CARES/CREEP

12 Pages·2012·0.33 MB·English

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CREEP LIFE OF CERAMIC COMPONENTS USING A FINITE ELEMENT BASED
INTEGRATED DESIGN PROGRAM (CARES/CREEP)
11111111111 1 1111111
BREAK
(cid:9)
Lynn M. Powers Osama M. Jadaan
(cid:9)
Cleveland State University University of Wisconsin-Platteville
(cid:9)
Cleveland, OH 44115 Plattevi/le, WI 53818
John P. Gyekenyesi
NASA-Lewis Research Center
Cleveland, OH 44135
ABSTRACT As design protocols emerge for these material systems, designers
The desirable properties of ceramics at high temperatures have must be aware of several innate characteristics of ceramics. These
generated interest in their use for structural applications such as in include the degrading ability of ceramics to carry sustained loading.
advanced turbine systems. Design lives for such systems can exceed Generally, time dependent failure in ceramics occurs because of two
10,000 hours. The long life requirement necessitates subjecting the different delayed failure mechanisms, slow crack growth (SCG) and
components to relatively low stresses. The combination of high creep rupture. SCG usually initiates at a preexisting flaw and continues
temperatures and low stresses typically places failure for monolithic until a critical crack length is reached causing catastrophic failure
ceramics in the Creep regime. The objective of this paper is to present (Weiderhom, 1974). Creep rupture, on the other hand, occurs because
a design methodology for predicting the lifetimes of structural compo- of bulk damage in the material in the form of void nucleation and
nents subjected to creep rupture conditions. This methodology utilizes coalescence that eventually leads to macrocracics which then propagate
commercially available finite element packages and takes into account to failure (Grathwohl, 1984).
the time varying creep strain distributions (stress relaxation). The creep Based on the two different delayed failure mechanisms presented
life of a component is discretized into short time steps, during which, above, probabilistic analysis and design methodologies are utilized to
the stress and strain distributions are assumed constant. The damage is predict the lifetime of ceramic components subjected to sustained
calculated for each time step based on a modified Monlcman-Grant loading conditions leading to failure in SCG mode. Several integrated
creep rupture criterion. Failure is assumed to occur when the normal- design codes such as CARES (Nemeth, et al, 1990), CARES/LIFE
ized accumulated damage at any point in the component is greater than (Nemeth, et al, 1993), and SPSLIFE (Saith, et al, 1994) are available
or equal to unity. The corresponding time will be the creep rupture life and have been demonstrated to be successful in predicting the failure
for that component Examples are chosen to demonstrate the probability for ceramic components subjected to fast fracture and SCG
CARES/CREEP (Ceramics Analysis and Reliability Evaluation of failure modes.
Structures/CREEP) integrated design program which is written for the However, no such integrated design codes exist-currently for
ANSYS ftnite element package. Depending on the components size and predicting the nonlinear behavior and lifetime of ceramic components
loading conditions, it was found that in real structures one of two subjected to creep rupture conditions. One reason for this is the type of
competing failure modes (creep or slow crack growth) will dominate. ceramics that existed until recently. These ceramics were processed
Applications to benchmark problems and engine components are using relatively large amounts of sintering aids that resulted in glassy
included. intergranular phases which become viscous at high temperatures, thus
limiting their creep resistance in the temperature range where ceramics
INTRODUCTION are needed most
Advanced structural ceramics are becoming viable materials for The advent of new techniques in ceramic processing technology
many high temperature applications including gasoline, diesel, and gas has yielded a new class of ceramics that are highly resistant to creep
turbine engine components. Attractive properties such as low density, at high temperatures (Ferber, et al., 1994, Ding, et al., 1994, Menon,
high strength, high stiffness, and corrosion resistance are allowing et al., 1994a). Such desirable properties have generated interest in using
ceramics to supplant alloys in these demanding applications. The result ceramics for turbine engine component applications where the design
is lower engine emissions, higher fuel efficiency, and more optimum lives for such systems are on the order of 10,000 to 30,000 hours.
design. These long life requirements necessitate subjecting the components to
Presented at the International Gas Turbine and Aeroengine Congress & Exhibition
Birmingham, UK — June 10-13,1996
This paper has been accepted for publication in the Transactions of the ASME
Discussion of it will be accepted at ASME Headquarters Ural September 30, 1996
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relatively low stresses. The combination of high temperatures and low continuum damage mechanics approach (Kachanov, 1960, Dunne, et
stresses typically places failure for monolithic ceramics in the creep al., 1990, Hayhurst, et at, 1975, Othman and Hayhurst, 1990), and the
and creep rupture region of a time-temperature-failure mechanism map internal (back) stress model (White and Hazime, 1995, Brown, et al.,
(Weiderhom, et al., 1994, Quinn, 1990). 1989, Kraus, 1980, LeGac and Duval, 1980).
