The unified constitutive theories for application to typical isotropic cast nickel base supperalloys used for air-cooled turbine blades were evaluated. The specific modeling aspects evaluated were: uniaxial, monotonic, cyclic, creep, relaxation, multiaxial, notch, and thermomechanical behavior. Further development of the constitutive theories to model thermal history effects, refinement of the material test procedures, evaluation of coating effects, and verification of the models in an alternate material will be accomplished in a follow-on for this base program

Dame, L. T.

Laflen, J. H.

Ramaswamy, V. G.

Vanstone, R. H.

English

Constitutive theories were evaluated against a large uniaxial and multiaxial data base that was generated as part of this work. The experimental approach was to determine the constitutive behavior of Rene 80 under a multitude of conditions that are important in the design of gas turbine blades and vanes. The experimental and analytical goals of this program were successfully accomplished. A new multiaxial constitutive model which can represent the complex nonlinear high temperature behavior of Rene 80 was developed. The model was extensively verified on data at several temperatures

NASA Technical Reports Server

N88- 11172
CONSTITUTIVE MODELING FOR ISOTROPIC MAIERIALS*
V.G. Ramaswamy, R.H. Van Stone, L.T. Dame, J.H. Laflen
General Electric Company
Aircraft Engine Business Group
INTRODUCTION
Accurate analysis of stress-strain behavior is of critical importance in
the evaluation of life capabilities of hot section turbine engine components
such as turbine blades and vanes. The constitutive equations used in the
finite element analysis of such components must be capable of modeling a
variety of complex behavior exhibited at high temperatures by cast
superalloys. The classical separation of plasticity and creep employed in
most of the finite element codes in use today is known to be deficient in
modeling elevated temperature time dependent phenomena. Rate dependent,
unified constitutive theories can overcome many of these difficulties and are
more suitable for the analysis of the complex behavior of high temperature
superalloys. However, many aspects of the unified theories had not been fully
evaluated prior to the initiation of this work, and thus these theories had
not been generally accepted for use in engine hardware design.
In this contract, constitutive theories were evaluated against a large
uniaxial and multiaxial data base that was generated as a part of the work.
Initially it was the intent to evaluate only available theories, however it
was found that no available approach was satisfactory in modeling the high
temperature time dependent behavior of Rene' 80 whicll is a cast turbine blade
and vane nickel base superalloy. Additional considerations in model
development included the cyclic softening behavior of Rene' 80, rate
independence at lower temperatures, and the development of a new model for
static recovery. The final constitutive model was implemented into a finite
element computer code which was developed as a part of the contract and which
was developed specifically for use with unified theories. The code was
verified by a re-analysis of the Turbine Tip Durability problem whicn was part
of the pre-HOST activities at General Electric [I]. This paper summarizes the
work on the second year of the contract; the first year's work was summarized
in last year's HOST Conference [2] and in the Annual Report [3]. Details of
the contractual efforts are given in the final report which is currently being
reviewed.
EXPERIMENTAL PROGRAM
The experimental approach in this work was to determine the constitutive
behavior of Rene' 80 under a multitude of conditions that are important in the
design of gas turbine blade and vanes. This required that thin wall specimens
be used as other NASA sponsored work has shown that thickness can be an
important factor in material response properties [4]. Consequently, all
*Work done under NASA Contract NAS3-23927.
307
https://ntrs.nasa.gov/search.jsp?R=19880001790 2020-03-20T08:33:33+00:00Z
specimens Were designed with a thickness of 0.03 inches. Similarly, the
experimental temperatures, strain ranges, strain ratios, hold times, and
strain rates were established through an evaluation of the operating
conditions in commercial jet engines.
In performing the experiments, the approach was to evaluate a series of
transient and steady state conditions in each specimen test by using a bloc¢
cycling method. This is illustrated in Figure 1 where several blocks of
strain ranges are used in one experiment - all other conditions, strain rate,
temperature, etc. are kept constant. By using several combinations of strain
range blocks in different sequences in a single test all combinations of
transient effects could be interrogated. The block length was selected to
produce cyclically stable hysteresis loops by the end of each block.
All uniaxial experiments were performed at the EMTL Laboratory of the
General Electric Company in Evendale, Ohio. The experimental results of each
test were automatically saved in digitized form in real time by using a ETS
data acquisition device. Prior to test, the number of load-strain pairs to be
saved in selected hysteresis loops was determined (between 200 to 400
points). Typically 50 hysteresis loops were saved in each test. After a
test, the data were permanently saved on tapes, before being loaded into
mainframe computer files which were used for detailed data analyses. Final
data analysis would include determining time derivatives by fitting a second
order polynomial to seven consecutive data points and differentiating. These
final data files could then be used in plotting data or determining constants
in constitutive theories.
