The basis of all crack growth calculations is the damage
integration package discussed in Section 5, which includes the models and
procedures used in estimating the effects of the load and environmental events
in the operational history that must be verified. To model the impact that a variable amplitude load history has on
the crack propagation characteristics of a structure, the damage integration
package must be able to predict the effects of load amplitude, stress ratio (R),
load sequences, and hold time events, as well as load frequency and waveshape
in the case of a material sensitive to environmental effects.
Testing for verification of the crack growth models in the
damage integration package should be conducted using middlecracked
panels. The middlecracked panel
geometry is characterized by widely accepted stressintensity factor
calibration and the results of spectrum tests with this geometry are easiest to
correlate. It is recommended that the
procedures outlined in Section 7.2 and in ASTM E647 relative to geometry, crack
measurement, and precracking be employed when using the middlecracked panel
specimen for nonconstant amplitude loading.
Additional tests should be performed on specimens with radial corner
cracked hole geometries and on specimens containing surface flaws in order to
verify methods that describe the change in crack shape as the crack grows. It is important that cornercrack and
surfacecrack geometries be included in any crack growth verification test
program in view of their relevance to the damage tolerance criteria. Radial cornercrackedhole specimens and
other partthrough thickness specimens require special preparation techniques. Typically, the radial cornercracked hole
specimens are prepared in two steps.
The first step is to introduce damage (EDM notch, saw cut, etc.) into a
hole that is undersized and precrack the specimen until a crack of sufficient
size appears. The second step is to
enlarge the hole, remove the initial damage, and leave a crack with the
required size in the specimen. It is
necessary in the first step during precracking to limit the stressintensity
factor levels so that the crack tip is not exposed to levels higher than what
will be experienced during the test start up.
Sometimes to preclude overload effects, the radialcracked specimen is
precracked subsequent to the second step.
The surface flaw (partthroughcrack) specimens are normally
prepared along the lines suggested by ASTM E740. While the objective of this standard is to describe a fracture
test of a partthroughcrack type structural geometry, the standard details
damage preparation techniques as well as precracking procedures.
Because each material responds differently to the same spectrum,
and because each load history will cause different amounts of damage in
different materials, a crack growth damage integration package will be based on
a combination of models and experimentally established constants. Typically, the effects of load amplitude,
stress ratio and load sequence are addressed through the use of a model that
effectively combines a crackgrowthratebased stressratio model with a
crackgrowthretardation model which in turn accounts for the effect of tensile
and compressive overloads, as well as multiple overload occurrences. The stressratio models as well as the
retardation models are empirically based as was discussed in Section 5. The tailoring of the retardation model so
that it adequately represents effects of a given spectrum and material is one
of the more difficult tasks of the damage tolerant design analysis and test
development activities.
The tailoring of the retardation model is based on crack growth
life predictions of test results using reliable baseline (constant amplitude)
crack growth rate data. In terms of
developing a good correlation between prediction and test results, the
following guidelines apply for each test.
First and foremost, there should be a good estimate of the crack growth
life based on the growth from crack initiation to test termination. Second, and normally just as important, the
shapes of the predicted and test crack growth curves should match as closely as
possible. Figure
7.4.16 illustrates these two points:
predictions A and B would be considered bad, even though the life to
failure was predicted correctly.
Correlations are considered good if the prediction of all relevant
points are within about 20 percent of the test data, as indicated by the shaded
region of the figure. Typically, a
number of tests with different conditions must be conducted before the damage
integration package can be accepted with confidence. It is recommended that each crack growth test be summarized with
crack growth life curves (predicted and test).
The next several paragraphs describe a verification test program for an
improved damage integration package.
Figure
7.4.16. Comparison of Analytical
and Experimental Crack Growth Curves
In a study for the (then) Flight Dynamics Laboratory, Chang
[Chang, et al., 1978; Chang, et al., 1981; Chang, 1981] conducted a series of
crack growth tests on 2219T851 aluminum alloy that were used to verify the
accuracy of an improved damage integration package imbedded within the computer
code EFFGRO. In Chang, et al., [1981],
Chang summarizes the results of ten constant amplitude tests (different stress
ratios), 20 tests where single and periodic overloads were applied, and 30
tests where multiple overloads and block loading conditions were studied. In
Chang [1981], Chang summarized thirteen tests where different flightbyflight
loading conditions were applied; eleven tests involved fighter histories, two
tests involved transport type histories.
Table 7.4.3 summarizes the test program and
Chang's ability to estimate the crack growth lives for the various types of
test conditions based on the life prediction ratio approach.
The life prediction ratio (N_{pred}/N_{test})
is the life determined from the prediction divided by the life from the test
and is calculated for each test. Table 7.4.3 provides a collective summary of all the
results that Chang developed, grouped in the same way that he presented the
results as well as in larger groupings.
For all the tests, the mean life prediction ratio is 0.987 and the
standard deviation of this measure is 0.35; the lowest and highest life
prediction ratios are 0.15 and 2.48, respectively. Table 7.4.4 shows how the life
prediction ratio statistics (mean and standard deviation) can be used to
estimate the error in a crack growth life calculation based on the improved
model. Note from Table
7.4.4 that the damage integration package will predict lives that range
between plus and minus (approximately) 60 percent of actual, 80 percent of the
time.
Table 7.4.3. Summary of Chang’s Improved Spectrum
Prediction Results Based on Tables
in Chang, et
al.[1981] and Chang [1981]
Chang’s Table No.

