A111D2 hTbflS? NBS i

I P^g^CATjONS

NBSIR 87-3564

Structural Reliability and Damage

Toierance of Ceramic Composites

for High-Temperature

Appiications

E. R. Fuller, Jr., T. W. Coyle, R. F. Krause, Jr. and T. J. Chuang

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Ceramics Division

Gaithersburg, MD 20899

April 1987

Issued June 1987

Prepared for - QQ nent of Energy

esearch & Technology Development

• U b 6 |.gy Material Program

?^87-3564

1987

C.2

INationai Bureau of Standards

f FOR HIGH-TEMPERATURE

I APPLICATIONS

I STRUCTURAL RELIABILITY AND DAMAGE

I TOLERANCE OF CERAMIC COMPOSITES

NBSIR 87-3564

Gaithersburg, Marylaud 20899

A125.C

, 6^sr ^ mi

E. R. Fuller, Jr., T. W. Coyle, R. F. Krause, Jr. and T. J. Chuang

; U.S. DEPARTMENT OF COMMERCE

\ National Bureau of Standards

^ Ceramics Division

I

Gaithersburg, MD 20899

' April 1987

||

Issued June 1987

~ Prepared for

; U.S. Department of Energy

> Fossil Energy

Advanced Research & Technology Development

Fossile Energy Material Program

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
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NBS-1 - STRUCTURAL RELIABILITY AND DAMAGE TOLERANCE OF

CERAMIC COMPOSITES FOR HIGH -TEMPERATURE APPLICATIONS

Semi-Annual Progress Report

for the period October 1987 through March 1987 to the

US Department of Energy, Fossil Energy,

Advanced Research & Technology Development,

Fossil Energy Material Program

under Interagency Agreement

Contract #DE-AI05-800R206179

E. R. Fuller, Jr., T. W. Coyle, R. F. Krause, Jr.

and T . - J

.

Chuang

National Bureau of Standards

Institute for Materials Science and Engineering

Ceramics Division

Gaithersburg, MD 20899

INTRODUCTION

The achievement of higher efficiency heat engines and heat recovery

systems requires the availability of high temperature, high performance

structural materials. Structural ceramics, and more recently, ceramic

matrix composites, have received particular attention for these

applications due to their high strength, and corrosion and thermal shock

resistance. Even with these positive attributes, improved reliability and

extended lifetime under service conditions are necessary for structural

ceramics to gain industrial acceptance. The problems with these materials

are mechanical and chemical in nature and are enhanced by the fact that

they are subjected to high temperatures, reactive environments and extreme

thermal gradients

.

With an objective of improved performance for heat engine/heat

recovery applications, the NBS program on structural ceramics and ceramic

composites addresses these problems through the determination of the

critical factors which influence mechanical and microstructural behavior.

The activities of the program are grouped under two major subtasks, each

designed to develop key data, associated test methods and companion

predictive models. The status of the subtasks are detailed in the

following sections.

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DISCUSSION OF CURRENT ACTIVITIES

SUBTASK A: INTERFACIAL AND MICROSTRUCTURAL COMPOSITE PROPERTIES

1.1 Measurement of Fiber/Matrix Interfacial Forces

Instrumented Indenter Testing

Introduction

A method based on the indentation technique of Marshall [1] has been

developed to characterize the mechanical behavior of the fiber/matrix

interface under applied shear loads. On a polished cross section of the

specimen, a force is applied to a fiber parallel to the fiber axis,

resulting in a displacement of the fiber relative to the matrix surface.

To determine the resistance to shear displacement along the fiber/matrix

interface it is necessary to know the force applied to the fiber, the

relative displacement between fiber and matrix, and the area of interface

over which the displacement occurs. A Vickers hardness indenter

instrumented to measure the load applied to the specimen and the

displacement of the tip of the diamond indenter is employed to apply the

force to the fiber. The resulting load- displacement curves can then be

used in conjunction with appropriate mechanics analyses to characterize the

behavior of the interface.

Modelling

The experimentally obtained curves of applied load versus the

displacement of the diamond indenter must first be corrected to give the

desired force -displacement curves. During the initial portion of the

loading curve the tip of the diamond penetrates the surface of the fiber

while simultaneously the fiber begins to slip down into the matrix. To

determine the displacement of the fiber surface relative to the surrounding

matrix, (u) , that part, (a), of the total displacement (5) due to the

penetration of the indenter into the fiber must be subtracted, i.e. u=5-a.

Assuming that the hardness of the fiber is constant, independent of load or depth of penetration, this correction can be calculated from the definition

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of hardness, the geometry of the indenter, the fiber hardness (Hf), and the

applied load (P) . With hardness defined as Hf =2P/d^ , where d is the

diagonal length of the indentation in the fiber surface , the geometry of

the indentation yields:

a = (F/2Hf)^/ 2/Tan $ (1)

where a is the depth of the indentation relative to the fiber surface, F

the force applied to the fiber, and $ the half- angle of the Vickers

indenter (74°). Initially all of the applied load acts on the fiber,

ie. F = P. Later in the loading process as the fiber slips down into the

matrix the edges of the indenter begin to penetrate the surrounding matrix.

This begins when d = 2R or at a total displacement (5) of;

8 = R/Tan # (2)

A portion of the load is now carried directly by the matrix and this must

be subtracted from the measured load to obtain the force on the fiber.

The calculation of r when the fiber slippage occurs through the entire

thickness of the sample is relatively straightforward if it is assumed that

the applied shear stress is constant along the interface (i.e. ignoring the

stress concentration near the free surface). When r is constant, a simple

force balance yields

r = F / 27t R t (3)

where t is the thickness of the specimen. In this case the applied load

should be independent of displacement for 8 less than given by Eq. 2.

