NASA Technical Memorandum ! 06475

ir -']_7

/sP

-":_ _-:_ Durability Evaiuiiti0n 6T-Ceramic

Components Using CARES/LIFE

Noel N. Nemeth

Lewis_ R_esea_rch Cent_er_......

Cleveland, Ohio

Lynn M. Powers

Cleveland State University

Cleveland, Ohio

m

and

Lesley A. Janosik andJ0hn P._Gyekenyesi

Lewis Research Center

---_ _--_ Cleveland, Ohio

Prepared for the

39th Intemational Gas Turbine andAer0engine Congress

sponsored by the American Society of Mechanical Engineers ....

The Hague, The Netherlands, June 13-16, 1994

_4 (NASA-TM-I06475) DURABILITY

EVALUATION OF CERAMIC COMPONENTS

USING CARES/LIFE (NASA) 15 p

rU/ A

N94-24682

Unclas

G3/27 0205033

https://ntrs.nasa.gov/search.jsp?R=19940020209 2019-07-08T12:31:36+00:00Z

DURABILITY EVALUATION OF CERAMIC COMPONENTS USING CARES/LIFE

Noel N. Nemeth

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135

Lynn M. Powers

Department of Civil Enginnering

Cleveland State University

Cleveland, Ohio 44115

Lesley A. Janosik and John P. Gyekenyesi

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135

ABSTRACT

The computer program CARES/LIFE calculates the timedependentreliability of monolithicceramiccomponentssubjected

to thermomechanical and/or proof testloading. This programis

an extensionof theCARES (Ceramics Analysisand Reliability

Evaluation of Structures) computer program. CARES/LIFE

accountsfor the phenomenonof subcriticalcrack growth (SCG)

by utilizing the power law, Pads law, or Walker equation. The

two-parameter WeibuU cumulative distribution function is used

to characterize the variation in component strength. The effects

of multiaxial stresses are modeled using either the principle of

independent action (PIA), the WeibuU normal stress averaging

method (NSA), or the Batdorf theory. Inert strength and fatigue

parameters are estimated from rupture strength data of naturally

flawed specimens loaded in static, dynamic, or cyclic fatigue.

Application of this design methodology is demonstrated using

experimental data from alumina bar and disk flexure specimens

which exhibit SCG when exposed to water.......

NOMENCLATURE

A

a

B

g

H

surface area; material-environmental fatigue constant

crack half length

subcritical crack growth constant

Shetty's constant in mixed-mode fracture criterion

g-factor

step function

i

K

k

m

N

n

Pf

Q

R

T

t

to

V

x,y,z

Y

C_

A

11

CY

ao

ranking of ordered fracture data in statistical analysis

stress intensity factor

crack density coefficient

WeibulJ modulus, or shape parameter

material-environmental fatigue constant

number of cycles

cumulative failure probability

cyclic fatigue parameter

ratio of minimum to maximum effective

stress in a load cycle

period of one cycle

time

time-dependent scale parameter

volume; crack velocity

Cartesian coordinate directions

crack geometry factor

angle between Ga and the stress ¢_1

angle between 6n projection and the stress 62 in

plane perpendicular to _l

increment

crack density function

3.1416

applied stress distribution

weibudl scale parameter

tensor stress components; principal stresses

(61 > 6 2>- o3)

1 Noel N. Nemeth
"c

tF

t2

c0

shear stress acting on oblique plane whose normal is

determined by angles a and

spatial location (x,y,z) and orientation (a,[i) in a

component

solid angle in three-dimensional principal stress

space for which o e >-Oct

angle in two-dimensional principal stress space for

which oe >_oct

Subscripts:

B Batdoff

c cyclic; critical

ch characteristic

cr critical

d dynamicfatigue

e,ef effective

eq equivalent

f failure; fracture

I crack opening mode

II cracksliding mode

!1"I crack tearing mode

i i'th

max maximum

min minimum

n normal;normalstress averaging

S surface

T transformed

u uniaxial

V volume

w Weibun

O characteristic

Superscripts:

- modified parameter

normalizedquantity

INTRODUCTION

Advanced ceramic components designed for gasoline, diesel,

and turbine heat engines are leading to lower engine emissions,

higher fuel efficiency, and more compact designs due to their

low density and ability to retain strength at high temperatures.

Ceramic materials are also used for wear parts (nozzles, valves,

seals, etc.), cutting tools, grinding wheels, bearings, coatings,

electronics, and human prostheses. Among the many requiremerits for the successful application of advanced ceramics are the

proper characterization of material properties and the use of a

mature and validated brittle material design methodology.

Ceramics are brittle and the lack of ductility leads to low strain

tolerance, low fracture toughness, and large variations in

observed fracture strength. The material as processed has

numerous inherent randomly distributed flaws. The observed

scatter in fracture strength is caused by the variable severity of

these flaws. The ability of a ceramic component to sustain a load

also degrades over time. This is due to a variety of effects such

as oxidation, creep, stress corrosion, and cyclic fatigue. Stress

corrosion and eycfic fatigue result in a phenomenon called

subcdtical crack growth (SCG). SCG initiates at an existing flaw

and continues until a critical length is reached, causing catastrophic crack propagation. The SCG failure mechanism is a

load-induced phenomenon over time. It can also be a function of

chemical reaction, environment, debris wedging near the crack

tip, and deterioration of-bridging ligaments. Because of this

complexity, models that have been developed tend to he

semi-empirical and approximate the behavior of subcritical crack

growth phenomenologicaUy.

The objective of this paper is to present a description of the

integrated design computer program, CARES/LIFE (1)(Ceramics

Analysis and Reliability Evaluation of Structures LIFE

prediction program). The theory and concepts presented in this

paper reflect the capabilities of the CARES/LIFE program for

time-dependent probabilistic design. To determine the validity of

the design methodology utilizedinthis software, time-dependent

reliability predictions from CARES/LIFE are compared with

experimental data (2) from uniaxially and biaxially loaded

alumina flexure bars and disks which are known to exhibit slow

crack growth in water.

PROGRAM CAPABILITY AND DESCRIPTION

ProbabUisticcomponent design involvespredictingthe

probabilityof failurefor a thermomechanicallyloaded

component from specimen rupture data. Typically these

experiments are performed using many simple geometry flexural

or tensile test specimens. A static, dynamic, or cyclic load is

applied to each specimen until fracture. Statistical strength and

SCG (fatigue) parameters are then determined from these data.

Using these parameters and the results obtained from a finite

element analysis, the time-dependent reliability for a complex

eornponent geometry and loading is then predicted. Appropriate

design changes are made until an acceptable probability of

failurehasbeanreached.Thisdesignmethodologycombinesthe

statistical natureofstrength-controlling flawswiththemechanics

ofcrackgrowthto allowformultiaxialstressstates,concurrent

(simultaneously occurring) flaw populations, and scaling effects.

