Illg, W.

English

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FACTORS IN EVALUATING FATIGUE LIFE OF STRUCTURAL PARTS
By Walter lllg
Langley Research Center
SUMMARY
Three facets of fatigue testing are discussed in relation to prob-
lems involved in evaluating the fatigue life of structural parts. These
facets are variable-amplitude loading, fatigue-crack propagation, and
equivalent fatigue loading. Experimental test results are included to
support conclusions.
INTRODUCTION
In the interest of safety and according to regulations, it must be
shown that an aircraft structure has a practically infinite life or a
safe life must be established. At present, theory alone is not suffi-
cient to evaluate the fatigue characteristics of a structural part. _c
only alternative is testing. Simple laboratory specimens are unsuitable
because of the many factors which must be simulated from the full-scale
parts. At the present stage of fatigue knowledge, testing the actual
part is the only sure way to evaluate the fatigue life of a piece of
aircraft structure. In this paper some recent NASA research, which
sheds light on a number of factors that are involved in any evaluation
of the fatigue life of structural parts, is discussed.
SERVICE LOADING
The first problem in testing is how to load a specimen to simulate
service loading. A record of actual stresses encountered in flight can
be obtained with the use of strain gages at critical points. The record
will depend a great deal upon how the aircraft is used. In the event
the same vehicle is to be used for more than one type of mission, the
flight record to be used intesting should be from that mission which
provides the severest load conditions. Each type of mission will include
a variety of maneuvers, such as taxiing, take-off, and climb, which have
characteristic load histories. The record should include sufficient
samples of all phases of the aircraft's mission to give an accurate
picture of the extremes and probabilities of occurrence of all loads.
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It may or may not be possible to combine the loads from different phases,
depending on the mean load. Schedules for phases having widely different
mean loads should not be combined. In the case of the helicopter, the
mean load in the blade for all phases will be practically identical since
it is dependent upon rotor angular velocity which is essentially constant.
The parts in other aircraft, however, will generally be subjected to
varying mean loads.
It would be very satisfying if the exact flight-lOading patterns
could be reapplied to the part in question in the laboratory; however,
the cost of such a procedure would be prohibitively high. On the other
extreme, cycling continuously at a single load range has been shown to
be incapable of reproducing all the effects of the varied flight loadings.
For instance, fatigue tests of transport wings (ref. l) indicated that
more cracks were initiated under variable amplitude than under constant
amplitude_ and the crack which finally caused failure was in a different
location for each type of loading.
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VARIABLE- AMPLI%_JDE TESTING
Since constant-amplitude loading is unrealistic and exact flight-
loading duplication is impractical, a compromise must be adopted. One
solution is to translate the flight record into a load program composed
of discrete steps which adequately represent the actual loads and which
can be handled in the laboratory. Figure 1 illustrates how a step-
loading schedule may be used to simulate a continuous spectrum. The
smooth curve is s representative stress spectrum found from actual ser-
vice conditions during one major phase of operations. The discrete
levels shown are chosen so that they represent a number of equal stress
intervals. The best number of steps to use has not been definitely
established. In NASA work at the Langley Research Center, eight steps
are generally used, and possibly no fewer than six should ever be used.
As figure 1 implies, all loads are assumed to cause fatigue damage.
Even though the lowest load step lies below the fatigue limit, it is
nonetheless important. One reason is that, after a crack appears, the
stress-concentration factor increases, and the lowest step may contribute
to crack propagation. For this reason, the test schedule should include
loads below the fatigue limit. As mentioned before, a similar schedule
will be obtained for each major phase of operation of the aircraft. The
various test schedules should be applied in the same proportion that is
expected to occur in service.
Once the magnitude and number of load steps have been determined_
the sequence of application must be considered. Tests on simple specimens
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under variable-amplitude loading have been conducted, and one discovery
has been the effect of the sequence of loading on the life. Figure 2
shows the relative effect of t_hree loading sequences on the fatigue life
of the specimens tested (ref. 2). Each of these patterns depicts a
different sequence of applying the same eight loads the same number of
times, each on the same type of simple specimen. The loading pattern
was repeated until failure occurred. The life for the random sequence
is given a value of 1 for purposes of comparison. Note that the lo-hi
sequence gave the shortest life while the hi-lo sequence gave the longest
life. The life obtained with the random sequence fell between the other
two. Thus, by change of sequence the results changed by a factor of 4.
In general, service loading of aircraft is of a random nature, in
which case, the laboratory test loads should be applied in random order.
Special cases may require other sequences to simulate the loading. The
number of cycles in each block (fig. 2) should be chosen so that the
specimen will survive at least l0 blocks.
