A high temperature, low cycle fatigue life prediction method was developed. This method, Cyclic Damage Accumulation (CDA), was developed for use in predicting the crack initiation lifetime of gas turbine engine materials, but it can be applied to other materials as well. The method is designed to account for the effects on creep-fatigue life of complex loading such as thermomechanical fatigue, hold periods, waveshapes, mean stresses, multiaxiality, cumulative damage, coatings, and environmental attack. Several features of this model were developed to make it practical for application to actual component analysis, such as the ability to handle nonisothermal loading (including TMF), arbitrary cycle paths, and multiple damage modes. The CDA life prediction model was derived from extensive specimen tests conducted on cast nickel-base superalloy B1900 + Hf. These included both monotonic tests (tensile and creep) and strain-controlled fatigue experiments (uniaxial, biaxial, TMF, mixed creep-fatigue, and controlled mean stress). Additional specimen tests were conducted on wrought INCO 718 to verify the applicability of the final CDA model to other high-temperature alloys. The model will be available to potential users in the near future in the form of a FORTRAN-77 computer program

Nelson, Richard S.

English

NASA Technical Reports Server

N91-24309
APPLICATION OF CYCLIC DAMAGE ACCUMULATION LIFE PREDICTION MODEL
TO HIGH TEMPERATURE COMPONENTS
Richard S. Nelson
United Technologies Corporation
Pratt & Whitney
E. Hartford, Connecticut
INTRODUCTION
A high temperature, low cycle fatigue life prediction method has been
developed by Pratt & Whitney under the sponsorship of the Lewis Research
Center (Moreno et al, 1984). This method, Cyclic Damage Accumulation, has
been developed for use in predicting the crack initiation lifetime of gas
turbiDe engine materials, but it can be applied to other materials as
well. The method is designed to account for the effects on creep-fatigue
life of complex loadings such as thermomechanical fatigue, hold periods,
waveshapes, mean stresses, multiaxiality, cumulative damage, coatings, and
environmental attack (Nelson et al, 1986). Several features of the model
were developed to make it practical for application to actual component
analysis, such as the ability to handle non-lsothermal loadings (including
TMF), arbitrary cycle paths, and multiple damage modes.
The CDA life prediction model was derived from extensive specimen tests
conducted as part of the contract activity on the cast nickel-base
superalloy BI900+Hf. These included both monotonic tests (tensile and
creep) and strain-controlled fatigue experiments (uniaxial, biaxial, TMFp
mixed creep-fatigue, and controlled mean stress). Additional specimen
tests were conducted on wrought INCO 718 to verify the applicability of
the final CDA model to other high-temperature alloys. The model will be
available to potential users in the near future in the form of a
FORTRAN-77 computer program.
FEATURES OF CDA LIFE PREDICTION MODEL
The CDA model is based on the fundamental assumption that an
instantaneous damage rate can be calculated and integrated on a
cycle-by-cycle basis until a damage of unity is achieved. The current
constants in the program reflect the definition of damage as the
initiation of detectable cracks (0.030 in. {0.76 mm.}) at the location
being considered. Other definitions of damage may also be modeled by
recalibration of the various constants. Different rates are calculated
simultaneously for whatever modes of damage may apply to a particular
material. Currently defined modes in the CDA program include transgranular
and intergranular fatigue, oxidation, and coating cracking.
One of the most significant features of the CDA model is its use of
ratios of stress/strain parameters rather than absolute levels. This
technique greatly simplifies practical application of the model to actual
Work performed under NASA Contract NAS3-23288; Dr. Gary R. Halford, LeRC,
serves as NASA Technical Monitor.
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components, since these ratios are generally easier to calculate than the
absolute levels. The model also makes use of total strain rather than
inelastic strain; this avoids the problem of having to calculate the very
small inelastic strains associated with the typically high design lives
for components made of modern superalloys. The transgranular damage model
incorporates a loading history term derived from primary creep data. This
captures the effects of overloads and other previous load excursions which
can set up compliant dislocation structures and thereby affect subsequent
fatigue behavior. Mean stress effects are handled through an exponential
term based on the ratio of maximum cycle stress to a reference maximum
stress. Subcycles are determined by the computer program using the
traditional rainflow cycle counting method, based on reversals of stress
range ratio rather than stress or strain alone.
Temperature effects are very important to any high temperature model,
and these are included in the CDA transgranular model in several ways.
