Fatigue behaviour of BS 2L65 aluminium alloy pin - aerade

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PROCUREMENT EXECUTIVE, MINISTRY
Aeronautical Research Council
Reports and Memoranda
FATIGUE BEHAVIOUR OF BS 2L65
R & M No.3835
OF DEFENCE
ALUMINIUM ALLOY PIN-LOADED LUGS
WITH INTERFERENCE-FIT BUSHES
by ...... ~
J.E. Moon
; 1 !~>,
Structures Department, RAE Farnborough, Hants
London" Her Majesty's Stationery
£7 NET
Office

UDC 620.178.3 : 669.715 : 621.886.1 : 621.886.4 : 621.822
FATIGUE BEHAVIOUR OF BS 2L65 ALUMINIUM ALLOY PIN-LOADED LUGS
WITH INTERFERENCE-FIT BUSHES
By J. E. Moon
Structures Department, RAE Farnborough, Hants
REPORTS AND MEMORANDA No.3835"
November 1977
SUMMARY
Cumulative fatigue damage has been studied in lugs with and without
interference-fit bushes. Fatigue tests'have been carried out under constant and
variable amplitude loading conditions and local stress measurements have been
made using the Companion Specimen Method.
Local stress measurements did not explain the large increase in life under
constant amplitude loading associated with fitting an interference-fit bush in a
pin-jointed lug, nor did they explain the reduction in life following a prestress
on such a specimen. However, the stress measurements in sequences representing
narrow band random loading were broadly consistent with actual fatigue test
results, and enabled more accurate life estimations to be made at the lower mean
stress tested, but at a high mean stress the measurements produced unsafe life
estimates.
* Replaces RAE Technical Report 77177 - ARC 37872

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LIST OF CONTENTS
INTR0 DUCTION 3
FATIGUE TESTS 4
2.1 Material and specimens 4
2°2 Fatigue tests and results 5
2.3 Life estimations and comparison with achieved performances 7
LOCAL STRESS HISTORY MEASURI~ENTS 7
3. I Method of measurement 8
3.2 Material and specimens 8
3.3 Summary of tests carried out 8
3.4 Results 9
DISCUSSION I 0
4. I Effect of passivating bushes 10
4.2 The effect of an interference-fit bush on the life of a lug 10
under constant amplitude loading
4.3 The effect of a prestress on bushed and unbushed lugs under 12
constant amplitude loading
4.4 The performance of bushed lugs under narrow band random 14
loading
CONCLUSIONS
Appendix A Local stresses in a bushed lug
Appendix B Fatigue testing facility and load spectra
Appendix C Cumulative damage calculations made using Miner's Rule
Appendix D Method of life estimation allowing for residual stresses
Table I Chemical composition and tensile properties of BS 2L65
aluminium alloy
Table 2 Fatigue test results
Table 3 Fatigue test results
Table 4 Fatigue test results
Table 5 Fatigue test results
Table 6 Fatigue test results
Table 7 Fatigue test results
Table 8 Fatigue test results
Table 9 Fatigue test results
Re feren~e s
Illustrations
Detachable abstract cards
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19
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25
26
27
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29
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Figures 1-43

I INTRODUCTION
A lug loaded by a clearance fit pin is a structural feature which has a
comparatively poor fatigue performance because fretting damage caused by relative
movement between the pin and lug bore occurs at a position of high stress
concentration and therefore leads to early crack initiation.
It has been found that the use of an interference-fit pin or bush can
greatly improve this performance, at least under constant amplitude conditions1°
For ease of assembly and maintenance it is usual practice to employ an inter-
ference-fit bush with a clearance fit pin rather than just a force fit pin as the
bush can be inserted into a sub-assembly whereas the pin has to be pressed into
a final assembly. The interference creates a compressive radial stress and a
tensile hoop stress in the lug in a similar manner to a cylinder under internal
pressure and it is generally believed that there are two main reasons why an
interference fit can improve the fatigue life of lugs 2. First, the frictional
force created by the radial stress decreases the amount of slip between the hole
bore and pin (or bush), and should therefore reduce the fretting damage. Second,
there is a reduction in the tangential stress amplitude at the point of crack
initiation. However, the interference does cause an increase in the local mean
stress which can be damaging in fatigue, but this is generally assumed to be of
only minor importance when compared with the reduction in amplitude. A fuller
explanation of the effect of the bush on local stresses can be found in
Appendix A.
The majority of research carried out investigating interference fits has
used constant amplitude loading, as in Refs I, 3 and 4, whereas components in
service usually experience load spectra which are of variable amplitude and
frequently random. It is well known that the use of constant amplitude loading
in fatigue evaluation can give misleading results. For example, whereas there
is a marked effect of fretting pad length on the life of a simple plain specimen
under constant amplitude loading~ the difference is greatly reduced under loading
which simulates service conditions 5. In addition Smith 6 found that whereas a
single tensile prestress applied to an unbushed lug before a constant amplitude
fatigue test increased the life, the reverse was true for the case of a lug
fitted with an interference fit bush. This implies that large load peaks in a
random spectrum may have a much different effect on a bushed lug than one with
just a clearance fit pin. It was therefore decided that in this programme, in
addition to constant amplitude fatigue tests of bushed and unbushed lugs, both
3

4
would be tested under narrow band random loading to simulate service conditions
in a simple way. This work is reported in section 2 which includes life predic-
tions for the random loading cases using Miner's Rule.
It has been shown that in many cases more accurate life estimations can be
made by considering the actual state of stress at the point of crack initiation,
rather than net section stresses. Section 3 presents local stress history
measurements in bushed and unbushed lugs using the Companion Specimen Method 7
which were made in order to try to explain some of the observed fatigue behaviour
and if possible to improve the life estimations made.
2 FATIGUE TESTS
All the results quoted for the unbushed lugs have been reported previously 8,
having been carried out as part of an earlier investigation. However, for
completeness, a full description is given of the specimens and tests for both
the unbushed and the bushed lug tests.
2.1 Material and specimens
All lugs, bushed and unbushed, were manufactured from bars of BS 2L65
aluminium alloy material obtained from one melt. The chemical analysis provided
by the manufacturers and tensile properties obtained from test pieces cut from
the same batch of material, are given in Table I.
Fig I shows the unbushed lug specimen which was pin-loaded at each end.
The same specimen was adapted to a bushed lug as shown in Fig 2 by enlarging one
of the holes and fitting a bush to accept the same size of pin; in this form
only the bushed hole was pin-loaded, the other end being clamped by wedge grips.
As the bushed and unbushed lugs had the same gross cross-section and pin size
they can be regarded as interchangeable components for the purpose of comparing
fatigue performance.
The bush, shown in Fig 3, was made of $80 stainless steel and cadmium
plated on its outer surface to prevent corrosion where the steel is in contact
with the aluminium lug. For purposes of comparison, some bushes underwent a
passivating process following plating, and some were untreated. The passivation
process is normal practice following cadmium plating and gives greater resistance
to corrosion. The bush had a nominal 0°27% interference in the lug, and in order
to facilitate insertion, was placed on a mandrel and cooled in liquid nitrogen.
The lug, preheated to 115°C was aligned in a jig below the bush and thus the
possibility of scoring the hole bore was minimised.