The calculation is more complicated when the sample thickness (t) is

larger than the length of fiber over which slippage occurs (1)

.

Marshall [1] has presented an approximate analysis for the case of t»l

.

The following description of the expected force -displacement relationship

is based on this analysis. Stress concentrations and Poisson's ratio

effects are ignored, and r is assumed to be constant, independent of

position and slippage distance. During loading the displacement of the

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fiber end involves slippage of the fiber relative to the matrix and a compression of the fiber over the length 1. The value of r can be obtained

from the slope of a plot of versus u:

=

4j? I? E

[1 - ^B(R/1)^]^

ru —

27rB(r/E^)

-{l - (4)

where Ef is the Young's modulus of the fiber and B a constant (~1) [1].

The terms in square brackets arise from consideration of the axial

compressive stress in the fiber at 1, the end of the sliding area. They

become negligible when the length over which slippage is occurring is much

greater than the fiber radius (1»R). This criterion is satisfied for

u » 37rBRr/Ef . On unloading, the fiber extends back towards the surface to relieve

the axial compressive stresses until, with F=0, these are balanced by the

interfacial shear tractions. During unloading r can be evaluated from the

slope of a plot of (AF)^ versus Au, where AF is the difference between the

maximum applied force and the current level of applied force and Au is

similarly the difference between the displacement at maximum load and the

current displacement:

(AF)2 = STT^R^EfTAu (5)

where the terms corresponding to those in the square brackets in Eq. 4 have

been omitted. Note that the slope given by Eq. 5 is twice that given by

Eq. 4. The slippage which occurs on unloading is therefore half that which

occurred during loading, so that when the fiber has been completely

unloaded the residual displacement of the fiber below the matrix surface

should be one -half of the displacement at maximum load.

Results and Discussion

A plot of F^ versus u is shown in Fig. 1 for a Nicalon SiC fiber in a glass ceramic (LAS III) matrix^. As described in Eq. 4 the slope of this

^United Technologies Research Center, East Hartford, CT.

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Force

Squared

(N‘2)

Fiber Displacement (urn)

Figure 1. Plot of the square of the force applied to a fiber versus the

displacement of the end of the fiber relative to the matrix surface

during an instrumented indenter test. The fiber diameter is 17.0pra.
ra

rj ' ' -

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curve is proportional to r over the range of u where the conditions l»r

and d < 2R are satisfied. The curve is nearly linear over the range 0.25//m < u < 1,25/zm, with a slope of 3.41 x 10^ N^/m. The fiber radius, R, is

8 . 5/im and the modulus, Ef , 200 GPa. From Eq. 4 (ignoring the terms in

square brackets) r is given as 7.0 MPa, in good agreement with other

measurements of r in this system. At large u the non-linearity can be

attributed to the indenter making contact with the surrounding matrix. The

curve also shows a change in slope at small u, shown more clearly at a larger scale in Fig. 2. The bracketed terms in Eq. 4 become important at

small u and would lead to an increase in the slope for a given constant r, as observed. It is not possible at this time to quantitatively compare the

projections of Eq. 4 with the detailed behavior at small u due to the

experimental uncertainties at such small displacements.

Other considerations would also tend to increase the force required to

cause the initial displacement of the fiber. If it is assumed that an area

of interface must first debond before sliding, this debonding region would

move from the surface down the interface into the bulk as loading

continued, leaving behind a growing area of frictional contact. Thus the

measured r could be viewed as the average of a constant small area of

relatively high effective r and a growing area of low r . Details of the

stress distribution at the interface near the free surface become important

when the assumptions of constant applied shear load along the interface and

constant r are relaxed. More sophisticated modelling and more precise

experimental results are necessary before the behavior in this region near

the initiation of fiber slippage is understood.

1.2 Characterization of Matrix Crack - Fiber Interactions

DCDC Fracture Specimens^

Introduction

A critical issue in the fracture behavior and mechanical performance

of ceramic matrix composites is the influence of the strength of the

^The processing aspects of this work were conducted with support from

the SDIO/IST program under ONR contract #N00014- 86 -F-0096

.

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Squared

(N“2)

Fiber Displacement (urn)

Figure 2. An expanded view of the low load, small displacement portion

of the curve shown in Fig. 4 emphasizing the non-linearity of the

behavior in this region.
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fiber/matrix interface on the interaction of a crack with individual

fibers. It is generally accepted that if a strong bond is present between

fiber and matrix, transverse cracks run directly through the reinforcing

fibers, which then have little effect on retarding propagation of the

crack. Although the strength of such a composite may be enhanced through

load transfer, the toughness is not appreciably improved and failure is

completely brittle. A weak interface leads to crack deflection, debonding

along the fiber/matrix interface and bridging of the crack by the fibers.

If the fibers do not break behind the crack tip, failure is noncatastrophic . However, if the interface is too weak, the fibers slide

freely through the matrix, and no improvement in strength or toughness is

obtained. Thus, a better understanding of the details of this behavior is

required before the optimum levels of interfacial strength can be

determined for a given fiber -matrix system.

This issue can be investigated experimentally by direct observation of

the interaction of a crack with a single fiber in an appropriate fracture

mechanics specimen. The double cleavage drilled compression (DCDC)

configuration [2] was employed because of the simple shape and loading

geometry. No guiding side grooves are required to keep the plane of the

crack in the center of this compress ively loaded specimen.