The objective of this paper is to describe an analytical methodol- Many types of ceramics, however, do not display tertiary creep
ogy and an integrated design program named CARES/CREEP (Ceramic behavior (Sundberg, et al., 1994, Cucio, et al., 1995, Ohji and
Analysis and Reliability Evaluation of Structures/CREEP) to be used Yamauchi, 1993, Lewis and Ostvoll, 1992, Sankar, et al., 1994).
for predicting the lifetimes of ceramic structural components subjected Therefore, it is appropriate for creep analysis of ceramics to use
to creep rupture conditions. This methodology utilizes commercially constitutive equations describing only the primary and secondary creep
available funte element packages and takes into account the transient regions. Many formulas, and combinations of these formulas exist for
state of stress and creep strain distributions (stress relaxation). The such formulation. One of these constitutive laws is known as the Baily-
creep life of a component is descritized into short time steps, during Norton time hardening rule (Kraus, 1980, Norton, 1929, Boyle and
which, the stress distribution is assumed constant. The damage is Spence, 1983) and is given by the following equation:
calculated for each time step based on a modified Monlcman-Grant
(MMG) creep rupture criterion (Menon, et al., 19946). The cumulative = a, (1)
S—
damage is subsequently calculated as time elapses in a manner similar RT
to Miner's rule for cyclic fatigue loading. Failure is assumed to occur
when the normalized cumulative damage at any point in the component
where e is the creep strain rate, a, t, and T are the stress, time, and
reaches unity. The corresponding time will be the creep rupture life for
absolute temperature. The material constants al, a2, a3, and Q are
that component.
determined from experiments and R is the universal gas constant. The
The CARES/CREEP program is made up of two modules, and is
Baily-Norton constitutive law was selected to describe the creep
currently customized to run as a post-processor to the ANSYS finite
behavior of ceramics in the CARES/CREEP code, because of its
element code. The first module is a parameter estimation program used
widespread use, and success in fitting the creep data as a function of
to compute the primary creep parameters based on the time hardening
stress, temperature, and time. Furthermore, this relationship, in
rule, the steady state parameters based on the Baily-Norton equation,
association with Prandlt-Reuss plasticity flow rule, satisfies four basic
and the creep rupture parameters based on the MMG criterion. The
requirements for multiaxial creep analysis (Kraus, 1980). These
second module, contains the coding for calculating the cumulative
requirements are: I) the multiaxial formulation must reduce to the
damage, and thus the creep rupture life for the component in question.
uniaxial formulation when appropriate, 2) the model contains constancy
of volume for creep conditions, 3) the model reflects lack of influence
BACKGROUND
of hydrostatic stress, and 4) principal directions of stress and strain
Engineers involVed in designing components against creep failure,
coincide. The constancy of volume requirement is a result of the
are generally interested in calculating the creep deformation and
original development of this theory for metals. Ceramics contain void
predicting the lifetime for these components when subjected to
which expand under creep conditions. A theory incorporating this
sustained multiaxial thermomechanical loading. Both endeavors, include
phenomena is not available for finite element calculations.
modeling the material's creep behavior using appropriate constitutive
equations, and subsequently choosing a rupture criterion suitable to that
Creep Rupture
material. This section contains a brief literature review on creep
The majority of current engineering design methodologies against
covering these two perspectives.
creep, fit into four major categories. The first is graphical, where the
time to reach a given strain, or fracture, at a given stress or tempera-
Creep Constitutive Relations ture is obtained from a creep life diagram. Some of the techniques that
The creep strain curve resulting from a constant load test is a
belong to this group are the Larson-Miller (Larson and Miller, 1952),
function of stress, temperature, and time. Many uniaxial constitutive
Sherby-Dorn (Orr, et al., 1954), minimum commitment (Manson and
laws have been proposed to describe such standard creep curves.
Ensign, 1971), Manson-Halferd (Manson and Halferd, 1953), Manson-
Currently, there exists two general formulations for creep modeling.
Succop (Conway, 1968), Quinn (1986), and Jones (1986) methods.
The first is referred to as the equation of state formulation and assumes
These approaches utilize parameters which when plotted against stress
that the material behavior depends on the present state only. The
would yield unique curves that can be used to predict the life of
second approach, named memory theory (Krempl, 1974), takes into
comporients subjected to creep rupture loading.
account that the material remembers the loading and temperature
The second category includes analytical methods to predict the
history and thus responds accordingly. At this point, most of the
creep life for structural components. The Monkman-Grant (MG)
material modeling discussed in the literature is based on the equation
method (Monlunan and Grant, 1956) is one of the most utilized
of state formulation because of its proven success and relative ease of
approaches for ceramics and is based on a power relation between time
use with computer programs. Thus, only models based on the equation
to failure and steady-state creep rate given by the following equation:
of state formulation will be reviewed
Several proposed constitutive relations are capable of simulating (2)
the entire creep curve (primary, secondary and tertiary). These laws
include the theta projection method (Evans and Wilshire, 1985, Evans,
et al., 1987, Foley, et al., 1992, Maruyama and Oilcawa, 1987), the
where tr is the time to failure and b, and 62 are constants. The above
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equation assumes that a unique curve can describe failure for a given however, planned for future enhancements of the code.