These issues are addressed within the CARES/LIFE program.

CARES/LIFE predicts the probability of failure of a

monolithic ceramic component as a function of service time. It

assesses the risk that the component will fracture prematurely as

a result of subedtical crack growth. The effect of proof testing

components prior to service is also considered. CARE, S/LIFE is

coupled to commercially available finite element programs such

as ANSYS, ABAQUS, MSCINASTRAN, and COSMOS/M.

CARES/LIFE is an extension of the CARES (3'4) program. It

retains all of the capabilities of the previous CARES code,

which include fast-fracture component reliability evaluation and

Weibull parameter estimation from inert strength (without SCG

contributing to failure) specimen data. CARES/LIFE can

estimate parameters that characterize SCG from specimen data

as well.

Finite element heat transfer and linear-elastic stress analyses

are used to determine the component's temperature and stress

distributions. The reliability at each element is calculated

assuming that randomly distributed volume flaws and/or surface

flaws control the failure response. The probability of survival for

each element is assumed to be a mutually exclusive event, and

the overall component reliability is then the product of all the

element survival probabilities. CARES/LIFE generates a data file

2 Noel N. Nemeth
containing element risk-of-rupture intensities (a local measure of

reliability) for graphical rendering of the structure's critical

regions.

CARES/LIFE describes the probabilistic nature of material

strength, using the WeibuLl cumulative distribution function. The

effect of multiaxial stresses on reliabiLity is predicted using the

principle of independent action (PIA), (s'6) the Weibull normal

stress averaging method (NSA), G) or the Batdorf theory. (s'9) The

Batdoff theory combines the weakest link theory and linear

elastic fracture mechanics (LEFM). Conventional fracture

mechanics analysis requires that both the size of the critical

crack and its orientation relative to the applied loads determine

the fracture stress. The Batdoff theory includes the calculation of

the combined probability of the critical flaw being within a

certain size range and being located and oriented so that it may

cause fracture. A user-selected flaw geometry and a mixed-mode

fracture criterion are required to model volume- or surfacestrength-limiting defects. Mixed-mode fracture refers to the

ability of a crack to grow under the combined actions of a

normal load (opening mode) and shear load (sliding and tearing

modes) on the crack face. CARES/LIFE includes the total strain

energy release rate fracture criterion, which assumes a crack will

extend in its own plane (coplanar). (9) Out-of-plane crack

extension criteria are approximated by a simple semiempirical

equation. (l°,lD Available flaw geometries include the Griffith

crack, peuny-shaped crack, semicircular crack, and notched

crack. The Batdorf theory is equivalent to the probabilistic

multiaxial theories proposed by Evans(12) and Matsuo.(13)

Subcritical crack growth is difficult to model because it is a

complex phenomenon often revolving a combination of failure

mechanisms. Existing models usually involve empirically derived

crack propagation laws that describe the crack growth in terms

of the stress intensity factor at the crack tip plus additional

parameters obtained from experimental data.

In CARF_,S/LIFE, the relations describing subcritical crack

growth arc din_tly incorporated into the PI.A, NSA, and Batdoff

theories. Subcritical crack growth is modeled with the power

law,(14'15)the Paris law, (16) and the Walker law(17'18) for static

and constant-amplitude Cyclic loading. These laws use

experimentally determined parameters which are material- and

environment-sensitive. The power law is used to model stress

corrosion cracking in materials such as glasses and alumina

exposed to H20. Elevated-temperature slow crack growth of

silicon nitfides, silicon carbides, and alumina aLsofollows power

law behavior.

Some polycrystalline ceramics are prone to strength

degradation due to mechanical damage induced by cyclic

loading. The Paris and Walker laws have been suggested as

modeLs to account for this behavior. (Is) The Walker equation is

functionally similar to the Paris equation with additional terms

to account for the effect of the R-ratio (minimum cycle stress to

maximum cycle stress) on lifetime.

CARES/LIFE is capable of predicting the change in a

surviving component's reliability after proof testing is performed.

Proof testing is the loading of all components prior to service to

eliminate those which may fail prematurely. The components

that survive the proof test-will have a lower (attenuated) risk of

failure in service. In CARES/LIFE the attenuated failure

probability iscalculatedusingthePIA,theWeibullnormalstress

averaging,and theBatdorftheories.The Batdorfmodelisused

tocalculatetheattenuatedfailureprobabilitywhen theprooftest

load and the serviceload are not in lineor have different

multiaxiai stress states. This feature is useful when the proof test

does not identically simulate the actual service conditions on the

component. The durations of the proof test and the service load

are also considered in the analysis.

Predicted lifetime reliability of structural ceramic components

depends on Weibull and fatigue parameters estimated from

widely used tests involving flexural or tensile specimens.

CARES/LIFE estimates fatigue parameters from naturally flawed

specimens ruptured under static, cyclic, or dynamic (constant

stress rate) loading. Fatigue and Weihull parameters are

calculated from rupture data of three-point and four-point flexure

bars, as well as tensile specimens. For other specimen

geometries, a finite element model of the specimen is also

required when estimating these parameters.

THEORY

Tune-dependent reliability is based on the mode I equivalent

stress distribution transformed to its equivalent stress distribution

at time t=0. Investigations of mode I crack extension (19) have

resulted in the following relationship for the equivalent mode I

stress intensity factor

gx_qCe,0 = o_Ce,t) x _ (D

where_q6P,t) istheequivalentmode Istresson thecrack,Y

isa functionofcrackgeometry,aCF,t)istheappropriatecrack

length,andW representsa location(x,y,z)withinthebody and

theorientation(a,_)of thecrackIn some modelssuchas the

Weibulland PIA,v/representsa locationonly.Y isa function

ofcrackgeometry;however,hereinitisassumedconstantwith

subcriticalcrackgrowth.Crack growthas a functionof the

equivalentmode Istressintensityfactorisassumed tofollowa

power law relationship

da(_P,t) hl

= A K,_,(_P,t) (2)

dt .tr.._--

where A and N are material/environmental constants. The

transformation of the equivalent stress distribution at the time of

failure, t=tf, to its critical effective stress distribution at time t=0

_sexpressed as(2°_D

°_,0(P'tr) j_tf oleq(_P,t) N dt °_Ieq20P'tf) _'_ (3) = 4-

B

3 Noel N. Nemeth
where

B

A y2 KI.-2c (N-2)

is a material/environmental fatigue parameter, Kic is the critical

stress intensity factor, and O_:q(_P,tf)is the equivalent stress

distribution in the component at time t=tf. The dimensionless

fatigue parameter N is independent of fracture criterion, B is

adjusted to satisfy the requirement that for auniaxial stress state,

all models produce the same probability of failure. The

parameter B has units of stress 2 x time.