Stable crack propagation is obtained in the DCDC specimen since the

applied stress intensity (K^pp) experienced at the crack tip decreases with

crack extension at a constant load. From the measured crack length (c) at

a given remotely applied compressive stress (<7app), K^pp can be calculated

from an expression of the following form [2]

Kapp = ^app A / [(c/r) /(c/r)] (6)

where the specimen dimensions are as defined in Fig. 3. The function

/(c/r) can be determined experimentally by testing specimens of known • Fracture mechanics analyses of this specimen have been performed [2-4] and

yield good agreement with the experimental results

.

6
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Figure 3

.

specimen.

Double -cleavage drilled- compression fracture mechanics

Compressive load opens cracks above and below centered hole.
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Experimental Procedure

Transparent specimens were produced by sandwiching SiC fiber^ between

borosilicate glass plates^ which were then fused together by heating in air

at approximately 850®C for 10-15 min. to produce transparent specimens.

The samples were loaded in compression with a screw- driven mechanical

testing machine^ at a crosshead displacement rate of 0.005 cm/min. The

strain contours visible in cross -polarized illumination were used to

monitor the length of the growing crack and to characterize the crack- fiber

interactions

.

Stress wave fractography [5] was utilized to monitor the shape of the

crack front and the relative velocity of the growing crack along the

specimen. Acoustic waves were propagated through the specimen during crack

extension by use of a ceramic piezoelectric transducer coupled to the

specimen. The transducer was driven with bursts of an 80-90 KHz sine wave

at a maximum of 30 V peak to peak. The burst frequency was 5 Hz; the burst

duration was 25% of the low frequency period. This technique produces

ripples on the fracture surface at a spacing determined by the frequency of

the acoustic excitation. These ripples can then be observed by optical

microscopy in reflected light using Nomarsky contrast. With a constant

excitation frequency, widely spaced bands indicate a region of rapid crack

extension while closely spaced bands indicate relatively slow crack growth.

Results and Discussion

Direct, qualitative observations of several aspects of the fracture

behavior in the specimen could be made in transmitted, cross -polarised

illumination at various magnifications. Typically the fiber could be seen

to bridge the crack for some distance behind the crack tip before breaking.

Evidence of localized strain at the fiber- crack surface intersection (Fig.

4) indicated that the bridging fiber was applying tractions across the

^SCS-6 SiC Fibers, Avco Corp. , Wilmington, MA.

^Corning 7740, Corning Glass works. Corning, NY.

^Instron Corp., Canton, MA.

7
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Figure 4. View perpendicular to fiber axes of DCDC specimen under load.

The cracks are seen edge -on with the crack tips located between the inner

and outer fibers. Strain contours are visible by virtue of the

transmitted cross-polarized illumination.
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crack faces. The shape of the strain contours ahead of the crack tip or behind the crack tip away from the crack surfaces gave only occasional

faint indications of localized strain which would show load transfer to the

fiber. Apparent delamination of the fiber ahead of the crack (Fig. 5) was

observed when a higher magnification was used for one specimen.

An optical micrograph of a region of the fracture surface which

includes a fiber, taken with Nomarsky contrast, is shown in Fig. 6. The

light and dark bands visible under these conditions represent "snapshots"

of the position and shape of the crack front at periodic intervals. It can

be seen that the crack front bowed around the fiber which was bridging the

crack before the center portion broke away and accelerated to reform a nearly straight front. A scanning electron micrograph of this area

(Fig. 7) shows that after bowing around the fiber the two sides of the

crack did not meet on the same plane. The resulting ligament would have to

have fractured before the center portion of the crack front could extend.

From the direct observations discussed above, the fiber appears to have

broken at some later time, after the ligament had fractured and the crack

front had moved well beyond the fiber. The chipping apparent around the

fiber in Fig. 7 would have occurred as the broken fiber was pulled out of

the glass matrix.

To quantitatively assess the influence of the fibers on the crack

propagation, the crack length was measured from photographs, such as shown

in Fig. 4, and used to calculate the apparent K^pp from the applied load

using Eq. 6. The results for several specimens are shown in Fig. 8.

Assuming that the crack is growing at a constant stress intensity,

K^ip = Kj0 for the glass matrix, the increase in the calculated K^pp for

crack lengths beyond the fiber position reflects the closure tractions

exerted by the bridging fiber (K^rac)-

Ktip = Kic = K,pp + (7) or Ktrac = Kic - K^pp (8)

The stress intensity factor due to a point force acting at a distance 5 behind the crack tip is given by [6]

8
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Figure 5. Higher magnification views in cross-polarized transmitted

light of region near reinforcing fiber. Crack- tip is seen approaching

and then passing the fiber as the remotely applied load is increased. Field of view is approximately 2.7mm wide.
^ • i

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Figure 6 . Optical micrograph of a region of the fracture surface

centered about a reinforcing fiber. Nomarsky contrast reveals the

periodic surface undulations caused by the applied acoustic waves,

crack was propagating from right to left. The field of view is

approximately 1mm wide.

i

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Figure 7. Scanning electron micrograph of area shown in Fig. 6. The

remnant of the ligament formed as the crack front swept around the fiber

can be seen to the left of the fiber. (Field of view approximately 1.1mm

wide .

)
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Crack Length (C/fl)

Figure 8. Plot of remotely applied K (calculated from Eq, 6) versus

crack length showing relative position of the reinforcing fiber.

Increase in the applied K required to propagate the crack reflects the

closure forces exerted by the bridging fiber.

= -72 F / (»r S)^'^ (9)

where the point force, F, may be a function of S. Thus, information

regarding the forces exerted by the bridging fiber as a function of crack

length can be obtained from data such as shown in Fig. 8.