Similarly, the tension torsion test results were available on cassette
tapes which could be used for detailed data analyses. These tests were
performed at the Turbine Technology Laboratory (TTL) of the General Electric
Company in Schenectady, New York under the direction of Dr. R. Williams.
These tests used a development extensometer from the Instron Corporation.
Additionally, a series of notched specimen test were conducted at Michigan
State University under the direction of Professor J. Martin. In these tests,
the notch root strains were measured using an ihterferometric displacement
gage.
THEORY DEVELOPMENT
Following a detailed literature review, General Electric selected the
Bodner model and a generic drag stress/back stress model for further detai|ed
evaluations with the Rene' 80 data. The intent in tlle evaluations with the
generic model was to perform an analysis of the Rene' 80 data to determine
which functional forms in suggested back stress/drag stress models were most
appropriate. Many of the results were presented in last year's paper. It was
found that neither the Bodner or the generic model were very adequate for
predicting the response properties of Rene' 80 at 18OO°F. Consequently a new
theory was developed which combined the Bodner exponential flow law with a
308
back stress formulation. The Bodner flow law had been found to be superior in
modeling the strain rate behavior of Rene' 80, and possess the ability to
predict essentially rate independent behavior at lower temperatures. These
are two essential aspects of the behavior of Rene' 80. Additionally, it was
found to be necessary to modify the evolution equations for tile back stress to
account for static recovery effects and to account for effects in the small
inelastic strain regime. Men these factors were included the final set of
equations could be written as:
[ : Z23K2)nl] (S-i_K_J)_ijI: D exp - A ( (I)
K2 : I12 (Sij - _ij) (Sij - _ij) (2)
_ij : _Sij + (l - ) _ijZ (3)
Rij I= fl _ijI fl
- _-- _ij
S
: m(z I - z) QI
(4)
(5)
_S
where
= 1J IJ
= -B(ae/°o) r (_s - _sat) (6)
_s(o) =_max, RijI(o) = 0, z(o) = Zo
The procedures for determining the constants in these equations have been
presented previously in [2,3]. Basically the procedure involves the
determination of most of the constants through the use of the monotonic strain
rate dependent stress-strain curves; only the saturated value of the drag
stress, Zl, is determined from cyclic tests (saturated hysteresis loops from
fully reversed cyclic tests are used in this case). Verification of this
method of determining the constants is presented in the form of correlations
with multiaxial, hold time/relaxation, and different mean strain test data.
That these equations are very accurate is shown through comparisons with
data. Figures 2, 3 and 4 show the correlation of the monotonic stress-strain
data at 1400°F through 1800°F, respectively. That the theory is capable of
predicting strain rate dependent as well as rate independent behavior is
309
apparent. Figure 5 shows a prediction of a compressive mean strain test
result. Figure 5(a) shows a comparison with the first two cycles, while
Figure 5(b) shows a comparison with the saturated hysteresis loop of this
test. Figures 6 and 7 show that the theory can predict the stress relaxation
behavior at high and low temperatures. Note that while the monotonic data at
1400"F exhibits little rate dependence there is still stress relaxation.
Creep comparisons are shown in Figures 8 and 9. These predictions depend
strongly on the form of the static recovery term. Note that the form that is
used in the current theory is much different than those used in other unified
approaches.
Multiaxial comparisons are shown in Figures ]0 to ]3. Figures lO (a)
and (b) show the axial and torsion comparisons, respectively, for a combined
tension-torsion (in-phase) test. Figure ll shows the data results and theory
predictions from a special nonproportional test where segments of proportional
cycles were used (see the insert of these two figures). Figure ]l compares
results from the first segment (cycle 5), and the last segment (cycle 32) of
this nonproportiona] loading experiment. That the predictions are accurate
illustrates that the theory is good for such conditions without considering
the additional hardening that has been found in some other materials.
Figures 12 and 13 show that the new theory can predict 90 deg. out of phase
tension/torsion experimental results at two temperatures with good accuracy.
Figures 14 and 15 show two predictions of the theory with test data from
combined temperature and strain cycling tests. The predictions are shown to
be reasonable considering that the predictions are based only on isothermal
test data.