Number of Tests

Type of Load History

Life Prediction Ratios (N_{pred}/N_{test})

Mean ± Standard Deviation

Lowest Value

Highest Value

2*

10

Constant amplitude

1.340 ± 0.500

0.81

2.48

3*


Single and periodic overload

0.783 ± 0.240

0.37

1.18

4*

30

Multiple overload and block

0.938 ± 0.30

0.15

1.60

2* and 3*

29

See above

0.974 ± 0.44

0.37

2.48

2*, 3* and 4*

59

All simple

0.956 ± 0.37

0.15

2.48


13

Flightbyflight

1.131 ± 0.22

0.80

1.46

2*,3*,4* and

72

All

0.987 ± 0.35

0.15

2.48

+ one
additional test reported but life estimate vague
* from Chang, et al. [1981]
++ from Chang [1981]
Table 7.4.4. Error Estimate in Life Prediction Ratio
Based on Assumed Normal Distribution
of All Chang’s
Results (72 Tests)
Probability of Maximum Error Occurring (%)

Formula For Estimating Errors

Life Prediction Data For Estimating Errors (See Table
7.4.2)

Lowest Error Expected (N_{pred}/N_{test})

Highest Error Expected (N_{pred}/N_{test})

±1

Mean ± 2.58 Std. Dev.

0.987 ± 2.58´0.35

0.084

1.89

±5

Mean ± 1.96 Std. Dev.

0.987 ± 1.96´0.35

0.301

1.67

±10

Mean ± 1.645 Std. Dev.

0.987 ± 1.645´0.35

0.411

1.56

By collectively evaluating the life prediction ratios for the
individual tests, for selective test groupings, and for the total number of
tests conducted, the engineer can evaluate both the effectiveness of the
modeling approach as well as the accuracy of individual tests. Improvements in the more fundamental
segments of the model might yield substantial improvements in all the life
prediction ratios, whereas isolated modification of some empirical constants
might only improve the predictability of a limited number of tests. It is recommended that life prediction ratio
data such as illustrated in Table 7.4.3 provide the
basis for justifying selection of damage integration packages. In fact, by using such schemes for different
crack geometries or load transfer situations, the engineer will have the
necessary confidence that crack growth life predictions for more complicated
cases can be made with the best possible reliability. See Saff & Rosenfeld [1982], Wozumi, et al. [1980], Rudd, et al. [1982], Dill, et al. [1980],
Abelkis [1980] and Lambert & Bryan [1978] for other examples of test
programs designed to verify the capability of a damage integration package.
In the design of a given airplane component, generality is not
required if the damage integration package applies well to the spectrum and
history of that component. The most applicable
prediction method has to be found. The
only basis for judgment of the applicability is a series of tests with the
relevant spectrum and stress history.
Therefore, it is recommended that some substantiation testing be
performed as soon as there is reasonable certainty with respect to the spectrum
shape. The experiments should be
performed on a flightbyflight basis, with landing loads included. A reasonable number of stress levels should
be used as discussed in Section 5.3.
The stress sequence within a flight should be representative for service
usage (Section 5) or arranged in a lohilo sequence. Block loading should not generally be applied. Experiments should be run for a few
different design stress levels and one or two clipping and truncation levels in
order to evaluate the effect of these changes on crack growth behavior, and to
justify proposed changes to the design spectrum for component and fullscale
fatigue testing. Figure
7.4.17 describes the results of one comparative study [Dill, et al., 1980].
Figure
7.4.17. Effect of Spectrum
Variations on Crack Growth Life Compared to Baseline (Design Mix) and to Two
Damage Integration Packages [Dill, et al., 1980]