Summary

Sample fabrication methods and experimental techniques have been

developed which allow crack- fiber interactions to be directly examined in a ceramic matrix. Qualitative information regarding fiber/matrix debonding,

fiber bridging, and pinning and bowing of the crack front at the fiber can

be obtained. Possibilities for quantifying the effects of bridging fibers

on crack extension in terms of the tractions exerted across the crack by

the fiber were demonstrated.

SUBTASK B: DAMAGE MODES AND FAILURE MECHANISMS

1.4. Elucidation of Damage Modes and Failure Mechanisms

Silicon Carbide Whisker Reinforced Alumina

The fracture toughness behavior of a silicon carbide whisker

reinforced altimina ceramic has been characterized as a function of

porosity. The alumina was hot pressed with 25 weight percent silicon

carbide whiskers to form composite materials whose porosity ranged

nominally from 1 to 11 percent. Controlled flaws of increasing size were

produced on polished surfaces of specimens by Vickers indentation loading

from 2 to 200 N. The flexure strength measured as a function of

indentation load indicates that the resistance to fracture of these

materials increases as a function of crack extension. Results are

analyzable in terms of fracture models containing ligamentary tractions in

the wake of the crack.

9
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a. Experimental Procedure

Four billets of a silicon carbide whisker reinforced alumina ceramic,

whose respective porosities ranged nominally from 1 to 11 percent, were

provided for this investigation through the courtesy of J . F. Rhodes of

ARGO Chemical Company [7,8]. A fine-grained alumina powder was hot pressed

with 25 weight percent silicon carbide whiskers, 0.45 to 0.65 /xm in

diameter and 10 to 80 /xm in length [9]

,

to form billets of the composite

material: 3 billets at 150 mm x 150 mm x 12 mm and a billet (nominally 1 percent porosity) at 100 mm diam x 15 mm. The silicon and carbon sources

were rice hull ash and rice hull hydrocarbons, respectively [9].

Samples were diamond- sawed from the billets to fabricate flexure

specimens, nominally 3 mm x 4 mm x 50 mm, with the prospective tensile

surface, 4 mm x 50 mm, normal to the hot-press direction. The sides of the

specimens were diamond- grounded flat and parallel within 30 /im. The

prospective tensile surfaces of the flexure specimens were polished with

9 /im diamond paste. The specimens were soaked and rinsed in ethyl alcohol

and dried in a hot air flow.

The porosity, p, of a flexure specimen was calculated by

p = 1 - Pb/Pt ( 10 )

where pj, and p^ are the bulk and theoretical densities, respectively. The

bulk density, pj, , was determined from the mass and bulk dimensions of the

specimen. The theoretical density, p^, = 3.762 g/cm^ , was calculated from

I/Z’t = + ^i/Pi (11)

where w^ is the weight fraction and p^ is the X-ray density of the ith

component: pj^ = 3.987 g/cm^ for AI2 O3 and P2 = 3.217 g/cm^ for SiC.

A flaw of variable size, controlled by Vickers indentation loading

between 2 N and 200 N, was placed in the center of the prospective tensile

surface of several of the flexure specimens . Care was taken to orient one set of the radial cracks of an indentation flaw in the direction of

prospective rupture . The indentations were made in air at room temperature

with a steady loading rate that required 15 s to produce a full load. The

10
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%Ti-'SL«iVf a3*aiid*l oi pallid *rf3 *u>ii bawa • tflo&aib eivw aolqsaS ^

aXiaao:? »vt'tt>“%qpaoiq ad5 d3lw ,«* 02 Jt Mr A ji nr f ylianinwi

arf^ Vv aabla afO? .oolj^aiii, jr.U iasrron ,ba Of x a» » .•oaVitiJa

arfT -«U 0£^fTid3J'4 Jai lajaq brja j»11 bfjbrurcni-bno*»lb •^aw a/ia«^&afB

rf:?iw badalloq aiiav •itmCl^aqr ad3 Jo mosmJxm oSlvt^

lodojia i^dJa ni beaitl? brri; r*iJ34aoc ajat# «{Taiil?aq« adT .a3trq C:no«a*lb lOH ^

^ .voi^ jia 3o4 » fll bai:di^b/i»

\d b^ibUnlAO o#'v rp.tjyoqt wis/XslJ u io »q ^TJiooioq arfT

(01)

..'! ,.

; t- • »dT .xiort^o^^^oi U. ft J^’ron bna a'tird aiii #*i» ,V baa 4^ aiU Vo ftitoimaotalk aAl9d^ t>n& A»*r aiO wotJ bo/tisn*i%b aar-ViA .yt-^lamib >i^

BoiV ba3Jili/i>i»^ ,VAl <* • .t^laaab ia:Uaio«i3 arfT fnm.ts^qo

I

(U) i^\x^ i' iV4 It

d3l adJ Vo y^la/fab xA3-X •.!: beta tsolJamiV orU b1

,ai^ “loV *ito\s ’-i-t • i<\ ‘‘via jOjiA io5 ^si:>\s S8«*C ^ . JiMiopnoaiP- ^ ^filtactl ^d balloTJrroa .asla aldaii-v wa^ 1 A ?A| ?

aIitrto3 avIjDaqaoiq aife 3'> ad3 cf1 ba^jslq aaw ,W OOS brta H 2 nar^adi.

•tno dnalto cu /laiaS a**r axaO *r»a«l:wuqe aiwralV anfc Jo Iotvom Id ^

i<) aoi:? 3 aiib Oda ni n qoija^otbfrl no Jo a^faaiQ lalbai aiMLlo ^^ar J

^au/rTii©q«a3 aobi So Tia nl *aiy fi*w aool3a3nabfli »dT ,aTii3qm tTUaaqtOTq

offT t*aof IJt»V A amiboiq ©J • Jt 3ad3 a3x7 ^olbaoi '^aoso • /tl
diamond pyramid contacted the specimen surface for about 30 s before it was

withdrawn to complete the load cycle. The lengths of surface cracks were

measured by optical microscopy, using a calibrated scale accurate within

2 /xm.

