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NATIONAL AERONAUTICAL ESTABLISHMENT
LABORATORY TECHNICAL REPORT
LTR - ST - 1409
A NUMERICAL INVESTIGATION OF THE EFFECTS
OF MARKER BLOCKS ON CRACK PROPAGATION RATES
FOR THE SNOWBIRD SPECTRUM
R.L. HEWITT
RAPPORT TECHNIQUE DE LABORATOIRE
UABLJSSEMENT AtRONAUTIQUE NATIONAL
3 SEPTEMBER 1982
I'
Conseil national
1+
National ResearchCouncil Canada de recherches Canada
NATIONAL AERONAUTICAL ESTABLISHMENT F'AGf s 13 tata1 PAGES ___ . ___ _ _ _ f,r, 2
REPORT
RAPPORT
IITABLISSEMENT AtRONAUTIQUE NATIONAL REPORT RAPPORT LTR-ST-1409 O,A(, ________________ _ _ LABORATORY / LABORATOIRE CATE DATE 3 September 1982 r IIHL Fe., r"RU.S __ 1 __ _ FlJR POIJ~. INTERNAL REFERENCE Rf rtf/ENeE LAB. ORDER COMM. LA8. _ _ _ _ _ FILE D088IER _ _ _ _ _ _ _LTR -
ST-1409A NUMERI CAL INVESTIGATION OF THE EFFECTS OF MARKER BLOCKS ON CRACK PROPAGATION RATES
FOR THE SNOWBIRD SPECTRUM
SU8MlrrED BV W. Wa11ace PR(SENTt PAR _ _ ___ _ LAaORATORV HEAO . . CHE~ OE LAaORATOIRE ApPROVED G.M. Lindberg ÄPPRouvt ____ __ . ____ . ___ _ __ _ _ OIRICTOR OIAfct[UA
THIS flf"QRT MAY NOT BE PUBLISHED WHOLLY OR IN PART WITHOUT THE WRITTEN CONSENT OF THE NATIONAl AERONAUTICAL ESTABLISHMENT
AUTHOR
AUTEUR _ _ _ _ _ ~R~.~L~.~H~e~w~i~t~t~ ___ _
CE RAPPORT NE OOIT PAS tTRE REPRODUIT. NI EN ENTIER NI EN PARTIE. SANS UNE AUTORISATION fCRITE DE l'fTABLISSEMENT AfRONAUTIQUE NATIONAL
COpy No.
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A NUMERICAL INVESTlGATION OF THE EFFECTS OF MARKER BLOCKS ON CRACK PROPAGATION RATES FOR THE SNOWBIRD
SPECTRUM
R.L. Hewitt
Stroc,tures and Materials Laboratory National Aeronautical Establishment
Crack growth behaviour of a crack from a circular hole in an aluminum plate has been studied numerically for loading conditions corresponding to the spar cap in the CL4lA Tutor aircraft in the Snowbird aerobatic role. The effect of using different randomization sequences for the fully
randomized spectrum has been investigated together with the effect of using a marker block consisting of all the cycles at one particular load level at the end of each randomized block of flights. A larger effect was observed by varying the randomization order than by using any of the marker block sequences selected, but both effects were considered minimal in terms of crack growth rates.
INTRODUCTION
In order to utilize the damage tolerance concept of aircraft design it is necessary to have a detailed knowledge of crack growth rates. In many cases the only source of this data is from component or full scale fatigue testing, and unless the critical crack is observable and its location is known, crack growth rates must be obtained af ter failure by fractographic means. This task has become more difficult in recent years because of
the introduction of randomized load spectra; unless there is a significant repeatable event within the spectra (such as a ground-air-ground cycle of a simple transport spectrum), it is of ten impossible to get meaningful crack growth data because of the lack of correlation between fatigue striations and applied load cycles.