material independent of temperature. This assumption was found to be
invalid for some ceramic materials (Ferber and Jenkins 1992, Luecke, THEORY
etal., 1993, Menon, etal., 1994a), which displayed stratification of the The creep response of a ceramic component must be evaluated in
MG curve depending on the temperature level. Thus, a modified Monk- order to determine its service life. Monolithic ceramics usually exhibit
man-Grant equation was introduced (Menon, etal., 1994b) to take the primary and secondary creep behavior, while failure occurs without
temperature into account and is given by the following formula: warning. The life of a component is determined by calculating the
damage over time. Creep of ceramic components is divided into two
cis phases: evaluating the nonlinear stress response and assessing the
In tf 0 d1 - d2 In + — (3)
T(cid:9) damage of the component
where di, d2, and c13 are constants. The MG and the MMG criterions Nonlinear Stress Response
were found to be very successful in describing the creep rupture The creep curve is broken up into three stages: primary, secondary
behavior for ceramics, and thus are used heavily in the ceramics and tertiary. The models for this response were built to match the
literature, For this reason, these criteria were selected as the basis for experimental data with the ANSYS creep equations. The three regions
predicting the creep life of ceramic components in the CARES/CREEP of the creep curve are considered separately. Primary and secondary
code. Note that the MMG criterion collapses to the MG criterion when creep may be modeled within the finite element software where tertiary
d3 is set equal to zero. creep is not taken into account. The tertiary stage is usually not
Differential formulations constitute the models making up the third modeled since it implies impending failure. ANSYS contains a library
category of approaches for creep rupture prediction. Continuum damage of strain rate equations characteristic of materials being used in creep
mechanics (Kachanov, 1960, Dunne, et al., 1990, Hayhurst, et al., design applications. The creep strain rates for primary and secondary
1975, Othman and Hayhurst, 1990), and internal (back) stress concepts creep are a function of stress, strain, and temperature.
(White and Hazime, 1995, Brown, et al., 1989, Kraus, 1980, LeGac ANSYS does not divide creep into unique stages as is done in
and Duval, 1980) belong to this category. conventional creep physics. Both primary and secondary creep are
Probabilistic formulations make up the fourth category for creep assumed to be in effect simultaneously. Thus the material constants for
rupture life prediction. Currently, most ceramic researchers utilize these relations must be computed so to account for this effect The total
deterministic approaches to describe creep deformation (hence, creep creep strain is given by
parameters), and to even predict creep rupture lives. Ceramic creep
deformation, and thus creep parameters, display less stochastic and L a= eP + e (4)
s
more deterministic behavior compared to fast fracture and slow crack
growth failure data. An indication of that is the absence of the so
called "size effect" (Weiderhom, etal., 1994), which is a characteristic where is the primary and ; is the secondary components of creep
for the probabilistic behavior of brittle fracture in ceramics. strain. The primary creep strain rate is given as
However, some ceramics tend to display significant scatter in the
creep rupture data (IChandelwal, et al., 1995). The advent of new
ceramic fabrication techniques, such as HIP with low levels of sintering 5 l
tp = a; t; exp - ± (5)
phases, have resulted in materials that are highly resistant to creep.
These improved fabrication methods yield thinner amorphous grain
boundary phases which are subsequently crystallized using heat
treatment. For such materials (Ferber, et al., 1994, Menon, et al.,
1994a) cavitation was found to control the creep deformation, while The secondary creep strain rate is given by
SCG controlled failure. This type of failure mechanism could be one
of the reasons contributing to the significant scatter in the creep rupture e. (cid:9) = C.2 a; exp I - C—ID I (6)
data, and thus fuels the argument for utilizing probabilistic rather than T
deterministic procedures for predicting the creep life of ceramic
components.
c;
The theoretical development for stochastically predicting the creep where are constants and parameters determined from creep experi-
life of ceramic structures is not well developed and still is in its ments. These constants are not numbered sequentially since i is the
infancy. One theory is based on the premise that both SCG and creep location of the value in the ANSYS data table.
failure modes are acting simultaneously (Lange, 1976). Mother, Typically, data available from creep experiments will be in the
combines continuum damage mechanics and the Weibull distribution, form of a creep response curve where the strain is recorded as a
assuming that the failure processes for SCG and creep are separable function of time when a constant load is applied. In order to evaluate
(Duffy and Gyekenyesi, 1989). material properties, several of these tests should be conducted at
A probabilistic creep theory is not well developed at this point varying stress levels and temperatures. After subtracting the elastic
Also, data to support the probabilistic treatment is not available. The strain from the total strain, the first step in parameter estimation is to
CARES/CREEP code (at this time) utilizes a deterministic approach to determine the parameters for secondary creep. To evaluate the material
predict creep life. Incorporating probabilistic creep life prediction is, parameters for equation (6), the minimum creep rate, dc/dt, is evaluated
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for each specimen. This value may be obtained graphically or by 0 s D s 1
assuming the creep response curve is linear over a fixed time and
performing a least squares best fit analysis on the data. The second
method is preferable for computer algorithms where large amounts of where 1>C1 for an undamaged component and l>1 for a failed
data are processed numerically. The time where linearity begins varies component. If failure is assumed to occur at time, t=tf, then the
for each specimen. This value is defined as the primary to secondary damage, D, is equal to unity at that time. A nonlinear analysis divides
transition time, C. the time into steps over which the stress and strain rates are assumed
Once the minimum creep rates for all of the specimens are known, to be constant The cumulative damage is subsequently calculated as
the parameters C,, Cs, and Cs, may be determined. An iterative time elapses in a manner similar to Miner's rule for fatigue loading.