Loading pins were manufactured from S94 steel, and in the case of the
unbushed lugs had a diametral clearance of between 0.03% and 0.21% of diameter
in the lug, while in the case of the bushed lugs the clearance in the bush was
between 0.63% and 0.74% of diameter, the larger clearance being necessary to
prevent seizure between the steel pin and bush.
2.2 Fatigue ' tests and results
All the fatigue tests were carried out on a modified Schenck resonant
machine which was capable of applying either constant amplitude or narrow band
random loading. Further details of the machine and waveforms applied are to be
found in Appendix B. Loads were monitored throughout tests by measuring the
root mean square value and displaying this on a pen recorder.
In this report stresses are quoted primarily in terms of
~ Load
Pin bearing stress = nominal pin diameter x lug thickness
so that a direct comparison can be made between equivalent bushed and unbushed
components carrying the same load. The use of net area stress is less satisfac-
tory because the two types of lug have different net areas due to the presence
of the bush and thus would sustain a different load for the same net stress; in
addition, the designer is often concerned with pin loads in a joint design.
However, to aid understanding and interpretation~ values of net stress, based on
the unbushed lug net area, are given in brackets following the pin bearing stress.
Fatigue tests on lugs fitted with interference fit bushes were carried
out under the following loading conditions:
(a) Constant amplitude loading over a range of stress amplitudes at two levels
(b)
(c)
of tensile mean stress.
Constant amplitude loading following two values of prestress. A prestress
is defined as a single large tensile stress applied at the beginning of
the test and then reduced to the mean stress of the subsequent fatigue
test.
Narrow Band Random (NBR) loading at two levels of tensile mean stress.
In the above tests the steel bushes were not passivated following cadmium
plating, whereas it is normal practice in the aircraft industry to passivate
bushes. In order to investigate the effect of this process further tests were
carried out using lugs fitted with passivated bushes under:

6
(d) Constant amplitude loading over a range of stress amplitudes at one tensile
mean stress°
(e) Narrow Band Random loading at two rms levels of alternating stress and one
tensile mean stress.
Specimens were tested to failure or 10 7 cycles, whichever occurred first.
Cracks were initiated by fretting between the bush and lug hole and led to
failure through the net section. A typical failure is shown in Fig 4.
The following table details the locations of the tabulated results and
associated S-N curves for each condition.
Form of Loading
Constant amplitude
~R
tt
It
t! !I
T! It
It
Mean
stress
MN/m 2
153 (95)
153 (95)
225 (14o)
153 (95)
153 (95)
153 (95)
153 (95)
225 (14o)
Prestress
gN/m 2
0
0
0
4o2 (25o)
474 (294)
0
0
0
Bushes
passivated
No
Yes
No
No
No
No
Yes
No
Table
No.
2
3
4
5
6
7
8
9
Fig No.
5
6
7
i
Fig No. of
comparison
I0
i ii i,
8 ~13
The S-N curves are based on a faired line passing as close as possible to
the log mean endurances at each stress level. All failed specimens are indicated
on these figures by a circle and dot, whilst a circle with an arrow indicates an
unbroken specimen.
In Figs 10-13 where comparisons are made of results under different condi-
tions, individual test points are omitted for clarity.
The unbushed lug data plotted in the comparison graphs, Figs 11-13, were
obtained in an earlier investigation 8 and only the faired S-N curves are
presented in this report.

2.3 Life. ' estimations and comparison with achieved performance
Miner's Rule is the most common method of predicting the life of components
under service loading using data obtained in the laboratory under more simple
loading, usually constant amplitude. Briefly, it sums linearly the damage
accumulated by the various levels of alternating stress contained in the service
spectrum. Miner's Rule was used to predict the lives of lugs under random
loading using constant amplitude data, as described in Appendix C for the
following cases:
(a) NBR loading at 153 (95) MN/m 2 mean stress using constant amplitude
data at that mean stress. The results for the passivated bushes
data is plotted in Fig 14, along with the achieved performance curve.
(b) As (a) but for the ease of unpassivated bushes. As only one rms
stress level was used at this mean stress the result is not plotted
on an S-N diagram, but is included in Fig 16, which compares the
accuracy of Miner's Rule for various conditions and will be explained
later.
(c) NBR loading at 225 (140) MN/m 2 mean stress using constant amplitude
data obtained at the same mean stress. The results for unpassivated
bushes are compared with the achieved performance in 9~ig 15.
The accuracy of Miner's Rule is usually judged by the ratio:
~ achieved life
predicted life
Thus values of D > 1 indicate a conservative or safe prediction, whereas
values < I indicate an optimistic or unsafe prediction. The results of the
e~%lculations for the conditions (a), (b) and (c) were used to obtain values of
~, which are all plotted in Pig 16.
For comparison, values of Z ~ n for unbushed lugs under NBR loading are
plotted in Fig 17.
3 LOCAL STRESS HISTORY MFASURmENTS
The interference modifies the initial stress state in the lug and it is
widely believed that it also reduces the local stress amplitude at the point of
crack initiation. It was therefore decided to study the local stress history in
a bushed lug in order to aid understanding of the ways in which a bush can affect
7

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the fatigue life of a lug. Theoretical analysis of the interference fit case is
difficult, so it was decided to make direct measurements on the lug using the
Companion Specimen Method 7.
3. I Method of measurement
Briefly, the Companion Specimen Method consists of reproducing on a plain
specimen the stress and strain history at a position of stress concentration on
another specimen. A strain gauge is attached at the point of interest in the
latter specimen, generally where the fatigue crack is likely to start, and the
strain history is recorded whilst the specimen is subjected to the desired load
sequence. The recorded strain sequence is then applied to a plain specimen,
made of the same material as the component, and by measuring the loads applied,
the corresponding stress history in the component is determined.
3.2 Material aud s~ecimens
All lug and plain specimens were cut from 2 bars of BS 2L65 aluminium
alloy from the same melt as those used in the fatigue test programme. The lug
specimen is shown in Fig 18 and the bush of $80 steel material in Fig 19. At
one end of the lug the hole was enlarged to accept a bush having a 0.27%
(0.076 ram) diametral interference, to be loaded by a 25.4 mm diameter pin. The
other end was machined to take the pin alone without the bush to enable a direct
comparison to be made between a bushed hole and an equivalent unbushed hole.
Thus the specimen represented exactly the bushed and unbushed lugs used in the
fatigue test programme. The strain gauges in both holes were placed as shown
in Fig 18, mid-way through the thickness of the lug. In order to clear the
gauge the bush had a hole drilled in its centre and was split, half being
inserted from each side, see Fig 19. The gauge was attached to the lug before
inserting the bush, in this way the strain due to the bush alone could be
measured. The loading pins had a slot milled along their length to accommodate
the gauge leads in the bushed hole, and both the gauge and its leads in the
unbushed hole. The plain specimen is shown in Fig 20.
3.3 Summarry of t_ ests carried_~out.
The load sequences employed, shown in Fig 21, were designed to represent,
in a simple way, the essential features of the fatigue tests reported in
section 2, as it was hoped that the Companion Specimen data could be used to aid
interpretation of the fatigue test results.