FINITE ELEMENT IMPLEMENTATION
The theory discussed in the previous section was implemented into a new
3-D finite element code which uses a 20-noded brick element. The program uses
a dynamic time incrementing procedure to minimize cost while guaranteeing an
accurate solution. The inelastic rate equations and state variable evolution
equations are integrated using a second order Adams-Moulton predictor
corrector technique. Piecewise linear load histories are modeled in order to
simplify input. Further economics have been achieved by improving the
stability of the initial strain method and further reducing the number of
equilibrium iterations. The program was developed on an IBM PC AT and has
been successfully installed on the NASA-Lewis CRAY computer.
SUMMARY
The experimental and analytical goals of this program were successfully
accomplished. A new multiaxial constitutive model which can represent the
complex nonlinear high temperature behavior of Rene' 80 was developed. The
31o
model was extensively verified based on data at several temperatures. The TMF
and nonproportional cyclic modeling capabilities of the model were
demonstrated. The model was implemented in a 3-D finite element code which
was installed on the NASA-Lewis CRAY.
REFERENCES
I. McKnight, R.L., Laflen, J.H., and Spamer, G.T. :'Turbine Blade Tip
Durability Analysis", NASA CR165268, February 1982.
e Ramaswamy, V.G., Van Stone, R.H., Dame, L.T., and Laflen, J.H.,
"Constitutive Modeling for Isotropic Materials," NASA Conference
Publication 2339, October 1984.
o Ramaswamy, V.G., Van Stone, R.H., Dame, L.T., and Laflen, J.H.,
"Constitutive Modeling for Isotropic Materials", Annual Report, NASA
CR17485, March 1985.
311
Figure 1. Typical Strain Limits Imposed During Cyclic Experiments
Rene'80
760°C
Experiment Model E --(M-1)
o .2
A --- .02
+ .'. .002
Figure 2. Monotonic Tensile Response of Rene'80 at 760°C
312
o
Rene' 80
871°C
Experiment Model _ (M-1)
o .2
.02
+ --- .002
Figure 3. Monotonic Tensile Response of Rene'80 at 871°C
ReneL80
982UC
Experiment Model _ (M"I)
o x .2
0 --- .06
.02
+ - - .002
! !
•08 .12 .'16
STRRIN mlO "t
Figure 4. Monotonic Tensile Response of Rene'80 at 982°C
313
Q. Rene'80
982°C
/
/
/
/
'Experiment
1 "1"
-.028 -.018 -.008
STRAIN 110 "t
(a) First Two Cycles
!
.002.
0
0
(__
(3:
Q_
w
cOO"
cO
LI.J
n,-
I---
cOB
!
0
0
I
.12
Rene'80
982°C
)eriment
Model
-'.o8 -'.o4
STRAIN =I0 -I
(b) Cycle 78
!
0
Figure 5. Cyclic Response of Rene'80 with Mean Strain
314
m Rene '80
_] 982°C
Experiment
Model
o
o
'-.oso -'.02s o' .b_s .bso
STRAIN II0 "I
Figure 6. Stress Relaxation in Rene'80 at 982°C
(Cycle No. 60)
(:)
o_
Go
o
o_
or
(I_
_r-
w
cOo
cO
LJJ
OC
cOoo
I
Rene '80
760°C
Experiment
Model
o
o
co
'-.0s0 -'.o2s o' .62s .6s0
STRAIN IlO "_
Figure 7. Stress Relaxation in Rene'80 at 760°C
(Cycle No. 94)
315
-iI
Z
/_OOO(9®®®®_-
/,_AA "--_ _'Experiment
_Model
°o sb _o _o 2_o
TIME (SECONDS)
300 MPa
217 MPa
Figure 8 Creep Response of Rene'80 at 982°C
O
684 MPa
633 MPa
s.
.j.
/
/
/
+ + + +
Model
553 MPa
% 2_ sb 7_ _bo
TIME (SECONDS) 110 _
Figure 9 Creep Response of Rene'80 at 760°C
316
o
o.
rr'o.
r
O0
09
bJ
e_, (3"
09
.J
X i
C_
o
o
!
(a)
Rene'80
982°C
Experiment
el
!
OB
! !
-'.04 0 .04
AXIAL STRAIN .10 "I
.0B
c}
_- Rene '80
982°C
(b)
Figure 10.