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-To alleviate this problem on a recent test of a Canadair CL-4lA Tutor aircraft in an aerobatic role, the Structures and Materials Laboratory of NAE utilized a marker block within an otherwise randomized load spectrum (1). The marker block consisted of all the cycles of one particular intermediate load level grouped together at the end of a block of flights. Although it was anticipated that the introduction of the marker block would have little effect on the crack growth rates, it was not studied in detail. In addition, it has been suggested (2) that the choice of marker block level should be optimized. If the load level of the marker block is increased the marker block will be observed cIos er to initiation, but the crack growth behaviour will probably be more distorted.
Thus there is a need to investigate the effect of marker block level on both crack propagation rate and detectability. Because of the large number of variables involved, it was decided to initiate the study numerically rather than experimentally. A series of crack growth predictions was made using the USAF crack propagation program CRACKS IV for a simple crack using load conditions corresponding to the main spar cap of the Tutor aircraft in the Snowbird aerobatic role. The effects of both different randomization sequences of the laad spectrum and different load levels in the marker block were studied and the results discussed.
ANALYSIS
Crack growth predictions were obtained using the USAF crack propagation program CRACKS IV which has been modified slightly for use at NAE (3).
Details of the input are provided below. Material
The purpose of this investigation was to study the effeèt of marker blocks in a general sense rather than to predict the effect on a
particular part. The choice of material was therefore arbitrary to some extent. It was intended to use the Grumman crack closure retardation model in CRACKS IV developed by Bell and Creager (4) since this model can account for compressive loads. Since the
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-Grumman retardation parameters were only available for 2219-T85l aluminum, this was the material chosen for the study. However, difficulties were encountered in using the Grumman model and these will be investigated separately. The Wheeler retardation model was
therefore used instead. The material was not changed however, and material parameters given by Chang et al (5) for 22l9-T851 were used as these have given good correlation with spectrum tests. The growth rates were expressed using Walker's equation as
da -
=
dN [ L'lk ] n C (l-R)l-m where C=
5.063 x 10-10 m = 0.60and n =' 3.83 for units of in/cycle and ksilirï
A fatigue crack growth threshold was expressed as a function of stress ratio, R, from the data given in reference 6. It was written
L'lk
th
=
0.21 (1 - 0.54R) where L'lk is again in units of ksifu GeometrySince cracks of ten start at fastener holes, the assumed geometry was for a single crack from a hole in an infinite sheet. The hole
radius was set at 0.25 inches and the initial crack length 0.1 inches. The tip of the crack was assumed to be in a condition of plane stress. Retardation Model
The Wheeler retardation model with an exponent of m
=
1.3 was used for most of the predictions.Load Spectrum
Full details of the derivation of the load spectrum used in the full scale fatigue test of the CL-4lA Tutor aircraft in the Snowbird
4
-test load spectrum which consists of a total of 4469 cycles at 20 different load levels and corresponds to one hundred equivalent flight hours (1 block of flights). The load sequence within a block was generated in a random manner on a draw without replacement basis.
The load history for the predictions was obtained in a similar manner, using the random number generator UDRAN which is available on the NRC-IBM system. The critical location in the fatigue test was the spar cap where the stresses were estimated as 2.727 ksi per g. The stresses for the program were therefore obtained directly from the load spectrum by multiplying by this factor.
The stresses were input to CRACKS IV directly from tape by effectively defining 23 individual mission segments which were each applied once within a block of flights. The first 22 missions each contained 200 load cycles or layers while the last contained 69, giving a total of 4469 cycles in the block of flights.
RESULTS
Randomized Spectra
Before studying the effect of marker blocks within a randomized spectrum, it was necessary to determine the influence of different random sequences alone. The order of cycles within a randomized spectrum, or load-time history, will depend upon the seed number used in the random number generator. It is therefore possible to get a very large number of different load-time histories for the same basic spec trum.
Using a low seed number, e.g. 1, produced a load-time history in which many of the large loads appeared very early in the sequence. The random number generator was therefore run until a relatively "even" load history was being produced, and a random number within this area was chosen as the initial seed number, and a complete load history of
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-4469 cycles generated. Four additional random load histories were then generated with the seed number for each being the last random number generated in the previous history.
The results for these five randomization sequences are shown in Figure 1 as crack length versus equivalent Snowbird flight hours.