Volume Flaw Analys|s

The probability of failure for a ceramic component using the

Bmdorf model (s'9'22) for volume flaws is

Pfv= 1 - exp - G d_v(_cr)

t VL o 4x dOcr

(4)

where V is the volume, 11v is the crack density function, oe

is the maximum value of %_q.ofor all values of _P, and fl is _'_

area of a solid angle projected onto a unit radius sphere in

principal stress space containing all crack orientations for which

the effective stress is greater than or equal to the critical mode

I strength, Oct.The crack density distribution is a function of the

critical effective stress distribution. For volume flaw analysis, the

crack density function is exp_ as

m V

"nv(a=_)) : kBv _c_

(5)

where kBv and m v are material constants. The solid angle is

expressed as

f_ = £2_ £x H(oi_,O,Ocr) sina da dl_ (6)

where

f

H(OieqO,Ocr)-- 101 _Ieq,O->Ocr

' L- cs_, o<°=

and a and 15are the radial and azimuthal angles, respectively, on

the unit radius sphere. The Wansformed equivalent stress O1eq,0

is dependent on the appropriate fracture criterion, crack shape,

and time to failure, tf. Equation (4) can be simplified by

performing the integration of Oct (_) yielding the time-dependent

probability of failure for volume flaw analysis

[ k.v f my Vl

O)

Fracture criteria and crack shapes available for time-dependent

analysis are identical to those used for fast fracture analysis in

CARES. (3,4) These fracture criteria include Weibull normal

stress averaging (a shear-imensitive case of the Batdorf theory),

the total coplanar strain energy release rate, and the noncoplanar

crack extension (Sherry) criterion.

For a stressed component, the probability of failure for volume

flaw analysis is calculated from equation (7). The finite element

method enables discretization of the component into incremental

volume elemen_ CARE.S/LIFE evaluates the reliability at the

Gaussian integration points of the element or, optionally, at the

element centroid. Suhelement volume is defined as the

contribution of the integration point to the element volume in the

course of the numerical integration procedure. The volume of

each subelement (corresponding to a Gauss integration point)(4_

calculated using shape functions inherent to the element type _ '.

Assuming that the probability of survival for each element is a

mutually exclusive event, the overall component reliability is

then the product of all the calculated element (or subelement)

survival probabilities.

Surface Raw Analysls

The probability of failure for a ceramic component using the

Batdoff model(8'9'22)for surface flaws is

P_ = I - exp

(8)

where A is the surface area, _S is the crack density function,

°e is the maximum value of o_1, 0 for all values of _F,and m

is _ arc length of an angle a projected onto a unit radius semicircle in principal stress space containing all of the crack

orientations for which the effective stress is greater than or equal

to the critical stress. Analogous to the argument for volume

flaws, equation (8) can be reformulated, yielding (_)

pfs(tf)_- i_expI_kBsf_, 1¢ ms ] (9)

The transformed equivalent stress _I-o is dependent on the

AI;_qw

appropriate fracture criterion, crack shape, and time to failure,

tf. The fracture criteria and crack shapes available for timedependent analysis are identical to those used for fast fracture

analysis. These fracture criteria include Weibull normal stress

averaging (a shear-insensitive case of the Batdorf theory), the

4 Noel N. Nemeth
totalcoplanar strainenergyreleaserate,andthenoncoplanar crackextension(Sherry) criterion.

Thefiniteelement method enables discretization of the surface

of the component into incremental area elements. CARES/LIFE

evaluates the failure probability at the Gaussian integration

points of shell elements or, optionally, at the element centroids.

The area of each subelement (corresponding to a Gaussian

integration point) is calculated using shape functions inherent to

the element type (4). Assuming that the probability of survival for

each element is a mutually exclusive event, the overall

component reliability is then the product of all the calculated

element (or subelement) survival probabilities.

Static Fatigue

Static fatigue is defined as the application of a nonvarying load

over time. For this case the mode I equivalent stress, OieqCP,t),

is independent of time and is thus denoted by O_=q(V/).

Integrating equation (3) with respect to time yields

Oleq.O(tP,tf) ----Oleq(W_ff OIe'q(_P) 2 + 1

B

(10)

Dynamic Fatigue

Dynamic fatigue is defined as the application of a constant

stress roteO(_F) over a period of time, t. Assuming the applied

stress is zero at time t=0, then

O_q_,t) = ctCe) t

(11)

Substituting equation (11) into equation (3) results in an

expression for effective stress at the time of failure

<(xP,t f) tf

Oleq,0(xp) = [ _ B + O_le_2Cp,tf)

(12)

Cyclic Fati.que

Cyclic fatigue is defined as the repeated application of a

loadingsequence.Analysis of the time-dependentprobability of

failure for a component subjected to various cyclic boundary

load conditions is simplified by transforming that type of loading

to an equivalent static load. The conversion satisfies the

requirement that both systems will cause the same crack

growth. (23) Implicit in this conversion is the validity of equation

(2) for describing the crack growth. The probability of failure is

obtained with respect to the equivalent static state.

Evans(_) and Mencik(23) defined g-factors, g(XF),for various

types of cyclic loading, that ate used to convert the cyclic load

pattern to an equivalent static load. For periodic loading, T is the

time interval of one cycle, and Oleq(_) is the equivalent static

stress acting over the same time interval, t1,as the applied cyclic

stress, OkqcOF,t), at some location _P. The equivalent static stress

is related to the cyclic stress by

a;q(_F) t! = _'1 _ieqc(_F,t)dt = tI T (13)

N

= g(XD O_q,mCt0 tx

The CARES/LIFE program uses the maximum cyclic stress,

Oieqc, eF), of the periodic load as a characteristic value to

normalize the g-factor. For a periodic load over a time t 1, the

mode I static equivalent stress distribution is

Oieq,O(_S,tf)= Oleq%ax(_) [2g (xI.V)tf °kqcmCP) + 1

B

(14)

The use of g-factors for determining component life is an

unconservative practice for materials prone to cyclic damage.

The Walker equation,(ID whichhas traditionally beenused in

metals design, has been suggested as a model of fatigue damage

for some ceramic materials.(18) The Walker equation describes

the crack growth increment per cycle, n, as

da(Tm) = A K_2(Tm) AK_(T,n) (15) dn

where

and AKIe(_F,n)represents the range of the stress intensity factor

over the load cycle. The subscripts max and min indicate the

maximum and minimum cycle stress, respectively. The cyclic

fatigue parameters A, N, and Q are experimentally determined.

The Walker equation reduces to the Paris law06) when N and Q

are equal in value. The integration of Eq. (15) parallels that of

Eq. (2), yielding the cyclic fatigue equivalent stress distribution

°leqc0 (xP'nf)= ,_a=_[1.R(xP,n)]Q Oieqc, N pP,n) dn

• - B (16)

+ _ (_,nf)

where R(xP,n) is the ratio of the minimum to maximum cyclic

stress, nf is the number of cycles to failure, and B is now

expressed in units of stress z x cycle. The parameters B and N

are determined from cyclic data.