®
®
)eriment
-Model
In phase Tension Torsion Cxclic -1
Response of Rene'80 at 982vC, .O02M
317
0-
C£C_-
(I_"*
w
ob
03
k--
03
OC
"111"I
03
c_
c)
N
I
- .04
Rene' 80
982°C
Experiment, Model Cycle
o,--,5
A ---j32
I I !
- .02 0 .02
SHEAR STRA IN I I0"I
I
.04
Figure 11 Comparison of Rene'80 Response Before and
After Non proportional loading (Paths A,F)
318
oo
a_o.
=
X I
¢Z
0
0
qP,
t-200
Figure 12.
Rene'80
982°C
®_®® ®
_Experiment
-'too o' lbo zbo
SHERR STRESS (lqPR)
Rene'80 Response to 900 Out of Phase
Tension/Torsion Cyclic Loading
o=
_1.°
=
o--I _.
X i
¢Z
oe_ Rene'_O
_¢m _ /_ "Experiment
,
'-zoo -1oo o tbo zbo
SHERR STRESS (HPR)
Figure 13. Rene'80 Response to 90 o Out of Phase
Tension/Torsion _clic Loading
319
(__
,mr
O.
OJ
Q-
w
fj_"
03
L_
n_
03_
I
Rene ' 80
TMF I 760°C
Experiment
Model
'-.o4 -:02 o' .b2 .b4
MECHRNICRL STRRIN =i0 "t
Figure 14. Rene'80 TMF Response (760°C-982°C Out of Phase)
0
,mr
cr
Q-
w
f,/3 O"
O3
la..I
I--"
"F
o Rene'80
0.
© TMF
0
0
qO
1649°C
)eriment
Model
'-.o4 -'.oz o' .b2 .b4
MECHRNICRL STRRIN =10 "=
Figure 15. Rene'80 TMF Response (649°C-1093°C Out of Phase)
320


Constitutive modeling for isotropic materials

The first year of progress on a NASA-Lewis contract with the General Electric Co is documented. The purpose of this contract (NAS3-23927) is to develop and evaluate unified constitutive equations for applications to hot-path components of aircraft gas turbine engines such as high pressure turbine blades and vanes. To accomplish this goal, uniaxial, notched, and multiaxial specimens made of conventionally cast Rene 80 are being tested under conditions that simulate engine operating conditions. To reduce the raw data, automated data reduction techniques are being developed that produce computer files containing the information needed to analyze proposed constitutive theories. Described are the analytical methods being developed to determine the parameters for these nonlinear unified theories by using the reduced data files. In another activity, a dedicated finite-element computer code is being developed to use unified theories in the structural analysis of hot-section components. This code was extensively verified for one such theory by successfully predicting the strain histories measured experimentally at the notch root of complex specimens taken from complex laboratory specimens

N8'7-I1212
CONSTITUTIVE MODELING FOR ISOTROPIC MATERIALS
V.G. Ramaswamy, R.H. Van Stone, L.T. Dame, J.H. Laflen
General Electric Company
Aircraft Engine Business Group
INTRODUCT ION
Accurate analysis of stress-strain behavior is of critical importance in the
evaluation of life capabilities of hot section turbine engine components such as
turbine blades and vanes. The constitutive equations used in the finite element
analysis of such components must be capable of modeling a variety of complex
behavior exhibited at high temperatures by cast superalloys. The classical
separation of plasticity and creep employed in most of the finite element codes in
use today is known to be deficient in modeling elevated temperature time dependent
phenomena. Rate dependent, unified constitutive theories can overcome many of
these difficulties and may be more suitable for the analysis of the complex
behavior of high temperature superalloys. However, many aspects of the unified
theories have not been fully evaluated. There is an urgent need for a
comprehensive evaluation and further refinement of the capabilities of unified
constitutive models for analysis of high temperature superalloy behavior.
OBJECTIVE
It is the purpose of this contract (NAS3-23927) to thoroughly evaluate the
unified constitutive theories for application to typical isotropic cast nickel base
superalloys used for air-cooled turbine blades and vanes. The specific modeling
aspects evaluated are: uniaxial, monotonic, cyclic, creep, relaxation, multiaxial,
notch and thermomechanical behavior. Further development of the constitutive
theories to model thermal history effects, refinement of the material test
procedures, evaluation of coating effects and verification of the models in an
alternate material will be accomplished in a follow-on for this base program.
