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DTD Handbook

Handbook for Damage Tolerant Design

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    • About
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    • Sections
      • 1. Introduction
      • 2. Fundamentals of Damage Tolerance
      • 3. Damage Size Characterizations
      • 4. Residual Strength
      • 5. Analysis Of Damage Growth
      • 6. Examples of Damage Tolerant Analyses
      • 7. Damage Tolerance Testing
        • 0. Damage Tolerance Testing
        • 1. Introduction
        • 2. Material Tests
        • 3. Quality Control Testing
        • 4. Analysis Verification Testing
          • 0. Analysis Verification Testing
          • 1. Structural Parameter Verification Techniques
          • 2. Residual Strength Methods-Verification
          • 3. Crack Growth Modeling-Verification
        • 5. Structural Hardware Tests
        • 6. References
      • 8. Force Management and Sustainment Engineering
      • 9. Structural Repairs
      • 10. Guidelines for Damage Tolerance Design and Fracture Control Planning
      • 11. Summary of Stress Intensity Factor Information
    • Examples

Section 7.4.3. Crack Growth Modeling-Verification

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 middle-cracked panels.  The middle-cracked panel geometry is characterized by widely accepted stress-intensity 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 pre-cracking be employed when using the middle-cracked panel specimen for non-constant 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 corner-crack and surface-crack geometries be included in any crack growth verification test program in view of their relevance to the damage tolerance criteria.  Radial corner-cracked-hole specimens and other part-through thickness specimens require special preparation techniques.  Typically, the radial corner-cracked 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 pre-crack 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 pre-cracking to limit the stress-intensity 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 radial-cracked specimen is pre-cracked subsequent to the second step.

The surface flaw (part-through-crack) 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 part-through-crack type structural geometry, the standard details damage preparation techniques as well as pre-cracking 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 crack-growth-rate-based stress-ratio model with a crack-growth-retardation model which in turn accounts for the effect of tensile and compressive overloads, as well as multiple overload occurrences.  The stress-ratio 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 2219-T851 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 flight-by-flight 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 (Npred/Ntest) 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 (Npred/Ntest)

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

Flight-by-flight

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 (Npred/Ntest)

Highest Error Expected (Npred/Ntest)

±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 flight-by-flight 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 lo-hi-lo 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 full-scale 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]