procedure (Sundberg, et al., 1994), is used to find these values as a The damage is expressed
function of is, a, and T. Equation (6) is rearranged twice to isolate
two of the variables for a least squares analysis. These relationships are
A t (cid:9) A t2 (cid:9) A t (cid:9) a (cid:9) t
D (cid:9) +(cid:9) + + (10)
41 (cid:9) tn (cid:9) tipi.It03
Cis (cid:9)
In[ es a ] = In(C7) - (7)
where tfi is the creep rupture time based on the loading conditions
during the i-th time step, At, is the duration of the i-th time step, and
and
n is the number of time steps to failure.
The creep rupture time for the i-th time step, tfi, is determined
ln exp (8) using an appropriate failure criterion. For the Monlcman-Grant criterion
given in equation (2), this time is
Initially, Cs is assigned a default or user supplied value, and then a tfi =
least squares best fit analysis is done to find C, and Cm. Using the
improved estimation on C10, equation (8) is evaluated for estimates on
the other parameters. This process continues until the solution
converges. where (cid:9) is the creep strain rate for the i-th time step. Substituting the
The primary creep parameters, C„ i=1,4, may be evaluated at this secondary creep strain rate into equation (11) yields
point Since ANSYS divides the creep response as given by equation
(4), the primary component of creep strain is evaluated by subtracting
te
the secondary creep strain from the total creep strain. The secondary (ci (cid:9) exIp C101\ (12)
creep strain is calculated using the secondary creep parameters
estimated for the material. The primary creep strain component is
evaluated over entire duration of the test The primary creep parameters
are evaluated by integrating equation (5): where a, and T, are the stress and temperature of the i-th time step.
Substituting equation (12) into equation (10) gives an expression for
C8 (cid:9) the damage
e = a; t I mq) - (9)
C3 + 1
D = C7b2 Ea (cid:9) b2c, (cid:9) 132 C(cid:9)io I (cid:9) t. (13)
Ti
• The constants C,, C,, C,, and C, are determined from multiple
regression using least squares analysis. All constants from equations (5)
and (6) are now known. These values are entered into the ANSYS data Failure is assumed to occur when the normalized cumulative damage
table, and the nonlinear creep fmite element analysis can now be at any point in the component reaches unity. The corresponding time
performed for a component will be the creep rupture life for that component
The modified Monkman-Grant (IVIMG) criterion may also be
Damage Assessment applied to compute the damage. Substituting the secondary creep strain
Due to stress redistribution during creep loading conditions, the rate into equation (3) yields
steady state (secondary) creep rate, a , also varies with time. Therefore,
the Monlanan-Grant failure criterion may not be used in the form in (cid:9) Cied2 + (cid:9)
equations (2) and (3) to predict lifetime. The following concept, based t = (14)
Ti(cid:9) Ti
on damage accumulation; can be used to predict service life with the
Mordcman-Grant criterion.
The component's predicted life is determined based on a damage
function, D. The damage function is generally defmed as
where a, and T, are the stress and temperature of the i-th time step.
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Substituting equation (14) into equation (10) gives an expression for
the damage Component Geometry Loads
Material Properties
Creep Test Data
n Cro ds oi4:4 t (cid:9) (IS)
DcC E
Ti
I Model denerationi
Parame or Estimation
CARES/CRPEST
Failure is assumed to occur when the normalized cumulative damage
I Heat Trans er Analysis I
at any point in the component reaches unity. The corresponding time
will be the creep rupture life for that component Primary & Secondary Nodal
Creep Strain Rate Temperatures
Parameters
PROGRAM CAPABILITY
The CARES/CREEP integrated design computer program predicts
Nonlinear Stressj__
the service life of a monolithic ceramic component as a function of its Analysis
geometry and loading conditions. CARES/CREEP couples commercial-
Modified
ly available finite element programs, with design methodologies to Moniunan-Orant Time-Varying
Parameters Stresses and
account for material failure from creep rupture. The code is divided Temperatures
into two separately executable modules, CARES/CRPEST and
CARES/CREEP, which perform: (1) calculation of parameters from Ceramics Analysis and Reliability
Evaluation of Structures
experimental data using laboratory specimens; and (2) damage
CARES/CREEP
evaluation of thermo-mechanically loaded ceramic components,
respectively. Finite element heat transfer and nonlinear stress analyses
are used to determine the temperature and stress distributions in the
Cumulabve amage Map 1
component The creep life of a component is discretized into short time
steps, during which, the stress and strain distributions are assumed con-
stant. The damage is calculated for each time step based on a modified Fig 1 Block diagram for the creep analysis of a monolithic ceramic
' Monlcman-Grant creep rupture criterion. Failure is assumed to occur component using CARES/CREEP.