APPROACH
The scope of the overall program covers several aspects of the development of
constitutive models for material behavior. The objectives of the base program is
being accomplished through a two year combined analytical and experimental
program. This is divided into several tasks, each task focusing on a specific
objective. First an extensive literature survey was made to identify possible
constitutive models for detailed evaluation. Based on the detailed evaluation, two
models have been selected for implementation into a finite element code. A
comprehensive uniaxial smooth specimen material test program is defined so as to
investigate the constitutive behavior patterns of Rene' 80, which is the base
material. These experimental results are being used for both the determination of
the material parameters and further evaluation of the predictive capabilities of
the two models.
pRECEI)I_IG PAGE BLANK N_T FIL_
293
https://ntrs.nasa.gov/search.jsp?R=19870001779 2020-03-23T15:01:13+00:00Z
The models will be evaluated for nultiaxial analysis capabilities, based on
multlaxial test data. Two types of multiaxial tests are being performed -
tension-tension type at a notch root using an extended ISG technique at Michigan
State University (MSU) (Ref. l) and tension-torsion type on hollow tubes at the
General Electric Turbine Technology Laboratories. The notch root behavior
prediction capability of the models will be evaluated based on several benchmark
notch verification experiments. This part is similar to the work conducted by
General Electric on the NASA sponsored Benchmark contract (Ref. 2).
The capability of the constitutive models to analyze the behavior of an actual
engine component will be verified by performing a finite element analysis of a
turbine blade tip, similar to that described in Reference 3.
PROGRESS
A. MODEL EVALUATION AND SELECTION
A comprehensive survey of various unified constitutive theories
available in the literature has been completed. From the 13 models
surveyed, 5 theories were selected for detailed evaluation. They are the
models of (1) Bodner et. al., (2) Krieg, Swearengen, Rohde (3) Miller
(4) Robinson and (5) Walker (References 4, 5, 6, 7, 8). Each of these
models was programmed as subroutines in a computer program, which performs
a simple numerical integration of the basic equations. All these models
involve a number of material parameters. For the purpose of evaluation of
the theories, constants available for different materials and temperature
in the published literature were used. Each model was subjected to a
variety of appropriate loading conditions, so as to evaluate their ability
to model several basic aspects of high temperature superalloy behavior.
These include: (1) strain rate sensitivity (2) creep (3) stress relaxation
(4) history dependence (5) cyclic hardening/softening (6) anelasticity.
In addition, the models were evaluated in terms of their complexities in
numerical implementation and material parameter evaluation.
During the course of this detailed evaluation, several generic features
of the models have become more evident, such as the roles played by the
backstress and drag stress. The numerical difficulties special to each of
the models have also become apparent. Based on this evaluation process,
two models were selected for further detailed investigation. These were
(1) the Bodner Model and (2) a generic backstress/drag stress model. In
the generic backstress/drag stress model, the specific functional forms
are being chosen based on the behavior observed in the Rene' 80 test
program.
B. EXPERIMENTAL PROGRAM
All specimens used in this program are cast as solid specimens and
machined to the desired configuration. Because of the desire to determine
thin wall constitutive relationships applicable to airfoils, the specimens
are tubular, with approximately .030 in. wall thickness. Tables la and Ib
294
Co
show all the monotonic tests and creep tests completed to date. Table Ic
shows all the isothermal cyclic tests that have been performed. The tests
cover a range of strain rates from .002 in/in/min to .2 in/in/min and the
temperature range from 538C (lO00F) to (982C) 180OF.
The tests are specially designed to meet the needs of constitutive
model development. At the same time, efforts were taken to maximize the
types of data obtained. For example, at the end of the strain rate
controlled monotonic tests, a stress relaxation test is performed. The
cyclic tests have an automatic data acquisition system, which is capable
of getting up to 200 data points for each hysteresis loop. Some examples
of this can be seen in Fig. 4.
The tension-tension multiaxial tests are being done by Prof. J.F.
Martin at MSU. These tests utilize an axisymmetric notched round bar with
three indentations at the notch root. Both the hoop and axial strains
will be measured using the interferometric strain gage, similar to that
used in the benchmark test program (Ref. 2).
Data reduction procedures also reflect the special needs of
constitutive model development. For each test, the elastic modulus is
first determined, based on the initial stress-strain readings. Then the
inelastic strain is calculated. Since time is recorded at each data
point, the time derivatives of all measured quantities is calculated.
Thus stress rate and inelastic strain rate is calculated at each point
using a 7 point sliding polynomial technique. All the results are stored
in a computer file which can be directly used as input in material
parameter eval uation.