FATIGUE-CRACK PROPAGATION
Under the application of any load schedule, the failure will take
place in two stages; the first stage is the period before a crack is
initiated, and the second stage is the period during which the crack is
propagated to failure. The interval between crack initiation and part
failure can be very important to an aircraft operator. Fatigue damage
is first visible during this interval in the life of a part. During
this time, the strength of the part decreases in a manner as shown in
figure 5. The dashed line represents the maximum repeated load encoun-
tered in service. The solid llne indicates the load which the cracked
part can still carry. As the crack grows, the strength decreases until
the part can no longer withstand the applied load, and failure occurs.
This interval between crack initiation and failure provides an opportunity
to inspect a part for fatigue damage. Two properties of the part must
be known to make it possible to set up a realistic inspection interval.
The first property is the rate of crack propagation under expected
stresses, and the second property is the crack length at which the resid-
ual strength equals the load and the part fails.
Prediction of the rates of crack propagation in simple specimens
at constant-amplitude loading is possible. Figure 4 shows some results
for 2024-T5 sheet specimens tested with the ratio of minimum stress to
maximum stress in a cycle R always at zero (ref. 3). The data for
many tests fall on a continuous curve when the rate of crack propagation
is plotted against a stress parameter which involves the local stress
at the tip of the crack. The dashed line represents a semiempirical
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expression used to correlate the data shown. The same curve may be used
to estimate the rate of crack propagation at other stresses and for other
size specimens. Crack propagation under variable-amplltude loading is
currently being investigated to understand more fully c_ack growth under
servlce-type loading.
The second property of the part which must be known (the residual
strength as a function of crack length) has also been investigated for
simple specimens. Some results are shown in figure 5 for 2024-T_mate-
rial (ref. 4). Note the sharp decrease in strength for small crack
lengths. The solid llne represents a theory for predicting strengths
for any crack length. This theory is based on a stress concentration
at the tip of the crack. When the local stress at the tip of the crack
reaches the ultimate strength of the material, the specimen will fail.
When the part is reasonably simple, this kind of data from simple speci-
mens can provide a fairly good estimate of the number of cycles which
the part can endure after a crack appears. For complicated structures,
the part itself would have to be tested to obtain all crack-rate data
and resldual-strength data. In any case, the part should be tested to
check the estimates made. From this information, an inspection inter-
val could be calculated which would make it reasonably certain that a
crack would be discovered before failure occurred. For the method to
be practical, the probable locations of cracks must be known and easily
accessible. Of course, in the event that the inspection interval is
found to be too short, the parts must be discarded before a crack appears.
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EQUIVALENT FATIGUE LOADING
In the course of an investigation of crack propagation, it may
sometimes be desirable to substitute one loading ratio R for another,
while maintaining identical rates of crack propagation. This procedure
might be desired for practical reasons such as testing mgchine capability.
Extreme care must be exercised in choosing an equivalent load. The fol-
lowing discussion illustrates how conventional methods for finding
equivalent loads can result in invalid crack-propagation test data. The
illustrative problem involves changing from a loading at R = 0 to a
loading at R = -1.
The conventional method of finding equivalent fatigue loads is
indicated in figure 6. The fatigue failure curves for unnotched speci-
mens are plotted for the two load ratios R = 0 and R = -1. The
ordinate is the maximum cyclic load and the abscissa is the total life.
The conventional method requires the determination of the load level at
R = -1 which gives the same llfe as the criginal load level at R = O.
However, the conventional method is invalid when dealing with the crack-
propagation portion of fatigue tests.
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Figure 7 shows the rates of fatigue-crack propagation for the two
load ratios R = 0 and R = -1 (ref. 3). The material is 7075-T6
alumlnum-alloy sheet. One set of tests was run with the minimum cyclic
load held at zero (R = 0)3 and the other set of tests was run with the
mean load held at zero (R = -1). These data show that, for the same maxi-
mum cyclic stress, the rates of crack propagation were the same even
though the load range for R = -1 was twice that for R = 0.
In a recent investigation of the crack propagation in a full-scale
helicopter rotor blade, the conventional method was used to change from
a service loading at R = 0 to a test loading at R = -i. Since fig-
ure 7 indicated that in simple specimens the maximum cyclic stresses
for similar cracking rates at R = 0 and R = -I are the same, axial-
load fatigue tests on small portions of the blade were performed to
check the results of the full-scale test. One specimen was subjected
to service loading and another specimen was subjected to the stresses
that were used in the full-scale test. The results of these tests are
shown in figure 8. The loading at R = -1, the so-called equivalent
loading, gave a much smaller rate of crack length than did the service
loading.
The result, then, of using an equivalent load obtained in the con-
ventional manner, was that the full-scale test not only did not yield
the answer that was sought but also gave a misleading indication of
comparatively slow crack growth.