First, time dependence (hold time, strain rate, etc.) is introduced
through the use of a multiplier term based on the integral of an Arrhenius
function. This will automatically handle any arbitrary periodic waveform,
eliminating the need to estimate average strain rate, frequency, or other
such parameters from a component loading history. Second, an additional
strain term is postulated to result from microscopic thermal expansion
mismatch within the material structure. This is added to the macroscopic
total strain, and the resulting strain range is used by CDA to compute the
life. Finally, temperature effects are included implicitly through the
temperature dependence of certain reference stress/strain quantities.
The second major damage mode currently active in the CDA model is the
intergranular mode. This is based on an integral of an Arrhenius function
which is calibrated to data from creep testing. This was found adequate
for many components which fail simply from cyclic loadlngs in the creep
regime. Other damage modes include cyclic oxidation (which modifies the
transgranular damage term) and coating cracking (based on the coating life
model from a companion NASA contract [Swanson et al, 1987}).
APPLICATION TO HIGH TEMPERATURE COMPONENTS
The CDA computer program is designed to accept one or more "defined
cycles" for which a complete stress/strain/temperature/time history is
known. These may be obtained from several sources, including simpl{fied
methods or full inelastic analysis programs. The program accepts this data
(interpolating where required) and directly integrates the rates of the
various damage modes until one of them reaches unity.
REFERENCES
Moreno, V., Nissley, D. M., and Lin, L. S., 1984, "Creep Fatigue Life
Prediction for Engine Hot Section Materials (Isotropic) Second Annual
Report," NASA CR-174844.
Nelson, R. S., Schoendorf, J. F., and Lin, L. S., 1986, "Creep Fatigue
Life Prediction for Engine Hot Section Materials (Isotropic) Interim
" NASA CR-179550Report,
Swanson, G. A., Linask, I., Nissley, D. M., Norris, P. P., Meyer, T.
G., and Walker, K. P., 1987, "Life Prediction and Constitutive Models for _
Engine Hot Section Anisotropic Materials Program," NASA CR-179594.
OVERVIEW
• Summary of Contract Activities
• Features of CDA Life Prediction Model
• Application to High'Temperature Components
• Future Research
THE CDA METHOD IS BASED ON EXTENSIVE HIGH
TEMPERATURE SPECIMEN TESTING
i
Base
program
(1982-84)
Option
I_ogram
(t984-Sa)
Program
extension
(1988)
CDA MODEL BEGINS WITH INTEGRATION OF DAMAGE
RATES FOR MULTIPLE MODES
For use as a practical design method, "Damage = 1" is defined as initiation of
a 0.030 in. (0. 76 mm.) surface length crack
• The basic equation for CDA is simply an integration of damage rate from
0 to 1:
1 = fNi dD dN
dN (1)"1
• This same calculation is performed simultaneously for multiple modes of
damage, as required for a given material. Currently defined modes
include:
1. Transgranular fatigue
2. Intergranular fatigue
3. Oxidation / environmental damage
4. Interactions of the above
TRANSGRANULAR DAMAGE MODEL UTILIZES A
STRESS AND STRAIN RATIO CONCEPT
Absolute inelastic strains can be small and dihicu_ to predict reliably for many
nickel-base superalloys
• The damage rate is calculated using the ratio of current parameters to
reference values:
dD_ 1 ( &_:T trill &o t_2(E.____.BEE/dN (N----_EF) A_T, REFI k_) _ _p / (2)
• A loading history parameter derived from primary creep data is also
included:
(__.P_.__)= f_p ( OMAX ) '£P,REF o£p,REF MAX, HISTORY (3)
TWO ADDITIONAL TERMS WERE NECESSARY TO
PREDICT BASELINE FAST RATE DATA
t| i, i ill
• The first predicts mean stress and R-ratio effects using a ratio based on
maximum tensile stress:
dD dD ( °MAX /
dN BASIC - dN e _OMAX,REFI (4)
• A threshold strain range was necessary to predict the high life, low strain
data for both B1900+Hf and INCO 718:
A£T -- A£TACTUAL -ArTTHRESHOLD (5)
STRAIN RATE EFFECTS CAN BE PREDICTED FOR ANY
ARBITRARY WAVEFORM
• i i
Permits direct appfication of CDA to practical component cycles
* The basic transgranular damage rate (product of the previous terms) is
modified by a time & temperature dependent term:
-[Qlldt
fTD = 1 +J" AleBl°e \R-T! (8)
• This eliminates the need to estimate hold time, average frequency, or
other similar parameters for complex loading cycles typically experienced
by modern high temperature components
CLASSICAL (.,,UM"I.tI..AT IVE DAMAGE, EFFECTS ARE ALSO
PREDICTED BY -]tiE CDA MODEL
Real components see a spectrum of loads during their service life
• Non-linear damage accumulation is included ill a modifying function for
the basic transgranular damage rate:
G(D) = (lifE) (/]-tl) Df_+ fL (7)
where p _dD/dNaAsic! (8)
• Subcycles are computed using the rainflc, w cycle counLing method based
on reversals of slress range ratio
• The primary creep ductility term automatically reduces the damage done
by sul_cycies when their maximum slress is lower than lhat of the major
cycle
THE RATIO CONCEPT PERMITS CDA TO HANDLE
NON-ISOTHERMAL LOADIN_._
Marly practical appfications involve varying temperature
• The referer_ce stresses and strains are functions of temperature for each