EVALUATION OF MATERIAL PARAMETERS
It has been widely recognized that one of the major sources of
difficulty in the use of unified constitutive theories is the
determination of the material parameters. No generalized procedures of
determining these material parameters are currently available.
Considerable effort has been made to develop such a method in the present
contract.
The approach that is adopted is to develop a computer program which
directly uses the various test results as input and generates the various
material parameters as output. The computer program developed is kept as
flexible as possible, so that different functional forms can be used.
Such an approach also assures consistency in the treatment of the various
test data. However, it should also be noted that, while conceptually
simple, such an approach can be very challenging, mainly due to the
non-linear equations involved. Such a computer program has been developed
for a generic backstress-drag stress model.
295
The generic backstress-drag stress model is described by the following
set of equations for the uniaxial case:
.I =(___) N sgn (a-_) 1
.I _I
= fl c - f21 I_ - R1 2
.I El
= gl c g21 IZ - R2 3
(I)
In the above,
Z
= Inelastic strain rate
= Backstress
= Drag stress
R1 and R2 are static thermal recovery functions.
fl and gl are the hardening functions.
f2 and g2 are the dynamic recovery functions.
Equations l, 2 and 3 are a set of coupled non-linear differential
equations. The specific forms for the various hardening and recovery
functions are significantly different for the various models that have
been published. The approach taken in this project is to choose those
forms that appear most appropriate for Rene' 80 behavior. To determine
the various material parameters involved, an iterative approach is used.
In this, a set of starting assumptions are made which are subsequently
relaxed. Then successive non-linear optimizations are performed in
equations l, 2 and 3 using the experimentally measured quantities as the
basis.
Rene' 80 test data at 982C (180OF) has been analyzed in detail using a
computer program incorporating the procedure described above. Some of the
notable results are as follows:
fl = constant, f2 = constant appears to work reasonably well for this
case. The constants in Rl have been found using slow strain rate
monotonic and creep tests. However, the overall contribution of the above
term seems extremely small, as compared to the hardening and dynamic
recovery terms.
296
(z)
(3)
(4)
(5)
Fig. la shows the results of the iteration procedure after 5 iterations,
using only the high E monotonic test (.2 in/in/min). It appears that
parameters determined using the computer program can reproduce the stress
strain behavior reasonably well. Fig. Ib shows the same result, but using
only the small strain rate monotonic test (.002 in/in/min). The constants
for these two strain rates are significantly different.
The monotonic based constants are not able to predict the cyclic
behavior. Fig. 2a and 2b show the cyclic loop predictions using monotonic
based constants. Fig. 3a indicates that softening is continuing. In the
model, the drag stress equation constants control cyclic softening.
Fig. 3 shows the results of using constants based on all monotonic tests.
It is seen that these parameters overpredict the high _ tests and
underpredict the low E tests. Thus, although the model appears good for a
specific strain rate, it does not seem capable of representing the entire
strain rate spectrum used here (0.002 in/in/min to 0.2 in/in/min).
Fig. 4a shows the comparison of the test data and model prediction for a
cyclic test at .2 in/in/min. The result shown is for the 96th cycle.
The initial hardening shown in the plot is to be disregarded, because the
prediction was made for only 2 cycles and not the entire 96 cycles.
Fig. 4b shows similar results as above for the 0.002 in/in/min cyclic
test. Both Fig. 4a and 4b indicate that the procedure works well for each
strain rate. However, the material parameters are significantly different
for the two cases. Here again, the difference is believed to be caused by
the drag stress equation parameters, as in the monotonic case. This
points to the limitations of the particular model in representing a wide
range of strain rate behavior.
Current work is evaluating the Bodner model, and extending the analysis to
lower temperatures where less strain rate sensitivity is anticipated.
(D) FINITE ELEMENT CODE IMPLEMENTATION
The 2-D finite element code containing Bodner's constitutive model has
been completed and tested. The 2-D finite element code utilizes two
dimensional constant strain triangles and an incremental initial strain
iteration technique. To facilitate the simulation of arbitrary load
histories, the load history is partitioned into piecewise linear segments
with steady state thermal conditions during each segment. In order to
simplify input, reduce convergence problems and minimize cost, a dynamic
time stepping procedure is incorporated. The 3-D finite element code
using 20 noded isoparametric bricks is currently being developed.
