NASA Technical Reports Server (NTRS) 20000056864: Slow Crack Growth Analysis of Advanced Structural Ceramics Under Combined Loading Conditions: Damage Assessment in Life Prediction Testing

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SLOW CRACK GROWTH ANALYSIS OF ADVANCED STRUCTURAL CERAMICS UNDER COMBINED
LOADING CONDITIONS - DAMAGE ASSESSMENT IN LIFE PREDICTION TESTING
Sung R.Choi"
Ohio Aerospace Institute, Cleveland, Ohio 44142, USA
[[email protected]]
John P. Gyekenyesi
NASA Glenn Research Center, Cleveland, Ohio 44135, USA
[[email protected]]
ABSTRACT mechanics specimens in which the crack velocity measurements are
Slow crack growth a,-udysiswas ped'onnedwith tJ_eedifferent made. Constant s_xess-ratetesting detcrmmes the strensth for agiven
loading histories including constant s_'css-mteJconstanstlress-ratc applied s_-ess; whereas, constant stress and cyclic stress testing
testing (Case I loading), constant skess/constant stress-rate testing measures time to failure for given constant stress and cyclic stresses,
(Case IIloading), and cyclic stress/constant stress-rate testing (Case ITI respectively. Of these test methods, constant stress-rate testing has
loading_ Strength degradation due to slow crack growth and/or been widely utilized for decades to chamcter_ SCG behavior of
damage accumulation was determined numerically as a function of ceramic materials at both ambient and elevated temperatures. The
percentage of interruptiontime between the two loading sequences for advantage of constant stress-rate testing over othermethods lies in its
agiven loading history. The numerical solutions were examined with simplicity: Strengths aremeasured in aroutine manner at four to five
the experimental data determined at elevated temperatures using four applied stress rates by applying either displvzement-control mode or
different advanced ceramic materials, two silicon nitrides, one silicon load-contromlode. The SCGparan_tm'sfor l_e-prediction/desisn are
carbide and onealumina forthe Case Iloading history,and aluminafor simply calculated from a rehtionship between strength and applied
the CaseHloading history. Thenumerical solutions were inreasonable stress rate. Because ofits advantages, conatant stress rate testing has
agreement with the experimental data,indicafin8 that notwithstandin8 been devdoped as an ASTM test standard (C1368-97) to determine
some degree of creep deformation presented for some test materials SCG parameters ofadvanced ceramics at ambient temperature [1]. The
slow crackgrowth was agoverning mechanism associated with failure advantages of constant stress-rate testing have also promoted an effort
forallthetest materials. to develop a companionteststandardtoevaluate SCG parametersat
elevated temperatures, which is underconsi_on within ASTM C28
Advanced Ccramics Committee [2].
INTRODUCTION One ofthedifficulties possibly encountered in elevated-temperature
testinigsthatd,ependinogntesctonditio(ntsesrtatet,imet,emperature
Advanced ceramics m¢ candidate materiedfsorhigh-temperature and environment) and material, the identification of agoverning failure
structuralapplications inheat engines and heat recovery systems. One mechanism may be obscured by the presence of possible multiple
of the mayor limitations of thesematerialsin hightemperature mechanisms, particu_y with a combination of SCG and creep [3-6].
applications is delayed failure, where slow crackgrowth (alsocalled Thus, the determined SCG parameters cannot be soldy representative
'fatlgue"or 'suberitical crackgrowth') of inhenmt flaws caneccur until of one single process, slow crack growth, butacombination of the two
a critical size for catastrophic failure is attahe& Therefore, it,s competing mechanisms. They may also act in series, i.e., creep
important to evaluate accurately slow crack growth (SCG) behavior followedby SCO. TheunderlyinbgasisoftheaforementioneSdCG
with aspecified loading condition so that reasonable life prcdiclinn of testin-gconstansttress-ractoen,stanstums andcyclic stress testing -is
ceramic components ise_ thecrackvelocitfyormulationinwhichcrackpropagationtypically
Thereareseveralmethodsof determin_ SCG of advanced followsapower-lawrelationI.ftheSCG mechanismisdominantfora
ceramics.Typicallyt,heSCG ofco'a_csisdeterminedbyapplying givenmaterial/temperatu/reenviromentalsystem,thenthe SCO
constant_xe=B-rate(also c.BJ]ed"dynamic fatigue"), co_ant stress parameters obtained, in principle at least, should be in a reasonable
(abocaged"mariefatigue"or "stress r.ptmd') or cyclic stress (also. range ofaccuracy, resardle_ oftest method. Fmltmmore, one mnst be
called "cyclic fi_t_,ue")togroundspecimensortoprecrackefdracture able to predict life and/or strength from any loading history that could
"NASAgeaiorReddem ResearchSdentlst,GlennResearchCenter,Cleveland,OH44135(Allcorrespondence=tothisaddress)
Thisisapreprintorreprintofapaperintendedforpresentationataconference.