Strength tests were conducted on specimens under 4-point flexure in

dry nitrogen at room temperature. The gear-driven crosshead of a universal

testing machine was operated at a constant load-point displacement speed of

5 mm/min, producing a loading rate of 145 N/s on the material, until the

applied load attained its maximum value, F, required to rupture the

specimen. The load was transmitted to the specimen through 6 mm diameter

rollers . Loading was measured by a linear load transducer and was recorded

on a constant speed chart. The load transducer was calibrated at the full

scale of the chart with a known 10 kg mass, which was converted to force

units by the local acceleration of gravity, 9.801 m/s^ . The flexure

strength, S, was calculated from

S = 3(ii-i2)F/2BW2 (12)

in which the loading spans were = 40 mm and J^2 = 10 mm and in which the

nominal dimensions of the specimen were B = 4 mm and W = 3 mm. Following

rupture of a specimen, it was examined by optical microscopy to confirm

whether or not the fractured surface passed through a radial crack of the

indentation flaw.

b . Data Analysis

According to the energy principle, incremental crack extension, dc,

can occur when the applied stress -intensity factor, K, is equal to or greater than the crack- extension resistance of the material, Kj^ . The

criterion for the onset of crack- extension instability, leading finally to

failure, is the point of tangency,

dK/dc = dK^/dc (13)

An equilibrium position will be attained at K = Kj^ , if dK/dc < dKj^/dc.

11
* snUu ,xT>^^oi5l» io^i^qo yd be^u8l- .«r

ni fi»ni^)£tl? Zfnib^ ao b®30A/bno-. r :^®w ada«o fbg;i»i:Jt

A 2t^ 6w»-'ieBoio a/TT *xu3»!r*q«*0:^ aoox 3b X'®,;

*Ht3 liJ^W .iAlXA30iT ®tf3 »to e\» lo A3AT sfftbBOl • ^rtlaiiboxq .ai«\fw e

<>3 3 ,i*oXAV A3l bwxiAJi® bAoI bAiiqq®

j.»3s«ai.b flww ^ ilj^u»3ff3 fr«Slr>®q* odi o? ebw baol ArtT ,n®«^o*q«

&®bzo3Ax^%Av br* xoaiibarjixd bBoX jaanlX yd b»xjie»#« jjiahAoJ .A^i-Xox

Hi'l « 3A b#3Btc;il »3 AJiiV x*»3oba4iaa3 baoX *iiT .:?7Bdo bABq*. iaa3%.'i<'3 m OQ

fc-y-zo^ 01 b»3Ts^n«ki> rfotifv «BA« 01 nvoccX a Hliv 3X4da add ai«o«

a^tmalX orif ‘t\as 10S.<? lo n*jl?»ioX«z>A laaol ®Ki yd all.-ui

•^l!l i^dJaXtt^iaD «

t

•ill dodffw iiJ t>06 aa 01 « boa |a«i A «*»•<?* yilbaoX md$ ni

nn!vi»oXioT OB C * W bn* * *? a'liw .TdAl^oqa sdJ 5o tfrolenaaib iAXilaiob

aailnod o3 yqooaaxal# itoldqo yd bajnpiiojm® tav ai .aaoiioaqa a 5o axi/dqui

io 03 iivupa ai ,xoi 9* i '^janaiai-iaaida bailqqA oii3 oadw Ti;bo»- f»3

OflT , pi .XaXtpi*® «d3 ’t* ajij^ialtax iToimii»l)tO-iiSBXo *^d5 ctAds isaAox^

Id l»^A‘^rt#®a€>AXqtt|b .inloq-baoX JaaJOJioa a| 3a baiaxaqo »>av anliteatf fn^iaaai

•lii lo ^eoATO lalbai a -loai^aq »3J i lut baxiiiaiai^ arb don to loddadw.

.wAiy ^To^^a1asb^l

lUyi^nA tt^A ^

lA?nat 3 lorti aXqiOfiilq ygia^^a *d3 03 jniMoaaA*

%

,Db .ffoXairalxa aio*

ylXftal^ yilbaal .yiilidajtni noJtnaixa-jloBXo ^6 latJ^o adi lol uoX^ailxa
When a sufficient load, P, is applied to a sharp indenter in contact

with a material and the indenter is then unloaded, semi-circular radial

cracks, Cj , will develop in the material [10], The driving force of the

crack system may be characterized by a residual stress -intensity factor.

where x is a constant dependent on the material and indenter geometry.

When a freshly- indented material is subjected to a small bending

stress, a, a bending stress -intensity factor, Kj, , will be superposed upon

Kj. . The crack system will grow as long as (K^. + Kj, ) 2: Kj^ . The bending

stress -intensity factor may be expressed as

where Y is a configuration coefficient which is dependent on specimen and

flaw geometry. Catastrophic failure ensues when the criterion of Eq. (13)

is satisfied. This condition occurs when a = S.

