................. :.....i ....--_

Subodh K. Mital

Institute for-Computational Mechanics in Propulsion

Lewis Research Center ........ : .....

Cleveland, Ohio

and

Christos C,II Chamis

Lewis Research Center

Cleveland, Ohio

(NA_A-TM-]0?565) FIg-R PUSHOUT T-ST: A NgO-21i31

THREE-DIMENSIONAL FIN!IE ELFMENT

COMPUTATInNAL SIMULATION (NASA) 1_ P

CSCL IID

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April 1990

Unclas

0277020

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FIBER PUSHOUT TEST: A THREE-DIMENSIONAL FINITE ELEMENT

COMPUTATIONAL SIMULATION

Subodh K. Mira1*

Institute for Computatlonal Mechanics in Propulslon

Lewis Research Center

Cleveland, Ohio 44135

and

Chrlstos C. Chamlst

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135

SUMMARY

A fiber pushthrough process has been computatlonally simulated using

three-dlmensional Finite element method. The interface materlal is replaced by

an anlsotroplc material with greatly reduced shear modulus In order to slmulate

the fiber pushthrough process using a linear analysis. Such a procedure is

easlly implemented and is computatlonally very effective. It can be used to

predict fiber pushthrough load for a composite system at any temperature. The

average interface shear strength obtained from pushthrough load can easlly be

separated Into its two components: one that comes From frictional stresses and

the other that comes from chemical adheslon between fiber and the matrix and

mechanical interlocking that develops due to shrinkage of the composite because

of phase change during the processing. Step-by-step procedures are described

to perform the computational slmulatlon, to establlsh bounds on Interfaclal

bond strength and to interpret interfacial bond quality.

INTRODUCTION

Bonding phenomena between fiber and the matrix (Interfaclal) are generally

regarded as playing an important role In the mechanical behavior of composite

materials In general, and ceramic matrix composites In partlcular. Bond degradatlon is often a critical factor in determining the ultimate strength of a

composite material, as well as its fatigue resistance, impact resistance and

other important properties. The strength of the bonding between fiber and the

matrix plays a major role In the ability of the composlte to brldge cracks or

deflect cracks along the interface, thereby, contributlng to the compos|te

fracture toughness (ref. I). In order for such fracture toughening to occur,

the fiber matrix interface must exhibit Just the right degree of bonding. If

the bonding is too strong, for example, the composite behaves 11ke a monollthlc

materlal, as a result cracks propagate through the material and it generally

results In brlttIe fracture.

"Work funded by Space Act Agreement C-g9066-G.

tSenlor Aerospace Scientist.
Previous researchers have conducted experiments on ceramic flber/ceramlc

matrix composites to estlmate shear bond strength and Interfaclal friction

stress. Typlcally, In these experiments, referred to as pushout tests, free

ends of a fiber in a unidirectional composite specimen with a ground and polIshed surface normal to the fiber axis are subjected to point loads at various

temperatures as shown schematically in flgure l(a) and (b). The loads required

for elther Interfaclal debondlng or Interfaclal sliding are measured and

related to Interfaclal propertles. Marshall (refs. 2 and 3) used a conventlonal Vlckers mlcrohardness diamond Indenter to depress frlctlonally bonded

SIC fibers In a LAS (11thlum alumlnoslllcate) matrix. Laughner (ref. 4) and

Brun and Slngh (ref. 5) have used slight variation of the above technlque to

find the flber pushout load In a composite specimen. Morscher et al. (ref. 6)

have studied the interfaclal shear strength of AVCO SCS-6 flber-relnforced

reactlon-bonded SI3N 4 (RBSN) composite as a function of temperature: Fiber

pushthrough experiments were conducted with a diamond Indenter and a hlgh temperature mlcrohardness tester.

In view of the success of three-dlmenslonal flnlte element computational

simulation of composite mlcromechanlcal behavlor (ref. 7), it is appropriate

and tlmely to computatlonally simulate the flber pushthrough process. The

objective of the present report is to descrlbe a computational simulation procedure to simulate the fiber pushthrough process, to identify the dominant

parameters in the planning of physlcal experiments and to Interpret results

obtained therefrom.