when the normalized accumulated damage at any point in the compo-
nent is greater than or equal to unity. The corresponding time will be
the creep rupture life for that component CARES/CREEP produces a
cumulative damage plot for graphical rendering of the structure's the modified Monlcman-Grant equation, may be evaluated from this
critical regions. data. After the title and elastic modulus, the input file consists of a
A schematic representation of the integrated design process is header line for each test which contains the test temperature and load,
shown in Fig. I. The CARES/CREEP algorithm makes use of the followed by two columns, strain and time, The data set ends with a
nonlinear stress analysis capabilities of the ANSYS finite element marker to indicate the start of a new data set The second available data
program. Before building a model in ANSYS, the creep response of the option yields secondary creep and Monkrnan-Grant parameters. For this
material must be known. An input file containing these parameters is data set the strain vs. time curves are not required, but the minimum
generated by the parameter estimation module of CARES/CRPEST. strain rate (secondary creep strain rate) and time to failure are input
This module is written in FORTRAN 77 and has as its input data from The input consists of four columns of data, with one line of data for
creep tests. After the parameter estimation and nonlinear analysis has each test specimen. The data entries are temperature, stress level,
been completed, the second half of the CARES/CREEP program may minimum strain rate, and time to failure.
be run. This module is executed from within the ANSYS program and CARES/CREEP is an ANSYS macro which computes the damage
is written in APDL (Ansys Parametric Design Language). APDL for each element The damage is evaluated for the modified Monlcman-
routines usually take the form of an ANSYS macro which is a -Grant failure criterion as given in equation (10). Finite element
sequence of ANSYS commands recorded on a file for repeated use. By analysis is an ideal mechanism for obtaining the stress -distribution
recording these commands on a macro, they can be executed with one needed to calculate the survival probability of a structure. Each element
ANSYS command. When this execution is completed, a damage map can be made arbitrarily small, such that the stresses can be taken as
of the component is displayed in the graphics window. This map constant throughout each element (or subelemenft. In CARES/CREEP,
consists of a contour plot of the component's damage at the time when the damage calculations are performed at the element centroid, or
failure has taken place, or at any design life. optionally, at the node points. Using the nodal points enables the
The parameter estimation module computes the Norton, Bailey— element to be divided into sub-elements, where the stresses and
Norton and modified Monlcman-Grant coefficients from uniaxial creep temperatures are calculated.
tests. Experimental data may be in one of two forms. The first is the
more complete set of data. A standard creep test involves applying a Input Information
constant load over a period of time or until the specimen fails. The The CARES/CREEP analysis is closely coupled to the ANSYS
strain is recorded as a function of time for varying test temperatures general purpose finite element package. As a result of this integration,
and loads. All parameters, primary and secondary creep strains and for the input for CARES/CREEP is centered around ANSYS input and
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Table 1 ANSYS structural elements with creep capabilities where PREP?, SOLUTION, and POST1 are ANSYS process opera-
tions, ETCHG and /INPUT are ANSYS commands, and CARESCR is
the CARES/CREEP macro. The ANSYS program is divided into
Thermal Structural Geometry Nodes
several processors each serving a particular purpose. The general
preprocessor (PREP?) is where the model is built Boundary conditions
2-0 PLANE35 PLANE2 Triangle 6
are applied and the solution is obtained in the SOLUTION phase. The
PLANE55 PLANE42 Triangle 3
evaluation of the results of a solution takes place in POST1.
Quadrilateral 4
A typical input file for the CARES/CRPEST code is given in
PLANE77 PLANE82 Triangle 6
Fig. 2. The '/' commands are used for program control and general
Quadrilateral 8
information. Program control includes SCRIT, PSRATIO, DATAOPT,
3-0 SOLID70 50LID45 Tetrahedron 4 START, STOP, and END. The purpose for each of these is shown in
Prism 6 Fig 2 with two exceptions. The SCRI keyword directs which stress will
Hexahedron 8 be used in the creep calculations. The options for this command
SOLIDS? SOL092 Tetrahedron 10 correspond to input for the ANSYS vget command. The DATAOP
keyword specifies which type of data will be supplied for the creep
Shell SHELL43 Triangle 3 response of the material. The FULL option, DATA0P---1, is demon-
Quadrilateral 4 strated in Fig 2. The SECOND option, DATA0P.--2, indicates
SHELLS! Line 2 secondary creep rates will be input The data includes stress, tempera-
ture, secondary creep strain, and time to failure for each specimen
tested. Secondary creep strain rate parameters are calculated from this
data.
restrictions. The requirements for a CARES/CREEP analysis do not
extend beyond those for the appropriate ANSYS analysis. This program Output Information
nms as a macro, so information from the ANSYS database does not Output for this program is divided into two parts depending on
need to be extracted for further manipulation outside the finite element which program is executed. The CRPEST output contains a summary
program. of specimen data and the estimated parameters. An echo of the
ANSYS contains a vast element library which includes elements command parameters and their interpretation is also included. For the
for structural, thermal, magnetic and electronic field, and fluid analysis. iterative solutions the values at each step are also given.