Sequence (a) was designed to investigate the effect of prestress on local
stress during subsequent constant amplitude loading. It represented tests at an
rms alternating stress of 64 (40) MN/m 2 and a mean of 153 (95) MN/m 2 with three
nominal values of prestress:
(1) 0
(2) 402 (250) MN/m 2
(3) 474 (294) MN/m 2
Previous experience using the Companion Specimen Method on a similar
material indicated that applying the two prestresses in sequence would not have
produced a different result to applying them separately on virgin specimens.
Sequence (b) was designed to represent narrow band random loading at
153 (95) MN/m 2 mean stress. Section 2 presented results of fatigue tests at two
levels of rms alternating stress under these conditions and this sequence
enabled the local stress behaviour to be compared before and after a load
representing the highest peak in each spectrum.
Sequence (c) was similar in principle to sequence (b) except that it was
designed to help interpret random fatigue tests carried out at a mean stress of
225 (14o) MN/m 2.
3.4 Results
Fig 22 is a typical example of a graph for a bushed hole of local strain
vs pin bearing stress, this particular plot being for a specimen loaded through
sequence (a), simulating the prestressed constant amplitude tests. The corres-
ponding local stress vs local strain diagram obtained from a plain specimen is
shown in Fig 23. For comparison Fig 24 shows a pin bearing stress vs local strain
diagram obtained from an unbushed hole under the same conditions, and Fig 25 is
the corresponding local stress vs local strain diagram. These graphs, along with
similar ones for the other sequences were analysed in order to obtain the local
stress range and local mean stress during each load cycle. These results were
then used to construct the following graphs:
Figs 26 and 27 - Comparison of local stress histories in a bushed and an
unbushed lug under constant amplitude loading, at 2 mean stresses.
Fig 28 - The effect of a prestress on local stress histories in a bushed
and an unbushed l~under constant amplitude loading.
Figs 29-33 - The effect of peak stress in a random spectrum on local stress
histories during subsequent smaller net stress cycles, at 2 mean stresses
and several rms alternating stresses.

10
4 DISCUSSION
4.1 ~ s i v a t i n g bushes
It is normal practice, when using a steel bush in an aluminium alloy lug,
to cadmium plate the bush. Plating is usually followed by a passivation process,
which consists of dipping the bush in a solution that deposits a fine chromate
layer on the cadmium plating, in order to give a greater resistance to corrosion.
Most of the bushes used in this programme were cadmium plated but not passivated;
however a limited number were treated in order to assess the effect of
passivation.
Fig 10 shows only a small effect of passivation on life under constant
amplitude loading over most of the alternating stress range. The most signifi-
cant effect was at the longer endurances, where the fatigue strength was reduced
by about 45% in the passivated case° This effect was probably due to an increase
in fretting damage brought about by the hard chromate particles deposited in the
passivation process.
Only a limited number of specimens were available to assess the effect of
passivation under NBR loading. The results, presented in Fig 8, did not show
any significant effect. However, an insufficient number of specimens were tested
to draw any definite conclusion. The possibility that passivation affects the
fretting damage would be less under random loading, as large load peaks in the
spectrum are likely to cause earlier crack initiation than under constant
amplitude loading.
4.2 The effect of an interference-fit bush on the life of a lu~ under constant
amplitude loadin~
When comparing the behaviour of bushed and unbushed lugs, it should be
remembered, as stated in section 2.1 that the unbushed lugs were double ended,
whereas the bushed lugs were pin-loaded at one end only. Thus, in the unbushed
case, failure occurred at the weaker of two holes° This caused a slight lowering
of the log mean life, but it is considered that this was of only small magnitude,
because of the small scatter exhibited by pin-loaded lugs.
Fig 11 shows log mean endurance curves for lugs with and without bushes.
Comparing the bushed and unbushed performance first at the lower mean stresses,
which were similar in the two cases, it will be noted that the effect of the
interference was to increase fatigue life considerably, which is in accordance
with the findings of other workers 1'2'3'4. It should be pointed out that the

curve presented for the bushed lugs is for the case of passivated bushes. The
effect of increasing the mean stress was to reduce performance of both the bushed
and unbushed lugs, the effect being much more damaging in the bushed case even
though the change in mean stress was less. Furthermore, whereas the S-N curves
for the unbushed lugs at the two mean stresses tended to converge at long
endurances, this was not so for the bushed lugs and the increased mean stress
caused a reduction of about 64% in fatigue strength at around 4 x 106 cycles.
The reduction was so great that the S-N curve for the bushed lugs crossed over
both unbushed curves. This result was checked by testing 4 unbushed lugs at
225 (140) MN/m 2 mean stress and an rms alternating stress of 8 (5) MN/m 2. None
of the unbushed specimens failed after 107 cycles, whereas 4 bushed specimens
had all failed with a log mean endurance of 5 x 106 cycles at the same stress
level, confirming that bushed lugs had an inferior performance to the unbushed
lugs at 225 (140) MN/m 2 mean stress and low alternating stress. It was found
that the main effect of passivating bushes under constant amplitude loading at
the low mean stress was to reduce the fatigue strength at long lives. As the
increased mean stress reduced this strength to a very low value it seems probable
that passivating bushes would have little if any effect at the high mean stress.
Reference can now be made to the local stress measurements to see if they
explain the observed fatigue behaviour. From the changes in local stress during
the first occurrence of each magnitude of stress cycle in sequence (b) and (c)
of Fig 21~ the local mean stress and stress range can be calculated for bushed
and unbushed lugs over a range of alternating stresses at the two mean stresses.
This information can be found in Figs 26 and 27. This shows that in general,
during any net stress cycle, the local stress history in the bushed lug displayed
a higher mean stress and a lower alternating stress than the unbushed lug, which
agrees with the ideas put forward in the introduction.
The next step was to quantify these findings in terms of effect on life.
In order to construct a local mean-local alternating stress diagram for unbushed
lugs over a range of fatigue lives, an S-N curve had to be constructed for
unbushed lugs at 225 (140) MN/m 2 mean stress. This was done by using the results
of constant amplitude tests at three mean stresses 8 to draw Fig 34 which is a
net alternating-net mean stress diagram for unbushed lugs. The constructed S-N
curve derived from this is shown in Fig 37 as the dotted line. The local stress
diagrams for constant amplitude loading in Figs 26 and 27 can then be used with
the unbushed S-N curves to construct the local mean-local alternating stress
11