E

G

P

R

Sis-yleld

T

Tc

tl

U

c_

¢

Oln

NOMENCLATURE

Young's modulus

Shear modulus

fiber length

flber pushout Load

fiber Radlus

In-sltu yield shear strength

temperature

consolldatlon temperature of the composite

thickness (width) of the interface

fiber displacement at the far end

coefficient of thermal expansion

flber diameter ( - 2.R)

Polsson's ratio

normal stress acting on the interface

2
Subscripts

f

m

In

11

22,33

flber

matrix

interface

is the longitudinal (along the fiber) dlrectlon

are transverse (to the fiber) directions

FUNDAMENTAL CONCEPT

The concepts adopted to expedite the computational simulation arise from

the physics of the fiber pushthrough process and are summarized In thls section. The collectlve results cited in the references indicate that the maxlmum

interFaclal shear stress occurs just Inslde the loaded end of the specimen.

Debondlng Initiates at that locatlon. As the load Is Increased on the flber,

interfacial fracture progresses until the full fiber length Is debonded and the

fiber just slldes out from the other end. In order for progressive fracture

to occur, the local Interracial shear stress must exceed the corresponding

strength. As the interfaclal bond shear strength Is approached, the interfacial shear stiffness decreases rapidly. The process Is nonlinear and the

full shear stress/straln behavior for the Interface bond Is generally needed

In the simulation. An alternate approach is used, herein, to take advantage of

the rapid reduction in shear stiffness. Thls approach is readily implemented,

is computatlonally effective and to the authors' knowledge, it Is applied to

computationally simulate the Interfaclal bond fracture for the first time.

A hypothetlcal shear stress versus shear strain curve for the interface

material behavior Is shown In flgure 2. The curve Is Initially linear (OA),

representing a reversible or recoverable shear deformation upon unloadlng. As

the shear straln increases, progressive nonlinearity (AB) occurs, which now

Includes deformations which are irreverslble or unrecoverable. In thls region,

the Instantaneous shear modulus keeps on decreasing. Eventually, the shear

modulus becomes almost zero, and the shear strain becomes unbounded, meaning

fracture of the Interface and the fiber Just pushes through. The advantage of

the present approach is the use of the approximate magnitude of the shear modulus near point B (fracture load, refer to fig. 2) to estimate the shear stress

in the Interface at flber pushout. Hence, a sequence of progresslvely reduced

shear moduII, corresponding to tangent shear modull (region AB) are used In the

present simulation. Point B (flg. 2) represents shear strain In the interface

at the fiber pushout. Thus, the load at fiber pushout is kept the same whether

the linear material with reduced shear modulus or the real material with its

nonllnear behavior is used. In the present work, a linear analysls is done

with reduced shear modulus, which substantially slmpIifles the computational

effort and mlnlmlzes the tedious calculatlons that are normally required. A

somewhat slmI1ar type of procedure Is used In the design of c1vll engineerlng

structures which are subjected to seismlc loads (refs. 8 and 9).

As mentioned before, the flber pushthrough process Is nonllnear. Hence,

In a fiber pushout nonlinear slmulatlon, the applled load Is Increased In small
increments untll the final fiber pushout load is reached. In the present

procedure, thls nonllnear process Is simulated by replaclng the interfaclal

materlal with an anlsotropic material with reduced shear modulus, and maklng

the slmulatlon process linear up to the pushout load. This type of slmulatlon

provldes a direct means to estimate the Interfacial shear strength in the composlte and to determlne the stress dlstrlbutlon in the interface region at the

instant of flber pushout. Due to the difference between the consolldatlon temperature and the use temperature of the composlte and also due to the mlsmatch

between the thermal expansion coeff|clents of flber and the matrix, there is a

residual normal stress actlng on the interface. The effect of the normal

stress dlstribution on the interface and on flber pushout load is readlly taken

Into account as will be explained in the followlng sectlons.

The critical Interfaclal shear stress, and thus, the fiber pushout load Is

effected by the normal stress actlng on the interface. This Is In llne with an

earlier experimental work (ref. 6), which showed that the flber pushout load

does depend upon the temperature at which the flbers are being pushed out.

FINITE ELEMENT MODEL AND SIMULATION PROCEDURE

The three-dlmenslonal flnite element model used In this procedure consists

of a group of nine fibers, all unldlrectlonal, In three by three unit cells

("nine cell model") as shown in flgure 3. The composite system consists of

0.35 flber volume ratlo SIC/TII5 metal matrix composite with the properties as

shown in table I.

