The purpose is to determine the ability of currently available P-I integrals to correlate fatigue crack propagation under conditions that simulate the turbojet engine combustor liner environment. The utility of advanced fracture mechanics measurements will also be evaluated during the course of the program. To date, an appropriate specimen design, a crack displacement measurement method, and boundary condition simulation in the computational model of the specimen were achieved. Alloy 718 was selected as an analog material based on its ability to simulate high temperature behavior at lower temperatures. Tensile and cyclic tests were run at several strain rates so that an appropriate constitutive model could be developed. Suitable P-I integrals were programmed into a finite element post-processor for eventual comparison with experimental data

Kim, K. S.

Laflen, J. H.

Malik, S. N.

Vanstone, R. H.

English

NASA Technical Reports Server

N88- 1174
ELEVATED TEMPERATURE CRACK GROWTH*
S.N. Malik, R.H. Van Stone, K.S. Kim, J.H. Laflen
General Electric Company
Aircraft Engine Business Group
Cincinnati, Ohio
INTRODUCTION
Critical gas turbine engine hot section components such as blades, vanes,
and combustor liners tend to develop minute cracks during the early stages of
operation. These cracks may then grow under conditions of fatigue and creep
to critical size. Current methods of predicting growth rates or critical
crack sizes are inadequate, which leaves only two extreme courses of action.
The first is to take an optimistic view with the attendant risk of an
excessive number of service failures. The second is to take a pessimistic
view and accept an excessive number of "rejections for cause" at considerable
expense in parts and downtime. Clearly it is very desirable to develop
reliable methods of predicting crack growth rates and critical crack sizes.
To develop such methods, it is necessary to relate the processes that
control crack growth in the immediate vicinity of the crack tip to parameters
that can be calculated from remote quantities, such as forces, stresses, or
displacements. The most likely parameters appear to be certain path-independ-
ent (P-I) integrals, several of which have already been proposed for
application to high temperature inelastic problems. A thorough analytical and
experimental evaluation of these parameters needs to be made which would
include elevated temperature isothermal and thermomechanical fatigue, both
with and without thermal gradients.
In any investigation of fatigue crack growth, the problem of crack closure
should be addressed in order to develop the appropriate crack growth model.
Analytically, this requires the use of gap elements in a nonlinear finite
element code to predict closure loads. Such predictions must be verified
experimentally through detailed measurements; the best method for measuring
crack closure has not been established in previous studies.
It is the purpose of this contract (NAS3-23940) to determine the ability
of currently available P-I integrals to correlate fatigue crack propagation
under conditions that simulate the turbojet engine combustor liner
environment. The utility of advanced fracture mechanics measurements will
alsn be evaluated and determined during the course of the program. These
goals are to be accomplished through a two year, nine task, combined
experimental and analytical program. To date an appropriate specimen design,
a crack displacement measurement method, and boundary condition simulation in
the computational model of the specimen has been achieved. Also, the
experimental testing and data acquisition is continuing. Alloy 718 has been
*Work done under NASA Contract NAS3-23940.
329
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selected as the analog material based on its ability to simulate high
temperature behavior at lower temperatures in order to facilitate experimental
measurements. Tensile and cyclic tests were run at several strain-rates so
that an appropriate constitutive model could be developed. Available P-I
integrals have been reviewed and the most suitable ones have been programmed
into a finite element post-processor for eventual comparison with experimental
data. These experimental data will include cyclic crack growth tests under
thermo-mechanical conditions and, additionally, thermal gradients.
A REVIEW OF P-I INTEGRALS
The utility of the J integrals [I] as a parameter for predicting crack
growth in the elastic-plastic regime is rather limited. The theoretical basis
of the J integral does not allow the extension of its usage to nonproportional
loading and unloading in the plastic regime, nor can it be utilized in the
