Astm stp 1157 1992

4 EVALUATION OF ADVANCED MATERIALS is not susceptible to cyclic fatigue and undergoes only static fatigue where failure or any crack growth is attributed to stress corrosion [5,6].. For

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S T P 1157

Cyclic Deformation, Fracture, and Nondestructive Evaluation

of Advanced Materials

M R Mitchell and Otto Buck, editors

ASTM Publication Code Number (PCN)

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Library of Congress Cataloging-in-Publication Data

Cyclic deformation, fracture, and nondestructive evaluation of

advanced materials / M R Mitchell and Otto Buck, editors

(STP ; 1157)

Based on papers presented at a symposium held in San Antonio, Tex

Nov 12-13, 1990

"ASTM publication code number (PCN)."

Includes bibliographical references and index

ISBN 0-8031-1444-3

1 Composite materials Fatigue Congresses 2 Non-destructive

testing Congresses I Mitchell, M R (Michael R.), 1941-

II Buck, Otto III Series: ASTM special technical publication ;

is 0-8031-1444-3/92 $2.50 + 50

Peer Review Policy

Each paper published in this volume was evaluated by three peer reviewers The authors addressed all of the reviewers' comments to the satisfaction of both the technical editor(s) and the ASTM Committee on Publications

The quality of the papers in this publication reflects not only the obvious efforts of the authors and the technical editor(s), but also the work of these peer reviewers The ASTM Committee on Publications acknowledges with appreciation their dedication and contribution

to time and effort on behalf of ASTM

Printed in Ann Arbor, MI Aug 1992

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Foreword

vanced Materials, contains papers presented at the symposium of the same name held in

San Antonio, Texas, 12-13 November 1990 The symposium was sponsored by A S T M

Committee E9 on Fatigue and its Subcommittees, E9.03 on Fatigue of Advanced Materials

and E9.01.07 on Research on Nondestructive Evaluation of Advanced Materials M R

Mitchell, Rockwell International, and Otto Buck, Iowa State University, presided as sym-

posium chairmen and are editors of this publication

Downloaded/printed by

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Small-Crack Behavior and Safety-Critical-Design C r i t e r i a for Cyclic F a t i g u e i n

M g - P S Z C e r a m i c s - - A A STEFFEN, R H DAUSKARDT, AND R O RITCHIE

M o d e l i n g C r a c k G r o w t h Resistance in Ceramics and Ceramic-Matrix C o m p o s i t e s - -

J LLORCA AND M ELICES

Thermomechanical Cyclic D e f o r m a t i o n of M e t a l - M a t r i x C o m p o s i t e s - -

M KARAYAKA AND H SEHITOGLU

F a t i g u e C h a r a c t e r i s t i c s of Heavily Cold-Roiled Cu-20Nb B s BINER AND

W A S P I T Z I G

Effect of Tensile M e a n Stress o n F a t i g u e B e h a v i o r of Single-Crystal and

Directionally Solidified S u p e r a l l o y s - - s KALLURI AND M A, MCGAW

Mechanical Properties of Amorphous and Roll-Drawn Polypropylene

D M C C A M M O N D , A N SINCLAIR~ A N D L A S I N C L A I R

T h e I n f l u e n c e of C o n s t i t u e n t P r o p e r t i e s o n the C o m p r e s s i o n B e h a v i o r of Laminates

w i t h D i s c o n t i n u i t i e s - - D L CRANE, W L BRADLEY, AND D L BARRON

Cyclic Creep Effects in Single-Overlap Bonded Joints Under Constant-Amplitude

Testing R A CHERNENKOFF

I n t e r p r e t a t i o n of L a b o r a t o r y T e s t I n f o r m a t i o n for R e s i d u a l S t r e n g t h a n d Life

P r e d i c t i o n of C o m p o s i t e S y s t e m s - - K L REIFSNIDER

Crack Resistance, Fracture Toughness, and Instability in Damage-Tolerant

A l u m i n u m - L i t h i u m A i l o y s - - R J H WANHILL, L SCHRA, AND

W G J ' T H A R T

Ultrasonic Wave Technique to Assess Cyclic-Load Fatigue Damage in Silicon-

Carbide Whisker Reinforced 2124 Aluminum Alloy Composites -

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Nondestructive Characterization for Metal-Matrix Composite Fabrication

Split Spectrum Processing of Backscattered Rayleigh Wave Signals to Improve

Detectability of Fatigue Microcracks M T RESCH AND P KARPUR

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STP1157-EB/Aug 1992

Overview

The implementation and usage of tailored engineering materials in structural and engine

design requires our understanding of their cyclic deformation behavior and fracture resist-

ance With such knowledge, we can proceed to determine the mechanistics of material

response to service environments and establish inspection procedures and intervals com-

mensurate with consumer usage This particular symposium, which is the first of several

planned on this topic, was outlined to encompass the cyclic deformation and fracture of

advanced metallic, ceramic and polymeric monolithic, and composites, as well as method-

ologies for nondestructive evaluation of these same material systems Such a joint venture

required the cooperation of Subcommittees E9.03 on Fatigue of Advanced Materials and

E9.01.07 Research on Nondestructive Evaluation of Advanced Materials

Organization of presentation first covers crack initiation and propagation in monolithic

and composite ceramics principally at elevated temperatures Several interesting ramifica-

tions of phase changes occurring at high temperatures and their influence on smooth and

notched fatigue behavior are examined Contributions of matrix cracking, fiber bridging

and pull out, and their effects on crack propagation are explained Experimental method-

ologies and techniques for these "difficult to test" materials as well as short/long fatigue

crack propagation threshold behavior is discussed Modeling of crack growth resistance in

ceramic and ceramic matrix composites is followed by constitutive modeling of a metal

matrix composite for cyclic, isothermal, and thermomechanical behavior

Initiation and growth of cracks are discussed for an in situ metal matrix composite (MMC)

The influence of mean stresses on the fatigue behavior of single crystal and directionally

solidified (DS) alloys as well as crack resistance and toughness of light weight alloys are

presented in two subsequent papers

Constituent properties of a polymeric laminate with discontinuities is followed by creep

effects in bonded polymer composite joints and the interpretation of test information for

residual strength and life prediction of composite systems complete the cyclic deformation

and fracture portion of this STP The latter presentation by K L Reifsnider of Virginia

Polytectnic Institute and State University received "Best Paper" award for this symposium

The final topic covered in the symposium was nondestructive evaluation (NDE) of tailored

materials A b o u t fifteen years ago, N D E began to evolve from testing with improved in-

strumentation along with a better understanding of materials behavior N D E aims to detect

and characterize flaws and microstructural changes in materials, and based on consideration

of physical mechanisms controlling materials behavior in a specific application, to predict

future performance and reliability of the component In the present publication, ultrasonic

surface wave and acoustic emission techniques are applied to monitor cyclic fatigue damage

(microcracks) in whisker reinforced metal matrix composites and homogeneous materials

The so-called acousto-ultrasonic technique (a sophisticated form of the well-known "coin-

tapping") as well as acoustic microscopy are used to determine damage due to monotonic

loading of ceramic composites Finally, one paper describes the application of eddy current

in combination with ultrasonic techniques for process control of metal-matrix composites,

with the possibility to provide on-line, closed-loop control of the fabrication parameters

The symposium chairmen affably acknowledge the authors and reviewers of manuscripts

Their participation as well as that of the A S T M staff has made this publication possible It

is hoped that the subject matter of this symposium will generate interest and stimulate