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diagram of Fig 35. The local stress diagrams of Figs 26 and 27 were then used
with this mean-alternating stress diagram to estimate the lives of the bushed
lugs over the range of net stresses applied. These estimates are plotted along
with the achieved bushed and unbushed performances in Figs 36 and 37.
Considering first Fig 36, which compares the estimated and achieved
performances at mean stress = 153 (95) NN/m2 it can be seen that the local
stress measurements predicted that fitting a bush would produce a small improve-
ment in endurance over an unbushed lug, typically increasing endurance by a
factor of 1.5-2. However, the actual achieved performance of a bushed lug was
approximately 6-7 times greater than an unbushed lug over most of the alternating
stress range. The predicted and achieved performance curves only converged at
low alternating stresses° Thus, although the local stress measurements predicted
that an interference fit bush should give rise to some improvement in life, the
actual achieved performance was much greater. A possible explanation is that the
interference did reduce fretting damage significantly, and this is the main
reason for the large increase in endurance observed in fatigue tests.
Turning next to Fig 37, which is similar to Fig 36 just described, except
that the mean stress was 225 (140) NN/m 2, it will be noted that the local stress
measurements predicted that the bush would increase endurance of the unbushed
lug by a small amount over all the stress range. Again the predictions were in
poor agreement with the observed fatigue behaviour. At higher alternating stresses
the bushed lug demonstrated a large increase in performance, which was possibly
due to the reduced fretting damage. However, at low alternating stresses the
performance of the bushed lugs was inferior to that of the unbushed lugs despite
the fact that local stress measurements indicated that the reverse should have
occurred. This is difficult to understand and does not support the earlier
supposition about the reduced effect of fretting.
4.3 The effect of aLprestress on bushed an d unbushed lugs under constant
~.~litude loading
As stated earlier, it has already been established by several workers that
t~e ~.~se of an i~terference fit bush can improve the f~tigue life of lugs under
constant amplitude loading. The main purpose of this programme was to investi-
gate the effects of bushing under variable amplitude loading. Smith 6 has
reported that whereas a single tensile prestress applied at the beginning of a
fatigue test could improve the life of an unbushed lug, the reverse was true for
the case of a bushed lug. This result implies that large load peaks in a

variable amplitude spectrum may have a much different effect on a bushed lug
from that on one with just a clearance fit pin. It was decided to check Smith's
results on the particular lug used in this investigation. Two levels of prestress
were applied to bushed lugs at one level of rms alternating stress. Results were
available from an earlier investigation 8 for unbushed lugs with similar levels of
prestress. Fig 12 compares the behaviour of the bushed and unbushed lugs
subject to a prestress. The constant amplitude curves for no prestress have been
drawn for both bushed and unbushed lugs, and are compared with log mean endurances
at one level of rms alternating stress for the prestressed results. It can be
seen that a prestress had opposite effects on bushed and unbushed lugs, repeating
Smith's findings. In the case of the unbushed lug, a prestress increased fatigue
life, the larger the prestress, the larger the increase. However, the effect of
a prestress on a bushed lug was to reduce life, the larger the prestress, the
greater the reduction. It should be noted that the prestresses applied were
fairly large, being approximately in the range 0.5-0.6 of the ultimate tensile
strength.
Seguence (a) used in the local stress measurements, shown in Fig 21, was
designed to investigate the effect of two levels of prestress on local stress
during subseguent constant amplitude loading, and the results are plotted in
Fig 28 which shows the effect of the prestresses on local stress range and local
mean stress. Considering first the effect of prestress on an unbushed lug it
can be seen that the local stress range was virtually unaffected by both values
of prestress. However, the mean stress was reduced by 57% and 93% respectively
by the two values of prestress. This behaviour is attributed to the creation of
compressive residual stresses following local tensile yielding which led to the
observed increase in fatigue life. This is a well known phenomenon and there are
design codes, such as the ESDU rule 9 which can be used to take account of it in
life prediction. Turning next to the case of the bushed lug the two values of
prestress increased the local stress range by 7% and 11% respectively. Reference
should again be made to Appendix A for an explanation of this effect. The local
mean stress was reduced slightly more than in the case of the unbushed lug. The
beneficial effect of reduced mean stress would be expected to oppose the detri-
mental effect of the increased stress range. Taking the case of the higher
prestress and using fatigue test data presented in this report, the observed 11%
increase in stress amplitude would be expected to reduce the life by about 40%.
However, the reduction in mean stress in the case of the unbushed lug caused an
13

14
increase in endurance of 160%. As there was a greater reduction in mean stress
for the case of the bushed lug, an equal, if not greater effect on life would be
anticipated which would more than offset the effect of the increase in stress
range. As the fatigue tests showed a reduction in life following a prestress,
this cannot be attributed to the change in local stress conditions described
above. Other possible explanations include:
(i) An increase in fretting damage caused by a relief in radial stress.
(ii) The presence of very high stress gradients such that the strain gauge was
not responding to the true local stress situation.
Both these points are currently being investigated using the Moir~ Fringe
Method. This will give the in-plane surface strains on the lug following bush
insertion and will study the effect of several values of preload.
4.4 ~erformance of bushed l~ under narrow band random loading "
The performance of bushed and unbushed lugs was also compared under NBR
loading at different mean stresses. It should be noted that the use of a
resonant machine for this evaluation is not entirely satisfactory because for a
given level of alternating stress, the amplitude distribution tends to vary with
mean stress and specimen type. This is due to the large change in stiffness of
the double pinned lug as the load passes through zero during large negative-going
amplitudes, resulting in truncation of the largest amplitudes, and it follows
that truncation of the high alternating stresses will be more pronounced for low
values of mean stress.
Fig 13 indicates that whereas there is only a very small effect of mean
stress on unbushed lugs, there is a pronounced effect on bushed lugs; this is
similar to the results under constant amplitude loadingo However, the question
of relative sensitivity of constant amplitude and NBR performance to mean stress
level is more accurately examined by studying life predictions based on load
spectra which were actually achieved, and using the appropriate constant amplitude
data.
As outlined in section 2.3, Miner's Rule was used to estimate the endurances
of the lugs. The predictions for the bushed lugs are plotted along with the
achieved performances in ~j~ 1~and 15. These results were used to plot Fig 16,
! achieved life l
which presents values of L = predicted life'~ uncer all conditions. It
will be noted that under most conditions Miner's Rule using nominal stresses was