presence of a temperature gradient and material inhomogeneity. A typical
example where all these limiting factors are operative would be the hot
section components of a gas turbine in mission cycles.
In recent years there has been a considerable effort to modify and
reformulate the J integral for applications in various areas of fracture
mechanics. Consequently, a number of new path-independent (P-I) integrals
have emerged in the literature. A critical review of these integrals is
presented by Kim[2]. Notable among them are the Blackburn J*[3],
Kishimoto J[4, 5], Athuri ATD and AT_[6,7], and Ainswortn J_[8]
integrals. In the present pPogram the theoretical bacKgrouhd of these
integrals has been examined with particular attention to whether or not the
path-independence is maintained in the presence of nonproportional loading;
unloading in the plastic regime; and a temperature gradient and material
inhomogeneity. The relation among the P-I integrals, salient features and
limitations were investigated. The physical meaning, the possibility of
experimental measurements, and the computational ease were also examined. In
view of the requirements associated with performing the tasks in this program
the following conclusions were made.
i) The J,* J, ATp andATp* integrals maintain the path-independence
under the thermomechanical cycles which will be used in the tests in
this program and will be simulated numerically in subsequent tasks.
Although the physical meaning of these P-I integrals needs to be
further pursued, they would be the logical choices for further
evaluation in this program.
ii) The Jc) integral is a modified version of J to include thermal
strain. Therefore, it cannot be used witi_ substantially
nonproportional loading and unloading in the plastic regime. It
would be worthwhile, however, to investigate the utility of
operationally defined J and possibly Jo for the test cycles in this
program.
330
All selected P-I integrals have been implemented in a postprocessor to U_e
General Electric nonlinear finite element program, CYANIDE. Numerical values
of the integrals will be evaluated and examined for cracks subjected to
various situations such as monotonic/cyclic 1oadings, unform/non-uniform
temperature distributions, stationary/propagating cracks, etc. Best
formulations suitable for all situations will be selected and used to
correlate with the test results. The relationship between the analytical CTOD
(or CMOD) displacements and the values of P-I integrals will De established to
identify the displacement which must be measured to determine operational P-I
integral.
EXPERIMENTAL PROGRAM
Alloy 718, a y-y" nickel-base superalloy, has been selected as the analog
material because over the temperature range from 800F to 1200F it shows very
large changes in creep behavior. This permits the use of Alloy 718 to
simulate the behavior of combustor liner materials while still performing
experiments at relatively low temperatures. Tensile, creep, and cyclic
constitutive tests have been performed on Alloy 718 over the temperature range
from room temperature to 1200F to identify the constitutive properties to be
used in finite element calculations. Tensile and cyclic tests have been
performed over strain rates different by a factor of 20, and no strain rate
sensitivity was observed, even at the higher temperatures where high creep
rates occur. This will permit the use of classical plasticity and creep
analysis in the Finite Element (FEM) analysis.
The primary specimen to be used in this study is a single edge crack (SEN)
specimen with buttonhead grips. The buttonnead grips permit better load
reversals and alignment, especially for compressive loads. The gage section
has a rectangular cross-section with a thickness, width, and gage length of
2.54, I0.2 and 15.gram (O.lO, 0.40, and 0.625 inch) respectively. The
relatively low gage length was selected to avoid buckling during the elevated
temperature cycling with large plastic cyclic strains. The overall length of
the specimen is 5 inch (127m) including the cylindrical shanks and
buttonheads.
The SEN tests are performed in a strain control mode wit|_ the experimental
setup shown schematically in Figure I. The controlling extensometer will be
mounted at the center of the lO.2mm wide surface of the specimen. Two other
displacement gages, one to monitor crack mouth opening displacement (CMOD) and
one to monitor the displacement on the face opposite the crack moutil, will
also be used. The purpose of the CMOD gage is to detect when crack closure
occurs. A standard 12.7mm (0.5 inch) elevated temperature extensometer has
been modified to have a gage length of approximately O.76mm (0.03 inch) and