Becausechangesmaybemadebeforeformalpublication,thisismadeavailablewiththe
understandingthatitwillnotbecited orreproducedwithoutthepermissionoftheauthor.
be a combination of consent s_ess-rate/constant s_s-rate, constant
sb'ess/constent stress-rate, or cyclic stress/constant stress-rate loading
sequence_ There have been some _ental attempts to evaluate
the degree of crack growth or damage accumulation by determining
'fast'-fracture "residual" strength of silicon nitride specimens thathad
been subjected to and then interrupted from tensile cyclic loading at
elevated temperature [7]. However, in general, both analytical work 8
and systematic experimental data on this subject rarely exist in the
literature.
Consequently, the purpose of this workis to better understandhow
damage (SCG, creep or both) was accumulated with time for given
loading history leading to failure of advanced structural ceramics at
elevated tempemture_ Numerical sohfons of strength degradation in
TIME,J
conjunction with crack growth were obtained for each loading history
with a major assumption that the governing failure mechanism was
slow crack growth. Included in the test matrix were two typical
_ethods of constant stress-rote ("dyna_c_ fatigue") andconstant stress CASE"n"w_o (b)
( static fatigue" or "s_ess rupture") tes_g. The SCG and related D /
V
parameterswere determined on the basis of these test results. Then, a
combination of two different loading sequences was applied to test
specimens and the corresponding strengths were measured to see how
s_ength degradation in the form of SCG/damage accumulation took 8
place during the combined loading sequences. The combination of
loading used in thistesting included slow test rate/fast test rate (which
is a combinallon of constant stress-rate/constant sVess-mte testing, l.t L
called here Case Iloading history) and static loading/fast test rate (a
combination of static stress/constant s_ess-rate testing, called Case II
loading). Thetesting was interrupted afterthe fu'stloading sequence at
aspecified time, and then the specimens were fractured at the second TIME, J
loading sequence using a fast test rate of typically 33 MPa/s. The
experimental results were compared with thenumerical solutions.
CASE"HI"LOADING (c)
THEORETICAL BACKGROUND
Approach
Numerical solutions of strength, crack size and other required 8
variables forvarious loading histories arelXeSontedinthissection. The
schematic loading historyconsidered inthis study is depicted in Fig. 1.
The first one, Fig. l(a), called Case I loading, was acombination of __ J'_'ij f
two constant s_ss-rate testing with afast testrateafteraslow testrate.
A specimen was subjected to alow stress rate. Then, the testin8was
interrupted at aspecified time J'muand resumed with afast stress rate
until the specimen fractured. The second loading history, Fig. l(b), TIME,J
called Case 17loading, was a combination of constant stress and
constant stress-rote test_-_. The testing was started initially with a
constant _ inte_zuptedataspecified test time3.nand thenresumed Fig. 1 Schematics of three loading histories considered: (a)
by applying a fast stress rate until the specimen broke. The third Case Iloading, (b) Case IIloading and (c) Case III loading
loading history, Fig. l(c), called Case 111loading, which was a
combination of cyclic stress and constant s_ess-rate testing, was simply
a_placement of astatic stress used in the Case II loading with cyclic second loading, i.e., ¢= 1)which is either constant slress-r_e, constant
_rem. The ratio (¢) of inten_tion time totimeto failure is defined as stress or cyclic stress, see Fig. 1. The case for _ - 0 rcprcsmts the
fonows:
second loading sequ_ce with no the fu_t loading sequeace. The
intezrup6on time was chme_ such thattheratioranged typically from p
=Oto 90%.