5 Noel N. Nemeth
Evaluation Of Fatigue Parameters from Inherently

Flawed Specimens

Lifetime reliability of structural ceramic components depends

on the history of the loading, the component geometry, the

dis_'ibution of pre-existing flaws, and the parameters that

characterize subcritical crack growth. These crack growth

parameters must be measured under conditions representative of

the service environment. When determining fatigue parameters

from rupturedata of naturallyflawed specimens,the statistical

effectsof theflaw distributionmust be consideredalongwith the

strengthdegradationeffectsof subcriticalcrack growth. In the

following discussion,fatigueparameter estimationmethods are

described for surface flaw analysis using the power law

formulationfor constantstressrate loading(dynamic fatigue).

Analogous formulationsfor volume flaws,staticfatigue,and

cyclicfatiguehave also been developed.(I)

For the uniaxialWeibull distributionthe probabilityoffailure

is expressed as

f m, ]

Pfs(tf)= 1 - exp kws f ol,0(xP)dA

A

(17)

where _F represents a location (x,y) and oi, o denotes the

transformed uniaxial stress analogous to Oieqc,O as defined in

equation(13).The Weibull crackdensitycoefficient B givenby

A d =

NS-2

CNs + 1) Bws aos

] l_ms

Aef I

In [1--_._)J

i/_s+D

(21)

where

The constants Ad and Aef are obtained by equating risks of

rupture. Aef is a modified effective area required for the timedependent formulation. For the uniaxial Weibull distribution, the

expression for the modified effective area is

= f IOi(_Is'tf) 1_sNs dA (22)

Aef A L of )

where ol(_F,tf) denotes the maximum principal stress

distribution. For multiaxialiy stressed components, the Batdorf

technique is used to evaluate fatigue parameters. The analogous

formulation for A©f is then

1

kw$ =_

m s

ooS

(18)

The Weibull scale parameter, OoS, correspondsto the stress level

where 63.21 percent of specimens with unit area would fail and

has unitsof stressx area 4. CARES/LIFE normalizesthe

variousfracturecriteriato yieldan identicalprobabilityof failure

for the uniaxialstress state.This is achieved by adjustingthe

fatigue constant B. For the uniaxlal Weibull model this adjusted

value is denoted by B w and for the Batdorf model it is denoted

by B B.From the dynamic fatigueequation(12),substitutingBws

for B, Ns for N, the uniaxial stress o I for O_q, and rearranging

equation (17) while assuming that

o_(xF,tf) tf > > 1 (19)

(Ns+I) Bw s

the median behavior of the experimental dynamic fatigue data

can be described by

_f0.s = Add II(Ns+I)

where of_ isthe median rupturestressof thespecimen and b

represent_the stressrateatthelocationof maximum stress.The

constant Ad is

Acf = 2kB---_ AJA[ : %'_" J dl_ l

(23)

dA

where the normalized Batdorf crack density coefficient is

BS= kBs/kws. Equation (21) is applicable except that BBS

replaces Bws. The relationship between Bss and Bws for a

uniaxial load-is established by equating the rise of rupture of the

Batdorf model with that of the uniaxial Weibull model (D

f r _sNs ] l_s

,cjoi Ce,tr) dA

B___ A

BBS " _sNs

2_:BS f_'_ O1eq (XF,tf)dcxdA

A

(24)

As N s becomes large,equation(24) approaches unity.

The terms A d and N s in equation (21) are determined from

experimentaldata.Taking the logarithmof equation(20) yields

(20) 1 (25)

In °fo_s= In A d + _ Ind

................. Ns+ I __

Linear regressionanalysisof the experimental data is used to

solve equation (25). The median value method is based on least

squares linear regression of median data points for various stress

6 Noel N. Nemeth
rates. Another technique uses least squares linear regression on

all the data points. A third option for estimating fatigue

parameters is a modification to a method used by Jakus.(25) In

this procedure, fatigue parameters are determined by minimizing

the median deviation of the logarithm of the falhre stress. The

mediandeviationisthemean oftheresiduals, wheretheresidual

isdefned as theabsolutevalueofthedifferencebetweenthe

logarithmof thefailurestressand thelogarithmof themedian

value.In CARES/LIFE thisminimizationisaccomplishedby

maximizingm s 0Ns + I) estimatedfrom thedataversusthe

fatigue exponent.

To obtain Ad based on the median line of the distribution the

following steps are taken. Experimental data at a sufficient

number of discrete leveis of applied stressing rate are

transformed to equivalent failure times tTi at a fixed stress rate

Or (equating failure probabilities using equation (17))

(26)

where the subscript T indicates a transformed value, the

subscript i denotes each observed data number, and

tfi = off let i. In CARES/LIFE the value of 0 T is taken as the

lowest level of stressing rate in the data set. With the data

defined by a single Weibull distribution, parameter estimation is

performed on the transformed data using

(27)

where the characteristic time is

I "It/(Ns+1)

NS--21

(Ns+ 1) B°°s ]

t T0S = IFms .N s /

Aef 0 T J

(28)

CARES/LIFE performs least squares or maximum likelihood

Weibull parameter_estimation as described in Pai (26) to solve

equation (27) for ms (N s ÷ 1) and tT0s. Substituting _r for

inequation(20)and solvingfortherupturestressinequation

(27)correspondingtoa 50% probabilityoffailure,_ro_, yields

A d = t TOS T n

(29)

This value of Ad is used with the fatigue exponent N s eslimated

either with the least squares (using all experimental rupture

stresses)or mediandeviationmethod.The fatigueconstantB is

obtainedfrom equations(21)or (28).

EXAMPLE

This example demonstrates the use of CARES/LIFE to predict

the time-dependent reliability of components under multiaxial

loads. The data for this example is from experimental work

performedby Chao and Sherry(2)on aluminadisksand bars

exposed to water at room temperature.Chao and Shetty

investigated the relationship between stress state and timedependentstrengthdegradation,specificallyto determineif

strengthdegradationdue toslowcrackgrowthinbiaxialflexure

canbe predictedfrom inertfracturestressesanddynamicfatigue

assessedin simpleuniaxialtests.Time-dependentreliability

predictionsforthealuminafromCARES/LIFE arecomparedto

theresultsobtainedby Chao and Sherry.

Details regarding specimen preparation and testing are given

in reference 2. Two batches of an alumina ceramic were purchased from the same vendor. The fLrstbatch was in the form of

plates (127x127xS ram) and rods (50.8 ram diameter, 76.2 mm

length). The plates and rods were made from the same powder

lot with identical isostafic pressing and sintering conditions. The

second batch of alumina, in the form of rods, was purchased

subsequently to examine dynamic fatigue under biaxial stresses.