conservative, the exception being for the case of the unpassivated bushes at the
lower mesA% stress
where~ ~. was just less than one. Similar results are plotted
in Fig 17 for unbushed lugs, which shows ~.~ varying from 1.5-4.75 for the
cases considered. Thus Miner's Rule was generally conservative for both bushed
and unbushed lugs under NBR loading.
Refe~ng to the earlier discussion of the effect of mean stress; similar
values of n were obtained at the two mean stresses and therefore as there
was a large effect of mean stress under constant amplitude loading it follows
that there is a similarly large effect under NBR loading. This contrasts with
the behaviour of unbushed lugs which exhibit only a small effect of mean stress
under both constant and variable amplitude loading 8.
Local stress measurement sequences (b) and (c) of Fig 21 were designed to
look at the local stress histories in bushed and unbushed lugs under simulated
random loading. Considering first sequence (b) which simulates NBR loading at
a mean stress of 153 (95) MN/m 2, the local stress history measurements for this
sequence are presented in Figs 29 and 30. These figures show the effect of the
largest peak stress in a fatigue test at two particular rms stress levels, on
subsequent smaller cycles in the spectrum. Thus the local stress ranges and
local mean stresses are plotted for the case before and after the largest
peak stress. The effects observed in general were not as great as for sequence
(a) described earlier, although similar basic trends can be identified as
follows:
(i) Effect on local mean stress
The peak stress in the spectra reduced the local mean stress of subsequent
smaller cycles by inducing compressive residual stresses. The reduction was
generally not as great in the bushed case as in the unbushed one. Due to this
effect alone, Miner's Rule would be expected to be conservative for both bushed
T-~
and unbushed lugs, although ~ would be slightly higher for the unbushed lug.
(it) Effect on local alternatin G stress
The peak stress had only a small effect on stress range for both bushed and
unbushed lugs, which would not be expected to affect significantly the life
prediction of either lug.
As these local stress measurements were broadly consistent with the observed
fatigue behaviour it was decided to use them to make modified predictions of the
fatigue lives. This was done by adjusting the constant amplitude S-N curve
15

16
used in the calculations, allowing for the reduction in mean stress. The method
adopted is described more fully in Appendix D. For the case of meau stress =
153 (95) MN/m 2 the method was only applied to the tests using passivated bushes,
since this is the normal practical situation. The results are summarised in
Fig 38 whloh presents values of over the alternating stress range tested.
It can be seen that the life predictions were more accurate than those in which
no allowance was made for residual stresses, although at the higher rms stress
the estimate was on the unsafe side, ~ N being 0.75.
Turning next to sequence (c), which simulated N~R loading at a mean stress
of 225 (140) ~/m 2, the results of the local stress measurements are presented
in Figs 31-33, each figure representing a random spectrum at a particular rms
alternating stress level. Thus each figure shows the effect of the peak stress
at a particular rms stress level on the local stress histories during subsequent
smaller load cycles"
(i) Effect on local mean stresses
Before the application of the peak stress~ the mean stress in the bushed
lug was slightly higher than that in the unbushed lug for the same net stress
range due to the initial interference hoop stress. It can be seen that at all
three rms stress levels the peak stress in each spectrum reduced the local mean
stress under subsequent loading in both the bushed and unbushed lugs. The
reduction was approximately the same in both cases~ and was larger for the higher
rms stress levels. Therefore, due to this effect alone, Miner's Rule would be
expected to be equally conservative for both bushed and unbushed lugs.
(ii) Effect on local alter~ stress
At all three stress levels the peak stress in the spectrum had a small
effect on local stress range during smaller cycles. The effect was minimal in
the unbushed lugs, but in the bushed lug there was a tendency for the local
stress ranges for the lower net stresses to be increased slightly. Typically
the local stress range was increased by 5-10% for the lowest two or three net
stress ranges. This would have a detrimental effect on fatigue life but this
would probably be considerably smaller in magnitude than that caused by the mean
stress reduction.
These local stress measurements were used to estimate the fatigue
endurances, making allowance for the reduction in mean stress, in a sim~
manner to that employed for the results of sequence (b). The resultant ~Nn

values are plotted in Fig 38, which shows that the estimates lay well over on the
unsafe side, varying from 0.12 %o 0.75. It should be noted that it was
assumed in the calculations~ when constructing the local mean-local alternating
stress diagram, that the bushes were passivated. Thus these predictions were
less satisfactory than those in which no allowance was made for residual
stresses, particularly because conservative estimates became unsafe.
There are several possible reasons for these poor estimates of life, which
include the following:
(a) The method employed to adjust the basic S-N data for the life estima-
tion, allowing for residual stresses, may have been in error,
particularly in the construction of the local mean-local alternating
stress diagrams where a Goodman-type straight line relationship was
assumed. However, it should be noted that the same assumption was
made for the lower mean stress results using sequence (b), and
reasonably accurate estimates resulted.
(b) At the high mean stress employed in these tests, the largest load
5 CONCLUSIONS
peaks may have effectively loosened the bush leading to an increase
in fretting damage and thus earlier crack initiation. It will be
recalled that a large prestress applied at the start of a constant
amplitude fatigue test decreased life and a similar mechanism was
postulated to explain the result. At the higher rms stresses the
peak load in the random sequence was of a similar magnitude to the
prestresses applied before the constant amplitude test. Fig 38
shows that the estimates became more unsafe for the higher levels of
rms alternating stress and thus higher peak loads, which is consis-
tent with the finding that the greater the prestress~ the greater the
reduction in constant amplitude life.
Studies of cumulative fatigue damage have been made comparing lugs with and
without interference-fit bushes by carrying out fatigue tests at tensile mean
stresses under constant amplitude and narrow band random loading conditions and
making local stress history measurements using the Companion Specimen Method.
The observed fatigue behaviour was only partly explained by the local stress
measurements. The following observations were made:
17

18
(i) Under constant amplitude loading the bush effectively reduced the
amplitude and increased the mean value of the local stress. Although
only a small effect on fatigue endurance would be expected, a large
increase in endurance was observed under all conditions tested apart
from the case of a high mean stress with a low alternating stress.
It seems possible that the reduction in fretting damage caused by
the presence of the bush was an important factor but does not
explain the single above-mentioned case.
(ii) The effect of tensile prestress on the unbushed hole was to reduce
considerably the local mean stress, and the expected increase in
endurance under constant amplitude loading was observed. When the
same prestress was applied to the bushed hole an even greater reduc-
tion in local mean stress occurred, accompanied by some increase in
the local stress amplitude; but instead of the expected increase in
endurance there was in fact a reduction. A possible explanation is
that the prestress loosened the bush which caused an increase in
fretting damage.
(iii) Under narrow band random loading the occasional peak loads maintained
a low level of mean stress by inducing compressive residual stresses
following local tensile yielding in both bushed and unbushed l~s,
whilst having virtually no effect on local stress ranges, and ~N
was generally greater than one. When allowance was made for th-@ ~
lowering of the mean stress in the bushed lugs, improved life esti-
mates were produced for fatigue tests at 153 (95) MN/m 2 mean stress,
while worse, unsafe estimates were found for a mean stress of
225 (140) MN/m 2. It is possible that the large load peaks loosened
the bush in this case in a similar manner to the effect of a
prestress noted in (ii).