Also shown on this figure is the experimentally determined crack growth curve from the 2024-T4 spar cap (1). It should be emphasized that the experimental curve was not obtained for the same geometry or material as the numerical results and has been included merely to indicate that the growth rates in the numerical examples are realistic. It is clear from Figure 1 that the randomization sequence does alter the predicted crack growth slightly. Af ter 15,000 equivalent flight hours the predicted crack length varies from 2.81 to 3.12 inches. This change is quite small, however, and in a practical case we would be more concerned with how many flight hours it takes to grow a crack to some detection limit or some critical crack length. The table included on Figure 1 shows that the flight hours calculated to grow the crack to 2 inches varies by less than 200 hours in 14,000. This is not significant.
Randomized Spectra with Marker Blocks
The predictions for load-time histories with marker blocks were obtained from the random history generated using a seed number of 967347175 which produced a crack growth eurve in about the middle of the group for the fully randomized histories. The marker block was produced by removing all the cycles corresponding to a eertain load level from the laad-time history and then adding them to the end of the bloek of flights. Thus, using load level 10 for example as the marker bloek, the 64 cycles corresponding to the 5.252 g cycle were
removed from the fully randomized load history and then added on at the end. Predictions were obtained for histories with six different marker bloeks corresponding to laad levels 5 to 10. All the results were indistinguishable from the fully randomized history when plotted
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-in the form of Figure 1, and showed a difference -in crack length af ter 15,000 equivalent flight hours of less than 0.03 inches.
Orde red Sequences
Since the inclusion of marker blocks in the load-time history had shown no significant effect on the crack growth curve, it was decided to ,check the sensitivity of the Snowbird spectrum to more substantial ordering effects. Predictions were therefore obtained for load histories in which the loads were ordered from low to high and from high to low within each block of flights. They were input to the program in the same single load format as for the random histories. The results are shown in Figure 2 together with the crack growth curve for the "middle" random history and also the curve obtained neglecting retardation effects.
The ordering has more effect than the marker blocks or different randomization sequences, but is still not large. The time to grow a crack to 2 inches is reduced to 13,000 equivalent flight hours for the high-low format from 14,000 hours for the random format. The effect of retardation is considerable, however, as the crack grows to 2 inches in 5500 equivalent flight hours if retardation is neglected, a factor of 2! times faster.
To determine if the ordering effect would be significantly altered by the amount of retardation assumed, a set of predictions was obtained with the Wheeler exponent set at 2.0 rather than 1.3. Af ter 15,000
equivalent flight hours, the crack length of about 0.6 inches differed by less than 0.03 inches for the ordered and random histories and so the effect does not seem very different.
DISCUSSION
From the results presented above it appears that the introduction of a marker block at the end of an otherwise random load-time history generated from the Snowbird spectrum has a negligible effect on crack growth predictions using the Wheeler retardation model. This would suggest that the introduction
ed
8.
,
.
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1
1
Jrve ;par md lot ~x1000
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ICES
2
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0::: ( UFIGURE 3
View of RHS notch surf ace first to develop a crack. The crack was detected in block 51 flight 133. The micrograph is from a replica of the notch surface. Taken across the thickness of the plate. The left hand edge seen in the photo is the surf ace of the plate specimen the
transducers are mounted on. There are numerous cracks in this area but at this magnificat ion they are not visible.
x24
-- -- -- -- -- --
-FIGURE 4
Micrograph from replica shows major crack as it appears with no load applied to specimen.
x 120
FlGURE 5
Same area as above but with 20 KIP (2.6g) load applied. Note how
cracks become more visible and at this load level an indication is showing on the ultrasonic trace but not large enough to trigger the gate as initially set.
FIGURE 6
Illustrating the effect of a 30 KIP (3.8g) load showing numerous cracks.
At this load level the cracks just trigger the gate. It should be noted that because of the various crack sizes there are a number of spikes in the gated area with different amplitudes.
x 24
FIGURE 7
Area with largest crack will be referred to as Site "A". Load 30 KIP.