This material had identical chemistry and preparation as the fu'st

batch. The measured properties of the frost batch include a

fracture toughness, KIc, of 4.13 MPa • _, Young s modulus,

F., of 297.2 GPa, and a Poisson's ratio, v, of 0.23.

Bar specimens were cut from the plate stock and disks were

cut from the rod stock. Specimens were either tested in a dry

nitrogen environment at 100 MPa/s to obtain inert (fast-fracture)

strengths, or in deioulzed water at various stress rates to obtain

the time-dependent fracture strengths. The specimens were

carefully prepared to minimize machining damage or failure

from edge flaws. The uniaxial specimens were nominally

3x4x45 mm. These specimens were loaded in either four-point

flexure with an outer support span of 40 mm and an inner load

span of 20 ram, or in three-point flexure using a 40 mm support

span. The disk specimens were nominally 3.175 mm in thickness

and 50.8 mm in diameter. They were loaded under uniform

pressure on one face and supported on the other face by 40

freely rotating ball bearings spaced uniformly along a 49.53 mm

diameter circle. Fractography showed that all specimens broke

due to a single population of randomly oriented surface flaws.

Table 1 lists the fast-fracture Weibu11 parameters, estimated

using the maximum likelihood method, for the various specimen

configurations and loads. The values shown correlate very well

to those of reference 2 for the Weibull shape parameter and

characteristic strength. The results for the 90% confidence

intervals differ somewhat from reference 2 due to the methods

of estimation. CARES/LIFE uses the technique from Thoman,

BalnandAntic(27),whilereference2 usesabootstraptechnique.

The 90% confidenceintervalon the Weibull modulus

significantly overlapsforbothbar and disktests.This is an

indication that the strengthresponseiscontrolledby the same

flaw population. Confidence bands on the characteristic strength

may only be compared for identical specimen loading and

geometry due to the size effect. The confidence intervals

obtained for the two disk tests using CARES/LIFE are shown to

overlap. The large confidence interval for the batch 2 specimens

is due to the small sample size of 7 specimens. In reference 2

the discrepancies in average strength between hatch 1 and batch

7 NoclN. Ncmeth
2 disks were attributed to material processing differences. This

will be further discussed.

Fatigue parameters were estimated from a-point bend bar

specimens loaded in dynamic fatigue in water. At least fifteen

specimens each were tested at stress rates of 0.02, 0.1, 1.0, 10.0,

and 100.0 MPa/s. Figure 1 shows a plot of the individual failure

stresses of the 95 specimens tested. Superimposed on this figure

are median lines and 5% and 95% confidence bounds on this

data as estimated with the median deviation technique. Table 2

lists the estimated fatigue parameters using the median value,

least squares, and median deviation techniques. The median

deviation technique shows best agreement with Chao and Shetty

for this case. In reference 2, the power law is used in the

following form

da(t) = Vc (K_ql N

dt _ K1c )

(30)

where V c is the critical crack velocity. The CARES/LIFE

program is formulated using the fatigue constant B and,

therefore, V¢ is not explicitly calculated. However, for

comparison, Vc can be computed from CARESK,IFE results

using the fracture strength relation(z)

I

of= ct 2Klc (N s+ 1) I l-Nsf2

V c Y Ns (N s - 2)tiNs a'-N-

(31)

where ai is initial crack size and af is the crack size at failure.

The subscript S denotes surface-flaw-dependent properties.

Assuming ai >> af and rearranging the above expression yields

2 K_ s (Ns + 1) ail-Nsr2

Vc Y Ns (Ns-2)

1

d_q_l"

O2)

Equating equations (32) and (20) results in

2 KNs (N s + 1) ait-Nsf2

Vc ffi (33)

AdNs+l Y Ns ('INs - 2)

The initial crack length ai and fatigue constant A d are evaluated

here for a failure probability of 50 percent. The crack geometry

factor Y for a semicircular crack is 1.366 O). Crack length ai was

determined from equation (1) using the strength determined from

inert testing (Table 1) for a 50 percent probability of failure.

Chao and Shetty (2) estimated that Ns was 40.7 and Vc was 9.1

m/s for Y equal to 1.24. The differences between the various

parameter estimates in CARES/LIFE and reference 2 are not

considered significant. The fatigue velocityVc isparticularly

sensitivetoN sasshown inequation(33).Table2 alsoliststhe

fatigueconstantsBws _d BBS. BBS is determinedfora

semicircularcrackandnoncoplanarcrackextensionwitha shear

sensitivity constant of C = 0.82 (3). The differences between Bws

and BBS are small since N s is relatively large. Finally, the

Weibull modulus can be directly estimated from the fatigue data

using the relation ms--'ms/(NS-2) when N s and ms are known.

For example, using the median deviation method ms = 25.0,

which is consistent with the results shown in Table 1.

To obtain disk specimens for dynamic fatigue tests, a second

batch of material (of identical dimensions as the first material

batch) was secured by Chao and Shetty (2). Seven of these

specimens were broken under inert conditions and a total of 35

specimens were broken at stressing rates of 0.02, 0.1, 10.0, and

100.0 MPa/s. Table 1 lists the fast-fracture Weibull parameters

of the (batch 2) disks and Table 3 gives the estimates for the

fatigue parameters. Table 3 shows only BBS, since Bws is

formulated only for the uniaxial stress state. Figure 2 shows a

plot of the individual failure stresses as well as the median line

and 5% and 95% confidence bounds estimated with the median

deviation technique. One data point was flagged as an outlier (at

100 MPa/s); however, it was not rejected and had Little effect on

the overall results. Batch 2 material showed a stronger than

expected average strength relative to the batch 1 materiaL Chao

and Shetty (2) attributed this to a small increase of KIc in the

material. Although batch 2 was unexpectedly strong, the rate of

strength degradation was similar to that of the batch 1 four-point

flexure data. Reference 2 reported that the 90% confidence

intervals of N s for both batches showed significant overlap. This

was further confirmed in Table 4, which shows the ratio of the

natural logarithm of the characteristic strength of the batch 2

disks to the natural logarithm of the characteristic strength of the

batch 1 four-point flexure specimens at each stressing rate

(maximum likelihood estimates). If the rate of change of strength

degradation were stress-state dependent, then the strength ratio

would systematically change with suessing rate. However, Table

4 shows no suchchange.Therefore,the differencesbetween

fatiguexponentsN s in Table 3 and Table 2 appearto be

reflecting expected statistical variation.

The effect of' multiaxial stress states on the material is

assessedby comparingthedifferencein inertstrengthbetween

theuniaxiallyoadedfour-pointbendspecimenand thebiaxially

loadeddisL Assuming that small crack-likeimperfections

controlthe failure,the materialstrengthin multiaxialstress

statescanbe correlatedtotheeffectsofmixed-modeloadingon

theindividualcracks.0_'9)Shetty(Il)developeda simpleequation

describingtheabilityof a cracktoextendunderthecombined

actions of a normal and shear load on the crack face using an

empirically determined parameter, C. For a semicircular crack

this equation is(3)

(34)

whereon and x arethenormalandshearstresses,respectively,

actingon theflawplane.