significantly improved resolution of CMOD displacements.
A DC potential drop system is used to monitor crack size. The
load-displacement data is periodically recorded using an ETS data acquisition
system. Figure 2 shows two examples of hysteresis loops obtained from typical
331
tests with AE =_(Cmin = -Cmax). Figure 2a shows an example of nominally
elastic cycling and a crack depth of approximately 0.51ram (20 mils). Even at
this small crack length, the CMOD is detecting closure. Also note the
displacement sensitivity of the CMOD loops is twice that of the other types of
loops. Figure 2b shows an example of elastic-plastic strain cycling. The
CMOD loop for this cycle shows crack closure and opening at very similar
values of CMOD even though the nominal stress is much different due to net
section plasticity. In both cases the back face extensometer shows a bias
toward negative strains indicative of bending within the gage length.
The experimental work is in progress and will measure the crack growth
response of Alloy 718 under isothermal, TMF, and temperature gradient
conditions. Some additional tests were performed with a 12.7ram (0.5 inch)
extensometer in place of the CMOD gage to provide verification of analytical
results.
NUMERICAL COMPUTATIONS
Numerical implementation and verification of the PI-integral
post-processor program was completed and is reported in the Annual Progress
Report [9]. A pre-processor program for automatic generation of finite
element two-dimensional meshes for crack problems was also completed and
discussed in detail in the Annual Progress Report [9]. Tnis mesh generator
program allows a gradual transitioning of the elements size from relatively
coarse in the remote stress field to very refined near the crack-tip region.
Prior to performing detailed FEM analyses for crack closure, efforts were
made to evaluate simplified boundary conditions which would eliminate the need
for analyzing the whole specimen (including the buttonhead). In order to
verify the plane stress type stress field in the gage-section of the SEN
specimen, a full-specimen three-dimensional (3D) analysis using 20-noded
isoparametric brick elements was made by using the 3D-CYANIDE code. It was
found that in the gage section there was very little variation in
through-the-thickness stresses, strains, and displacements. Therefore, a 2D
plane-stress model of the "full-specimen" was developed to investigate the
influence of prescribed buttonhead displacements on the displacements in the
"gage-section portion" of the specimen. Figure 3 shows the full-specimen
model for the 2D-CYANIDE analysis which contains 566 nodes and I002 constant
strain elements. The near crack-tip mesh refinement was validated by
prescribing constant displacement boundary conditions and computing stress
intensity factor (KI) from the post-processor J integral. For the elastic
response, Figure 4 shows a comparison of computed KI values with the Tada,
Paris and Irwin handbook solution having a maximum difference of 7% for
various a/w ratios. Similar comparisons made in the plastic regime using the
elastic-plastic fracture mechanics handbook [lO] solutions showed equally
encouragi ng results.
The next step was to compare the computed load-displacement variation from
the elastic-plastic analysis with the measured normal displacement data
obtained from three 12.7mm (0.5 inch) extensometers positioned as shown in
332
Figure I. Figures 5, 6 and 7 show the results obtained for an a/w ratio of
0.265. Solid lines represent test data curves for the first load cycle,
whereas the circular symbols represent the computed values, and the square
symbols represent test data for the second cycle. The monotonic stress-strain
properties of Alloy 718 were used in the 2D-CYANIDE full-specimen analysis.
It could be seen that the experimental first cycle load versus displacement
data at each of the three extensometer locations compare very well with the
computed values. The regions of extreme plasticity were modeled very
satisfactorily by the 2D-CYANIDE analysis. Figure 8 shows Uy displacements,
normal to the crack plane, near the end of gage-section. It-could be seen
that the uy displacement varies approximately linearly across the
gage-secti6n width for all the seven load cases plotted in Figures 5, 6
and 7. For the larger displacement cases the uy displacement near the back
face (X = 0.4 inch) developed slight deviations from linearity. The most
significant implication of Figure 8 is that due to linear variation of normal
displacement across the specimen width near the end of the gage-section, only
two extensometers are needed to accurately predict displacement response.