¢ =Jim (1)
Ji In many cases, slow crack growth of advanced ceramics under
mode I loading above the fatigue limit, either by stress c(m_on at
ambimt temperature or by grain boundary sliding at elevated
where J-, is the interruption time andJ! is time to failure of a test
teml_atmes , can beexpressed by the following empirical power-law
specimen, subjected to only the first loading sequence (withoutthe
relation[g]
The normalized SIF, K*, in constant mess-rate and cyclic (sinusoidal)
where v, a, tare crack velocity, crack size, and time, respectively. A
and n arethe material/environment-dependent SCG peraraeters. Kiis mess testing canalsobe expressed, respectively [13,14]
the mode I stress intmsity factor (SIF), and K,c is the critical SIF or
fracture toughness of the _ subjected to mode I loading. The g"=d*J[C*]1/2 (9)
simplistic analytical solutions of strength in constant mess-rate testing .I+R I-R . 07a
andof time-to-faihue inconstant stress and cyclic stress testing canbe K*=i---_---+--_--sm[(T-_-):o]*}_ [C*_]2 (I0)
approximatedasfollows [9-11]:
where R is themess (or load) ratio, defined asR = _/_ with ¢_
_r:=D_[a]vj'* (3)
being the minimum applied mess in cyclic loading, and 07is the
t/,=D,[a]-* (4) angular velocity. The normalized SIF for constant s_ess loading is
simply reduced to the case with bothR = 1.0and o*m =o* inEq. (10l
t_=D_[urn]-* (5)
The differential equation Eq. (8), together with Eqs. (9) and (10),
was solved numerically using afourth-order Rungz-Kutla method fora
where _/is the fracture strength corresponding to the applied stress given loading history. The initialcondition was C* ffil.OatJffiO. The
instability conditions were K* = 1.0and dK*ldC* > O. The solution in
rate (_) in constant mess-rate testing, t_ is the time to failure cyclic loading was independent of frequency [14]; hence an arbitrary
subjected to aconstant applied mess (_-)in constant stress testing, and value of wa/A = 100 was used in the analysis. At interruption time,
t_ isthe timeto failure subjected tothe maximum applied stress (am_) Jilt, the corresponding variables including crack Kze, mess, stress
incyclic mess testing. The parametersD's canbeexpressed as follows intensity factor and time were provided to the next (second) loading
[9-11]: sequenceso thatthe requiredvariables were determined until an
instability condition was reached. Includedinthe typical input data
D a = [B(n + l)Si"-21]1('0 were n,R, d * and O*m_. The major assumption in the analysis was
that only one mechanism, i._, slow crack growth, was associated with
D, =BSI "-2 (6) failure.
Ir
Results of Numerical Solutions
0 Stren_h
Normalized sVe.gth (o*/) as a function of percent of interruption
where $_isthe inertstrength andB =2Kio/[Af(n-2)] with Y being the
time (¢ =J'n/Jf)for the Case Iloading history is shown in Fig. 2. Six
crackgeometry factor inthe relation ofKi =YcraIn. j(t) isaperiodic
different values of n tanging from n = 5 to 160 were employed. For
functioinncyclilcoadingspecifieidno(t)= triO(0witharangeof0_
each n value, the initial slow stress rate of _*= Ixl0 "swas followed
j_t)_la,nd ris the period. The SCO perameters nandB (orA) canbe
by the second loading which was chosen as a"* = lxl0 "4,lxl0 "3,lxl0 "2
obtained by a linear regression analysis with _ental data in
conjunction with an appropriate equation, Eq. (3), (4) or(5), depending and lx10 q. The choice of this range of d* was based on the typical
onthetype ofloading. range of applied mess rates commonly used in the actual constant
Toobtain more gene_diz_ convenient andaccurate SCG analysis, sUes,s-rate testing [1]. Forthe case ofn = 5_ SCG susceptibility
several parameters that are commonly specified in the conventional is high,thestrengthdegsdationwithrespecttothestrengthat0,= 0
analytical solutions (Eqs. 3to 6) have to be minimized. This can be depends on intetruptlon time, particularly with increasing stress rate.
done by using anormalization scheme, asused in the l_fevious stu_es The nmximum strength degradation of about 16%and 10%occurred
[12,13]. The normalized variables utilized in the numerical approach at ¢p--90%, respectively, forthe highest mess rateof d *= lxl0 "_and
were asfollows [13,14]: for the lowest rate of dr*-- lxl0 "4. This i_cates that the initial
loadingup to_ ffi90 % resulted in somewhat appreciable en_
K*=_, Kt "j=At;_ C* =_;a _* cr growth/damage-accumulation. For n = I0,the nat_atum meogth
K ;c a_ a.o =-_i; degradation was about 3 %both at d*= lxl0 "t and lx104. For the
(7)
case of higher resistance to SCG, n Z20,themength degradation was
_. _,____"
negligible with less than 0.6 % at ¢ - 90 %, indicating that crack
growth/damage-accumulation rarely occurred during the first loading
where K*, J,C*, o*, o*mx and d *are,respectively, normalized stress sequence. Therefore, Ris concluded that for n> 20 which is file case
intensity factor, normalized time, normalized crack size, normalized formostsiliconniUidesand silicon carbides at devated temperatures
applied stress, normalized maximum applied stress (in cyclic loading) the first loading sequence would not have any significant influence on
and normalized mess rate. a_ is the critical crack s/ze in the inert crack growth/damage, leadin8 to negligible strength degredation. The
condition, or is the initial crack size. Using these variables, the crack second loading rote, which is at least one orderof magnitude greater
propegatiornateofEq.(2)yields than the first one, contruls exclusively the strength via crack growth.