1

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2 EVALUATION OF ADVANCED MATERIALS

participation in the sponsoring A S T M committees We welcome your cooperation and

contributions to the Second Symposium on Cyclic Deformation, Fracture, and Nonde-

structive Evaluation of Advanced Materials planned for November 1992, in Miami, Florida

M R Mitchell

Rockwell International Science Center, Thousand Oaks, CA 91360;

symposium chairman and editor

Otto Buck

Iowa State University, Ames Laboratories, Ames, IA 50011; symposium chairman and editor

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C.-K Jack Lin, 1 Thomas A Mayer, ~ and Darrell F Socie t

Cyclic Fatigue of Alumina

Cyclic Deformation, Fracture, and Nondestructive Evaluation of Advanced Materials, ASTM

STP 1157, M R Mitchell and O Buck, Eds., American Society for Testing and Materials,

Philadelphia, 1992, pp 3-27

loading was studied Smooth cylindrical specimens of 99.8% alumina were cyclically loaded

at both room temperature and 1200~ to produce stress-life curves A decrease in strength

was observed with an increase in temperature Macroscopic fracture surfaces were found similar

for both temperatures A fiat semicircular region that originated from the surface indicated a

period of stable crack growth The size of this zone agreed with the estimates from the fracture

toughness of the material and maximum load during the fatigue cycle Lifetimes of static

fatigue specimens tested at 1200~ appeared to be shorter compared with cyclic fatigue tests

The viscous boundary phase may be the primary contributor to the improved fatigue resistance

under cyclic loading Specimens with two circumferential notches were loaded cyclically at

1200~ to simulate a component and study notch sensitivity effects A further decrease in

strength was observed as a result of the stress concentration However, the alumina became

increasingly less sensitive to the stress concentration factor, K,, at the lower stresses, suggesting

a fatigue notch factor, KI, that is less than K,

notch effects, high temperature

Ceramic materials are rapidly being developed for an increasing number of engineering applications, for example, in advanced heat engines They offer combinations of thermal

and mechanical properties that are unavailable in other materials These desirable properties

such as high specific strength, high-temperature resistance, erosion-corrosion resistance, and

high hardness give ceramic materials the potential for use in more efficient engines requiring higher operating temperatures Although many of the engineering ceramic components were

subjected to cyclic loading at elevated temperatures for prolonged periods, the study of fatigue in ceramics is still inadequate and inconclusive, in particular at elevated temperatures

In the ceramic literature, static fatigue (or stress rupture) has been used to describe the

fracture of a ceramic component subjected to a constant load If the fracture occurs under cyclic loading, it is termed cyclic fatigue

Polycrystalline alumina is representative of a class of modern structural ceramics Although

a considerable amount of research has investigated its physical and mechanical properties [1], very little is known about its cyclic fatigue behavior at room temperature and even less information exists regarding its high-temperature fatigue properties Research that investigated the fatigue properties of alumina did not begin until about 1956 [2-4] Since that time, several researchers have tested alumina cyclically and the results are conflicting with regard to the causes of the observed damage Some of the work has concluded that alumina

1Graduate research assistant, graduate research assistant, and professor, respectively, Department

of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL

61801 Mr Mayer is currently at Ford Motor Co., Dearborn, MI 48121

3 Copyright 9 1992 by ASTM lntcrnational www.astm.org

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is not susceptible to cyclic fatigue and undergoes only static fatigue where failure or any

crack growth is attributed to stress corrosion [5,6] To the contrary, much of the work done

has determined that alumina does indeed exhibit a cyclic fatigue effect at room temperature

[3,7-15], while still other research has observed a cyclic effect only under certain conditions

[16-18] Also, certain studies have simply reported cyclic fatigue data for alumina in the

In an early study, Krohn and Hasselman [17] subjected a polycrystalline alumina'to room-

temperature four-point bend tests including static tests and cyclic tests at various frequencies

and amplitudes Within the scatter of the data, no clear cyclic fatigue effects can be seen

except, perhaps, at the highest frequency (40 Hz), as most of the measured cyclic data lie

suggested that cyclic fatigue in that alumina at room temperature was essentially a mani-

festation of stress corrosion [5]

However, some other data indicate alumina does exhibit cyclic as well as static fatigue

For example, room-temperature uniaxial tension-compression tests using another polycrys-

on fatigue lifetime as the specimens under constant loading took " a much longer time" to

fatigue crack growth at room temperature in edge-notched specimens of a commercial

polycrystalline alumina The application of cyclic compressive loads to the specimen results

similar experiments in vacuo (~10 -4 Pa) to verify that this crack growth was not simply the

result of stress corrosion

Several researchers have also investigated cyclic fatigue of alumina without attempting to

tilever bend tests on an alumina at room temperature and 1000~ and observed increases

results using rotary bend tests on another alumina at room temperature Furthermore, Ko

[21] went on to show that the fatigue strength of polycrystalline alumina increases with a

with an alumina content of 94% and 99.8% to cyclic uniaxial tensile loads and observed

decreases in lifetimes for both materials as the applied stress increases

Most of the preceding studies utilized either small bend specimens or larger plate-type

specimens with large cracks in them These various bend tests have been popular in the

testing of brittle materials because they are relatively simple to conduct and are easily

adaptable to testing at high temperatures It must be kept in mind that ceramics are very

sensitive to surface or volume flaws In bending test specimens, only a small portion of the

material is under the maximum stress and the chance of encountering a critical flaw in this

highly stressed region is small As a result, the strength of the material is overestimated

with these specimens These types of tests may be appropriate for screening work but are

not suitable for studying the mechanical behavior and extrapolating this information to

structures Long crack growth behavior is studied with large plate-type specimens where the

cracks are several millimetres long While such information regarding this behavior may be

useful, failure of a ceramic component will most likely have occurred long before the crack

reaches such lengths

Thus, tension testing of ceramics is necessary for reasons including: (1) there is smaller

scatter of test results due to a larger volume of material subjected to the maximum stress

in a uniaxial tension test specimen compared with small bending test specimens and a higher

probability of flaws existing in this larger volume; and (2) uniaxial homogeneous stress

distributions are necessary for fatigue tests at high temperatures to avoid the stress redis-

tribution effects

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LIN ET AL ON CYCLIC FATIGUE OF ALUMINA 5

In this investigation, a self-aligning grip system attached to a closed-loop electroservo-

hydraulic test machine was used to study the fatigue behavior of a polycrystalline alumina

conducted with the same test machine at 1200~ to compare with the cyclic fatigue tests

Cyclic loading tests were also applied to notched specimens at 1200~ to investigate the

notch sensitivity effects

Experimental Equipment and Procedure

Test Equipment

Widespread reliable tension testing of ceramic materials has not occurred because of

the difficulties associated with it For example, the gripping system utilized must subject

bending strains that cause variable stress states throughout the gage section of the specimen

leading to erroneous results and even greater data scatter No test standards for fatigue

testing of ceramic materials are available Where the ASTM Recommended Practice for

Constant-Amplitude Low-Cycle Fatigue Testing (E 606-80) allows bending strains as high

as 5% of the minimum axial strain range for a valid tension test of metallic materials, it is

accepted generally that this value is much too high for the testing of brittle ceramic materials,

To accomplish proper alignment and reduce bending strains, this investigation used a self-

The grip system consists of two major components: (1) a hydraulic housing assembly for

self-aligning, and (2) a pull rod assembly The grips originally used in this investigation were

equipped for high-temperature testing and had a water-cooled grip-head that attached to

the pull rod This grip-head then held a buttonhead specimen with a rounded split collet