material in the CI-)A library
This is sufficient for variable temperature components below the range
where TMF is a concern
• For TMF, an additional strain due 1o thermal expansion coefficient
mismalch ¢_as necessary t_-_correlab; tla_ dala
"rMF = J:" A '_(T) i" dl (9)
lO
THE SECOND DAMAGE MODE PREDICTS
INTERGRANULAR FAILURE MECHANISMS
Often components fail by cyclic loads which result in failure by creep mechanisms,
not fatigue
The damage rate for this mode is baSed on an Arrhenius function, but
with constants which are different from those used for the transgranular
mode:
o /Q2_
dO = fA2 e B2 e-_-_) dt
dN (10)
This rate is integrated cycle-by-cycle along with the transgranular damage
rate (and any other active modes) until some mode reaches a value of
unity
ENVIRONMENTAL DAMAGE CAN BE INCLUDED FOR
CYCLIC AND STATIC OXIDATION
Certain components can switch between these modes, depending on how they
are operated
• For cyclic oxidation, a multiplier factor based on a time-temperature
dependent integral is added to the transgranular damage model
• For static oxidation, a separate third damage mode can be calculated
which depends only on time and temperature, not cyclic variables such
as stress or strain
11
INTERACTIONS BETWEEN DAMAGE MODES
CAN BE EASILY INCORPORATED
• Where interactions are observed among the various damage modes
(creep/fatigue/environment), these are handled by combining damage
levels from those modes and integrating the result as a separate mode
• Almost any type of interaction may be modeled using this technique:
1. Linear (addiUve)
2. Non-linear
3. Power law
COATING LIFE PREDICTIONS UTILIZE THE MODEL
FROM A COMPANION CONTRACT
,T
Many modem superaltoys must be coated for oxidation protection ir_ actual service;
this must be accounted for by a practical system "
• First, a viscoplastic constitutive model is used to predict the local
stress/strain history in the coating itself
• This coating stress/strain history is next used to predict coating cracking
life (through the coating thickness)
Finally, this life is converted to an equivalent damage rate which can be
integrated along with the other active damage modes for the substrate
material
12
MULTIAXIAL STRESS/STRAIN STATES ARE CONVERTED
TO EQUIVALENT CDA VALUES
i llfm l l ill ii
Many actual components are analyzed using 3-D methods which produce full
tensors; these must be interpreted by a practical life system
• The applied stress/strain tensors are transformed into 100 different axis
orientations in the plane of the component surface to search for the crack
plane (with the "worst" orientation)
• Two different algorithms are currently implemented for choosing the plane
which experiences the worst damage:
1. Maximum normal strain range
2. Socie parameter (combination of shear and normal)
• New materials may use these or choose some other appropriate
parameter
THE EFFECTS OF COMPLEX STRAIN AND
TEMPERATURE HISTORIES MUST BE DETERMINED FOR
ACCURATE LIFE PREDICTIONS
+0 5%
Hot spol
crealed by iml_ngement Strain 0
of gas palh air
+0 5%
-0 5%
Sl(a_n O
-05%
Outer vane support
TMF crack location
A
I 10_O 15100500
/ \ T,..,
E
D
BC'_ J T_me
D
Crilical location
strain-temp-time histories
13
CDA USES THE GIVEN STRESS/STRAIN HISTORY :'
DIRECTLY TO PREDICT LIFE
• The CDA program accepts as input one or many "defined cycles" for
which a full stress/strain history is known. These may come from many
sources:
1. Actual rig data taken during specimen testing
2. Simplified methods using elastic input
a. Neuber's rule
b. Integrated energy density
3. Full inelastic analysis methods
a. Finite element
b. Boundary integral equation
• The program performs semi-log interpolation of damage rates to
determine intermediate values between the defined cycles
THE CDA PROGRAM CAN BE EASILY EXPANDED FOR
NEW MATERIALS OR METHODS
"The only thing constant is change ..."
• The current CDA equations are sufficient for most current nickel-base
alloys; a new set of constants can be generated for materials other than
B1900+Hf or INCO 718
• The program is modular so that new equations, damage modes, or even
completely different life prediction methods can be added if desired
• The program is written in standard FORTRAN-77 and has run on
machines from PC's to mainframes; source code will be available for
distribution soon
14
FUTURE RESEARCH
Practical methods must undergo continuous improvement and continue to adapt
to new materials and analytical methods
The extensive database for F31900+Hf, including both constitutive and
creep-fatigue data, provides an excellent opportunity for evaluating new
prediction methods
TMF cycle path effects (such as CW vs. CCW elliptical cycles) are not
fully explained by the current CDA formulation; possible new methods
include:
1. Equilibrium stress/strain methods
2. Micromechanical models
Q The CDA model could be applied to the constituent materials in
advanced systems such as metal matrix composites
15
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Application of cyclic damage accumulation life prediction model to high temperature components

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