The f_ber dlameter used is 8.8 mlls (223 _m). The length to diameter

ratio (_/@) of the model is 6.8 and the thickness (width) of the Interface, tI,

Is 6.8 percent of the flber diameter. The computer code MSC/NASTRAN version 65

(ref. lO) has been used to perform the slmulatlons. A compressive load Is

applled on the surface of the fiber as described in the different cases below.

For interface, an anlsotroplc materlal is assumed (MAT9 property card In

MSC/NASTRAN). As mentloned before, for this material, shear modulus G Is

reduced, thus effectlng only the shear stiffness of the Interface, where the

nonllnearity domlnates In the fiber pushout process. The normal stresses to

normal stralns coefficients in the elastlclty matrix are kept same as those

for the matrix materlal. When the load Is applled on one end of the fiber, it

pushes out from the other end. To define the fiber pushthrough, the following

procedure Is adopted" a fiber pushthrough test is slmulated using the actual

materlal properties. In the present model of the specimen, the Interface Is

dlvlded Into 16 elements ("bays") along the length (longltudlnal dlrectlon).

Interface materlal propertles are assumed the same as those of the matrix material, except the shear strength of the Interface is assumed to be 30 ksl, which

is approximately 50 percent of matrix shear strength. A compressive load Is

applied on the flber as shown in figure l(b). Load Is applled gradually and

the interface elements are allowed to debond when the shear stress in an element reaches its assumed shear strength. Once, an element Is debonded, its

shear modulus is reduced to near zero. Debonding progresses gradually along

the interface as the applled load Is Increased. F_gure 4 shows the shear

stress dlstrlbution in the interface as it gradually debonds (load is applied

at X/L - I end). Figure 5 shows the applied load versus the f_ber displacement at the far end of the specimen. When the interface is completely
debonded, there Is a drop In the load and the fiber Just pushes out resisting

only the frictional stress. The peak load when the complete fiber is debonded

is defined as the fiber pushthrough load, P. The shear strain at the far end

of the Interface at the load - when the interface has Just completely debonded,

wlll be used to define fiber pushthrough In the simulations, when the reduced

shear modulus of the interface Is used. In the case, when the interface Is

gradually allowed to debond, the pushout load, P comes out to be 56.7 Ib for

zero residual stress in the interface. The shear strain at the far end of the

interface at Fiber pushout Is 0.03 (3 percent), which corresponds to a relative

displacement between fiber and the matrix equal to 0.002 times the flber diameter, for the thlckness of the interface being used. For an Interracial residual stress of -14 ksi (the normal stress that develops In the interface, when

the composite Is cooled down from processing temperature to room temperature,

AT - 1630 °F) and F (coefficlent of friction) assumed to be 0.2 andO.4, the

frictlonal stresses (_.ain) are -2.8 ksi and -5.6 ksl respectively. With these

frictional stresses applied, the fiber pushout load comes out to be 62.5 and

67.0 Ib respectively, as the interface is gradually allowed to debond. Hence,

For the simulations when the pushthrough Is llnearized by reducing the shear

modulus of the interface, the flber 0ushthrough is deflned when the relative

dlsplacement between fiber and the matrix at the far end of the specimen equals

0.002 times the fiber diameter. Once, the fiber pushout load Is known, the

nomlnal (average) interfacial shear strength Is

P (I)

as = 2.I.R._

where R and P. are fiber radlus and length, respectively.

CASES STUDIED, RESULTS/DISCUSSION

The cases Investlgated, typical results obtained and their relevance to

composite behavior are described In thls section.

REFERENCE CASE

Reference case Is deflned as the case when the fiber is pushed without

resldual stresses In the interface, that develop due to fabrlcatlon process

(about 1700 to 70 °F for SlC-Til5 metal matrix composite). Specifically, it

is assumed that the composite is free from any resldual thermal stresses that

develop due to thermal expansion coefficient mismatch between fiber and the

matrix. The fiber pushout load, P, Is found from flnite element simulations as

the shear modulus, G, of the Interface varies. As mentioned before, the fiber

pushout Is defined at the load when relatlve dlsplacement between the fiber and

matrix at the far end equals 0.002 tlmes the flber diameter. The flber pushout

load, P, versus the shear modulus of Interface, Is shown in figure 6. The

pushout load varies nonllnearly with shear modulus below 0.3 mpsi (approxlmately) and linearly above this value. Thls may be interpreted to mean that

the pushout load varies llnearly for strong Interfacial bond and nonllnearly

for weak Interfaclal bond. It should be mentioned once agaln, that an anlsotropic materlal has been used for the interface such that the coefficients in

the elastlcity matrix for normal stress - normal straln are the same as those

for the matrix material. Only, the shear modulus, G, of the interface material

has been reduced, making it rather soft In shear. For the fiber pushout load
of 56.7 Ib, the value of G turns out to be 330 ksl or 0.33 mpsl. The average shear stress on the Interface, os computedfrom equation (1), comesout

to be 33.8 ksl. For this case, G _ lO_s. This provides an Initlal estimate

for G of about lO times the Interfacial fracture shear stress (or reduced

matrix yield stress) to be used In the computational simulation.