The failureresponseofthebiaxialflexurespecimensand the

three-pointflexurebars is predictedusing the Weibull

8 Noel N. Nemeth
parameters (Table 1) and fatigue parameters (Table 2; median

deviation results) estimated from the four'point flexure bar

rupture tests. The prediction for the three-point bars is compared

to experi-mental results to confirm the expected Weibull size

effect. The disk prediction is compared to experimental results

in order to make assertions regarding the effect of multiaxial

stress states on the fast-fracture and fatigue fracture of the

material.

For this analysis, the disk predictions are based on a finite

element model of the disk as shown in Figure 3. Brick and

wedge solid elements are used to model a 7.5° sector of the disk

and appropriate boundary conditions are applied corresponding

to a 49.53 mm diameter ring support and a pressure load on one

face. A gradient is imposed on the nodal spacing such that the

smallest elements have the highest tensile stresses. This is

required to obtain a satisfactory convergence of the reliability

solution and is independent of the mesh size needed to obtain

accurate nodal stresses. To perform surface flaw reliability

analysis quadrilateral and triangular shell elements are attached

to the surface nodes on the disk tensile face in order to obtain

surface stresses and areas. The shell elements are very thin and

have membrane properties only. These elements are such that

they contribute negligible stiffness to the model. Verification of

the accuracy of the finite element model is obtained by comparison to available closed form solutions. Chao and Sherry (2)

calibrated the applied pressure on the disk to the measured strain

at the center of the disk. The swain calibration was used to

correlate the fracture stress with the fracture pressure. The

CARES/LIFE analysis uses these reported fracture stresses rather

than the actual applied pressure on the disk. Reliability predictions for the three-point flexure bar are obtained from closed

form solutions of the effective area-(t'3)

Probability of failure predictions are made for the disk and

three-point bar in the fast-fracture condition and also for

dynamic loading at a stressing rate of 1 MPa/s in water. The

fracture strength distribution of dynamically (constant stress rate)

loaded specimens is characterized by a Weibull distribution with

a Weibuli modulus, rodS, of o

INs+ 11 (35)

rods = _)ms

For this analysis rods has a value of 25.58. Table 5 lists the

estimated WeibuU parameters obtained from bars and disks

loaded in this condition. In all cases the estimated Weibull

modulus is somewhat higher than predicted; however, the predicted value was within the 90% confidence bounds. Table 5

shows that the Weibull modulus did increase from the inert

condition, as expected. If the Weibull modulus value of ms=25.0

obtained directly from the four-point fatigue data were considered, then mdS would be 26.9, which is in better agreement

with Table 5.

The CARES/LIFE program is designed to predict reliability for

static fatigue or constant-amplitude cyclic loading. To predict

reliability for dynamic loading, an equivalent static loading time

is computed using the approach given in equation (16). In this

case, the g-factor is equal to 1/(Ns+I) multiplied by the time to

failure. Figures 4 and 5 are the resulting Weibull plots of these

predictions for various levels of shear sensitivity parameter C.

In Figure 4 a value of C of 0.82 is usedwhich corresponds to

an approximation of the maximum tangential stress mixed-mode

fracture criterion. The dashed line in the figure denotes the

results from reference 2. The small differences indicated are

mainly due to the different C and crack geometry factor, Y,

used and are not due to the different values used for the fatigue

parameters. This figure also shows a good correlation between

predicted and experimental results for the three-point flexure

bars, which confn'ms the size effect expected in fast-fracture and

fatigue. The CARES/LIFE prediction Lines for the three-point

flexure bars superimpose on the three-point bar prediction lines

of reference 2.

Figure 5 shows predictions for C values of 0.82, 0.90, and

>>1 (solid, long dashed, and short dashed line, respectively).

Since in this example the CARES/LIFE fracture predictions are

normalized to the (uniaxial stress state) four-point flexure data,

then the choice of a fracture criterion only effects the predictions

for the(biaxialstressstate)disks.The C valuesof 0.82and

much greaterthanone representheextreme bounds on the

expectedmixed-mode shearsensitivityof the flaws in the

material.The valueof C>>1.0 representsa shear-insensitive

fracturecriterion, while_=0.82 ishighlyshearsensitive.The

0.90valuerepresentsa choiceof C thatbestfitsto bothinert

and fatiguediskdata.OptimizingC in thismanner was not

consideredinreference2.From thisfigurestressstateeffectsare

adequatelyaccountedfor,bothin fast-fracture and subcritical

crackgrowthconditions.

CONCLUSION

The use of structural ceramics for high-temperature

applications dependson thestrength,toughness, and reliability

of thesematerials.Ceramic componentscan be designedfor

service ff the factors that cause material failure are accounted

for. This deign methodology must combine the statistical nature

of strength controlling flaws with fracture mechanics to allow

for multiaxial stress states, concurrent flaw populations, and

subcritical crack growth. This has been accomplished with the

CARES/LIFE public domain computer program for predicting

the Kme-dependent reliability of monolithic structural ceramic

components. An example has been given to Rlnstrate the use of

this design methodology in CARESKJFE for predicting the

effects of component size, stress distribution, stress state, and

subcritical crack growth on the lifetime reliability. Potential

enhancements to the code include the capability for Wansient

analysis, three-parameter Weibutl statistics, creep and oxidation

modeling, flaw anisotmpy, threshold stress behavior, and

parameter regression for multiple specimen sizes.

REFERENCES

1. Nemeth, N.N., Powers, L.M., Janosik, L.A., and

Gyekenyesi, J.P., "Ceramics Analysis and Reliability

Evaluation of Structures LIFE prediction program

(CARES/LIFE) Users and Programmers Manual",

TM-I06316, to be published.

9 Noel N. Nemeth
2.Chao,L.Y.,and Shetty,D.IC,"Thne-DependentStrength

Degradationand Reliabilityof an Alumina Ceramic Subjected to Biaxial Flexure," Life Prediction Methodologies

and Data for Ceramic Materials, ASTM STP 1201,

C.R. Bdnkman, and S.F. Duffy, Eds., American Society for

Testing and Materials, Philadelphia, 1993.

3. Nemeth, N.N., Manderscheid, LM., Gyekenyesi, J.P.,

"Ceramics Analysis and Reliability Evaluation of Structures

(CARES)', NASA TP-2916, Aug. 1990.

4. Powers, LM., Starlinger, A., Gyekenyesi, J.P., "Ceramic

Component Reliability With the Restructured NASA/CARES

Computer Program', NASA TM-105856, Sept. 1992.