Some room-temperature tests were conducted initially with the buttonhead specimens to

occurring at the shoulder of the buttonhead were observed Similar observations were also

the authors in this study to eliminate the buttonhead and the associated failures outside of

the gage section of the specimen The elimination of the buttonhead substantially reduces

specimen fabrication time and cost With only a simple change of collets, this new grip-head

is capable of gripping smooth-shank specimens of diameters ranging from 3 to 20 mm The

hydraulic pressure is transmitted from two hand pumps, one for gripping pressure and one

for release pressure, to the grip-heads through loops of very flexible medium-pressure

hydraulic lines that are fastened securely to the O R N L housing to minimize the lines' moment

arm on the grip-heads Even when fully pressurized (a pressure of approximately 6.90 MPa

is used), the hydraulic lines do not impart significant side forces to the grip-heads Numerous

tests have also shown that no slippage of the specimen in the grips occurs This grip-head

attaches to the pull rod in the O R N L grip housing and thus still utilizes the self-aligning

O R N L design For high-temperature tests, an aluminum water cooling jacket with cooling

lines was pressfit on each grip-head These jackets did not adversely affect the alignment

of the system

Excellent alignment of the load train was verified through several room-temperature

bending strain tests using a strain-gaged alumina specimen with the water-cooling lines

attached to the grip-head and the cooling water running Calculations showed the maximum

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of the applied axial strain Electrical noise in the system did not allow accurate bending

strain measurements at lower loads and the bending strain is expected to be even lower at

Once proper alignment of the specimen load train is achieved, conducting high-temper-

ature tension tests presents the crucial problem of heating the specimen to the desired

temperature without affecting the alignment Although many methods of specimen heating

atures Induction heating has an advantage over resistance furnace in that the heat can be

focused onto the test specimen's gage section so that the ends of the specimen are heated

only through conduction Thus, with alumina's low thermal conductivity, the ends of the

specimen are of sufficiently low temperature to allow gripping simply with the water-cooled

grip-heads mentioned earlier and pull rod extensions are not necessary

Alumina is an electrical and magnetic insulator and cannot be heated directly with in-

duction power; therefore, a silicon carbide susceptor is heated directly which then heats the

specimen through radiation The details of the various components of the induction furnace

Material and Specimen Preparation

The specimens tested in this investigation were made from extruded rods of AD-998

alumina (nominally 99.8% alumina) supplied by Coors Ceramic Company of Golden, Col-

orado The grain boundary phases and impurities in this alumina contain SiO2, MgO, cal-

cium, sodium, and iron The average grain size of this material is about 6 ~m, and some

grains are as large as 25 p~m The manufacturer provides the room-temperature properties

of this material as follows: specific gravity = 3.90, elastic modulus = 345 GPa, flexural

strength = 331 MPa, and compressive strength = 2071 MPa

Specimens of three different geometries (see Fig 1) were ground from the supplied rods

using diamond grinding wheels First, the length of each rod was ground to a uniform

diameter with a 150-grit diamond wheel such that its entire length was concentric The

specimen details such as the buttonhead and the gage section were then ground (also with

a 150-grit diamond wheel) into the rod The semicircular notches were introduced with a

100-grit diamond wheel

The buttonhead design (see Fig l a ) was used with the original grip-heads supplied with

the grips, while the smooth-shank specimens (Fig lb) were tested using the new grip-head

design The double-notch geometry (Fig lc) was tested for two reasons

Factors [33] gives a value of K~ = 2.15 for a single notch of the dimensions used here A

finite element analysis to determine the value of K, for the double-notch specimen config-

uration was made using the P O L O - F I N I T E code at the University of Illinois Due to

symmetry, only a quarter of the structure was modeled and the remainder of the structure

was defined by choosing the axisymmetric option of the two-dimensional eight-node-iso-

parametric element and defining the appropriate boundary conditions This finite element

code gave a value of K, = 2.13 when the effect of the second notch was considered The

notch design allows the specimen to more closely simulate an actual component so that the

alumina's sensitivity to stress concentration can be studied Second, testing of this specimen

may also provide information about the evolution of fatigue damage Failure will originate

from one of the two notches The second notch would be sectioned and examined for possible

evidence of fatigue damage

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under cyclic loading while static fatigue tests were conducted on another set of smooth- shank specimens Only cyclic loading tests were performed on double-notch specimens For high-temperature testing, the specimen was preheated to 1200~ in air over a period

of 100 min (for smooth specimens) or 120 min (for double-notch specimens) The specimen then remained at 1200~ for 30 min (smooth specimens) or 45 min (double-notch specimens)

to allow the specimen to reach thermal equilibrium

The specimens for the high-temperature cyclic fatigue test were tested to failure with a sinusoidal loading waveform and an R-ratio of 0.1 The room-temperature specimens were tested to failure at an R-ratio of 0.075 with a triangular loading path All cyclic fatigue tests were conducted at a frequency of 2 Hz In the event that failure did not occur even after

106 cycles, the test was then terminated Static fatigue specimens were tested to failure in the same test machine under constant loads

Results and Discussion

Comparison of Cyclic Fatigue at R o o m and High Temperatures

Room-temperature tests were conducted with buttonhead specimens, and the results agree very well with data produced by the developer of the O R N L self-aligning grip system using

a similar test system, material, and specimen geometry (see Fig 2) Thus, it was determined that the test frame was working properly and producing valid data

(arrow designates interrupted test)

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Tests at 1200~ were conducted on the smooth-shank specimens These results are graph-

ically compared to the room-temperature results in Fig 2 Each data point represents a

single test at various stress levels Tensile strength was plotted as a single cycle to failure

A substantial decrease in strength was observed with the increase in temperature The stress-

life curves show that the fatigue strength (at 106 cycles) at room temperature was about

damaging at high temperatures

Notch Sensitivity Effects

Double-notch specimens tested at 1200~ produced the results shown in Fig 3 These

data are compared to the smooth specimen data in Fig 3a where maximum nominal stress

is plotted versus life A further decrease in strength is seen as a result of the stress concen-

in Fig 3b, the results take on a different look It is seen that a notched specimen has

approximately the same tensile strength as a smooth specimen, but as the applied stress

decreases and the lifetimes increase, the alumina becomes increasingly less sensitive to the

is less than K~ This phenomenon is observed generally in metals, and K i has been defined

as [34]

S~unnotched)

to be that stress at which failure does not occur after one million cycles In this case, the

fatigue notch factor appears to be approximately 1.2, much lower than the stress concen-

tration factor of 2.13

extrapolate fatigue strength data obtained from small laboratory specimens to the design of

actual structural parts, Kuguel considered geometric factors such as "the notch, the size and

shape effects, and the influence of different types of loading." In particular, the concept of

the highly stressed volume of material was discussed Kuguel proposed that the volume of

material that experiences, for example, 95% of the maximum stress in the specimen should

be considered because of the statistical nature of fatigue rather than simply the maximum

stress alone Thus, even though the notched specimen is subjected to a higher maximum

stress than in the smooth specimen, a much smaller volume of material actually experiences

this high stress Kuguel put forth the following relationship for specimens in bending

\LI

where V,, is the volume of material that experiences 95% of the maximum stress in the

notched specimen, 11, is the volume of material that experiences 95% of the maximum stress

in the smooth specimen, and a = 0.034 for most metals In this study, V, = 0.92 (mm 3)

and Vs = 1.06 • 103 (mm 3) are given by geometry analysis and stress distribution from

finite element analysis If we use a = 0.034, this relationship predicts a value of 1.68 for

K r in this study that overestimates the experimentally determined value by about 40% This

overestimate is not a surprising result because the strength of a brittle material such as