TEMPERATURE EFFECTS ON FIBER PUSHOUT LOAD

As the composite Is cooled down to temperatures lower than consolidation

temperature (or reference temperature - assumed to be the stress free state),

some residual normal stresses (Oln) will develop in the interface region.

These residual stresses may be tensile or compressive. The magnitude of these

stresses depends upon the difference between the reference (consolidation) and

use temperatures and extent of _ 'mlsmatch between fiber and the matrix. For

example, at higher temperatures close to consolidation temperature, the thermal

stresses wlll be low, but at room temperature, when AT is large, these thermal stresses are significant.

In the simulation procedure, it is assumed that the effective shear modulus of the Interface can be modified to Include the effect of the thermal

stresses as followsG - Go±(p-Oin).F (2)

where _ Is the coeff|cient of frlction between the fiber and the matrix materials, Oln Is the Interfaclal normal stress, GO Is the effective shear modulus

at zero InterfacIal normal stress and F is a scaling factor. Equation (2) Is

shown graphlcally in figure 7. If the normal stress acting on the interface Is

compresslve, it will result In higher shear resistance (interlocking) between

the rough surface of the flber and the matrix and, thus, will result In higher

load needed to push the fiber through. This is reflected in figure 7 as follows: compresslve normal stresses will mean a higher G, which In turn means a

hlgher pushthrough load (fig. 6). In equatlon (2), GO reflects mainly chemical adhesion between fiber and the matrix as well as mechanical interlocking

between rough surface of the fiber and the matrix from shrinkage stresses that

develop due to the phase change during the processing of the composite. The

normal stress, Oln, Is mainly due to thermal expansion mismatch. From the slmulation, where the interface Is gradually allowed to debond, we know the fiber

pushout load for a given value of Oln and assumed values of _. Then, by

using equation (2) and P versus G curve, the value of F has been found

to be ~lO.O from

G-Go F

IJ'Oln

The normal stress on the interface versus the temperature Is shown in

figure 8. The consolldatlon temperature is taken as 1700 °F. As seen in figure 8, the variation of normal stress versus the temperature Is almost linear.

The normal stress _n the Interface at consolidation temperature is approximately -l.O ksl (compressive) as shown in figure B.
For a given temperature, the Interfacla] normal stress Is known from flgure B. Then, for a given value of _ and GO (F assumed to be lO.O), we calculate G from equatlon (2), which in turn, gives us a pushthrough load from

flgure 6. Thus, the pushthrough load is implIc|tly a funct|on of temperature.

Figures 9(a) and (b) show pushthrough load, P, versus GO for different values

of temperatures and p. The effect of p at consol|datlon temperature |s

small (because Oln Is small) and hence neglected. An average curve for consol|dat|on temperature (T c) Is, therefore, adopted.

Figures 9(a) and (b) are proposed to be used wlth experlments as follows:

flrst, we conduct a pushthrough test at some temperature near the consol|datlon

temperature and knowlng the pushthrough load, determine GO . Then, conduct a

pushthrough experiment at temperature Tl and knowing the pushthrough load at

T I, determine the other parameter (_) of the model. It has been assumed, so

far, that _ and Go remain constant over a wide range of temperatures, even

though, the real material shear modulus might show dependence upon the temperature. If one conducts several pushthrough tests at dlfferent temperatures, a

regresslon technlque llke "least square method" can be used in conJunctlon wlth

equation (2) to find the "best flttlng" values of p and Go . Then, |twlll

also be clear whether _ and Go were indeed independent of temperature or

not.

Once, values of _ and GO are determined, for any given temperature one

can predict fiber pushthrough load uslng figure 9. One can determlne the average Interfaclal shear strength, slnce the Interracial normal stress is known as

a functlon of temperature, the part of Interfacla] shear strength that comes

from frlctlonal stresses can be separated. AS shown In flgure 9(b), the flber

pushthrough load at room temperature_ _ dependlng upon the value of p, can be

20 to 30 percent higher than the pushout load at consolidation temperature.