t
%' 1.2 *" 1.2
t • | • i • i • • ! • ! • j • , •
n-5 n- 10
t 01..80 i 0]..08
0.6 0.6,
°
0.2 0.2
l 0.4 l 0.4
0.0 • l s i J ¢ , i 0.0 , I I I | l
0 20 40 60 80 100 0 20 40 60 80 100
%OFINTERRUPTIONTIME,_p %OF INTERRUPTfON TIME,
._, 1.2
D _ 1.2 . , . , , . , .
n-20
r 1.0
1.0 g _ g
0.8 T T _" v
0.6 _ o
-_ ,_o' I
lx10"_[
0.2 lxlffz[ 0.2
l 0.4 --e-- lx10"1
0.0 , I i I i l a I • 0.0 • ' , t , l , , .
0 20 40 60 80 100 0 20 40 60 80 100
%OFINTERRUPTION TIME, % OF INTERRUFHON TIME,
%" 1.2
t:> • i i • i • i • _. 1.2 w • i • m • ! •
n-80 n-160
0.8 0.8
1.0 1.0
0.6 0.6
1x104
0.2 0.2 ----ee--- llxx11_04 I
0.4 : I 0.4 --e-- lx10"_
0.0 i ./ t i . i , | i , 0,0 • i . l , ! ,i I .
0 20 40 60 80 100 0 20 40 60 80 100
%OFIN'IERRUPTIONTIME,_p %OF INTERRUPTION TIME,
Fig.2 Numericalresultsofnormalized strength(o't) asi functionofpercentofInterruption time (p)for differentvaluesof
slow crackgrowth (SCG)parametern inCaseI loading
="
An analysis onhow acrackgrows under agiven loading historywill be a)Forn =10 (/Zig6.A). FortheCaseIloading(Fig.5A(a)_an
presented inalatersection. initiaclracksubjectetdoonlythefirsltoadingsequenceofd* = Ixl0"s
Theresults of strength asafunction of percent of interruptiontime (i.e., q_= 1.0) remained almost unchanged in size fora long time, but
(= _v)forthe Case Hloading history, a combination of constant stress started togrow veryquickly atJ >0.3848 xlOsuntil failure time of,//=
and constant stress-rate testing, Fig. l(b), ispresented inFig. 3. Two to 0.3849 x l0s. This indicates that the initial crack started to grow to
three different normalized applied stresses, ranging from cO = 0.2 to instability atatine greater than 95%of failure time. Therefore, any
0.95 depending on n value, were used for each n value. Since the inten'up6on of loading below ¢ ffi95 % did not give any significant
susceptibiltiotSyCG decreasewsithincreasinng,higher applied stress crack growth so that the resulting strength al_ the second loading
withnarrowrangewasemployedforhighern value.Two testrotesof s_ucnce remained unchanged (compared with the strength at ¢ = 0),
o*"= Ixl0"3andIxl0qwereusedinthesecondloadingsequence.As irrespective of intcm_ption time. This is also reflected as an
intheCaseIloadingf,orn< 10,strengtdhegradatiownassignificatnot insignificant s_ength degradation with respect to the _ength at¢ =0,
interruptitoinme,particularaltybothlowerapplieds_essandhigher as shown in Fig. 2 for n = 10. Similar behavior as in the Case I
s_essrateofb *= Ixl0q.Forn_ 20,strengtdhegradatiofnoragiven loading was aLso observed in the Case II loading (see Figs. 5ACo)).
valueof¢ was independenotfeitherappliedconstansttress(oj)or Most major crack growth occurred close to and/or at failure time.
appliedstresrsate.However,theoveraldlegreeofstrengtdhegradation However, during the first static loading sequence, an initial crack
occurrinfgorthewholerangeofn'swasgreateirntheCase11loading started to grow earlier and greater in size than that of the Case I
than inCase I loading. Forn= 5, the maximum s_ength degradation loading.Hence, the resulting critical cracksizeafterthesecond
of 42 %occurred at<p= 90% with aloading combination of o* = 0.2 loadingsequenceof b *= Ixl0"lwas increasedwithincreasing
and b *= lxl0 "l. For n =lO, about 20 percent strength degradation interruptitoimne (_).As aresult, strength degradatioansafunctioonf
was observed at _= 90 % for the combination of o_ = 0.3 andd'* ffi ¢ became much greater,compared with thatof the Case Iloading (see
Ixl0 "l.Forn>20, the maximum strength degradation of 10%, 5%, 3 Fig. 3forn = 10)_ Forthe Case HI loading, crack growth behavior in
termsofinterruptitoinmewas almostidenticatlothatoftheCaseH
% and 1% took place, independent of ci"*, forn=20, 40, gOand 160,
loading, as canbe seen by compming Fig. 5ACo)with Fig. 5A(c). The
rcspcctivdyM.ore_cy ofstrengtdhegradatioonninterruption
only difference between Case IIand HI loading lied in time to failure:
time(_),comparedwiththeCaseI loading,impliesthatthefirst,
Time to failure foragiven nis always greater in cyclic (R =0.1) than
constant-_ess loading sequence resulted in more crack
in constant stress (R = 1.0) loading [11,14]. Therefore, the resulting
gro_damage-accumulation,thusloadingtolowerstrengtwhhenthe
strength asafunction ofpercent of interruption time (_) renmined the
damaged sl>ecimen was subjected to the second constant stress-rote
same for either Case H(static) or Case HI(cyclic) loading history, as
loading sequence.