In order to verify the 2-D finite element code with Bodner's model a
number of uniaxial test cases were run and compared with published
results. (References 9-11). In addition, a large two dimensional model
(Fig. 5a) of the benchmark notch specimen (Reference 2) was constructed
29/
and run with three different loading histories and compared with published
experimental results. An example of these comparisons can be seen in
Figure 5b. The overall performance of the finite element code with
Bodner's model was quite good. The cost of running the code is comparable
to one using a conventional uncoupled plasticity and creep constitutive
model.
REFERENCES
I. Bofferding, C.H. III, "A Study of Cyclic Stress and Strain Concentration
Factors at Notch Roots Throughout Fatigue Life", M.S. Thesis, Michigan State
University, 1980.
2. Domas, P.A., Sharpe, W.N., Ward, M. and Yau, J., "Benchmark Notch Test for Life
Prediction" NASA CR-165571, June 1982.
3. McKnight, R.L., Laflen, J.H., and Spamer, G.T., Turbine Blade Tip Durability
Analysis, NASA CR 165268, 1982.
4. Bodner, S.R. and Partom, Y., "Constitutive Equations for Elastic Viscoplastic
Strain-Hardening Materials," ASME Journal of Applied Mechanics, ASME, June
1975.
5. Krieg, R.D., Swearengen, J.C., Rohde, R.W., "A Physically Based Internal
Variable Model for Rate Dependent Plasticity" Proceedings of ASME/CSME PVP
Conference, 1978.
6. Miller, A., "An Inelastic Constitutive Model for Monotonic, Cyclic and Creep
Deformation (Part I and II)", Journal of Engineering Materials and Technology,
April 1976.
7. Robinson, D.N., Swindeman, R.W., "Unified Creep-Plasticity Constitutive
Equations for 2 I/4 Cr-l Mo Steel at Elevated Temperature" ORNL/TM-8444.
8. Walker, K.P. "Research and Development Program for Nonlinear Structural
Modeling with Advanced Time-Temperature Dependent Constitutive Relationships"
NASA CR-165533.
9. Stouffer, D.C., Bodner, S.R., "A Relationship Between Theory and Experiment For
a State Variable Constitutive Equation," Mechanical Testing for Deformation
Model Development, ASTM STP 765, 1982.
lO. Bodner, S.R., "Representation of Time Dependent Mechanical Behavior of Rene' 95
by Constitutive Equations", AFML-TR-79-4116, November 1978.
II. Stouffer, D.C. "A Constitutive Representation for InlO0" AFWAL-TR-SI-4039, June
1981.
298
(a) TENSILE
TABLE I
SPECIMEN TEST MATRIX
OR_NAL PAGE IS
OF POeR QUALITY
(b) CREEP SPECIMEN TEST MATRIX
Test
Temlpereture ••rein Pt;8
C (r) 0.002 .In-: O.OZ .I.-1 .06 .In-1 _-1
538 (1000) i T + 8R T + SR
648 (1200) T + SR
760 (1400) T + SR
871 (1600) T + SR
982 (1800) T + SR T + SR T T + SR
T indicates • constant sir•in fete tension tesL ter_lnmted •t • strmin
O_ 0.03.
$R Ls • stress relaxation Lest to be porfo_aed •L • ¢onmL•nt lit•in
of 0.03.
XnLtLaL AppLied
Test TemPer$tur• Sires| L_v•I|
C (Y) mP• (kmL)
982 (1800) 110 (16.0)
982 (1800) 217 (31.5)
982 (1800) 303 (44.0)
871 (1600) 493 (71.5)
871 (1600) 414 (60.0)
B71 (1600) 312 (45.3)
750 (1400) 554 (00.3)
760 (1400) 605 (99.3)
760 (1400) 634 (92.0)
1093 (2000) 114 (16.6)
(c) UNI-AXIAL FATIGUE SPECIMEN TEST MATRIX
(Ic_xl or IcmLnl - o.oo15. 0.0030. o.oo,5)
Continuously Cycled Tilt! (Strlin Controlle_)
Tomt llo, Tel_•ritur• - C (Y)
1 538 (1000) m
2 871 (1600) m
3 982 (1800) m
4 538 (1000) m
5 871 (1600) o
6 982 (1800) o
7 538 (1o00) ÷1
8 538 (1000) +1
9 871 (1600) +1
10 871 (1600) -1
11 982 (1800) -1
12 982 (1800) -1
S(cJ_ "1)
0.2
0.2
0.2
0.002
O, 002
0.002
0.2
0,002
0.2
0.2
0.2
0 1 O0 2
HoLd Time Temt8 (A¢ - m. • , 0.2 min -1. mtrmin controlled)
Tempermture MaxLmul or MLnL_
Test Mo. -C(F) Striin HoLd
13 538 (1000) HlxLr_am
14 538 (I000) Maximum
15 811 (1600) gaxlmum
16 871 (1600) _|ximum
17 871 (1600) _inlmum
18 871 (1600) _inlmum
19 982 (1800) RLnimum
20 982 (1800) 8inlmum
Hold Time _Sec)
12
120
12
120
12
120
12
120
299
Figure la.