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FIG 3 Comparison o f all cyclic fatigue data: (a) with maximum nominal stress plotted versus lifetime

and (b) with m a x i m u m stress (considering Kt) plotted versus lifetime

10

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LIN ET AL ON CYCLIC FATIGUE OF ALUMINA 1 1

alumina is expected to be very dependent on the amount of material exposed to high stress

[36] These limited data suggest that the simple approach used for metals will probably not

be appropriate for ceramics Additional tests and probabilistic analyses are necessary to gain more understanding of the notch effects on the cyclic fatigue behavior of ceramics

Comparison of Static and Cyclic Fatigue at High Temperature

Static fatigue tests at 1200~ were conducted on smooth-shank specimens These results are compared to the cyclic fatigue results in Fig 4 where the maximum applied stress is plotted versus lifetime in time base The predicted lifetime for cyclic loading that is also shown in Fig 4 is computed from the results of static loading using a procedure that will

be discussed later The ratio of measured cyclic lifetimes to those of static tests is from 10

at higher applied stresses to 100 at lower applied stresses

Most of the mechanical failure of ceramic materials occurs from "preexistent flaws." These "preexistent flaws" are introduced into the materials during either processing or machining Thus, the lifetime of mechanically loaded structural ceramic components is restrained by subcritical crack growth of preexisting flaws Preexisting flaws may grow under constant or varying loading to critical sizes for spontaneous propagation and lead to final failures of ceramic components In the following paragraphs, a crack growth model is applied

to examine whether cyclic fatigue failure can be attributed to the accumulation of static fatigue failure or if there exists some other cyclic effect on failure time

I I I I

LIFE TO FAILURE, (Hours)

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The subcritical crack growth for ceramics is described usually by the following power law

[37]

V = da/dt =- A K ' ] = A ( Y ( ~ / ' ~ ) " (3)

where V is the crack velocity, a is the crack size, t is time, A and n are material constants,

KI is the stress intensity factor, Y is a geometric factor, and (r is the applied stress

The applied stress, or, can be expressed generally as cr = (r,,f(t), where o- m is the m a x i m u m

applied stress a n d 0 -< f ( t ) -< 1 for tensile loading The failure time, tf, can be o b t a i n e d

from the integration of E q 3 as follows

a/q2-,,)/2 _ t-/(2-n)/2 _, = [(2 - n)/2]AY"(rT, [ [f(t)]"dt (4)

where al and af are the initial and final crack sizes In most cases n > > 1, thus a, (z ,~/2 > >

@2-,)/2 F o r static fatigue tests with f ( t ) = 1, the lifetime, t~r , is given by the following

approximation from Eq 4

tsy ~ [2/(n - 2 ) ] A - ' Y "a}Z-")/2(rm" (5)

For fatigue tests performed u n d e r a cyclic loading waveform with a time period r, the time

to failure, tee, can also be o b t a i n e d by simplifying E q 4 as follows

t c r ~ [ 2 / ( n - 2)A-1 Y -~ a, (2 n)/2-n /f ~ ffm r [f(t)]"dt } 1 (6)

In E q 6, tcr = NI" T is used to get the approximation for Nf > > 1

The ratio of cyclic fatigue to static fatigue lifetimes u n d e r the same m a x i m u m applied

stress is t h e n given as

r = tcz/tsi = ~ t)]"dt (7)

For a sinusoidal waveform, f ( t ) = (1 + R)/2 + [(1 - R)/2] 9 sintot, where to = 2~r/T and

R is the stress ratio

Linear regression analysis of the static fatigue data shown in Fig 4 indicates that failure

m a y be described satisfactorily as ts~ = 5.72 x 1014(r~ 8-3z (in hours and MPa) with a relatively

high correlation coefficient value of 0.941 This gives the crack growth e x p o n e n t , n, a value

of 8.32 With n = 8.32, R = 0.1, a n d r = 0.5 s, r i s given as 4.90 from Eq 7 The predicted

cyclic fatigue lifetime is then plotted as a dashed line in Fig 4 Predicted cyclic fatigue

lifetimes are slightly shorter than the measured lifetimes u n d e r higher applied stresses, while

the deviations increase with the decrease of applied load; the m e a s u r e d cyclic fatigue lifetimes

are more t h a n a factor of 10 larger than the predicted lifetimes u n d e r lower applied loads

It is obvious that lifetimes of cyclic fatigue specimens are u n d e r e s t i m a t e d by this prediction

m e t h o d using the static fatigue data T h e preceding comparison indicates that there is

apparently a beneficial cyclic effect on the failure time from repeated loading as compared

to static loading

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Comparison with Other Studies

The literature survey shows a limited number of studies that directly compare static and

observations will be compared with other researchers' investigations on the influence of

cyclic loading on the fatigue behavior of ceramics at elevated temperatures

It is noted that the prediction method discussed previously is based on the assumption

that both cyclic and static fatigue failures are dominated by slow crack growth, and the

stress intensity factor, KI, is the only dependent variable in describing the crack velocity

during slow crack propagation The literature is conflicting regarding this assumption

with frequency <5 Hz at 1400~ and found that there was no enhanced cyclic effect on the

slow crack growth rate as the measured cyclic crack velocity was predictable from the static

velocity data That observation provides a verification for the assumption that cyclic crack

growth is essentially due to the static crack growth mechanism Similar observations were

established for silicon nitride up to 1200~ and for silicon carbide up to 1400~ with uniaxial

tension tests in both static and cyclic loading The cyclic loading tests were conducted at R

= 0.5 and with a triangular waveform The period of a loading cycle ranges from 1 to 7

min as the stressing rate was kept constant at a value of 0.6 MPa/s Within the scatter of

the data, no true cyclic fatigue effects could be detected either for silicon nitride at 1000,

1100, and 1200~ or for silicon carbide at 1400~ as the predicted cyclic lifetime agreed very

well with the measured data It was therefore concluded that fracture in both static and

cyclic fatigue for those two ceramic materials at high temperatures were essentially caused

To the contrary, this assumption may not be applied completely to another silicon nitride

under bending tests at 1200~ in a study reported by Fett et al [40]; the predictions based

on static loading data also substantially underestimated the measured cyclic lifetimes under

sinusoidal loading waveform with a frequency of 30 Hz This is similar to the observation

in the current study

phenomena regarding the assumption that cyclic fatigue is primarily attributed to static crack

growth mechanisms In their investigation, the measured cyclic lifetime was obtained from

uniaxial tension-compression tests (R = - 1) under a sinusoidal waveform with a frequency

frequency at high temperatures A t 20 Hz, the measured cyclic lifetime was much larger

than the predicted value based on the static fatigue data and slow crack growth model

However, the cyclic lifetime with a frequency of 0.01 Hz was within the range of the predicted

lifetime from the experimental data under static loading

The preceding comparison indicates that in addition to slow crack growth other high

temperature mechanisms (such as creep, microstructural instabilities, or a mechanical cycle

effect or a combination thereof) need to be considered in lifetime predictions for ceramics

tribution due to creep in bending tests, the measured lifetimes of cyclic fatigue tests are still

much larger than the modified predictions A further consideration of the adhesive effects

of viscous grain boundary phases on the crack surfaces was used to make predictions com-

boundary phases may be also applied to explain the observations in the present study Figure

5a shows that a finger-like glassy boundary phase spreads on an alumina grain facet on the

fracture surface of a failed specimen In the cyclic case with high frequency (for example,

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features) and (b) a viscous boundary phase bridging the crack faces

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crack closure effects and carry a part of the applied load by bridging the crack surfaces