shown inFigs. 2and 3forn = 10.
The results of s_ength asafunction of interruptiontime (_) forthe
Case HIloading, acombination of cyclic stress andcomtant stress-rate
b)Forn = 20 (Fig.5B).Forthecaseofn= 20,theoveraltlrendin
loading, see Fig. 1(c), is shown in Fig. 4. The second constant stress-
crackgrowthbehaviorwas verysimilartothecaseofn = I0.Note
rote loading sequence was l_eceded by the first, sinusoidal cyclic stress
againthataninitiaclrackstartetdogrowclosetoand/oratfailurteime,
witha R-ratioofR = 0.I,untilthespecimenfailed.Two tothree
indelxazlent of the type of loading history. However, because of
different normalized _um applied stzesses, ranging from o*_ ffi higherresistancteoSCG incaseofn = 20 the critical cracksizeat
0.2 to0.95, were used foreach nvalue. Note that Cr*m_applied in the
instability between q ffi0and 0.9 was all smaller (and less dependant
CaseM loading was identical in magnitude to o* applied intheCase lI onmtoxruptiontime) thanthat of the case forhigher SCG susceptibility
loading.As inthecase]Iloadingt,wostresrsotesofd *= Ixl0"3and
with n = 10. As aconsequence, strength degradation as a function of
Ixl0qwerealsousedinthesecondloadingsequence.Comparingthe interruption time (_v)was less significant compared with that ofn = 10
results inFigs. 3and4,it canbe readily evident thatforthe given nand (see Figs. 2through 4forn=20).
o*ma = c_strengtdhegradatioinntheCaseHIloadingwasalmostthe
sameasthatintheCaseIIloading.Itshouldbenotedthatconstant Based onthenumericalresults onstrm_ and crack growth, itcanbe
stres(si.eR.,= 1.0)resultisnmuch longerliftehancyclisctreswsithR mnmari_ that strength degmhtion due to crack growth or damage
ff0i.1[I1,14].However,intermsofstrengtdhegradatioansafunction accumulation as a result of the first loading sequence depends on
ofpercentofinterruptitoinme,eitherconstansttres(sCaseIIloading) interruptitoinme¢ andSCG pmmnc_ n fora givenloadinghistory.
orcyclicstres(sCaseHIloadingy)ieldedthesameresult. The _ degradaticofndegreeof crackgrowth/damage-
accumulatioansafunctioonfint_wptiontimewassignificafnotrlower
_IQw Crack Growth SCG pmmnetem n_;10, butbecameinsignificantwith increasing SCG
Typical examples of crack growth/damage-accumulation subjected immme_ of n > 20. This trend was observed more dominant forthe
to the three diffcrent loading histories are iTesented inFig. 5forbothn
Case Iloading than the Case lIor HIloading history. Thelmy factorthat
=I0 and20. The figuresshow how aninitiaclrackgrowswithtime governssuch strengthdegradationor crackgrowthbdmviorwasthatan
during the whole loading history until failure occurs. The loading initial crackstartetdogrowtypicalcllyose toand/oratfailurteimeaftear
combinations employed for each n were as follows: d* ffi lxlO"5
subs_tisllylongincubatiotnime.Thislongincubatiotnime,uniqueto
(la)/d* = Ixl04forCaseIloading0*= 0.5(la)/d*= Ixl0q (2e) ceramic materials exhibiting n >20, was also abasis oftheaccelerating
fcfCaseIIloading;¢r*m_= 0.5(la)/d* = Ixl0"](2_) forCaseHI test methodology in constant stressda_ testing where depending on n
loading.Noteagainthatthecaseof<p= 1.0representosnlythefirst valueapixopriatpercloadingcanbe_plied to testspecimens_or to
loadingsequenceapplied. testing thus saving asignificantamountof testtimes [15].