5. Barnett, R.L., Connors, C.L., Hermaun, P.C., and Wingfield,

J.R., "Fracture of Brittle Materials Under Transient

Mechanical and Thermal Loading," U.S. Air Force Flight

Dynamics Laboratory, AFFDL-TR-66--220, 1967.

(NTISAD--64997S)

6. FreudenthaI, A.M., "Statistical Approach to Brittle Fracture,"

Fracturea..yol. 2: An Advanced Treatise) Mathematical

Fundamentals, H. Liebowitz, ed., Academic Press, 1968,

pp. 591-619.

7. Weibull, W.A., "The Phenomenon of Rupture in Solids,"

Ingenoirs Vetenskaps Akadanien Handlinger, 1939, No. 153.

8. Batdorf, S.B. and Close, J.G., "A Statistical Theory for the

Fracture of Brittle Structures Subjected to Nonuniform

Polyaxial Stresses", Journal of Applied Mechanics, VoL 41,

No. 2, June 1974, pp. 459-464.

9. Batdoff, S.B., and Heinisch, H.L, Jr., Weakest Link Theory

Reformulated for Arbitrary Fracture Criterion. Journal of the

American Ceramic Society, VoL 61, No. 7--8, July-Aug.

1978, pp. 355--358.

10. Palaniswamy, K., and Knanss, W.G., On the Problem of

Crack Extension in Brittle Solids Under General Loading,

Mechanics Today, Vol. 4, 197g, pp. 87-148.

11. Sherry, D.IL, ]_ftxed-Mode Fracture Criteria for Reliability

Analysis and Design with Structural Ceramics. Journal of

En_zineering for Gas Turbines and Power, VoL 109, No. 3,

July 1987, pp. 282-289.

12. Evans, A.G., "A General Approach for the Statistical

Analysis of MultiaxialFracture',Journal of the American

CeramicSociety,Vol.61,1978,pp 302-306.

13.Matsuo,Y.,Trans.of theJapan societyof Mech,anical

Engineers,VoL 46,1980,pp.605--611.

14.Evans,A.G.,andWiederhom,S.M.,"CrackPropagationand

FailurePredictionin SiliconNitrideatElevated

15.

16.

17.

Ig.

19.

20.

21.

22.

23.

Temperatures",Journalof Maten.'.al Science,Vol.9, 1974,

pp. 27O-278.

Wiederhom,S.M.,FractureMechanicsofCeramics.Bradt,

R.C.,Hassclman,D.P.,andLange,F.F.,eds.,Plenum,

New York,1974,pp.613--646.

Paris,P.,and Erdogan,F.,"A CriticalAnalysisof Crack

PropagationLaws",Journalof BasicEngin.cering,VoL 85,

1963,pp.528-534.

Walker,IC, "The Effectof StressRatioDuringCrack

Propagationand Fatigue for 2024---T3and 7075--T6

Aluminum',ASTM SIP 462,1970,pp.1-14.

Dauskardt,R.H., James, NLR., Porter,J.R., and

Ritchie,R.O.,"CyclicFatigueCrackGrowth inSiCWhisker-Reinforced AluminaCeramicComposite:Longand

SmallCrack Behavior",Journalof theAmericanCeramic

S_iety_Vol.75,No. 4, 1992,pp.759-77!.

Paris,P.C.,and Sih,G.C.,StressAnalysisofCracks.AS'I'M

STP 381, 1965, pp. 30--83.

Thiemeier, T., "Lebensdauervorhersage fun Keramische

Bauteile Unter Mehrachsiger Beanspruchung",Ph.D.

dissertation, Universityof Karlesruhe,Germany,1989.

Stunner,G.,Schulz,A.,andWittig,S.,"LifetimePrediction

for Ceramic Gas Turbine Components',ASME Preprint

91-GT-96, June 3--6, 1991.

Batdorf, S.B., "Fundamentals of the Statistical Theory of

Fracture", Fracture Mechanics of Ceramics, VoL 3, eds.,

Bradt, R.C., Hasselman, D.P.H. and Lange, F.F., Plenum

Press, New York (1978), pp. 1-30.

Mencik, J., "Rationalized Load and Lifetime of Brittle

Materials",Communications of the American Ceramic

S_iety, Mar. 1984, pp. C37-C40.

24. Evans, A.G., "Fatigue in Ceramics" International Journal of

F_ture, Dec. 1980, pp. 485-498.

25. Jakus, K., Coyne, D.C., and Ritter, LE., Analysis of Fatigue

Data for Lifetime Predictions for Ceramic Materials. Journal

of Material Science, Vol. 13, 1978, pp. 2071-2080.

26. Pal, S.S., and Gyekenyesi, J.P., Calculation of the Weibull

Strength Parameters and Batdorf Haw Density Constants for

Volume and Surface-Haw-Induced Fracture in Ceramics,

NASA TM-100890, 1988.

27. Thoman, D.R, Baln, L.J, and Antle, C.E., Inferences on the

Parameters of the Weibull Distribution. Technometrics,

VoL I l, No. 3, Aug. 1969, pp. 445--460.

I0 Noel N. Nemeth
TABLE l-Weibull parameters estimated from inert data.

S_cimen Weibull

modulus,

m s

90% confidence Characteristic

bounds on strength,

m s °o s

MPa

90% confidence

bounds on

oes

MPa

Scale

parameter,

OoS

MPa •mm 2/_

3-point

4-point

Disk

Disk Coateh2)

25.43

23.76

22.25

28.98

20.47, 29.91 385.9

19.13, 27.95 353.4

17.12, 26.81 338.7

13.28, 40.88 351.4

382.0, 389.9

349.6, 357.3

334.1, 343.5

341.5, 362.2

414.7

425.8

436.4

423.2

TABLE 2-Fatigue parameters for 4-point bend bar_,

Estimation

method

Fatigue Fatigue Fatigue Fatigue Crack

constanh exponent, constan_ ¢onstan_ velocity,

Aa Ns B,, s BBs V_

MPa z -s MPa 2 • s m -s -1

Median Value

Least Squares

Med Deviation

Reference 2

2.339 x 102 36.04 4.590 x 10"l 4.579 x 10"1

2.336 x 102 40.84 5.631 x I0"z 5.617 x 10"z

2.337 x 102 41.23 4.783 x 10.2 4.771 x 10.2

-- 40.7 -- --

1.162

8.176

9.373

9.1

Estimation

method

TAgI.E 3--Fatigue parametersfor disk (batch 2) specimens.