Appendix A
LOCAL STRESSES IN A BUSHED LUG
A.I The effect of an interference fi 3 on local stress histor~ in a lug
In the Introduction it was stated that with the introduction of an
interference-fit bush there is a reduction in stress amplitude at the point of
crack initiation. The reason for this can be explained by imagining the bush as
a stiff spring in compression inside the hole in the lug, as shown in Fig 39.
The spring produces a tensile stress and strain in the lug material surrounding
the hole. The load transmitted by the pin is modelled by the load at point A,
which is at the top of the spring, where it contacts the lug bore. On applica-
tion of a tensile load at this point~ the material surrounding the hole will
experience a tensile strain, which will allow the spring to extend and thus
relieve some of its compression. As a consequence the tensile stress in the lug
due to the spring is decreased. Thus~ referring to Fig 40, the lug material will
experience an increase in tensile stress due to the external load and a reduction
in the tensile stress due to the spring. The net effect is that the local stress
amplitude under external loading is reduced by the presence of the interference
fit. However, the hoop stress created by the interference will cause an increase
in local mean stress, but this has usually been assumed to be of only minor
importance when compared to the reduction in stress amplitude.
A.2 The effect of a ~restress o n l oca! stress range in a bushed hole
In section 4.3 during the analysis of local stress measurements investi-
gating the effect of prestress it was observed that the local stress range in
the bushed lug was increased during subsequent constant amplitude loading. A
simple explanation of the increase in stress range after the application of a
prestress can be made by referring once again to Fig 39, where the spring
represents the bush. If a sufficiently large load is applied at point A such
that local yielding takes place, then the hole in which the spring is held will
be permanently deformed. Thus the compression in the spring will be reduced~
which means that the stress range over which the spring can help reduce local
stress is reduced, as it can only work in compression.
19

20
FATIGUE TESTING FACILITY AND LOAD SPECTRA
The tests were all carried out on a modified Schenck resonant fatigue
machine operating at 27,4 Hzo Either constant amplitude or narrow band random
loading could be applied~ control being achieved in a similar manner to that
described by Edwards10o The original out-of-balance mass exciter was replaced
by an electrohydraulic exciter in the case of the unbushed lugs, The bushed
specimens were tested at a later point in time when an electromagnetic exciter
replaced the electrohydraulic one,
The spectrum shape was measured at all stress levels used by means of a
levels-crossed counter 11o All spectrum measurements were made when the electro-
magnetic exciter was in use~ including those for the unbushed lugs~ It was
considered that the type of exciter would make no difference to the response of
the machine and hence the spectrum shape, The levels-crossed counter measured
the cumulative number of times the stress exceeded a series of amplitude levels
(exceedings)~ equally spaced over the range of the spectrum° In this report
the resttlts of these measurements are plotted in the form cumulative number of
exceedi~s on a logarithmic scale against the non-dimensional quantity
amp..litude,, Ievel
J
root mean square value of waveform °
Plotted in this way true Gaussian narrow band random loading would produce
a straight line, In practice there is a truncation of the higher levels of load
due to mechanical damping, as can be seen in Figs 41 and 42,

Appendix C
CDNULATIVEDANAGE CALCULATIONS MADE USING MINER'S RULE 12
Miner's Rule states that if a component is subjected to a variable ampli-
tude loading sequence containing stress amplitudes ~ q (q = 1,2,3 ... p),
then the fraction of the total life used up by any single stress cycle at stress
amplitude ~q is given by I/N where N is the expected number of cycles to
q q
failure of the component under stress amplitude ~ q alone.
Therefore the total fraction of the fatigue life used up by the variable
amplitude waveform is
q=p
..%
= q
where n is the number of cycles of stress amplitude
q q
variable amplitude waveform.
The rule predicts failure when
q=p n
-~ = I
N
= q
The accuracy of the rule is generally judged by computing the ratio
q~0 n
contained in the
for specimens which have been tested to failure. Since the rule predicts failure
when
)N = I~ the computed value of the ratio at failure is equal to the ratio
achi eve--£ life
'p'redict=e'd life"
When carrying out the predictions in this report the actual measured load
spectrum for the particular condition and stress level was used in all cases.
It was necessary in carrying out the predictions to use S-N curves which
extended above the stresses actually tested. This was done by extrapolating to
the static failure point.
21

22
~ETHOD OF LIFE ESTIMATION ALLOWING FOR RESIDUAL STRESSES
Section 4.2 described the construction of Figs 26 and 27 which present the
local stress histories in bushed and unbushed lugs under constant amplitude
loading. This, in combination with the relevant S-N curves enabled the local
mean-local alternating stress diagram of Fig 43 to be drawn for bushed lugs. It
was decided to construct the diagram for the case of passivated bushes, since
this is likely to be the situation met in practice. Fatigue results were avail-
able at only the low mean stress for passivated bushes but at both low and high
mean stress for non-passivated bushes. However it was found, in section 4.1 that
zt the lower mean stress passivation had little effect except at long lives where
~t reduced the fatigue strength. As the higher mean stress reduced the fatigue
strength at long lives to a very low value, see Fig 11, passivation could have
had very little further effect and thus it was assumed that the S-N curves for
both passivated and unpassivated bushes at the higher mean stress were identical.
It will be noted that a Goodman-type straight line relationship was assumed on
the mean-alternating stress diagram.
Having plotted the mean-alternating stress diagram new S-N curves could be
constructed at any new local mean stress. The local mean stresses for the random
spectra tested were obtained from the local stress measurements, see ~igs 29-33,
and new S-N curves were constructed for each random spectra case, which were used
with the appropriate spectrum measurement to calculate the fatigue life allowing
for residual stresses.