A thermomechanical analysis of a ceramic component would involve
the thermal and structural elements. ANSYS contains several elements
with creep modeling capabilities. A list of the 2-dimensional, 3-dimen- MTLE,Example Problem #1
(cid:9)
sional, and shell elements is given in Table I. Additional elements with /EIVIOD,400.E1-09 elastic modulus
(cid:9)
creep capabilities include beam and pipe elements which are not /MATTD,1 material number
(cid:9)
commonly used to model ceramic components. All 2-D structural /SCRIT,1 stress for damage calculation
1 - equivalent
elements have 2 degrees of freedom per node and may be used for
2 - maximum principal
plane stress, plane strain or axisyrnmetric analysis. The 3-0 structural (cid:9)
/PSRAT,0.333 default tp,/tt ratio
elements, which would be most commonly used for ceramic component (cid:9)
/DATA0P,1 full time-strain history
analysis have 3 degrees of freedom per node. /FAILCR,1 (cid:9) failure criteria option
The 3-D hexahedron element with midside (20), SOLED95, nodes does 1 - modified Monianan:Grant
not have creep modeling features. If midside nodes are desired for a 2 - Monkma.n-Grant
(cid:9)
3-dimensional analysis, the 10-node tetrahedral element, S0LI092, /RGAS universal gas constant
(cid:9)
must be used. /TOFFST specifies the offset temperature from
The required steps for a CARES/CREEP thermomechanical absolute zero to zero
1st specimen
analysis are;
/START stress temperature tps
cc (cid:9) ! time-strain, paired data
PREP7-Construct the model with thermal boundary
•••
conditions
/STOP
SOLUTION-Heat transfer solution
! 2nd specimen
ETCHG-Change element type to their corresponding element /START stress temperature tps
type, in this case, thermal to structural time-strain, paired data
!
/INPUT,CRPEST,ANS-Read CRPEST input from a file
generated by CRPEST /STOP
SOLUTION-Apply mechanical BC's and loads and solve
//END
POST I -Enter POST I for postprocessing
CARESCR-Execute CARES/CREEP to calculate accumulated Fig 2 CRPEST input file.
damage
6
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The first part of all CARES/CREEP output data contains an echo
of ANSYS runtime statistics and CARES/CREEP control input. The )
r
u
damage for each element is output at the time to failure as well as the o
h
time history of the elements with the highest accumulated damage. The I/
cumulative damage for each element is stored in an element table e (
at
within ANSYS so that the cumulative damage map may be constructed. R
After the CARES/CREEP macro is executed, this map appears in the ep
e
ANSYS graphics window. The data is stored in the element table for Cr
l
future use. a
nt
e
m
EXAMPLES eri
Benchmark problems of creep life prediction for ceramic compo- p
x
nents under multiaxial loading are used to validate the CARES/CREEP E
program. Two examples of ceramic components under multiaxial loads
are presented here. The first example is the spin disk which was a part
1E-05 (cid:9) 1E-04 (cid:9) 1E-03 (cid:9) 1E-02
of AlliedSignalts program to develop and demonstrate life prediction
methods for ceramic components of advanced vehicular engines (Cucio, Analytical Creep Rate (1/hour)
et al., 1994). The failure mechanisms for this example were found to
be a combination of creep and slow crack growth. The second problem
was a silicon nitride notched tensile specimen which was analyzed as Fig 3 Experimental vs. analytical creep rates for NT 154 ceramic
a part of Saint-Gobain/Norton advanced heat engines applications from Saint-Gobain/Norton.
program (Sundberg, et al., 1994). Both of these efforts were sponsored
by the Department of Energy as a part of the Ceramic Technology
Project.
strain rate is plotted as a function of the analytical secondary creep
Spin Disk strain rate, Fig. 3. The analytical value is found using equation (6) and
This example demonstrates the use of CARES/CREEP and the constants estimated for the material and the stress and temperature
CARES/LIFE to predict the time-dependent behavior of ceramic conditions of the individual specimen. If the analytical and experimen-
components under multiaxial loads. The data for this example are from tal creep rates are equal, the data point will lie on the line in Fig. 3..
work done by AlliedSignal Aerospace on the life prediction methodolo- Since all of the points are relatively close to the line, the estimated'
gy for ceramic components (Cucio, et al., 1995). This work included parameters for this material adequately characterize the secondary creep
tests on silicon nitride NT154 for a variety of uniaxial and multiaxial rate of the individual uniaxial test specimens. The primary creep
specimens. The uniaxial tests were conducted on three- and four-point parameters as given in equation (5) were calculated and are C,=-
bend and tensile specimens at temperatures ranging from ambient to 5.14x1045/Pat°5 hour021, C2=1.05, C,4.785, and c=25290°K.