Fatigue Fatigue Fatigue Crack

constant, exponent, constant, velocity,

Ns Vo

MPa 2 • s m • s -t

Median Value

Least Squares

IVied Deviation

Reference 2

2.293 x 102 35.68 2.675 x I0"] 1.894

2.313 x 102 41.79 3.959 x 10.2 16.22

2.304 x 102 36.23 .2.649 x 10"1 1.988

-- 36,6 -- 2.4

11 Noel N. Nemeth
TABLE 4-C0mparison of 4-point and disk (batch 2)

characteristic st_n_,, s

Su'essing 4-point Disk Strength

rate, strength, strength, ratio,

On Oes=,_

_" Oos °0s

On Oes4..__

lvtPa.s -1 MPa MPa

0.020 2.145 x 10 z 2.116 x 102 0.9975

0.100 2.250 x 10 z 2.195 x 102 0.9954

10.00 2.531 x l02 2.492 x 10= 0.9972

I00.0 2.628 x 102 2.620 x I02 0.9995

Inert 3.534 x 102 3.514 x 102 0.9990

TABLE 5-Weibull parameters estimated in water (1 MPa/s).

Specimen Weibull 90% confidence Characteristic 90% confidence

modulus, bounds on su'ength, bounds on

ElldS rods O'oS o os

MPa MPa

3-point

4-point

Disk

27.83

26.70

32.66

21.20, 33.70 255.6

20.54, 32.17 236.3

24.87, 39.53 215.9

252.7, 258.5

233.6, 239.0

213.8, 218.1

12

Noel N. Nemeth
2";5

25o

P}

r_

9.OO

,1 V I

f _"l II

.. =. A:.

w .._e

I / •

[ I I I

0.01 0.1 1 10 100 lO00

LO,U)Z,',Tae,X'r_:(U_oa/s)

Figure 1 .--.Dynamic fatigue of alumina four-point flexure bars in water.

Median regression line (solid), and 5% and 95% regression lines

(dashed) estimated with the median deviation technique.

v

!

E,

O

.¢

m

F---7

99 • 3 PL.--Inert 0 // /

90 : 3 PL--Fatigue

8050ZC10 O Oisk--Fot]gi_/_

0' ,j!'' /,/

= /

I:l,

1

150 200 250 300 350 4_00

FRACTURE STRESS (laPs)

Figure 4.--Weibull plot showing fast-fracture three-point and disk

specimen strengths measured in an inert environment, as well as

three-point and disk specimen fracture strengths dynamically

loaded at a rate of I MPa/s. Solid lines are corresponding

CARES/LIFE predictions for C = 0.82. Dashed lines are corresponding predictions from reference 2.

2-t6

i"

=P.5

2OO

J

// i

/;_'_l _ ""

.i" _ -._

I I I I

0.01 0.1 1 iO lO0 1o00

LOADINGRATE (_,,/s)

Figure 2.--Dynamic fatigue of alumina pressure-on-disk flexure specimens in water. Median regression line (solid), 5% and 95% regression

lines (dashed) estimated with the median deviation technique.

Figure 3.---Finite element model of a 7.5 ° sector of the disk.

Arrows indicate pressure load on disk,

t=

D

t.4

[.,

£

en

0

99 !

90

80

50

20

10

5

Obek--FoUgue

i

1

150 1'75 200 225 250 275 _00

FRACTURE STRESS (_a)

Figure 5.--Weibull plot showing three-point and disk specimen dyrmmtc fatigue strengths that were loaded at a rate of 1 MPais. Solid

line corresponds to CARES/LIFE prediction for C = 0.82 (shear-sensitive criterion). Long dashed line corresponds to the disk prediction for C" = 0.90 and the short dashed line corresponds to the

disk prediction for C>> 1.0 (shear-insensitive criterion).

Nocl N. Nemcth

13
Form Approved

REPORT DOCUMENTATION PAGE OiaNo. 0704-01_

Public reporting burden for this collection of infon'nation _ estimated to average 1 hour per .response. including the time Ior reviewing instructions, searching existing data sources,

g_hefing _ rnamtaalin_ the da__ needed., and corr,, let.=ng .and rev.=ewtng !he collection .of information. Send co.n'_, nts r.egardmg this b u_en e.stimate orany other" aspect ol this

COllection o_ inlorrnatK_,n, iP.ouolng suggestmns for reaucmg mrs ouroen, to wasnlngzon Heaoquaners ._.erVlCeS, utrec'(orate 1or intor_lon uperatlon$ ano Heport$, 1215 Jefferson

Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-018_), Washington, DC 20503.

1. AGENCY USE ONLY (Leave b/ank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

January 1994 Technical Memorandum

4. TITLE AND SUBTITLE

Durability Evaluation of Ceramic Components Using CARES/LIFE

6. AUTHOR(S)

Noel N. Nemeth, Lynn M. Powers, Lesley A. Janosik, and John P. Gyekenyesi

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135-3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, D.C. 20546-0001

5. FUNDING NUMBERS

WU- 505--63-5B

B. PERFORMING ORGANIZATION

REPORT NUMBER

E-8402

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM- 106475

11. SUPPLEMENTARY NOTES

Prepared for the 39th International Gas Turbine and Aeroengine Congress sponsored by the American Society of Mechanical Engineers, The Hague, The

Netherlands, June 13-16, 1994. Nod N. Nemeth, Lesley A. Janosik, and John P. Gyckenyesi, NASA Lewis Research Center and Lynn M. Powers,

Cleveland State University, Department of Civil Engineering, Cleveland, Ohio 44115. Responsible person, Noel N. Nemeth, organization code 5250,

(216) 433-3215.

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Unclassified - Unlimited

Subject Categories 27 and 39

13. ABSTRACT (Maximum 200 words)

The computer program CARES/LIFE calculates the time-dependent reliability of monolithic ceramic components subjected to thermomechanical and/or proof test loading. This program is an extension of the CARES (Ceramics Analysis and

Reliability Evaluation of Structures) computer program. CARES/LIFE accounts for the phenomenon of subcritical crack

growth (SCG) by utilizing the power law, Paris law, or Walker equation. The two-parameter Weibull cumulative distribution function is used to characterize the variation in component strength. The effects of multiaxial s_resses are modeled

using either the principle of independent action (PIA), the Weibull normal stress averaging method (NSA), or the Batdorf

theory. Inert strength and fatigue parameters are estimated from rupture strength data of naturally flawed specimens loaded

in static, dynamic, or cyclic fatigue. Application of this design methodology is demonstrated using experimental data from

alumina bar and disk flexure specimens which exhibit SCG when exposed to water.

14. SUBJECT TERMS

Fatigue; Weibull; Batdorf; Reliability; Ceramic; Design

17. SECURITY CLASSIFICATION

OF REPORT

Unclassified

18. SECURITY CLASSIFICATION

OF THIS PAGE

Unclassified

19. SECURITY CLASSIFICATION

OF ABSTRACT

Unclassified

15. NUMBER OF PAGES

15

16. PRICE CODE

A03

20. LIMITATION OF ABSTRACT

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribedby ANSI Std. 7_39-18

298-102