_'- 1.2 • , .... - , •
_" 1.2 _ n=5" , ,"_ . .... I n"lO
l.OI
0.8 IxlO'_
0.8 lxlO 4
o,Fl-.:-.:::I
0.2 [E°'=°°'3=10"3 I
I 0.4 _ * Ix104 I 0.4 0*=0.7J
r [-_- o.=0.7I
0.0 " " ' ' ' " ' " ' " 0.0 • e • I • s • i •
0 20 40 60 80 I00 0 20 40 60 80 100
% OF INTERRUPTION TIME, _p % OF INTERRUPTION TIME, _o
I • i • I • _'- 1.2 ! I |
_" 1.21-n-20, . •n-40
lxlO "t
lxlO"
01..80' lxlO.S :
_ 0.8 ixI0.3_"'_--'q_.,-_
0.6 r_ 0.6
0.2 0.2 J._T°."_°-'I
l 0.4 ]__,.v_..°o*'_=00.8"5] l 0.4 o.=0.7
0.0 I I , ! . 1 , I • 0.0 I I t I , u • i ,
0 20 40 60 80 IOO 0 20 40 60 80 I00
%OF INTERRUFI'ION TIME, _p %OF INTERRUPTION TIME,
_" 1.2 I t • e ! • *_" 1.2 • I • t • ! !
n-80 lxlO.i n=160 lxlO"
1.0
ixl04 IxlO4
0.8
0.6 l°.4!I
il°--,I
0.2 0.2 ' a,_.9
0.4 _ o-=0.91 o*=0.93
0.0 t I ' ! ' l , I , 0.0 , t , , I , • •
0 20 40 60 80 100 0 20 40 60 80 100
%OF INTERRUFI'ION TIME, _o %OF INTERRUPTION TIME, 9
Fig. 3 Numerical results of normalized strength (ohf) as a function of percent of Interruption time (4P)for different values of
slow Prick growth (SCG) parameter n in Case II loading
_,- 1.2 . 0 . , .... •
n-lO
_'- 11..20 1.0
io. lxlO"l
0.8 Ixl04
0.6
o,_.oI5
00..62 _ 0.2 o._.o.,i
l 0.4 0.4
00 0.0 • I • I • I • I •
0 20 40 60 80 100 20 40 60 80 100
%OF INTERRUFrlON TIME, %OFIN'rERRUFTIONTIME,_p
! ! ! , _" 1.2 I ! ! !
_'... !.2 _ n'20' n'40
lxlO"1
Ixl0"I 1.0
e
lxl04 :
0.8
l0o.6 _ .:.-Ii:xl0,4," 0.6
0.2 --e-- a*,,-0.5 0.2 °'-'°"1
o,,I,'0.8 l 0.4 a*ma'0.7 I
0.0 ;' 7 _ . , 0.0 , I • I t 1 • I .
0 20 40 60 80 100 0 20 40 60 80 100
%OF INTERRUPTIONTIME, %OFI_ERRUPTION TIME,
*_'b- 1.2 ....... , b 1.2 • , • , • ° • , •
Ixl04
1.0 'rt-80 _r 1,0 n-160 IxlO'St $
lxlO 4 "--
0.8 0.8 lx104
0.6 0.6
R-0.1"
-,- o._..oI.,
0.2 0.2 I
o,_..oI.,
0.4 °""0"9 I l 0.4
0.0 • I , I t I • I . 0.0 , • | • I i | i I I
0 20 40 60 80 I00 0 20 40 60 80 100
% OF INTERRUPTION TIME, % OF INTERRUPTIONTIME,9
Fig.4 Numericalresultsofnormalizedstrength(o'f) asafunctionofpercent ofInterruptiontime (p)for differentvalues of
slow crackgrowth(SCG)parameter ninCaseIilloading
U 5
r
CASE "I"LOADING
4 n-iO; 10_/104 m 4 n=20; 10"5/10"l
_'I.0
q,,.o
I
I 2! _ _=0.6-0_ (a}
-----------_-- ,L
lip 101 102 103 104 11_ 106 10o 10! 102 l0s 104 105 10_
NORMALIZED TIME, J
NORMALIZED TIME, J
_ , | , , I D0 5 , ....
4 CASEv"r_If1"0L;O0.A51D1I0N4G 4 nC,A-2S0E;0".5H/1"0LO"lADING
l 3 q_l.0 3
q_l.O I
2 --_
I _ (b) l 21 _-0._.9_ (b)
1, I ] I I I I I [ I
10o 10! 102 103 104 l0s 106 l0° 10' 10s 10_ 104 l0s 10_
NORMALIZED TIME, J
NORMALIZEDTIME,J
C.) 5 ...... 5 ......