To facilitate analysis of the data, a parametric representation of the

fracture resistance as a power- law function in crack extension is used

where and c^ are constants, and r“ ^ is a constant which measures the

susceptibility to R-curve behavior (i.e,, the susceptibility for a rising

fracture resistance with crack extension). When r“ ^ = 0, Eq. (16) gives

completely brittle behavior with = Kj,- . Using Eq. (16), a solution

of the fracture mechanics equations gives [11]

Kj. = xPc'3/2 ( 14 )

Kb = Y(TC^/2 (15)

(16)

S = CP'^ (17)

in which the R-curve susceptibility is given by

r"i = (1 - 3b)/(2+2b) (18)

12
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.fl

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|

C#l>

»\«-=’* - ^

y-r'!».*o»3 f>3.t*brt; brt# ItlTlMv »i'J no aroJxJoqo^ 3n*3«ji09 • »1 -

'

liotJ » o b^3uobfl*-X-I<<»o^ ‘ ,

noot. b*«oqi.v» H ili* « •^' •»;.»•'«

jn:t:!»<i oriT s (<!* * P''> •* *TM- *• ''*** ***"<^* io»i» «rr . ^

aa b#«*aiqx» t**

tei)

OTit * ^

•tfa'

ta. noala*^* no 5i.*bn»q.l) 3B.i»pooa noiJkV^llnoo . .1 T .^»rf» -U

<Cl) p3 aadir aaO«n» *:

j 3 » t> #f%rfv aiuu^dO cioi^lbfioo iliH

»T& nol3*3A#i^3q^»=t aiT5*tm7iq B ,»JBh •ftr 5i» U-XB «t ’;;^3

^ el Jloal^ Ai noliamll ^TirfsAti

aiu

(sn

« i

*K3 e^oiiwe d^ldw SABimnoG m *1 ^‘1 IWB #3b ta^

ftiilali *» 70^ v^Uldlaq.:^B #H5 . .P ^tkvKd^ o5

ae^vlg <dn ?3 .0 - ^‘*1 irtidW (nu:af*<i3*B alGGio afaiv

.,0131.100 - .(»t) ,nt.O .„!f - ^ rtalv «*vo.l.d

(Xlj «iiold4W/p* #j1a* iri3f9ABi? '#11^

'!* ' * 2 i :U)

rd^ t3lildi3q*!>*i>% %irsi/:»-.<5 erl^ dolrihr

I

(dS4S)\(d£ - I> i --

St
and the coefficient of crack- extension resistance is given by

= YC(Ab)’’= (1 + b)^ ^ ( 19 )

When Kj. = Kj^ , the coefficient A is defined in terms of the initial

indentation flaw size, Cj , as

( 20 )

c . Experimental Results

Thus far only two of the four billets of the whisker- reinforced

alumina ceramic have been characterized. Table 1 gives the mean porosity,

p, and the standard deviation of the mean from measurements on 24 flexure

specimens from each of the two billets. In general, specimens from the

edges of the billets tended to be slightly less porous.

Figure 9 shows the bending strength as a function of indentation load

for the selected porosities of the material. A straight line, the

logarithm of Eq. (17), was fitted by a method of least squares to evaluate

the coefficients b and C for each porosity. Table 1 gives these values and

their standard deviations. Only those indentation loads which correspond

to the fractured surface having passed through a radial crack of an

indentation flaw are considered valid points for the fit. The open circles

which are arbitrarily plotted at logio(l*) = ^ correspond to strengths of

non- indented specimens. A plateau of strength which is invariant with

indentation load exists over a region of small indentation flaws for each

porosity, but the range of this plateau decreases with decreasing porosity

of the material. An estimate of effective size of intrinsic flaws of a selected porosity could be made by the intersection of a plateau line with

the straight line of the least- squares -fit. The dashed line describes a slope of -1/3, which would indicate a fracture toughness invariant with

crack size, as would be expected in the region of large crack size.

Figure 10 shows the half-length of surface crack as a function of

indentation load for the selected porosities of the material. The dashed

line is a least- squares -fit to the observed data. In principle an

alternate value of b could be deduced from the slope of this fit, (l+b)/2.

13
fi. id n»v»g t! nolan»S«»-da*'« lo »rfJ 6^ .

(9f>

IM r) **' <iA>:>v *

* '\rrf *•

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8A • r- Villi nolii *ri*hal

(Ot)

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JjLiosMiiagr.

i.Wtoi«J.3-7*3t.ld«%.a3 50 i3.IUd 3005 .ria ovd ylno i»4 »c^I

.VJjtoioq «**• .d3 MViJ. ‘ .bs;n»3o»3.rto fr».d ovod oliL«30a o-tiaul*

o3U«»i5 no ».}ttmmnvi^en «oil oaM nol3»)v»b 53aba*J« *n o«* .

oria «035 »n.«iUq. ,U«*n»S «o3 odd 5o da.* -oal

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liool /toio*7a.ba* 1« c«?; -«oi . .• d38»'f '’^ *<t3 «'»«*• • •tustlM ' «l

flda ..nlJ driai*«‘ * i.l3«3** •d- io o»lJJ.030<, b.Jo.U. *<t» 3ol

03«/J.v« od tM.opa d«*i ^

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ta,oq..Tro> .b.oI noii.ar«^.l ^oda ^clnO ~.ol3.tv*b ti.r,i»3. Jl.dd

u io ^ 3.30 lAlb.3 • ifc'Jos'Jd b»«t.q snmri »3b53«» b»»-3o.3l *<t» o3

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So .*f3»o.3d. 03 booqwrK.!. 0 - C^:-o>aal -* b.ddolq »" .'1’^^'^

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ffl ^ ^ - A. ^ do., tol .V.11 ot.ld.do.bnt II.O. in Ootg« . dovo .d.to. bool ooi-.3n.bnl

^dl.oioq 3nle..do.b ddlv n.od.Iq .Idd 1« sgo.3 odd di-d .<dt q

. lo a*.il Olwilddol lo .*t. 0v;-)o.ll. So .rwold.* n* Uli.d«. odd lo

ddlV^«Ttl . In no'3>...o3nt «ld X- *b«. .d tlooo Xdl..3 oq b.d0.1 ..