lee
$44J
480
,4L_O
P 140
)
18o
Ill
61
U
f
I'I S-0G
O J2-0g
-- Model
[] Test Data
.Ill .04 .111 .N ._O .1_ .14 .11; .l| .N
STRAII4 SlOtS-I
Rene 80 982 C (1800 F) Monotonic Test at 0.2 in/in/min.
400
F igure lb.
35e
28e
S _40
T
J_
£
S
S he
(
F_
P
160
)
81
441
i
.1
i,+I_
r,i
imS
I_ &-K
--Model
[] Test Data
.11 .14 .el .ll .ll .1! .14 .t6 .ll .tl
STRMI_ 8|08t-1
Rene 80 982 C (1800 F) Monotonic Test at 0.002 in/in/min.
300
SOO
4OO
Itoo
S 10O
T
R
E
S
$ e
(
M
p
|
-iNto
°_
-oo¢
-,IS -.04 -,O] *.It
Figure 2a.
O SII-N
-- Model
[] Test
-.It • 111 .N .03 .1¢ .IS
STWMII_ IZl_t-I
Rene 80 982 C (1800 F) 0.2 in/in/min Cyclic Test.
Model Prediction Using Monotonic Based Material Parameters.
181
++I
S IO
T
II
[
$
S O
¢
R
P
A -4O
J
-in
-IIi
-141
-.ii -.04 %13 %11 -.01
STRAZN
Figure 2b.
O Ull*ll
__ Model
[] Test
l ,I! .Ol_ .05 .14 .Ol
llltt-|
Rene 80 982 C (1800 F) 0.002 in/in/min Cyclic Test.
Model Prediction Using Monotonic Based Material Parameters.
301
141
S-e6
0 J-l_;
• lt-tE
+ J:_-es
x I1-OS
in/in/min
.2
.06
.02
.002
Test
Q+
0
Mode I
mmm
o..o..
• ".(HI ,14 ,N .141 .1O .1_ .14
+TRmlm |Zlu-!
.11 .++t .2e
Figure 3. Rene 80 982 C (1800 F) Monotonic Tests.
302
Figure 4a.
ORIQINAL PAGE IS
OF POOR QUALITY
Me
if
D 9II-K
__Model
[] Test
-.eS -.e¢ -.l| -.N -.el .Ol .e| .e3 .e¢ .eS
SThZ*_ Illsl-l
Rene 80 982 C (1800 F) Cyclic Test 0.2 in/in/min, 96 th Cycle.
Figure 4b.
t_
IN
S 61
T
R
£
S
S t
(
M
P
.4e
)
-1|o
.441
e5 U81-SI
Model
[] Test
-.0S -.04 *.0) ".M -.01 • .01 .0t ,e3 .04 .elSTIA|N 81088-L
Rene 80 982 C (1800 F) Cyclic Test 0.002 in/in/min, 58 th Cycle.
303
II",,,[/\/",Ayl_y _./_...-,_
/\./-_/_./,d/ xj \/_\ /_ j'.,,,./-._-
\/\/\/\ _\,£x /\/\ ./\ .../._/_
/\/\/\/_\/WYN/\ ./\/'_/_/
X/\/\/\/ \fX'/\ /_ /_,,,,/'\/_
/
/r
J"C'_.
Figure 5ao Finite Element Mesh for Benchmark Notch Specimen.
ORIGINAL PAGE IS
OF POOR QUALITY
NEb_ONS LOAD (LBS)
31136 7000
26688 6000
22248 5000
17792 4000
13344 3000
8896 2000
4448
-.4
-4448
-8896
-13344
-17792
Figure 5b.
i000
ST_IN (%)
.8 1.0 1.2
200
LOAD (LBS)
4000
2ooo[ ,
-2000 r- 50 I
-4000 ¥
TIME (SEC)
i I I I)'
!50 200 1250
Bodner Model Predictions for Benchmark Notch Specimen.
304


Constitutive modeling for isotropic materials

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