1400°C. Confirmatory tests were designed to simulate the stress, size, The strain as a function of time for a uniaxial specimen whose
and loading conditions that represent actual engine components. Three temperature and applied load were 1371°C and 145 MPa, respectively,
multiaxial tests were conducted: notched tensile, tension-torsion, and is shown in Fig. 4. The experimental results (solid line) and the
the spin disk. analytical strains (dashed line) are plotted. Both a primary and
Life predictions for the spin disk were chosen to validate the secondary creep regime are present The analytical curve was generated
CARES/CREEP code. Smooth uniaxial test specimens were used to using the material constants given above. The analytical curve is the
determine the creep parameters and consequently serve as a basis for sum of the primary and secondary creep strain in order to be compati-
these predictions. The tension test is the preferred method for charac- ble with the creep modeling in ANSYS. The analytical creep response
terizing the high-temperature properties of the silicon nitride. The is plotted with its primary and secondary creep components separated
uniaxial test geometry consists of a flat dog-bone with tapered holes to in Fig. 5. Both Figs 4 and 5 are shown to demonstrate the manner in
account for the relief of out-of-plane alignment. The highest creep which the creep strain is handled within the ANSYS•program. The
strain rates should be confined to the gage section rather than the correlation of the analytical and experimental data is exceptional for
pin-loaded holes. The creep characteristics of silicon nitride (NT154) this specimen. Typically, experimental creep rates within a factor of
when isothermally loaded in uniaxial tension at temperatures in the two of the analytical creep rate are within acceptable limits for these
1200-1400°C range have been investigated. The strain as a function of materials.
time for each test is known. The total data base consisted of 83 The mesh for the spin disk is shown in Fig. 6. The ANSYS model
specimens for various temperatures and loads. With this information contains 1126 axisymmetric elements (PLANE82). The maximum
the primary and secondary creep may be characterized for this material. diameter of the disk is 0.137 m. The height of the disk is 0.0483 m
6 Iterating over equations (7) and (8), the secondary creep rate including the shaft. A rotational velocity was applied to the disk. The
parameters converged after 52 iterations. The parameters, C,, C,, and disk is constrained in the shaft to prevent rigid body translation in the
Clo, are 2.78x 1041/Pr hour, 6.94, and 114000°K, respectively. These vertical direction. The temperature distribution in the spin disk is not
parameters are assumed to be material constants. To determine if they uniform in the shaft region. This distribution is plotted in Fig. 7. The
vary from one specimen to the other, the experimental secondary creep temperature of the body of the disk is 1370°C.
7
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0.016
0.014-.
0.012 —
0.010 —
0.008 —
00 .
0.006 —
0.004 —
0.002
0.000
0 20 (cid:9) 40 (cid:9) 60 (cid:9) 80 (cid:9) 100 120
Time (hours)
Fig 4 Creep Strain as a function of time for a smooth tensile speci- Fig 6 Axisymmetric finite element mesh for the spin disk.
men at 1371°C and 145 MPa.
0.012 (cid:9) so.cc
in 1026
0.010 — El 1064
'a 1103
ri
E 1141
lo•
0.008 — ..= 1179
.9 1217
Analyti • 1256
0.006 — • 1294
• 1332
0.004 — M 1 3 7 0
11\
0.002 — Primary
Secondary
0 000
(cid:9)
0 20 (cid:9) 40 (cid:9) 60 (cid:9) 80 100 (cid:9) 120
Time (hours)
Fig 5 Components of creep stain as a function of time for a Fig 7 Temperature distribution in the silicon nitride spin disk.
smooth tensile specimen at 1371°C and 145 MPa.
The creep life of the spin disk was estimated at 5500 hours. The center of the disk. As time passes, the maximum value resides on the
life of these components in laboratory experiment was approximately surface, Figure 9b. At life as low as 100 hours, the surface stress is
10 hours. Test results indicated that the disks did not fail in the creep close to the maximum value in the interior of the disk. Fast fracture
regime. Possible failure mechanisms included slow crack growth and and slow crack growth analysis are most closely a function of the
surface (machining) damage. A fast fracture and slow crack growth maximum principal stress.
analysis was conducted on the disks as well. The equivalent stress The results of a creep and a slow crack growth analysis cannot be
distribution as well as the maximum principal stress distribution were compared directly since the evaluated quantities are not the same. The
examined for the disks. The Von Mises (equivalent) and maximum creep life is found in terms of the damage sustained over the service
principal stress distributions are plotted as a function of time in Figures life of a component Failure due to fast fracture and slow crack growth
8 and 9 for a disk at 50,000 rpm. CARES/CREEP predictions were is quantified by assigning a probability of failure or survival to a
based on the equivalent stress in the disk. At time, Figure 8a, the component for a given lifetime. If that probability of failure is less than
equivalent stress is maximum in the center of the disk. The maximum one which has been established as acceptable for design than the
remains in the center for the duration of service, Figure 8b. The component may be suitable for that application. A general comparison
distribution of the maximum principal stress as a function of time is of the two analyses will be made in order to understand the mecha-
much different. At time, Figure 9a, the maximum value is at the nisms behind the failure of these disks.