FIGURE 8
Site "B" second largest crack with numerous smaller cracks 30 KIP load
x 120
FIGURE 9
Specimen STDNDT stopped at 61 blocks in Flight 79, gain reduced 2db to allow crack growth. Shows indication for the unloaded condition. Note the various peaks from the staggered crack pattern. Note that spike has to reach the white horizontalline to trigger gate.
FIGURE 10
Micrograph shows Site "A" crack as it appears with no load on the specimen. This shows crack growth due to extra 9 blocks and 79 FL TS after first detection.
FIGURE 11
Shows overall picture of the staggered crack formation. Load 13.5 KIP Site A bottom right.
x 59
FIGURE 12
Reflectroscope presentation with a 13.5 KIP (l.7g) load applied. This load is required to activate gate halting test. Af ter a 2db gain
reduction. Note the pulse just to the left of gate (horizontalline) is the edge of notch radius of the specimen.
-I .
I
i . • ,j i/t:'f
,
'11 1\.
,
!
1 1;, FIGURE 13AAppearanee of eraek at zero load. Sites A and B.
x 35
FIGURE 13B
Specimen at 16 bloeks past initial deetion. Shows traee at 58db gain and zero load. Gate initial trigger in bloek 67 FL T 64.
FLIGHT 14A
Reflectoscope trace gain 58db load zero
Flight 14B
Load zero, gain 64db.
FLIGHT 14C
FIGURE 15A Gain 58 db Load 2 KIP FIGURE 15C Gain 58db Load 7 KIP FIGURE 15S Gain 58db LOAD 4 KIP FIGURE 15D Gain 58db Load 9 KIP
FIGURE 16A
Gain 58db, Load 15 KIP.
FIGURE 168
Site A and B as they appear 15 KIP load. Note how cracks have merged.
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APPENDIX "A"
S-80 REFLECTASCOPE, CONTROL SETTINGS
MAIN SWEEP RANGE:
MAIN SWEEP CALIBRATION: SYNC: 2 inches 2.38 initial pulse PULSER RECEIVER PR-l DB GAIN 67 db
REJEC'l' : 1/5 from off REFERENCE: N.A.
F'REQ: 5 MHZ
l"IODE: VIDEO + ECHO
PULSE: 1/3 from ccw stop FILTER: OH'
GATE G'I'-l
START: COARSE: position ft 3, FINE: 1/10 from ccw stop
LE'NG'I'H: COARSE: position i2, FINE: (sufficient to cover area) l"IODE: AUTO
POLARITY: POS. at 50% LEVEL DISPLAY: ON
GATE: ON SYNC: lP
Note: Probes are inclined 10 towards the notcl! and are
pl~ced 1.5" in from the edge of specimen and approxi-mately 1.5" above the notch.
SENSITIVITY CHECK:
Once all the settings are correct and the probes are mounted on the specimen face it is necessary to check that the
",
required sensitivity is achieved. The first step is to insure that each probe surface has been cleaned and then coated with a layer of grease (Lubrex). The probe must th en be placed on the specimen under a spring holder. It 'is
necessary to wipe away any excess grease that may have spread in front of the probe. It is very important that the specimen surface from probe to notch is clean and free from any surface damage. The probe is positioned 1 1/2" above the notch such that the echo from the notch radius just appears
o
on the trace. The probe should be angled about 10 toward the notch radius. Once the probe is in position a small (pin head size or slightly less) dab of grease is placed on the specimen just at the edge and mid point of the ~adius. This should produce a spike on the trace in the centre of tbe gated area. By slightly rotating the probe while under the holder the max signal point is found. The procedure is repeated for the second probe. Once both probes are mounted and positioned a check is do ne by placing the small dab of grease on one side at a time to be sure each side will trig-ger the gate.
(J) -l IJJ al (,) LIJ o
70 CRACK DETECTION SURFACE WAVE
ALUM1NUM 1/4" PLATE SPECIMEN
60
50
40
0.01
CENTRE NOTCH UNDER LOAD
A
'"
' \ ~ ~SPECIMEN STDNDT 580 SYSTEM\
""
\
0\
\~KRAUTKRAMER
SYSTEMo
0 0'\
\
\
\
o
0.1CRACK LENGTH, INCHES
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