The sequencing effect due to retardation is largely dependent on the ratio between the highest and lowest loads in the spectrum and their frequency of occurrence.  As a result, it will depend upon spectrum shape.  Compare, for example, the fighter spectrum with the transport spectrum in Figure 5.4.6.  The relatively few high loads in the transport spectrum may cause a more significant retardation effect than the many high loads in the fighter spectrum.

The selection of the highest loads in the load history is critical to obtain a reliable crack growth prediction.  It was argued in Section 5.4 that it is not realistic to include loads that occur less frequently than about 10 times in 1,000 flights, because some aircraft in the force may not see these high loads.  This means that the spectrum is clipped at 10 exceedances.  No load cycles are omitted.  Only those higher than the clipping level are reduced in magnitude to the clipping level.  The effect of clipping on retardation and crack growth life was illustrated in Figure 5.2.4.

The question remains whether proper selection of a realistic clipping level is as important for a crack-growth prediction as it is for an experiment.  In this respect, it is important to know which retardation model is the most sensitive to clipping level.  As pointed out above, the sensitivity may also depend upon spectrum shape.  The effects can be determined by running crack growth calculations for different clipping levels, different spectrum shapes, and with two retardation models.

Calculations were made for the six spectra shown in Figure 5.4.6, by using the flight-by-flight history developed in Example 5.4.2.  The cycles in each flight were ordered in a low-high-low sequence.  Figure 5.5.4 shows the crack growth curves for the full spectra using the Willenborg model, and Figure 5.5.5 shows the curves using the Wheeler model.  The crack configuration was a corner crack from a hole, as indicated in the figures.  A limit load stress of 35 ksi was used for all spectra, and the material was 2024-T3 aluminum.

Figure 5.5.4.  Spectrum Fatigue Crack Growth Behavior Willenborg Retardation Model

 

Figure 5.5.5.  Spectrum Fatigue Crack Growth Behavior Wheeler Retardation Model

Subsequently, four significantly different spectra (A, B, C, and E) were selected.  Crack growth curves were calculated using the clipping levels S₂, S₃, S₄, and S₅ in Example 5.4.2.  The resulting crack growth curves for one spectrum are presented in Figure 5.5.6.  Also shown is a curve for a linear analysis (no retardation).  The crack growth life results for all spectra are summarized as a function of clipping level in Figure 5.5.7.  Test data for gust spectrum truncation are also shown.  Some characteristic numbers are tabulated in Table 5.5.2 for the four spectra as a function of crack growth model.

 

Figure 5.5.6.  Effect of Clipping Level on Calculated Crack Growth for Spectrum B-Trainer

Table 5.5.2.  Characteristic Value for the Four Spectra of Figure 5.5.6

Symbol		Spectrum	Linear Analysis (Flights)	Retardation Life (Flights)
				Willenborg Fully Retarded	Wheeler m = 2.3
A	▲  Willenborg ∆ Wheeler	Fighter	270	4,900	2,100
B	●  Willenborg ○  Wheeler	Trainer	460	14,200	7,900
C	■  Willenborg □  Wheeler	B-1 Class Bomber	140	700	700
D	▼Willenborg ▽  Wheeler	C Transport	1,270	6,700	11,600

 

Figure 5.5.7.  Effect of Clipping for Various Spectra

Figures 5.5.4 through 5.5.7 allow the following observations:

·        The two retardation models predict largely different crack growth lives for all spectra, except C.  The differences are not systematic.  Since there are no test data for comparison, the correct answers are not known.

·        With one exception, the two models essentially predict the same trend with respect to clipping levels.  This shows that they both have equal capability to treat retardation.

·        The steep spectra (fighter, trainer) are somewhat more sensitive to clipping level.  Apparently, the damage of the high cycles outweighs their retardation effect.

·        With extreme clipping, the analysis attains more the character of a linear analysis, indicating that the largest amount of damage in the linear analysis comes from the large number of smaller amplitude cycles.

·        Bringing the clipping level down from 10 exceedances per 1,000 flights (top data points in Figure 5.5.7) to 100 exceedances per 1,000 flights (second row of data points in Figure 5.5.7) reduces the life by only 15 percent or less for all spectra.

In addition, crack growth calculations were made to re-predict the gust spectrum test data shown in Figure 5.5.7.  The results are presented in Figure 5.5.8 where the calculated results are shown to be very conservative.  However, with one exception, they would all fall within the scatter-band of Figure 5.2.4.  The baseline data used were worst case upper-bound da/dN data.  This can easily account for a factor of two in growth rates.  If the growth rates were reduced by a factor of two, the calculations would be very close to the test data (dashed line in Figure 5.5.8).

Figure 5.5.8.  Calculated and Experimental Data for Gust Spectrum Clipping [Schijve, 1970; 1972]

One important thing has been disregarded so far.  As shown in Figure 5.2.1, compressive stresses reduce retardation (compare curves B and C).  Omission of the ground-air-ground (GAG) cycle in the experiments by Schijve (1970) shown in Figure 5.5.8 increased the life by almost 80 percent.  Apart from the GAG cycle, there are other compressive stresses in the spectrum.  All compressive stress effects were ignored in the crack growth calculations with the retardation models used for this analysis.

The top clipping level in Figure 5.5.8 is at 5 exceedances per 1,000 flights, the second level is at 13 exceedances per 1,000 flights.  From these results and Figure 5.5.7, it appears that an exceedance level of 10 times per 1,000 flights will combine reasonable conservatism with a realistically high clipping level.  This supports the arguments given previously to select the clipping level at 10 exceedances per 1,000 flights for both calculations and experiments.  The effect of clipping level should be calculated for a small number of representative cases to show the degree of conservatism.