. ..di30..b .nil —ii.1* -t)l e.3..<p.-3»‘«i dd8t.T3.,-dd

dJtv do.mvni i.wwtaon* «3i«o»*l » .d.olbni bluow doldw ,tSJ* 1« »qn^»

.sla do.30 M3“i »“ "'ib” ''•* ” '•“*

Jo ooidonoi . .. do.30 .0.130, So d38n.J-M~l .d3 .wod. 01 '

ai- m ma^ W — ^ -r — - bmjt»^ .dT .UK.J.- odd Ic. .»m.03 oq b«»o.I.. .rtd tol b.oJ oold.dOjbol

n. -iqiontdq ot ..Aob b.^..do •« od tlS-..3.op.-d«.J • .1 *"11

I >+l) ,JJl .Irfd to oqol*..dd »nl boaubab ad blooo d lo •‘•l^’ o3.ura.3lO
Table 1. Values of parameters that define crack- extension resistance, K^, , of a 25 wt percent silicon carbide whisker reinforced alumina ceramic at

various porosities. The uncertainty for each value is its standard

deviation.

Parameter® Billet 1 Billet 3

A. Porosity

p , percent 11.48 + 0.16 4.89 + 0.14

Number of measurements 24 24

Indentation Crack Length

logio (A) 8 . 0447 + 0.0243 8.1645 + 0.0212

X = Kg /Ac„

^ 0.095 0.088

Number of measurements 6 6

Bendinz Strength of Indented Beams

b 0.2759 + 0.0148 0.2657 + 0.0093

2.8808 + 0.0265 2.9258 + 0.0149

Number of measurements 13 18

Student's t,

90 percent confidence band 1.363 1.337

Crack- Extension Resistance

r 14.8 ± 4.0 12.5 + 1.8

Kg in MPa'm^'^^ 4.12 + 0.46 4.24 + 0.37

a Calculations correspond to P in N, C in M, S in MPa and = 1/im
^,”S , -jjr.aJt la»l •Oil##'

":fL a r>»076^Al«l

f fj' ./ #wl»v Hit# 10^ x^

II El” tIS

U hi
log

(S)

log

(S)

P,N

log (P)

Figure 9. Bending strength, S, as a function of indentation load, P, for

silicon carbide whisker reinforced alumina ceramics at selected

porosities. The solid line is a least- squares -fit, and the dashed line

describes a slope of -1/3.
f’

OS or 3

ooor

ooe

00^ 000

oos

oer

oos 00 f oa

T

ijru— T

XX^9oyoq 9nmi>\9q d.t t ( 0)

0001

ooa U

00%

I

ooc

M

ooa

par

,k:- i II.

e

"T

^ » vri#Ot^q (a)

o.e

i

'

c\> a.s

o e

*

„

i ®

J a.o

^

I «3

Inebni 0#iufqtiH #

beiulQua O

OS

<s) oo»

H r*c U»3n*-SnJ TOia;«n.l t M ,» ioXbn^ .« 'lO

b »,'•• 3» «oJ - >*0 ^.-li -Jir aao(»lAi ablSia-i rooHia

U b„. . . .i ..li bU«.^^

HI • »: I
log

(c.)

'09

Figure 10. Half-length of surface crack, Cj , as a function of

indentation load, P , for silicon carbide whisker reinforced alumina

ceramics at selected porosities. The dashed line is a least- squares - fit

,

and the slope of the solid line is derived from the strength

measurements

.

lurl
00 s 00 .

• oe

C^J OO*

In aoljou.^ • »4 . jO .is.T5 .o«^tu« io iUsn.i-^»h OJ

Mnlmtlt b»-jioiiUfi laJelrf* *«>ldit3 noallU ao* ,1 .6»oi

3 li-i8aiwa- 3 E0»i E a> ontl t.aria«J> •(« .o*l31«*ioq b.aaala* J*

^ rf,8n,«a ..* i»3i Mvlaab .1 ~.li bllot .rfa 1»«
However, evaluation of b from Eq. (17) is preferred because the variance of

(l+b)/2 would have to be 0.25 of the variance of b from the slope of the

strength data to provide the same variance of r. The solid lines in Fig.

10 describe the slope (l+b)/2 at the respective porosities of the material

where b was deduced from the strength data. Clearly, there is a bias in

the small crack region of indentation loads due to the failure to observe

the complete crack length by optical microscopy. Thus, the coefficient A

was evaluated as the mean logarithm of Eq. (20), using b from the strength

data and the Cj only from the large crack region of indentation loads

.

Table 1 gives these values of A.

Since Eq. (17) is believed to provide a reasonable fit to the observed

strength data, the supposition of Eq. (16) is confirmed as a reasonable

representation of the crack- extension resistance of the materials at

selected porosities. Table 1 gives the values of r and deduced from

Eqs. (18) and (19), respectively, using Y = 1.174 [11]. Figure 11 shows

crack- extension resistance, Kj^ , as the function of Eq. (16). The shaded

regions describe the range of critical stress -intensity factors that

correspond to the onset of instability of crack extension deduced from the

analysis for the two materials of selected porosities.