Table I
CHEMICAL COMPOSITION AND TENSILE PROPERTIES OF B S 2L6> ALUMINIUM ALLOY
mm
Chemical composition (nominal)% w/w
Tensile properties (measured)
4.4 Cu, 0.7 Mg, 0.7 Si, 0.6 Mn, balance A1
~s - 517 MN/m 2
0.1% proof - 462 MN/m 2
Elongation - 10%
23

24
CONSTANT AMPLITUDE LOADING
Table 2
FATIGUE TEST RESULTS
Mean pin bearing stress = 153 MN/m 2
(Mean net stress* = 95 NN/m 2)
Bushes unpassivated
Specimen No.
825
430
744
438
439
440
749
502
379
426
432
375
378
381
385
370
373
377
448
369
371
376
384
433
Rms pin
bearing stress
(MN/m 2 )
32.2
32.2
32.2
32.2
36.2
36.2
36.2
36.2
40.3
40.3
40.3
48.3
48.3
48.3
48.3
64.4
64.4
64 -4
64-4
80.5
8O.5
8O.5
8O.5
8O.5
J,,.
i
*Rms net
stress
(NNIm2)
20
20
20
20
22.5
22.5
22.5
22.5
25
25
25
3o
30
30
30
4o
40
40
40
5o
5o
5o
5o
5o
(UB) Unbroken
Life
( 104 cycles)
128.0
289.0
78.5
161o.o (uB)
147.0
96.0
328.0
69.1
122
63,7
58.8
38.2
123.0
82.6
67.0
21.8
26.3
21.8
24.3
7.8
19.1
11.9
7.2
7.4
* Based on net section area including bush wall
it
Loog4mean life
(10 cycles)
134
77.o
71.3
23.5
9.9

CONSTANT AMPLITUDE LOADING
Mean
Table 3
FATIGUE TEST RESULTS
pin bearing stress = 153 MN/m 2
(Mean net stress* = 95 MN/m 2)
Bushes passivated
i,,
Specimen No.
481
763
458
467
486
380
372
504
832
427
390
306
474
462
835
383
475
i
Rms pin
bearing stress
(MN/m 2)
i ii i l
16.1
24.2
24.2
24.2
32.2
32.2
32.2
48.3
48.3
48.3
64.4
64.4
64.4
64.4
80.5
8o.5
80.5
i ,
i
*R ms net
stress
(~IN/m2)
1o
15
15
15
20
20
20
3o
3O
3O
4o
40
40
40
5O
50
50
(UB) Unbroken
Life
(104 cycles)
1o2o
309.0
417.o
149.o
66.0
119.0
131.0
54- 2
38.0
49.7
15.8
24.6
23. I
10.7
7.9
7.6
6.4 i
* Based on net section area including bush wall
Log mean life
(104 cycles)
267
101.0
46.8
17.6
?.3
25

26
CONSTANT AMPLITUDE LOADING
Table 4
FATIGUE TEST RESULTS
Mean pin bearing stress = 225 MN/m 2
(Mean net stress* = 140 MN/m 2)
Bushes unpassivated
Specimen No.
746
457
743
450
653
472
838
745
499
686
451
654
489
835
75o
5o3
488
685
482
761
495
Rms pin
bearing stress
( lvJN/m 2 )
8.05
8.O5
8.05
8.O5
16.1
16.1
16.1
16.1
24 • 2
32.2
32.2
32.2
32.2
48.3
48.3
48.3 L
48.3
64.4
64.4
64.4
64.4
*Rms net
stress
(MN/m 2 )
10
10
10
10
15
20
20
20
20
3O
3O
3O
3O
4O
40
40
40
Life
(t04 cycles)
441.0
578.0
389.0
657.o
113.0
81.6
38.2
101.0
5o.I
26.7
39.1
72.8
14.8
8.6
19.8
18.1
IO.3
6.4
8.0
7.8
6.6
* Based on net section area including bush wall
i
j ,,i
Log4meau life
(IO cycles)
5o5
77. I
32.5
13.3
7.2

Table 5
FATIGUE TEST RESULTS
CONSTANT AMPLITUDE LOADING WITH A PRESTRESS
Mean pin bearing stress = 153 MN/m 2. Pin bearing prestress =
(Mean net stress* = 95 MN/m 2.) (Net prestress = 250 MN/m2.)
Bushes unpassivated
Specimen No.
478
756
505
455
Rms pin
bearing stress
(MN/m 2)
64.4
64.4
64.4
64.4
* Rms net
stress
(MN/m 2)
i
40
40
40
40
Table 6
FATIGUE TEST RESULTS
CONSTANT AMPLITUDE LOADING WITH A PRESTRESS
Life
(104 cycles)
17.7
19.7
13.6
16.4
Mean pin bearing stress = 153 MN/m 2. Pin bearing prestress =
(Mean net stress* = 95 MN/m2.) (Net prestress = 294 MN/m2.)
Bushes unpassivated
Specimen No.
468
830
754
827
Rms pin
bearing stress
(MN/m 2)
i, L
64.4
64.4
64.4
64.4
III I
* Rms net
stress
(M~/m 2)
4O
40
40
40
Life
(lO4 cycles)
10.1
11.5
10.3
9.7
* Based on net section area including bush wall
402 MN/m 2
Log mean life
(104 cycles)
16.7
474 MN/m 2
Log mean life
(104 cycles)
10.4
27

28
NARROW BAND RANDOM LOADING
Table 7
FATIGUE TEST RESULT~
Mean pin bearing stress = 153 MN/m 2
(Mean net stress* = 95 MN/m 2)
Bushes unpassivated
Specimen No.
484
454
477
Rms pin
bearing stress
(MN/m 2)
32.2
32.2
32.2
NARROW BAND RANDOM LOADING
i
. Rms net
stress
(NN/m 2 )
i , i
20
20
20
Table 8
m?IaUE ~ST R~s~S
Mean pin bearing stress = 153 MH/m 2)
(Mean net stress* = 95 MN/m 2)
Bushes passivated
Specimen No.
t i ,i
453
452
461
5OO
46o
748
Rms pin
bearing ~tress
(MN/m)
u , i q
32.2
32.2
32.2
45.9
45.9
45.9
I, ,L
*Rms net
st re s s
(MN/m 2 )
2O
2O
2O
28.5
28.5
28.5
i
Life
(lo4 cycles)
118.0
192.0
156.0
Life
(104 cycles)
258.O
189.0
156.0
165.0
I04.0
113.0
* Based on net section area including bush wall
i
i r 1 111,
Log4mean life
(10 cycles)
i i
152.0
i ii
Log mean life
(104 cycles}
i i i i
197
125

NARROW BAND RANDOM LOADING
Mean stress = 225 MN/m 2
(Mean net stress* = 140 MN/m 2)
Bushes unpassivat ed
Specimen No
i
470
485
464
463
473
490
493
494
711
491
487
466
483
826
492
459
Rms pin
bearing stress
(MN/m 2 )
16.1
16.1
16.1
16.1
32.2
32.2
32.2
32.2
48.3
48.3
48.3
48.3
64.4
64.4
64.4
64.4
Table
FATIGUE TEST RESULTS
i
*Rms net
stress
(MN/m 2)
10
10
10
10
20
20
20
20
3O
3O
3O
3O
4O
4O
40
40
(UB) Unbroken
Life
(104 cycles)
149.0
448.0
166o.o
319.o
66.2
46.2
42.5
78.2
28.4
21 -9
36.5
20.4
10.4
12.6
15-7
14.1
* Based on net section area including bush wall
Lo~mean life
(I oycles)
56.5
26. I
13.0
29