For comparison, in the experlments conducted by Morscher et al. (ref. 6), where

they used SIC-RBSN composite (:f > :m ), fiber pushthrough load at consolidation

temperature was twice the pushthrough load at room temperature. They also

reported that most of the failures occurred at carbon-carbon Interface within

the cellular flber itself, whlch exhibited very weak Intercellular bonding. In

our case, :m > _f, hence pushout loads at room temperature are higher than the

pushout load at consolldatlon temperature. The shear strength of the interface

has been assumed to be 30 ksI. If the interface shear strength Is lower, then

the percent of Increase In pushout load at room temperature wlll be greater for

the same value of p.

PROCEDURE FOR ESTIMATING THE PUSHOUT LOAD

The collectlve results from the computation simulations prevlously

described can be used to provlde step-by-step procedures for: (1) computationally slmulating interfaclal bond, (2) establishing upper and lower bounds on

the pushout load, and (3) providing some guidelines for assessing conditions at

the interface. The terms to be used In the subsequent development are defined

for clarity.

Term Deflnitlon

Perfect Interface Bond - The matrix fractures in shear. The surface of

the pushed-out flber Is covered wlth a layer of matrix materlal. No bare flber

surface Is exposed.
No Interfaclal Bond - The surface of the pushed-out fiber Is bare and

clear of any matrix residue.

Strong Interfaclal Bond - The surface of the pushed-out fiber has substantlal matrix residue.

Weak Interfaclal Bond - The surface of the pushed-out fiber has sparsely

dlstrlbuted matrix residue.

Strong Interface Bond

The pushout load for strong interfaclaI bond is slmuIated as follows:

(I) Obtain the room temperature properties of the fiber and the matrix

(constituent) materials and the processing condltlons.

(2) Generate a three-dlmenslonal finite element model as described In the

finite element model and slmulation procedure section.

(3) Perform the simulation descrlbed in the same sectlon as In Item (2)

above assuming that the interface fractures when the shear stress reaches the

shear yleld stress.

(4) Find the pushout load when the fiber at the far end advances about

0.2 percent of the fiber dlameter. Thls usually occurs near the peak load of

the load versus far end displacement curve.

(5) Thls Is the upper bound of the Interracial bond strength indicating

perfect bond at the interface as previously defined. Composites approachlng

thls value have near perfect bond at the interface and were manufactured by the

best quallty possible for interfaclal bond.

No Interface Bond

The pushout load for little (negllglble) or no Interfaclal bond Is simulated as follows:

(1) Same as for strong interface bond.

(2) Same as for strong interface bond.

(3) Determine the thermal (normal) stresses (ain) at the interface using

finite element analysis.

(4) Estimate the equivalent shear modulus from:

Ge ; p.Oln. F

wlth p _ 0.5 and F ; lO.

(5) Perform the slmulatlon procedure described In the temperature effects

on fiber pushout load section with G = Ge from step (4) above.
(6) Determine the pushout load as the load needed to advance the fiber by

0.2 percent of fiber diameter at the far end. Composites exhibiting this type

of pushout load have no interface bond and anything that can be done to Improve

it is worth the effort.

INITIAL ESTIMATES ON INTERFACIAL BOND

Initial estimates for strong and no interface bond can be obtained from

the curves presented herein as follows:

Strong Interface Bond

(l) Estimate yield shear stress of the matrix (Sis-yleld).

(2) Assume the Interface shear modulus (Gin) to be -lO Sis-yleld.

(3) With this value of Gin, determine the pushout load from figure 6.

(4) For example: graphite/copper composite

Sis_yleld _ 5 ksl; Gin = I0 x 5 = 50 ksl = 0.05 mpsl

Pushout load, P from figure 6 _ 5 lb.

No Interface Bond

(1) Determlne the product A_.AE.AT for the composite of Interest, where

a_ and AE are d_fferences In the _ and E between the fiber and the

matrix respectively. This gives an estimate of the thermal normal stress in

the interface. AT is the difference between the processing and operating

temperatures.

(2) Determine the product A<_.AE.AT for the composlte in sectlon on temperature effects on fiber pushout load (SIC/TilS).