Crack-tip shielding might occur in cyclic loading due to the wedging and bridging effects

from viscous fluids and reduce the effective stress intensity factor range and retard the crack

specimens (more description is given in a later section) demonstrate clear evidence of a

viscous boundary phase bridging the crack faces as shown in Fig 5b These viscous boundary

phase effects on the crack opening in static loading or cyclic loading with low frequency

stresses due to the viscous characteristics of glassy phases The definitions of low or high

frequency for cyclic loading are dependent on material, temperature, and environment For

instance, 2 Hz might be a high frequency for the alumina tested in this study, while it may

be classified as low frequency for the silicon nitride investigated in the study of Evans et al

[38]

Recently, Suresh and co-workers measured the static and cyclic (sinusoidal waveform)

found to give rise to a lower crack growth rate compared to static loading under the same

maximum stress intensity factor for both ceramics in their studies They also observed that

higher cyclic frequency (2 Hz) caused more crack growth retardation than lower cyclic

frequency (0.13 or 0.10 Hz) in both materials One of the possible contributions to the

improved cyclic fatigue resistance is due to the bridging of crack surfaces by the inherent

diminish with a decrease in cyclic frequency

The retardation of crack growth is more pronounced at lower applied load levels where

the thickness of the boundary phases becomes comparable with the crack-tip-opening dis-

placement This might explain the difference in measured lifetimes between static and cyclic

loading cases and the larger difference observed at lower applied stresses in the current

study

More tests are necessary to gain a more detailed understanding of the phenomena observed

in this investigation The mechanisms by which viscous boundary phases can affect fatigue

behavior in ceramics at elevated temperatures need to be documented in a systematic way

Fracture Morphology

The features of several of the fracture surfaces were also studied with SEM Figure 6a

shows the fracture surface of one of the specimens that was cyclically loaded at room

temperature, while the fracture surface of a smooth-shank specimen tested at 1200~ under

cyclic loading is shown in Fig 6b The macroscopic features are similar for both temperatures

A flat semicircular region (indicated by dashed lines) that originated from the surface may

represent a period of slow crack growth

Estimates of the alumina's fracture toughness, K~c, were made from the size of the semi-

circular flat area and the maximum stress applied during the fatigue cycle to examine whether

this zone truly indicates a period of slow crack growth The values of Kk were calculated

was obtained for the room-temperature specimens while estimates for the fracture toughness

of the high-temperature specimens were in the range 7.19 to 9.79 (MPa-m m) with an average

value of 8.25 (MPa-mVZ) Tschegg and Suresh [47] have determined the room-temperature

Trang 22

16 EVALUATION OF ADVANCED MATERIALS

1200~

Trang 23

LIN ET AL ON CYCLIC FATIGUE OF ALUMINA 1 7

fracture toughness of this alumina to be 3.35 (MPa-m 1/2) while other sources have reported typical room-temperature K~c values between 3.8 and 5.1 (MPa'm 1/2) for various aluminas [1] Considering the accuracy with which the final crack size could be determined (because

with published results (of the same order of magnitude) and suggest that the semicircular flat region is indeed a slow crack growth zone Higher Kic values may be expected from cyclic loading tests, as compared to pure tension tests, due to various extrinsic toughening mechanisms such as crack closure and crack-tip shielding

Although the slow crack growth regions in the smooth specimens of cyclic fatigue tests are macroscopically different from the fast fracture zones, no significant microscopic differences could be resolved as shown in Figs ? and 8, respectively, for room- and high- temperature specimens This fact may help explain the difficulty in defining the boundary

of the overload that was encountered in the fracture toughness calculations However, one major difference exists between the room-temperature and high-temperature fracture surfaces The crack growth (both slow and fast) at room temperature appears to be a mixed

intergranular/transgranular fracture mode while intergranular crack growth is much more

high temperatures, and crack growth around the grains requires less energy than does crack growth through a grain

All cyclic fatigue and tensile strength tests of double-notch specimens had failures initiating from surface flaws either at the notch root or around the notch root region A typical fracture surface of a notched specimen tested at 1200~ is shown in Fig 9 Again, a semicircular, flat, slow crack growth region occurs along with a rough, fast fracture zone However, the fracture surfaces of these high-temperature specimens resembled those of the room-temperature specimens in that failure appeared to be mixed with intergranular and transgranular cracking (see Fig 10)

The macroscopic features of the fracture surfaces of static fatigue specimens tested at

single semicircular flat region could be identified It is suspected that the origin of failure

in this specimen might occur at or near the edge of the fracture surface and be associated with rough areas (marked by R1-3) as opposed to the cyclic fatigue cases where a semicircular flat region surrounded the failure origin In addition to the major rough area (R1), some other smaller rough areas (R2 and R3) were also recognized These rough areas might be characteristics of slow crack growth of multiple macrocracks At higher magnifications, no notable microscopic differences in fracture features were observed between the rough and flat regions for this static fatigue specimen (see Fig 12) Both regions show that intergranular cracking is the predominant fracture mode except at some large grains where transgranular crack growth occurs

intermediate, or low maximum tensile stress) were axially sectioned, polished, and observed with SEM to seek possible evidence of the development of fatigue damage No formation

of any macrocrack except the failure crack was detected in the gage section of each sectioned smooth specimen This phenomenon also occurred in both broken and unbroken notch regions of all the sectioned double-notch specimens This implies that failure of the alumina,

formation and growth of a single primary crack rather than by simultaneous nucleation or growth of multiple macrocracks or both With careful documentation of specimen orien- tation, crack branching from the main failure crack was found to initiate within the fast fracture zones of few smooth-shank and double-notch specimens cyclically loaded at 1200~

as shown in Fig 13

Trang 24

temperature: (a) slow crack growth region and (b) fast fracture zone

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(a) slow crack growth region and (b) fast fracture zone

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However, examination of an axially sectioned static fatigue specimen tested under a lower

applied load at 1200~ revealed the existence of other macrocracks in addition to the failure

crack (see Fig 14) Thus, the failures of static fatigue specimens tested under the low loading

conditions in this study might occur by simultaneous nucleation or growth of multiple mac-

rocracks, or both This is supported by the observations of many isolated rough areas (slow

crack growth regions) in the fracture surface of a static fatigue specimen as shown previously

macrocracks was strain-rate dependent For the cyclic fatigue tests in the present study, the

maximum strain rate during loading period in each cycle is likely too high to produce any

multiple macrocracks

Conclusions

1 Equipment for the cyclic uniaxial tension testing of ceramic materials at room tem-

perature as well as elevated temperatures has been developed and tests on an alumina have

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and (b) fast fracture zone

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FIG ll Fracture surface of a static fatigue specimen tested at 1200~ (the letters R1-3 refer to rough

areas)

been successfully conducted Stress-life curves have been produced for the following spec-

imen types and temperatures: (a) smooth specimens at room temperature, (b) smooth spec-

2 Decreases in fatigue strength were observed with the increase in temperature and with

the introduction of notches

3 The notched specimens become increasingly less sensitive to the stress concentration

factor, K,, as stress decreases, suggesting the existence of a fatigue notch factor, KI, of

approximately 1.2 that is substantially less than the K, value of 2.13

4 With the same maximum applied stresses, cyclic loading provides a beneficial effect

on lifetime of alumina at 1200~ in comparison to static loading when the lifetime is con-

sidered a combination of the loading and unloading periods for the cyclic case Viscous

boundary phases may play an important role in this improved cyclic fatigue resistance