CONCLUDING REMARKS
It has been shown that many factors enter into the determination
of the safe life of a structural component subjected to fatigue loadin&
It is preferable to test actual parts because of the multitude of
items which must be duplicated in simple specimens to make a valid tes_.
Variable-amplitude testing is preferred to constant-amplitude
testing. The number of load steps for a given schedule should probably
not be less than six. The sequence of loading should be random for most
cases. The number of cycles per block should be such that at least
l0 blocks will be survived by the part.
Loads below the fatigue limit should be included since they can
affect the llfe of the part.
Inspection for cracks during the service life of an aircraft can
improve its safety. When the procedure discussed in this paper for
determining an inspection interval is used, the following properties
must be ascertained:
...... J| II
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(I) The probable location of fatiguecracks
(2) The rate of growth of all fatigue cracks
(5) The length of the crack at which the residual strength is no
longer greater than expected loads
When the rates of crack propagation are investigated, great care
should be taken in determining equivalent loads if theyare to be used.
REFERENCES
1. Whaley, Richard E.: Fatigue Investigation of Full-Scale Transport-
Airplane Wings - Variable-Amplitude Tests With a Gust-Loads Spectrum.
NACATN 4152, 1957.
2. Naumann, Eugene C., Kardrath, Herbert F., and Guthrie, David E.:
Axial-Load Fatigue Tests of 2024-T5 and 7075-T6 Aluminum-Alloy
Sheet Specimens Under Constant- and Variable-Amplitude Loads.
NACA TN D-212, 1959.
3- McEvily, Arthur J., Jr., and Illg, Walter: The Rate of Fatigue-Crack
Propagation in Two Aluminum Alloys. NACA TN 4394, 1958.
4. McEvily, Arthur J., Jr., Illg, Walter, and Hardrath, Herbert F.:
Static Strength of Aluminum-Alloy Specimens Containing Fatigue
Cracks. NACA TN 3816, 1956.
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D
SIMULATION OF CONTINUOUS STRESS SPECTRUM BY USE OF
REPRESENTATIVE STRESS STEPS
LOAD
AMPLITUDE
i I • I I I \
CUMULATIVE LOAD CYCLES
(LOG SCALE)
Figure 1
EFFECT OF TEST SEQUENCE ON FATIGUE LIFE
LO-HI Ht-LO RANDOM
ONE BLOCK
100,000
CYCLES
0.5 2.0
COMPARATIVE FATIGUELIFE
Fi_are 2
v..
-11
_-r! aa'E
: :m
......... :},*
332
LOAD
STRENGTHREDUCTIONDUETO CRACK PROPAGATION
- ZAPPLIED CYCLIC LOAD LURE
OCCURS
CYCLES AFTER CRACK INITIATION
Figure 3
RATE OF FATIGUE-CRACK PROPAGATION IN 2024-T5 SHEET
10-2
I0-3
i0-4
10-5
i0-6
0
CRACK
PROPAGATION
RATE,
I N./CYCLE
R =0 (MINIMUM STRESS=0)
/
!
#I/--THEORY
1 i I I I I
200 400
STRESSPARAMETER,KSI
]
F ig_Lre It
333
J.± ,•
i
z...._Z_
STATIC STRENGTH OF 2024-T3 SHEET
CONTAINING FATIGUE CRACK
lOO_
STRENGTH,
% OF ORIGINAL
I
80
6O
40
20
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I I I I I I I I
29 40 60 80
AREA CRACKED, %
Figure .5
METHOD FOR DETERMINING EQUIVALENT
MAXIMUM
CYCLI C LOAD
LOADING
SIMPLE-SPECIMEN FAILURE CURVES
\ R_O I#_ /"_ .
SERVlCELOAD, R=O - OI _/ _
I _'_,_,_._ R =0
...... R=.I
EQUIVALENT LOAD, R - -I
LIFE (LOG SCALE)
Figure 6
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CRACK
PROPAGATION
RATE,
IN./CYCLE
RATE OF FATIGUE-CRACK PROPAGATION IN 7075-T6 SHEET
- -I (COMPLETELY REVERSED LOADING1
10-2 -
J/
i0-3
I0"410-5 k _ _-._/ CRACK
I _ R : -I DATA
i0_6 / ------ R : 0 CURVE
I
10-7 I 1.. I t i 1 i I
2OO 4O0 6O0 80(]
STRESS PARAMETER, KSI
Figure 7
AXIAL-LOAD TESTS OF A PORTION OF A HELICOPTER BLADE
1.5-
/-SERVICE LOADING,R =0
1.0-
CRACK
LENGTH,
IN. TEST LOADING, = -I
Y
I I I l l I I
0 4 8 12 16 20 24 28 x IV'
CYCLES
F i6_Jre 8
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Factors in evaluating fatigue life of structural parts

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