CASE "m"LOADING q
4 m-lO; R-0.1; 4 CnA=2S0E; "RI-0_.'1L;O0A.D5/I1N0G"'
q_l.0
3 @=I.0 0.5/10"1•
3
_-o.6-o.9.._
_ 2 _.6._.9.
J
1 (c) ") ,o,
[ i I ' [ J I I I I I I
1_ 10! 102 10s 104 10_ 11_ 10_ 10e 10] 102 10_ 104 l0s 10• 107
NOR/4ALIZED TIME, J NORMALIZEDTIME,J
[A]n = I0 [B] n = 20
Fig. 5 Nurnedcal results of normalized crack size (C*) ms• function of time (J) for different values of Interruption time (IP)
In three Ioeding histodes: [A] For SCG parameter n ,, 10; [B] For SCG parameter n -"20
EXPERIMENTAL PROCEDURE EXPERIMENTAL RESULTS AND DISCUSSION
In orderto verify the numerical solutions, experiments to cover (a) Case ILoading
different loading histories as specified in Fig.l, was conducted at Theresultfsorthe Case I loadingtestfsor96wt%alumina, NC132
elevated temperatures. The nominal dimensions of rec_mgular-beam silicon niUide, ASS00 silicon nltride and Hexoloysilicon carbide are
test specimens in accordance with test method ASTM C-1211 [16] summarized in Fig. 6. The figure incloded flexure strensth as a
were 3mm by 4 mm by 50 ram, respectively, in height, width and function of percent of intetrup6on time ¢ for each material The
leagth. Test sp_imens were subjected to appropriate flexural loading horizontal line represents thestrength de.mined with zero interruption
depending on the type of loading history using SiC four-point flexure time ¢=0, thatis,the 'fast'-ffacture s_mgth evaluated at 33.33 MPa/s
fixtureswith 20-ram inner and 40-mm outer spans via [6,18]. The three materials including NC132 and ASS00 silicon
eleclromechanioaanld serve-hydraultiecstframes(ins_onModels nitrides and Hexoloy silicon carbide exhibited asomewhat appreciable
8562 and 8501). All test specimens were equilibrateadt test variation(in average sense) in strength between ¢ =0and p ffi80or 90
temperatures forabout20 min priortotesting. Four different materials %. Itisbelieved that this was atlributetdothe inherently large
including 96 wt % alumina, NC132 silicon nitride, ASS00 silicon slrength scatter, typical of advanced ceramics that ranges ommnonly
nitridea,ndHexoloysilicocnarbidewereusedintheCaseIloading, from 10 to 13 in We_ull modulus. By contrast, 96 wt % alumina
while ouly 96 wt % alumina was used in the Case II loading. The exhibited a very small scatter, thus re_ily concluding that the
reasonforthechoiceofaluminainbothCaseIandIItestinwgasthat difference in strength between _p= 0 and _ = 80 or 90 % was
unlike other materials, 96wt %alumina has exhibited a considerably insignificant,
small strengthscatter with aWdbull modulus typically greaterthan 20
at tither ambient and elevated temperatures [6]. Hence, it would be (b) Case IILoading
possible tosee material's response to fifeand strengthmore clearlyand Figure 7 showsthe results of constant stresstestingfor 96 wt %
accurately with even asmall number (about5at each condition) of test alumina at lO00°C. The slow crackgrowth parametersn andD, in Eq.
specimens. Also note thatthe alumim was very susceptible to SCG at (4) were determined asn = 9.8and Ds = 4.69x102° with units of 'MPa'
elevated temperatures _ 800°C with significantly low values of SCG in stress and 'second' intime. NotethatSCO parameter n detenn_ed
parameter ofn = 7-12 [17], so that it would be much easierusingthe from constant stress testing was in reasonable agreement with n = 8.3
aluminatoscrutinitzhee influence ofSCG/damage-accumulatioonn from constant s_ess-rate testin8 de,'mined from aprevious study [6].
thecombinedloadingseqtumcesmore accuratelyT.he expedm_tal The results oftheCaseIIloadingtestwsas presenteidnFig. 8, where
work for theCase IHloading was not conducted in this study, primarily strengths determined at 33.33 MPa/S, afterthe firstloading sequence of
duetolimited availability oftestspecimens. constant stress of 50 or 65MPa, was plottedas afunction of percent of
interruptitoimne (q_).As seeninthe figure, the slrength exhibitead
a) Case Iloading
significant scatterparticularly at ¢ = 75 and 90 %. much greater than
IntheCaseIloadtestingt,heloadinghistoriyncludeda slowtest
that exhibited in the Case I loadinghistoryfor the same alumina
rateof0.033MPa/sforthefastloadingsequenceandthenafasttest
material. It isbelieved that this was attributed to the fact thatno exact
rateof33.33MPa/sforthesecondloadingsequence.Thepercentage
failure time of each individual test specimen subjected to the Case iI
of intmuption time (¢ = t._t/) ranged from ¢ = 70 to 90 %. The loading could be known and that as a result the actual corresponding
average failure time (= t/)of test slx_imens only subjected to the fwst interruption time foreach test specimen could not be determined. This
loading sequence (with 0.033 MPa/s) was detennin_ from the will bediscussed in alatersection.