(3) Determine the equivalent shear modulus Ge for SiC/Til5 composite

From equatlon (2):

Ge = p.Oln. F (Go _ O)

e.g., AT = 1630 °F, _ = 0.5, F = 10, from figure 8, aln = 14 ksl

then, Ge = 0.5 (14 ksi) I0 = 70 ks_ = 0.07 mpsl

(4) Determlne the corresponding pushout load from flgure 6:

P --" 10 Ib

(5) Determine the ratio of products In steps (I) and (2).
(6) Adjust the pushout load In step (4) by the ratio In step (5). This Is

the required pushout load for the composite of interest.

(7) For example:

For graphite/copper composite,

A_.AE.AT : (4x10-6).(9xlO 6 psl).(1730 °F)

For S|CITil5 composite, r

A_.AE.AT = (2.7xlO-°).(49.7x106 psl).(1630 °F)

Then, the ratlo Is"

(4xlO-6).(9x106)/(1730 °F)

- 0.285

(2.7xlO-6).(49.7x106).(1630 °F)

The corresponding pushout load Is then,

P = 0.285 x lO = 2.85 Ib

a relatively small value. Improved estimates can be obtained when composite

micromechanlcs Is used to calculate the Interracial normal stresses (refs. II

and 12). The authors recommend that the user estimate the bounds of the Interfacial strength for his composite(s) of interest in order to become familiar

with the relative ease in applying these procedures.

The range between the two bounds on fiber pushout load for Gr/Cu composlte

is about 2.85 to 5.0 lb. The corresponding range for SIC/TII5 composite is

lO to lO0 lb. As can be seen, the bounds for the Gr/Cu composite are relatively close while those for the SIC/Til5 composite are relatively far apart.

These simple calculations show that there is not much that can be done to

increase the fiber pushout load In Gr/Cu composite by manipulating the interfacial conditions. On the other hand, the pushout load for the SIC/Til5 composite can be substantially increased by Increaslng the bond strength at the

interface. Another way to look at it is that Gr/Cu composites are rather

Insensitive to qual|ty control of the interfacial conditions while SIC/Til5

composites are not.

Weak Interfaclal bond can be computatlonally slmulated by following the

same procedures for the strong bond. However, for thls case the Interfaclal

elements are assigned different In-sltu yield shear strength (Sis_viel d ) values, ranging from 0 to that of the matrix; or respective shear mod_ll for the

Inltlal estimates (ref. 13).

GENERAL REMARKS

Though the results are not included here, the followlng observations were

made during the course of the present work:

(I) Whether the whole or part of the fiber surface is loaded, the total

load required for flber pushout remalns the same. Stress distributions In the

interface have also remained the same Indicating negllglble polsson ratlo

effect.

lO
(2) The fiber pushout load Is independent of the number of fibers loaded

slmultaneously. The normal stress dlstrlbutlon In the interface is also independent of whether one or several flbers are belng pushed through. Thls suggests negllglble flber Interactlon, at least for the composite system and the

fiber volume ratio Investigated.

(3) Normally, the fibers are pushed by an indenter. One has to ensure

that the tlp dlameter of the indenter Is smaller than the fiber diameter, so

that whlle Indentlng the fiber, It should not push against the matrix.

SUMMARY

A computational slmulatlon procedure has been developed to slmulate the

fiber pushthrough process. The procedure consists of three-dimenslonal finite

element slmulation method wlth a unlque representation of the interfaclal shear

stress behavior. The interface materlal has been replaced by an anlsotropIc

material wlth greatly reduced shear modulus in order to simulate the fiber

pushthrough process using a linear analysls. This procedure can be used to

predict fiber pushthrough load for a composite system at any temperature. The

average interfac1al shear strength and Its component two parts - one that comes

from frictional stress (due to normal stress) and the other that Is due to

chemical adhesion, rough fiber surfaces and the stresses that develop due to

the phase change durlng the processing of the composite, can be obtained. For

the composite system used, the flber pushout load is 20 to 30 percent higher

than the flber pushout load at consolldatlon temperature, due to hlgher frictional stresses. Step-by-step procedures are described to perform the computatlonal slmulatlon, establ!sh bounds on f!be r pushout load and to interpret the

Interfacial bond quallty.

REFERENCES

I. Marshall, D.B.; and Evans, A.G.: Fallure Mechanlsms in Ceramlc-Flber/

Ceramic-Matrix Composites. J. Am. Ceram. Soc., vol. 68, no. 5, May 1985,

pp. 225-231.