8
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MPa (cid:9) MPa
D
Co
C14 08
29 MN (cid:9) 21
44 34
50i 58 EN 47
72 60
87 73
1.101 86
116 im 99
m"130 •• 112
(a)
(b) (b)
(cid:9)
Fig 8 Von Mises stress distribution in the spin disk at time equal to Fig 9 Maximum principal stress distribution in the spin disk at
(cid:9)
a) zero and b) 5500 hours. time equal to a) zero and b) 5500 hours.
The cumulative damage for the spin disk after 5500 hours is
0
plotted in Figure 10. The damage is maximum and equal to one at the
0.11
center. CARES/CREEP than predicts a lifetime in creep of 5500 hours.
0.23
The slow crack growth analysis predicts much smaller lifetime. The 0.34
fast fracture (instantaneous) probability of failure is 0.001. After 100 0.45
0.57
hours, the probability of failure is 0.05. With probability of failures of
0.68
this magnitude, the disks would be expected to fail due to slow crack
0.80
growth. In addition, the spin disks were also found to fail at the 0.91
surface and the potential for damage due to surface finishing operations 1.02
may have contributed to their ultimate failure.
Notched Tensile Specimen
The aim of this example is to predict the multiaxial creep rupture
behavior of silicon nitride, NCX-5100, from data obtained from
uniaxial specimens (Sunfberg, et al., 1994). This effort was a part of
the study of the joining of silicon nitride to silicon nitride. Creep
experiments were conducted on two types of specimens. First, smooth
tensile tests were investigated in order to characterize the creep
Fig 10 Cumulative damage in the spin disk after 5500 hours.
response of the silicon nitride. Second, experiments on notched tensile
bars provided a multiaxial loading condition where the creep life may
be predicted from data obtained from the smooth tensile specimens. the relief of out-of-plane alignment The highest creep strain rates
The tension test is the preferred method for characterizing the should be confined to the gage section rather than the pin-loaded holes.
high-temperature properties of the silicon nitride. The uniaxial test The creep characteristics of silicon nitride (NCX-5100) when isother-
geometry consists of a flat dog-bone with tapered holes to account for mally loaded in uniaxial tension at temperatures in the 1275-1425°C
9
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1E-03
e"
0 (cid:9) 1E-05
(cid:9) (cid:9)
1E-07 1E-06 (cid:9) 1E-05 (cid:9) 1E-04 lE 03
Analytical Creep Rate (Lhour)
Fig 11 Experimental vs. analytical creep rates for NCX-5100
1.1Pa
ceramic from Saint-Gobain/Norton.
0
28
57
range have been investigated. The minimum creep rate, temperature, 85
114
stress, and time to failure for each specimen are known. The secondary
143
creep rate and Monlcman-Grant parameters were computed from this 171
data set. 200
Iterating over equations (7) and (8), the secondary creep rate 228
258
parameters converged after 14 iterations. The parameters, C7, C and
,
C10, are 7.858x1026/Pa" hour, 6.75, and 127560°K, respectively.
These parameters are assumed to be material constants. To determine
if they vary from one specimen to the other, the experimental second-
ary creep strain rate is plotted as a function of the analytical secondary
creep strain rate, Figure 11. The analytical value is found using
equation (6) and the constants estimated for the material and the stress
and temperature conditions of the individual specimen. If the analytical
and experimental creep rates are equal, the data point will lie on the
line in Figure II. Since all of the points are relatively close to the line,
the estimated parameters for this material reasonably characterize the
secondary creep rate of the individual uniaxial test specimens.
1111111/Sraltin
1011111MWASIM
San (cid:9)
11 10 .310,04: (cid:9)
Fig 13 Maximum principal stress in the notched tensile specimen at
We" ..........
time equal to a) zero, b) 10, and c) 100 hours.
00004.1%Atttle37t.
nlIt*Se•Setilt ”Aig
ifigrangOA!!! The mesh and load applied for this example is shown in Figure
12. The ANSYS model contains 1047 axisyrrunetric elements (PLANE-
;;;;;I:IgTVIV;
• ."• • • • •• 82), In addition to the axisynunetrical loading and geometry conditions,
the bar is also symmetrical in the longitudinal direction. One-half of
the bar is meshed as shown in Figure 12. The notch is on the outside
Fig 12 Axisymmetric finite element mesh for the notched specimen.
of the bar and its radius is 20% of the radius of the gage section of the
tensile specimen. The model was long enough in the direction of the
10
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