Analysis of the random errors in the strength measurements will

elucidate whether or not the Kj^ curves themselves , appearing to increase

with crack- extension, and the apparent difference in the Kj^ curves of the

two materials are significant. Table 1 gives the standard deviations of b

and log(C) for N measurements, following the statistical analysis of a straight line [12]. The standard deviations of r, , and Kj^ were

estimated by the law of propagation of errors. According to the principle

of least squares applied to the logarithm of Eq. (17),

Log(C) = <log(S)> + b-<log(P)> (21)

where <log(S)> = 2 log(S^)/N and P is assumed not subject to error. The

variables <log(S)> and b can be shown to be statistically independent [12], a necessary requirement for the validity of the law of propagation of

errors. When Eqs. (18) through (21) are substituted in the logarithm of

14
pj ( ]

, p3 8K>!X3t ^

30 0 9t« 03 tv ' Z I

•>ini. <* ?'?'t shJ'/o'jq 03 i- 1

;

.Afiu^ol rr<

bfam9%do erij o3

9 A •rf"' P0T3 ^ ** '* avods IJ -im -"I.i ^ -

bofcftd* »--r .(^0 P?.

'

lArfJ *303001 ^3l*n*3sil-»eal3» ^

erl3 »h>33 booubsb nol*o*JiEC> ioA^&o lo <3J

ilJtw eiuMJ93t?«AO« i -j '

d*AOT:»ni 03 arinoaqqa .

orfdi lo e«\nijo jX orb rl a >

d lo xaoX^AtVBb b'iaJ)fia3* 9ttS I ol*^**!

B 5o *l*^U.rr» lAol3*l3ft3ft »lfi

»3«y nX baa . Ji •! H biM :

!i 5 6fl* " \> d’* ‘ rfcjcla orf3

fi34.-b d3^<lo53t «•

'

t*i»c: ^ ,;o: 3i.3noonj to

-,‘tn ipiJjqo Y<i AdhtOi 93m

rarl3l3*]|oi naMt , \i f-% ta

*il3 BOl^ ' A !o ••oil«V »or^

; tHmd *l -r? ^

’ !

.*

. aoqqy* sd3

'

». ; .fi-. .'*'- ''*'7- • ri2 to nciOi

.,.- . : i -iHsT

•:»:•'!« I*"*

97q»1t^

‘ lioioq .

. bail {il ,, . bp8 c

. .' ; r.iTOOJC*

• *

L ;3

' '

1

!'

s.i ‘.*;j* -

..:>cs -if:'

.tii :._

j (b-*

-*7 s’ a

s \ " .’^1 bam

Cii *nil 3fi5 X 633» '

•l({2oal3q •iJ3 o3 |(iltrx»9eA ,W(»W», 'S*(ij

,(V1) .11 1*

•.'i'j* J Vftj arfJ »•

t 0

«f> c «-(o)^oi> *

-:(2';:4oi> e*l

t\? f «vs

'.? 3r:5tns7ii.*r*'* i^aae*#

(Sr*
Eq. (17), the standard deviation of log(Kj^), reflecting only random errors

in S , may be calculated as the square root of

var[log(Ka)

]

'aiog(KR)

2

var [<log(S)>] +

'aiog(KR)'

_a<iog(s)> 5b

var(b) ( 22 )

Table 1 gives the standard deviations of r and , and Figure 11 shows the

90 percent confidence intervals for the materials, being approximately ± 4

and ± 3.4 percent over the range of measurements at the selected

porosities, 11.5 and 4.9 percent, respectively.

15
•rij twud*

U *** ^ •*¥’ ± yj«i3*Aijeo^i|C*t» ^dS
MPa

CM

E

Figure 11. Crack- extension resistance, Kj^ , of silicon carbide whisker

reinforced alumina ceramics at selected porosities compared to that of an

alumina ceramic

.

J K»mNB$-114A (REV. 11-84)

I

• 1

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U.S. OEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions^

1. PUBLICATION OR

REPORT NO.

NBSIR 87-3564

2. Performing Organ. Report No. 3. Publication Date JUNE 1987

4. TITLE AND SUBTITLE

STRUCTURAL RELIABILITY AND DAMAGE TOLERANCE OF CERAMIC COMPOSITES FOR

HIGH-TEMPERATURE APPLICATIONS

5. AUTHOR(S)

E. R. Fuller, Jr., T. W. Coyle, R. .F. Krause, Jr. and T.-J. Chuang

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7. Con tract/ Grant No.

NATIONAL BUREAU OF STANDARDS

U.S. D^ARTMENT OF COMMERCE 8* Type of Report & Period Covered

GAITHBISBURG, MD 20899

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, State, ZIP)

NBS

10. SUPPLEMENTARY NOTES

f~

'1 Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200~word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey .meqtion it here) ^e achievement of higher efficiency heat engines and heat recovery systems

requires the availability of high temperature, high performance structural materials.

Structural ceramics, and more recently, ceramic matrix composites have received

particular attention for these applications due to their high strength, and corrosion

and thermal shock resistance. Even with these positive attributes, improved reliability and extended lifetime under service conditions are necessary for structural

ceramics to gain industrial acceptance. The problems with these materials are

mechanical and chemical in nature and are enhanced by the fact that they are subjected

to high temperatures, reactive environments and extreme thermal gradients.

With an objective of improved performance for heat engine/heat recovery

applications, the NBS program on structural ceramics and ceramic composites

addresses these problems through the determination of the critical factors which

influence mechanical and microstructural behavior. The activities of the program

are grouped under two major subtasks, each designed to develop key data, associated

test methods and companion predictive models. The status of the subtasks are detailed

in the following sections.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) composites; double-cleavage-drilled-compression; indentation; R-curve;

Sic fibers; SiC whiskers; shear resistance; strength

13. AVAILABILITY

IX~| Unlimited

I I For Official Distribution, Do Not Release to NTIS

r I Order From Superintendent of Documents, U.S. Government Printing Office, Washington,

20402.

14. NO. OF

PRINTED PAGES

DC

30

15. Price

(Xj Order From National Technical Information Service (NTIS), Springfield, VA 22161 $11.95

USCOMM-OC 83-6006
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