2. Marshall, D.B.: An Indentatlon Method for Measuring Matrix-Fiber

Frictional Stresses In Ceramlc Composites. J. Am. Ceram. Soc., vol. 67,

no. 12, Dec. 1984, pp. C259-C260.

3. Marshall, D.B.; and Oliver, W.C.: Measurement of Interfaclal Mechanical

Properties In Flber-Relnforced Ceramic Composites. J. Am. Ceram. Soc.,

vol. 70, no. 8, Aug. 1987, pp. 542-548.

4. Laughner, J.W., et al.: Simple Indentation Method for Measurement of

Interfaclal Shear Strength In SIC/SI3N 4 Composites. Ceram. Eng. Scl.

Proc., vol. 7, no. 7-8, July-Aug., 1986, p. 932.

5. Brun, M.K.; and Slngh, R.N.: Effect of Thermal Expansion Mismatch and

Fiber Coatlng on the Flber/Matrlx Interfac1al Shear Stress in Ceramic

Matrix Composites. Adv. Ceram. Mater., vol. 3, no. 5, 1988, pp. 506-509.

11
6. Morscher, G.; Pirouz, P.; and Heuer, A.H." Temperature Dependence of

Interfaclal Shear Strength in SIC-Flber-Relnforced Reactlon-Bonded Silicon

Nltrlde. J. Am. Ceram. Soc., vol. 73, no. 3, Mar. 1990, pp. 713-720.

7. Mltal, S.K.; Caruso, J.O.; and Chamls, C.C.: Metal Matrix Composites

Mlcrofracture: Computatlonal Simulation. Accepted as Invited Paper for

Presentation at the Symposium on Computational Technology for F11ght

Vehlc]es, Nov. 5-7, 1990, Washington, D.C.

8. Shlbata, A.; and Sozen, M.A." Substitute-Structure Method For Seismic

Design In R/C. J. Struct. Div., ASCE, voI. 102, no. STI, Jan. 1976,

pp. l-I8

9. Mital, S.K." Pseudo Non-Linear Seismic Analysis For Damage Evaluation of

Concrete Structures. Master's Thesis, The University of British Co]umbla,

Vancouver, Canada, May lg85.

I0. MSC/NASTRAN, User's Manual, Version 64, Vol. I and II. The MacNeal

Schwend]er Corporation, Los Angeles, I984.

11. Murthy, P.L.N.; Hopklns, D.A.; and Chamls, C.C." Metal Matrix Composite

Micromechanics" In-Situ Behavior Influence on Composite Properties. NASA

TM-I02302, 1989.

12. Caruso, 3.J.; Chamls, C.C.; and Brown, H.C." Parametric Studles to

Determine the Effect of Compllant Layers on Metal Matrix Composite Systems.

NASA TM-I02465, 1990.

13. Caruso, J.J.; Trowbridge, D.; and Chamis, C.C." Finite Element Applications to Explore the Effects of Partlal Bonding on Metal Matrix Composite

Properties. NASA TM-lO1482, 198g.

TABLE I. - PROPERTIES OF CONSTITUENT Fta_TERIALS OF SiC/Ti15

Modulus, E (mpsi)

Poisson's ratio,

Shear modulus, G (mpsi)

Coefficient of thermal

expansion _ (ppm/°F)

SiC fiber TilS Matrix Interface

62.0

0.3

23.8

1.8

12.3

0.32

.1.6

4.5

12.3

0.32

Varies from

0 to Gmatrix

4.5

12
P

FIBER _,\ I

MATRIX_,j 0 l ._ , i ' .

x

INTERFACEMATRIX

', _

IEE

u T- _,_ t i

.-'-FIBER

COMPOSITE _

,ES = u/t i

I i = THK. OF INTERFACE

by

(a) FIBER PUSH-OUT. (b) FIBER PUSH-THROUGH.

FIGURE I. - SCHEMATIC REPRESENTATION OF FIBER PUSH-OUT AND PUSH-THROUGH TECHNIQUES.

_- INTERFACIAL FRACTURE

/ (PUSH-THROUGH) B i

4

A f AEs / INSTANTANEOUS SHEAR MODULUS

/// ( dos/_,£s )

I / _ PROGRESSIVE NONLINEARITY

_//_--_--_REVERSIBLE DEFORMATION

0

SHEAR STRAIN

FIGURE 2. - SHEAR STRESS VERSUS SHEAR STRAIN CURVE FOR THE

MATRIX MATERIAL.