5 The fracture surfaces of the smooth specimens tested under cyclic loading at room

temperature and 1200~ were macroscopically similar, with both showing a flat, semicircular,

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region and (b) fast fracture zone

Trang 30

and (b) double-notch specimen (arrows indicate the loading direction)

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slow crack growth region and a rough, catastrophic fracture region of fast crack growth

However, the two fracture surfaces were microscopically different The room-temperature

fracture surface was mixed with intergranular/transgranular crack growth, while failure at

high temperature appeared to be predominantly intergranular

6 The fracture surfaces of the notched specimens appeared macroscopically similar to

those of the smooth specimens and were microscopically similar to the room-temperature

smooth specimens in that fracture was a mixed intergranular/transgranular mode in nature

7 The fracture surfaces of smooth specimens tested under static loading at 1200~ show

different macroscopic features from those of cyclic fatigue specimens; the slow crack growth

region might be associated with a rough surface Intergranular cracking is the prevailing

fracture mode

8 All of the failures of the cyclic fatigue specimens were dominated by the formation

and growth of a single crack, while the failures of the static fatigue specimens tested under

low loading conditions at 1200~ might occur by simultaneous nucleation or growth of

multiple macrocracks or both

A c k n o w l e d g m e n t s

This work was supported by the U.S Department of Energy under Contract DE-AC02-

76ER 01198 The authors gratefully acknowledge the assistance by Mr D Miller for ma-

chining the specimens Dr P Kurath, Mr R Brown, and Mr A Siljander are sincerely

thanked for their technical help in the laboratory

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References

[1] Dorre, E, and Hubner, H., Alumina: Processing, Properties, and Applications, Springer-Verlag, New York, 1984

[2] Williams, L S., "Fatigue and Ceramics," Mechanical Properties of Engineering Ceramics, W

Kriegel and H Palmour, Eds., Interscience Publishers, New York, 1961, pp 245-302

[3] Williams, L S., "Stress-Endurance of Sintered Alumina," Transactions, British Ceramic Society, Vol 55, No 5, 1956, pp 287-312

[4] Mizushima, J S and Knapp, W J., "Behavior of a Ceramic Under Cyclic Loading," Ceramic News, Vol 5, No 12, 1956, pp 26-29, 36

[5] Evans, A G and Fuller, E R., "Crack Propagation in Ceramic Materials Under Cyclic Loading Conditions," Metallurgical Transactions, Vol 5A, 1974, pp 27-33

[6] Lathabai, S., Mai, Y W., and Lawn, B R., "Cyclic Fatigue Behavior of an Alumina Ceramic with Crack-Resistance Characteristics," Journal, American Ceramic Society, Vol 72, 1989, pp 1760-1763

[7] Shand, E B., "Stress Behavior of Brittle Materials," Bulletin, American Ceramic Society, Vol

38, 1959, pp 653-660

[8] Sedlacek, R and Halden, F~ A., "Static and Cyclic Fatigue of Alumina," Structural Ceramics and Testing of Brittle Materials, S J Acquaviva and S A Bortz, Eds., Gordon and Breach Science Publishers, New York, 1968, pp 211-220

[9] Sarkar, B K and Glinn, T G J., "Fatigue Behavior of High-A1203 Ceramics," Transactions,

British Ceramic Society, Vol 69, 1970, pp 199-203

[10] Guiu, F., "Cyclic Fatigue of Polycrystalline Alumina in Direct Push-Pull," Journal of Materials Science Letters, Vol 13, 1978, pp 1357-1361

[11] Ewart, L and Suresh, S., "Dynamic Fatigue Crack Growth in Polycrystalline Alumina under Cyclic Compression," Journal of Materials Science Letters, Vol 5, 1986, pp 774-778

[12] Ewart, L and Suresh, S., "Crack Propagation in Ceramics under Cyclic Loads," Journal of Materials Science Letters, Vol 22, 1987, pp 1173-1192

[13] Brockenbrough, J R and Suresh, S., "Constitutive Behavior of a Microcracking Brittle Solid in Cyclic Compression," Journal of the Mechanics and Physics of Solids, Vol 35, 1987, pp 721-742

[14] Suresh, S and Brockenbrough, J R., "Theory and Experiments of Fracture in Cyclic Compression: Single Phase Ceramics, Transforming Ceramics and Ceramic Composites," Acta Metallurgica, Vol

36, 1988, pp 1455-1470

[15] Reece, M J., Guiu, F., and Sammur, M F R., "Cyclic Fatigue Crack Propagation in Alumina under Direct Tension-Compression Loading" Journal, American Ceramic Society, Vol 72, 1989,

pp 348-352

[16] Chen, C P and Knapp, W J., "Fatigue Fracture of an Alumina Ceramic at Several Temperatures,"

Fracture Mechanics of Ceramics, Vol 2, R C Bradt, D P H Hasselman, and F F Lange, Eds., Plenum Press, New York, 1974, pp 691-707

[17] Krohn, D A and Hasselman, D P H., "Static and Cyclic Fatigue Behavior of a Polycrystalline Alumina," Journal, American Ceramic Society, Vol 55, 1972, pp 208-211

[18] Evans, A G., "Fatigue in Ceramics," International Journal of Fracture, Vol 16, 1980, pp 485-

498

[19] Glenny, E and Taylor, T A., "The High-Temperature Properties of Ceramics and Cements,"

Powder Metallurgy, No 1/2, 1958, pp 189-226

[20] Ko, H N., "Fatigue Strength of Sintered AI203 Under Rotary Bending," Journal of Materials Science Letters, Vol 5, 1986, pp 464-466

[21] Ko, H N., "Effect of Grain Size on Fatigue Strength of Sintered A1203 Under Rotary Bending,"

Journal of Materials Science Letters, Vol 8, 1989, pp 1438-1441

[22] Liu, K C and Brinkman, C R., "Tensile Cyclic Fatigue of Alumina at Room and Elevated Temperatures," Proceedings, Twenty-Fourth Automotive Technology Development Contractors' Meeting, Dearborn, MI, 27-30 Oct 1986, P-197, Society of Automotive Engineers, Inc., War- rendale, PA, April 1987, pp 191-200

[23] Mejia, L C., "High Temperature Tensile Testing of Advanced Ceramics," Ceramic Engineering and Science Proceedings, Vol 10, No 7-8, 1989, pp 668-681

[24] Liu, K C and Brinkman, C R., "Tensile Cyclic Fatigue of Structural Ceramics," Proceedings,

23rd Automotive Technology Development Contractors' Coordination Meeting, Dearborn, MI, 21-24 Oct 1985, P-165, Society of Automotive Engineers, Inc., Warrendale, PA, March 1986,

Trang 33

[26] Soma, T., Masuda, M., Matsui, M., and Oda, I., "Cyclic Fatigue Testing of Ceramic Materials,"

International Journal of High Technology Ceramics, Vol 4, 1988, pp 289-299

[27] Grathwohl, G., "Current Testing Methods A Critical Assessment," lnternational Journal of High

Technology Ceramics, Vol 4, 1988, pp 123-142

[28] Chen, I W and Bowman, K., "Dynamic Fatigue Testing of Advanced Structural Ceramics,"

Closed Loop (published by MTS Corporation), Summer 1988, pp 3-8

[29] Ohji, T., "Towards Routine Tensile Testing," International Journal of High Technology Ceramics,

Vol 4, 1988, pp 211-225

[30] Buddery, J H., "Furnace Design and Temperature Control," International Journal of High Tech- nology Ceramics, Vol 4, 1988, pp 181-202

[31] Liu, K C., "Ceramic Specimen Heating by Induction Power," International Journal of High