This simplification eliminated the need for three extensometers needed to
model gross specimen displacements.
Another interesting feature of the full-specimen 2D-CYANIDE analysis was
the magnitude of horizontal displacement, Ux, in the gage-section. Figure 9
shows the relationship of the uy versus ux displacement at each of the
nine x-coordinate locations near the end of gage-section for each of the seven
load values plotted in Figures 5, 6 and 7. It could be seen that ux
displacement is about 30 to 60% of the corresponding uy displacement at the
end of gage-section.
Another simplification to reduce computer cost was made by only modeling
the "gage-section portion" of the SEN buttonhead specimen. This gage-section
model of the specimen retains the same mesh refinement as shown in Figure 3
except that the model is extended only up to 0.3125 inch (7.94mm). It now has
only 359 nodes and 634 elements. This "gage-section portion" model was
prescribed with zero ux displacement at the top edge along which uy
displacements were applied either from the extensometer data or from the
"full-specimen" 2D-CYANIDE solution (shown in Figures 5, 6 and 7). The
extensometer data were taken only from the back-face (Figure 6) and middle-
gage (Figure 5) and were linearly extrapolated to simulate the actual data
acquisition from cyclic loading tests. Figures I0 and II show the results of
the "gage-section" portion model driven by the experimental uy data, and by
the "full-specimen" extracted data, along with the full-specimen response. It
could be seen that the elastic-plastic KI values, in Figure 10, obtained
from the post-processor J integral values for the full specimen and
gage-section portion models are within 5% of each other. The induced vertica]
load in the gage-section model is within 8% of the full-specimen model, as
shown in Figure If. The experimental data driven gage-section portion model
shows excellent agreement with the full-specimen analysis. These results were
obtained for upper bound crack length to be used in this program, and it is
felt that these conclusions will hold good for all tile lower crack lengths.
333
CONCLUDING REMARKS
The work to date has shown that the 2D gage section modeling accurately
simulates the behavior of the specimen as verified by experimental data. Work
is continuing to simulate crack closure with the GAP-CYANIDE Finite Element
Program. This effort along with the companion crack growti_ experiments will
be used to identify path-independent integrals which predict the crack growth
behavior under isothermal, TMF, and temperature gradient conditions.
REFERENCES
I. Rice, J.R., "A Path-Independent Integral and the Approximate Analysis of
Strain Concentration by Notches and Cracks," Journal of Applied Mechanics,
Vol. 35, 1968, pp. 379-386.
2. Kim, K.S., "A Review of Path-lndependent Integrals in Elastic-Plastic
Fracture Mechanics," General Electric Company, 1984, NASA Contractor
Report; Also presented in ASTM 18th National Symposium on Fracture
Mechanics, June 1985.
3. Blackburn, W.S., Jackson, A.D., and Hellen, T.K., "An Integral Associated
With the State of a Crack Tip in a Nonelastic Material," International
Journal of Fracture, Vol. 13, 1977, pp. 183-200.
4. Kishimoto, K., AoKi, S., and Sakata, M., "On the Path-lndependent
Integral-J," Engineering Fracture Mechanics, Vol. 13, 1980, pp. 841-850.
5. Aoki, S., Kishimoto, K., and Sakata, M., "Elastic-Plastic Analysis of
Cracks in Thermal ly-Loaded Structures," Engineering Fracture Mechanics,
Vol. 16, 1982, pp. 405-413.
6. Atluri, S.N., "Path-lndependent Integrals, in Finite Elasticity and
Inelasticity, With Body Forces, Inertia, and Arbitrary Crack-Face
Conditions", Engineering Fracture Mechanics, Vol. 16, 1982, pp. 341-364.
7. Atluri, S.N., NishioKa, T., and Na_agaRi, M., "Incremental
Path-lndependent Integrals in Inelastic and Dynamic Fracture Mechanics,
Engineering Fracture Mechanics, Vol. 20, 1984, pp. 209-244.
8. Ainsworth, R.A., Noale, B.K., and Price, R.H., "Fracture Behavior in the
Presence of Thermal Strains," Proceedings of Institute of Mechanical
Engineers, Conference on Tolerance of Flaws in Pressurized Components,
London, 1978, pp. 171-178.
334
9. Yau, J.F., Kim, K.S., MaliR, S.N., Van Stone, R.H., and Laflen, J.H.,
"£1evated Temperature Crack Growth," Annual Progress Report, General
Electric Company, NASA Contractor Report, 1985.
10. Kumar, V., German, M.D., and Shih, C.F., "An Engineering Approach for
Elasto-Plastic Fracture Analysis," EPRI Report NP-1931 (R.P. 1237-I),
Electric Power Research Institute, Palo Alto (CA.), 1981.
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Elevated temperature crack growth

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