13
LENGTH

: 6t8 FIBER

DIAM

FIBER

MATRIX

FIGURE 3. - REPRESENTATION OF NINE CELL MODEL.

14
40 -- 70

30

2O

lO

40

30

_z

z 20

cO

lo(-

o

I I I I I

(a) AFTER 10 BAYS BEBONDED.

I ...... 1 I I

(b) AFTER lh BAYS DEBONDED.

1

60

50

-=

o_,o

30

M

_ 20

10

,.--- INTERFACEBOND+ FRICTION

FRICTION

I I I I

.25 .50 .75 1.00

U/L

FIGURE 5. - APPLIED LOAD VERSUSFIBER DISPLACEMENTAT THE

END.

30

20

i

lO

I I I I I

.2 .4 .6 .8 1.0

X/L

(c) AFTER 15 BAYS I_-BONDED.

FIGURE 4. - SHEAR STRESS DISTRIBUTION IN THE INTERFACE.

.J

v

W200

t60

120

8O

40

m

.2 .4 .6 .B

SHEAR MODULUS, G (MPSI)

FIGURE 6. - VARIATION OF FIBER PUSH-OUT LOAD VERSUS SHEAR

MODULUS OF INTERFACE.

#

1.0

15
G o

p,F = tan Lp

G = GO + (I,I.01N.).F

• OIN"

FIGURE 7. - REPRESENTATION OF EFFECTIVE SHEAR MODULUS OF INTERFACE F_AffR[AL.

120

8O

8O

/T = Tc: Oin'

I I

(a) T = 10OO OF: Oin ' = -7 KSZ.

P

Ao.2

00.4

[] 0.6

/

=0

/

/

/

I

[]

5

o T

-4

-8

-12 tON

TEMPERATURE,

-16 1700 °F

-20 l I I I I

0 500 1000 1500 2000 2500

TEMPERATURE, OF

FIGURE 8. - VARIATION OF NORMAL INTERFACIAL STRESS VERSUS

TEMPERATURE.

GO

2O

_T = TC: Oin ' = O

I I I' [

.10 .20 ,30 .qO

GO , _PS!

(b) T = 70 OF: ain ' = -lq KS[.

FIGURE 9. - FIBER PUSH-OUT LOAD VERSUS Go.

]

.50

16
Report Documentation Page NationalAeronautics and

Space Administration

1. Report No. NASA TM-102565 2. Government Accession No. 3. Reclplent's Catalog No.

ICOMP-90-11

4. Title and Subtitle

Fiber Pushout Test: A Three-Dimensional Finite Element Computational

Simulation

7. Author(s)

Subodh K. Mital and Christos C. Chamis

9. Performing Organization Name and Address

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135-3191

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, D.C. 20546-0001

5. Report Date

April 1990

6. Performing Organization Code

8. Performing Organization Report No.

E-5389

10. Work Unit No.

510-01-0A

11. Contract or Grant No.

13. Type of Report and Period Covered

Technical Memorandum

14. Sponsoring Agency Code

15. Supplementary Notes

Subodh K. Mital, Institute for Computational Mechanics in Propulsion, Lewis Research Center (work funded by

Space Act Agreement C-99066-G). Christos C. Chamis, NASA Lewis Research Center. Space Act Monitor:

Louis A. Povinelli.

,_6. A_"-bsttact

A fiber pushthrough process ha_be_n computationally simulated using three-dimensional finite element method.

The interface material is replaced by an anisotropic material with greatly reduced shear modulus in order to

simulate the fiber pushthrough process using a linear analysis. Such a procedure is easily implemented and is

computationally very effective. It can be used to predict fiber pushthrough load for a composite system at any

temperature. The average interface shear strength obtained from pushthrough load can easily be separated into its

two components: one that comes from frictional stresses and the other that comes from chemical adhesion between

fiber and the matrix and mechanical interlocking that develops due to shrinkage of the composite because of

phase change during the processing. Step-by-step procedures are described to perform the computational simulation,

to establish bounds on interfacial bond strength and to interpret interfacial bond quality.

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

Composite; Fiber; Interface; Push-through Push-out;

Shear strength; Bonding; Simulation; Residual stress;

Thermal stress

18. Distribution Statement

Unclassified - Unlimited

Subject Category 24

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

Unclassified Unclassified 18

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