Technology Ceramics, Vol 4, 1988, pp 203-210

[32] Mayer, T A., "Cyclic Fatigue of Alumina," Masters thesis, University of Illinois, Urbana, IL,

1990

[33] Peterson, R E., Stress Concentration Factors, Wiley, New York, 1974

[34] Bannantine, J A., Comer, J J., and Handrock, J L., Fundamentals of Metal Fatigue Analysis,

Prentice Hall, Inc., Englewood Cliffs, NJ, 1990

[35] Kuguel, R., "A Relation Between Theoretical Stress Concentration Factor and Fatigue Notch Factor Deduced from the Concept of Highly Stressed Volume," Proceedings, American Society for Testing and Materials, Vol 61, 1961, pp 732-748

[36] Davies, D G S., "The Statistical Approach to Engineering Design in Ceramics," Proceedings,

British Ceramic Society, Vol 22, 1973, pp 429-452

[37] Wiederhorn, S M., "Subcritical Crack Growth in Ceramics," Fracture Mechanics of Ceramics,

Vol 2, R C Bradt, D P H Hasselman, and F F Lange, Eds., Plenum Press, New York, 1974,

pp 623-646

[38] Evans, A G., Russell, L R., and Richerson, D W., "Slow Crack Growth in Ceramic Materials

at Elevated Temperatures," Metallurgical Transactions, Vol 6A, 1975, pp 707-716

[39] Kawai, M., Fujita, H., Kanki, Y., Abe, H., and Nakayama, J., "Tensile Testing of Silicon Carbide and Silicon Nitride," Proceedings, First International Symposium on Ceramic Components for Engines, S Somiya, E Kanai, and K Ando, Eds., Elsevier Applied Science Publishers Ltd.,

London, 1983, pp 269-278

[40] Fett, T., Himsolt, G., and Munz, D., "Cyclic Fatigue of Hot-Pressed Si3N 4 at High Temperatures,"

Advanced Ceramic Materials, Vol 1, 1986, pp 179-184

[41] Masuda, M., Soma, T., Matsui, M., and Oda, I., "Fatigue of Ceramics (Part 3) Cyclic Fatigue Behavior of Sintered Si3N 4 at High Temperature," Journal, Ceramic Society of Japan, Vol 97,

1989, pp 612-618

[42] Suresh, S., "Fatigue Crack Growth in Ceramic Materials at Ambient and Elevated Temperatures,"

Fatigue 90, Vol 2, H Kitagawa and T Tanaka, Eds., Materials and Component Engineering Publications Ltd., Birmingham, U.K., 1990, pp 759-768

[43] Han, L X and Suresh, S., "High-Temperature Failure of an Alumina-Silicon Carbide Composite under Cyclic Loads: Mechanisms of Fatigue Crack-Tip Damage," Journal, American Ceramic Society, Vol 72, 1989, pp 1233-1238

[44] Ritchie, R O., "Mechanisms of Fatigue Crack Propagation in Metals, Ceramics and Composites: Role of Crack Tip Shielding," Materials Science and Engineering, Vol A103, 1988, pp 15-28

[45] Tzou, J.-L., Hsueh, C H., Evans, A G., and Ritchie, R O., "Fatigue Crack Propagation in Oil Environments-II A Model for Crack Closure Induced by Viscous Fluids," Acta Metallurgica, Vol

33, 1985, pp 117-127

[46] Rooke, D P and Cartwright, D J., Compendium of Stress Intensity Factors, H M Stationery Office, London, 1975

[47] Tschegg, E K and Suresh, S., "Tensile Fracture Toughness Measurements in Ceramics," Journal,

American Ceramic Society, Vol 70, 1987, pp C-41-C-43

[48] Hasselman, D P H., Venkateswarn, A., and Donaldson, K Y., "Contribution of Damage by Multiple Crack Growth to the Strain-Rate Sensitivity of a Polycrystatline Alumina at Elevated

Temperatures," Journal of Materials Science, Vol 24, 1989, pp 671-680

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Reji John 1 and Noel E Ashbaugh 1

Fatigue Crack Growth in Ceramics and

Ceramic Matrix Composites

of Advanced Materials, ASTM STP 1157, M R Mitchell and O Buck, Eds., American Society

for Testing and Materials, Philadelphia, 1992, pp 28-51

ABSTRACT: Reliable design of ceramic matrix composite components in aerospace appli-

cations requires the knowledge of the crack propagation behavior of these materials at elevated

temperatures The first part of this paper discusses a test setup using a centrally notched disk

to conduct mechanical fatigue crack growth testing of brittle matrices used in these composites

The specimen compliance is monitored using the laser interferometric displacement gage

system To evaluate this fatigue crack growth test setup, cyclic crack propagation is studied

in an alumina ceramic specimen Transmission electron microscopy of surface replicates show

evidence of irreversible microcracking at the crack tip that could provide the mechanism for

fatigue crack growth in this ceramic The second part of this paper discusses the results from

automated fatigue crack growth tests on silicon-carbide fiber-reinforced aluminosilicate glass

matrix composites at room and elevated temperatures using the compact tension geometry

Tests conducted at room temperature indicate high damage tolerance in these composites due

to energy dissipation through distributed matrix cracking around the tip, fiber bridging, and

fiber pull out In contrast, tests at 650°C reveal Mode 1 self-similar crack growth in these

composites and absence of fiber pullout

tolerance, elevated temperature, fatigue crack growth, fiber bridging, fiber pullout, fracture

(materials), microcracking, fatigue (materials), advanced materials

Ceramic matrix composites (CMCs) have been considered to be potentially useful as hot- section components in advanced engines and certain structures in aerospace vehicles Re- liable design of these components requires the knowledge of fatigue crack growth behavior

of the CMC at elevated temperatures The enhanced behavior of the ceramic matrix composite compared to the plain matrix is attributed to mechanisms such as crack arrest, retardation of crack growth, and distribution of damage by the reinforcing fibers [1] To clearly understand the reinforcing effect of the fibers during fatigue crack growth in the composite,

it is essential to determine the cyclic crack growth behavior in the plain brittle (glass or ceramic) matrix This paper is divided into two parts; the first part describes a new automated fatigue crack growth testing system for brittle materials using a centrally notched disk geometry, and the second part describes the results of fatigue crack growth tests on silicon- carbide fiber-reinforced aluminosilicate glass matrix (90/0)3 s composites at room temperature and 650°C using the compact tension geometry

1Associate and senior research engineer, respectively, Advanced Material Characterization Group,

Structural Integrity Division, University of Dayton Research Institute, Dayton, OH 45469

28 Copyright* 1992 by ASTM International www.astm.org

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JOHN AND ASHBAUGH ON CERAMIC MATRIX COMPOSITES 29

Fatigue Crack Growth Testing of Brittle Materials

This section describes the development of a new fatigue crack testing system for brittle materials This includes the specimen geometry and loading configuration, linear elastic fracture mechanics (LEFM) solutions for this geometry, crack opening displacement measurement using the laser interferometric displacement gage system, and a fatigue crack growth test on a COORS 2 AD998 alumina ceramic specimen