previous studies [6,18], and used here asareference valueto calculate
t_ for agiven value of ¢. Four ceramics including 96 wt %alumina, (c) Compwison of Experimental Data withNumerical Solutions
NC132 siliconniU'ideA,S800 siliconhi,de, and Hexoloysilicon The comparison of mength as a function of _ between the
carbideweretestedattemperatureosf1000,1100,1200and1371°C,
exl_-imental dataandthenumericalsolutionsforeachloading history
respectivelyT.ypicallya totalof fivespecimens,dependingon
• wasmadeandpresentedinFiss.9and I0. Thereducedslrensth(a,*)
materialw,ereusedateachvalueof_. The majormechanicaland
physicalpropertieosfthetestmaterialssuchas Young'smodulus, usedherewasdefined suchthatstrengthdeterminedatany givenvalue
density, fracture touglmess,strength and slow crack growth can be of ¢ wasnormalizedwith respectto thesUengthdeterminedat ¢= O,
found elsewhere [18]. whichis_ asfollows"
a,*= o'f, (ll)
b) Case flloading
Constantstress("static fatigue") testing for 96 wt %alumina was
first conducted in flexure at lOOff'C to determineSCGbehaviorand
thusto obtainthetime-to-failure data_Four differentappliedstresses where o', isthe strmgth atany given value of ¢,(which isdetermined
rangingfrom50to 100MPawereemployed,withatotaloffive tonine atafast test rate of 33.33 MPa/s after the tim loading sequence) and
specimenstestedateachappliedstress. TheCaseITloadin8 history
or4,.o is the strength determined at ¢ ffi0(which is simply the 'fast'-
consistedofaconstantstress(for thefast loading sequence)andafast
fracture strength determined at 33.33 MPa/s without any first loading
stressrate of 33.33 MPa/s (for the secondsequence). Two applied
sequence).
stressesof 50 and 65 MPa were usedin the first loading sequence.
Three different values of interruption time, _ =60, 75 and 90%, were
i) Case Iloading. As seeninFig. 9, except for96wt % alumina,
utilized ateach applied stress, with atotalthreeto five specime_ tested
the discrepancybetweeatheexpedm_tal mean-strengthdataandthe
ateach interruptiontime.
numericalsolutions wassomewl_t large. However,asaforementioned,
considering low Wdbull modulus (10-13) typical of many advanced
6OO 1000
' I • ! * ! i ' I . I ' I ! -
96 wt%ALUMINA (a) NC132 SLjN.;1100°C (b)
1000°C
i ° tD'-°
300 700
2OO
0 i ! . I • i i i • ! , I I I I i
0 20 40 60 80 100 0 20 4O 6O 80 100
PERCENT OF INTERRUPTION TIME,9[%] PERCENT OF INTERRUPTION TIME. 9 [%]
1000
• i • ! , ! ' I ! , ! , ! ,
ASS00 Si:N.:1200°C (c) HEXOLOY (SIC):1371"C (d)
_ 90O
o_
t°
700 3OO
l °
2OO
500
4OO I I i l i I i I I , 0 , I • i | I I I
0 20 4O 60 SO 100 0 20 40 60 80 IOO
PERCENT OF INTERRUPTION TIME,9 [%] PERCENT OF INTERRUPTION TIME. 9 [%]
Fig. 6 Experimental results of flexural strength as a function of percent of Interruption time (9) for Case I loading tests,
determined from 96 wt % alumina, NC132 and AS800 silicon nitddea, and Hexoloy silicon carbide at elevated
temperatures. Each solid line represents the mean strength at p=O.
200
I | I I
96wt%ALUMINA;IOO0°C
Prediction
o (_ eon_ stre_ tom
8O
7O Best-tit _
6O
5O
4O
EXP.DATA I
3O I l I I
]oo 101 lO2 10_ 104 iOs
TO FAILURE, tr[s]
Fig. 7 Experimental results of constant streu ("static fstigue") testing for 96 wt % alumina at 100000. A prediction made
from the constant stress-rate ("dynamic fatigue") testing data [6] was Included as a dotted line.