Specimen Geometry and Loading Configuration

A circular disk with a middle crack is adopted for the fatigue crack growth test specimen geometry A schematic of the geometry is shown in Fig 1 Following ASTM Terminology Relating to Fracture Testing (E 616-82) procedures, the geometry is designated as DM(C) (Disk with a Middle crack subjected to Compressive loading) This geometry has been used for monotonic mixed-mode fracture toughness tests on brittle materials such as sintered carbide [2], polymethacrylate (PMMA) [3], graphite and marble [4[, and alumina [5] One of the advantages of this geometry is the easy "gripping" of the specimen between the loading shafts by the applied compressive load as shown in Fig 2 This configuration is well suited for tension-weak brittle materials such as glass, ceramics, concrete, and rocks that usually tend to fail at the points of load application in the conventional testing config- urations The simple end fixture also facilitates the use of ceramic loading shafts for high- temperature testing In addition, the DM(C) geometry enables testing the specimens under positive Mode 1, negative Mode 1, mixed-mode and pure Mode 2 loading conditions The negative Mode 1 configuration can be used to study possible crack growth in brittle materials under cyclic compressive fatigue loading, similar to the work done by Suresh [6]

2Registered trademark of Adolph Co., Golden, California

Trang 36

Silicon Carbide Loading Piston

Disk Specimen

Furnace for Elevated Temperature Testing

FIG 2 Schematic of the test setup with the disk specimen

L E F M Solutions f o r the DM(C) Geometry

Yarema et al [2] provide series expressions for Mode 1 and Mode 2 stress intensity factors

(/s and K2, respectively) in terms of crack length (a), diameter (W), and inclination of the

crack to the loading axis These solutions compare well with the results from Atkinson et

al [3], Awaji and Sato [4], and Tweed et al [7], for notch depth ratio (2a/W) less than or

equal to 0.60 A n expression for K1 of the DM(C) geometry is obtained by the authors using

the results from Tweed et al [7] for 2a/W up to 0.9 and assuming that the limiting behavior

at 2a/W = 1.0 for K1 is the same [8] as that of the middle-cracked specimen, M(T) The

expression for K 1 is given by the following equation

where

F(~) = 1 - 0.61'88et + 2.6438a 2 - 5.3122a 3 + 6.1794a 4 - 3.0659a 5

X/] - ot

and a, W, B, and P are defined in Fig 1 This wide-range equation matches the results from

Tweed et al [7] within 0.5% and is assumed to be applicable for 0 < 2a/W <- 1.0

Trang 37

To conduct compliance-based automated fatigue crack growth tests, in addition to the K1 solution, an expression for the crack length as a function of the crack mouth opening displacement ( C M O D ) at the center of the notch is also required A new expression valid

conditions is derived by the authors using the method proposed by Fett et al [9] The resulting expression is given by the following equation

Laser Interferometric Displacement Gage System

A u t o m a t e d fatigue crack growth testing requires a nonvisual method for evaluating crack length The load versus C M O D data provides a convenient measure of specimen compliance from which the crack length is computed using Eq 2 In addition, material behavior such

as closure/bridging in the vicinity of the crack tip could be extracted from the load versus

C M O D data

For the determination of C M O D in high stiffness brittle materials at elevated temperatures, the measurement device must provide high resolution Hence, the laser interferometric

this purpose The I D G system facilitates noncontact displacement measurement useful for elevated-temperature testing This system has a resolution of the order of 0.004 Ixm essential

A schematic of the laser I D G system is shown in Fig 3 The laser beam incident on indentations made on both sides of the crack by a hardness tester is reflected by the angled facets The reflected beams interfere, creating fringe patterns on both sides of the crack

acquisition The C M O D is then computed using the relative displacement between the fringes formed on one side of the crack with respect to that on the other side

The laser I D G system requires pyramidal indents on a polished surface of the specimen Since indentation on brittle materials would initiate fracture, a measurement technique using metallic tabs is developed for this purpose based on the method proposed by Jenkins et al

[13] The elevated temperature environment requires nonoxidizing tabs (for example, plat- inum), but for the development of the technique, steel tabs are used To glue the tabs to the specimen an alumina-based ceramic adhesive (Ceramabond 569, A r e m c o Products Inc., New York) is used This adhesive sets at room temperature and has a temperature limit of

Trang 38

The advantages of the preceding displacement m e a s u r e m e n t technique include: (a) displacement measurements on composites and nonmetallic materials using the laser

I D G system at elevated temperatures, (b) displacement measurement across wide notches

in standard geometries such as C(T) and SE(T), even in metals, and (c) strain measurements

in unnotched tension specimens with tabs glued across the gage length One possible dis- advantage is the averaging of displacement across the glued area Hence, it is preferable to maintain the tab size as small as possible

Trang 39

Fatigue Crack Growth Test on A l u m i n a Ceramic

An alumina (COORS AD998) ceramic disk specimen is machined to a diameter of 51

mm and a chevron notch cut in the center using a circular diamond saw [5], Fig 1 The average notch width is 180 txm The metallic tabs are glued across the notch at the center

of the disk as discussed earlier The specimen is then subjected to cyclic loading with a stress

frequency of 5 Hz at room temperature in laboratory air A servocontrolled hydraulic

is used for this purpose

The alumina disk specimen is first precracked so that the crack tips are sufficiently away from the chevron notch The specimen is removed from the test setup for observation under the microscope to measure the crack length From the measured elastic compliance, C, and

GPa, which is within 5% of the modulus value provided by the manufacturer

After precracking, a fatigue crack growth test with a constant load amplitude is conducted

on the same specimen A typical load versus displacement plot for the ceramic specimen is shown in Fig 5 This figure includes a plot of both the load and CMOD data (a) as well as the load and differential-displacement data (b) A slight nonlinearity at the top of the load- CMOD trace is noticed throughout the test from the beginning Neglecting this portion, a least square procedure is used to fit a straight line (c) to the unloading data between the upper and lower windows (UW and LW, respectively) The slope of this line is equal to the elastic unloading compliance, which when substituted in Eq 2 gives the compliance crack

3.405

linear fit to unloading portion of load versus CMOD for the alumina ceramic

Trang 40

length The deviation of the measured displacement from the least squares fit is then mag- nified three times and plotted as the load and differential-displacement data in the same figure Following the conventional methods, the closure load corresponds to the deviation

of the load versus differential-displacement data from the straight line

The data shown in Fig 5 are obtained at a crack length of 14.2 mm after about 6.3 million cycles into the test Note that the total CMOD is only equal to 1.64 i~m The compliance crack length is plotted agaifist the applied cycles in Fig 6 At selected intervals, crack lengths are measured optically and plotted in the same figure The optical crack lengths are always marginally less than the compliance crack length As shown in Fig 6, the compliance crack growth data are discontinuous and jumps in crack length of about 0.3 mm are observed Occasionally, the data show an apparent decrease of compliance crack length in contrast to the optical measurements This can be attributed to the actual changes in the specimen compliance during the tests because the compliance crack lengths are calculated from the measured compliance These compliance changes might be occurring due to crack bridging and microcracking at the crack tip It should be noted that some of the jumps in compliance measurements occur when the specimen is removed from the machine for optical measurements

To calculate the growth rate, a second order polynomial is fit to the compliance crack length versus cycles plot in Fig 6 and used in conjunction with 1Eq 1 The resulting crack

curve is seen in this figure highlighting the brittle nature of the material [t should be noted that the fracture toughness of this material is about 4.5 MPa V m

At the end of this test, the intact specimen is unloaded and surface replicates are taken near the crack tips These replicates are then viewed under a transmission electron micro-

Tiêu đề	Cyclic deformation, fracture, and nondestructive evaluation of advanced materials
Tác giả	M. R. Mitchell, Otto Buck
Trường học	University of Washington
Chuyên ngành	Advanced Materials
Thể loại	Special Technical Publication
Năm xuất bản	1992
Thành phố	Philadelphia

Định dạng
Số trang	345
Dung lượng	9,43 MB