3O
No
4
6
7
8
Author
WoA.P. Fisher
W.J. Winkworth
Oo Gok~l
W.AoPo Fisher
Ho Yeomans
DoJo White
PoRo Edwards
RoJ. Ryman
CoRo Smith
J.Ho Crews Jr
H.Fo Hardrath
J.Eo Moon
PoRo Edwards
REFERENCES
Title etc
Improvement in the fatigue strength of joints by the
use of interference fits.
ARC R & M No.2874 (1952)
Estimation of endurance of light metal alloy lugs with
interference fit bushes.
RAE Library Translation 1861 (1975)
Further fatigue tests on loaded holes with interference
fit bushes.
RAE Technical Note Structures 210, ARC 19462 (1956)
The fatigue strength of large single pinned and double
pinned connections made from alloy steel FV 520B.
Io Mech. E. Applied Mechanics Group Proceedings
1968-1969, Volume 183 Part I
Studies in fretting fatigue under variable amplitude
loading conditions.
RAE Technical Report 75132, ARC 36737 (1975)
Linear strain theory and the Smith Method for
predicting fatigue life of structures for spectrum
type loading.
ARL Report 64-55, April 1964
A study of cyclic plastic stresses at a notch root.
Exp. Mechanics 23, pp 313-320 (1966)
Fatigue behaviour of pin-loaded lugs in BS 2L65
aluminium alloy.
ARC R & M No. 3834 (1977)
Cumulative fatigue damage calculations (effect of
correcting mean stress at stress concentrations).
Data sheets on fatigue No 71028.
Engineering Science Data Unit. Royal Aeronautical
Society (1971)

No
m
I0
11
12
Author
P.R. Edwards
E.M. Power
M.A. Miner
REFERENCES (Concluded)
Title T etc
A controller for random and constant amplitude loading
on resonant and electrohydraulic fatigue machines.
RAE Technical Report 72226, ARC 34525 (1973)
The analysis of random data for fatigue testing.
Paper presented at the SEE symposium "Statistical
Aspects of Fatigue Testing" held at Warwick University
12 February 1975
Cumulative damage in fatigue.
J. Applied Mechanics, Vol 12, No 3, pp AI59-A164 (1945)
31

_3
Scale 4
Nominal dimensions in mm
I I
I I
I I
I I
I I
25.4 dia
165,1
2 5/..0
Fig 1 Unbushed lug
I I
I I
I I
I I
I I
I
/.4.5
"11

3
Scale /.
Nominal dimensions in mm
This hole incidental
/
This a r ea ~ ~ ~ I ~ ~ ~ , , ~ ~,~~~
clamped
254.0
Fig 2 Bushed lug
i~
II
II
Jt
i I
itl
II
11 J!
25.4 dia
$80 stainless steel bush
-,, / t
!
~D
m
W
"TI
~o

I
t -t-
Scale 2:1
Material $80 steel
Nominal dimensions in mm
25.40 dia
28.65 dia
I
I
I
I
I
I
I
I
I
I
L
.!
v
)
Fig 3 ~nterference fit bush
\
,,.-:.
¢",1
Chamber 4 5 =
xO.6
Fig 3

Fig 4 Failed specimen
e .

?0-~
-- 60-~
E =
ol
Z ~
120
E
zl00
:E 50- 2 80
= ~0-,~
.~ 60
e- ¢_
o ~
~ 30 -~
j,_ m
f-
: 20
L_ i'~
E
~o
"~- 20
10 -<
0 - Oi
10 104 105
Endurance (cycles)
106
Bushed lug 0.27% interference
25.4 mm dia pin
Frequency = 27Hz
Stress scale is rms. Forpeak
amplitudepamUltiplYun ssivated by
. ® ~® ®
\
I t I I
107
Fig 5 Constant amplitude loading at mean stress = 153(95) MN/m 2. Bushes unpassivated
"11
i i
C11

60-
E
?0-
120 -
100 -
z
~ES0 P 80 -
U~
U~
h0- --
= ~ 60 -
.o
~ 30- "~
~ 20 c ~
< 10
- 0
20 -
-
103
Bushed lug 0.27% interference
25./, mm dia pin
Frequency = 27Hz
Stress scale is rms. For peak
amp|itude multiply by V2"
® bushes pass|vat.ed
I I I I
10/` 105 106 107
Endurance (cycles)
Fig 6 Constant amplitude loading at mean stress = 153(95) MN/m 2. Bushes passivated
"11
01

70-
E
120 -
~100 -
~-" 60 - ~
E
Z m
~ 50 - N 80-
~ E
. - -
E
" 60 -
Q..
E 30 - ul
a,.
o~ E 40 -
e-
20 -: . ~
E .,..
.,., C
~ 20 -
10 ~
0 0
10 3
I ! I
104 105 106
Endurance (cycles)
°
Bushed lug 0.27% interference
25.4mm dia pin
Frequency -- 27Hz
Stress scale is rms. For peak
amplitude multiply by
bushes unpassivated
Fig 7 Constant amplitude loading at mean stress = 225(140) MN/m 2. Bushes unpassivated
I
10 ~r
"11
mo
¢Q

?0-
120 -
~EIOC -
60 - z
50 - ~ 8C -
ffl
~ ~0 - .E
e- e-
~ 30 - "~.
E m
60 -
=" E Z.0 -
03
¢-
=--
~20 - o-
c-- o - -
+~ r-
-~ < ~ 20 -
0- 0
103
Bushed lug 0.2'/% interference
25.l, rnm dia pin
Frequency = 2? Hz
® Bushes passivated ~ ~
+ Bushes unpassivated
I 1 I I
10/' 105 106 107
Endurance (cycles)
Fig 8 Narrow band random loading at mean stress = 153(95) MN/m 2
®
'11
n ,
cO
00

A
E
?0-
6O
Z
:E 50
--Z
w
E
u~
ul
t~3
t/1 C:7
-~ 40 ,.
Q;
r- ¢..
~ 30 -'~
E i-- m
E
1-
=50 -
~ N
.1_, e-
4 ~
_
120 -
00-
80-
60-
/.0-
20-
0
103
Bushed lug 0.24%
25.4 mm dia pin
Frequency = 2?Hz
Bushes unpassivated
interference
I I I ,,]
104 105 106 107
Endurance (cycles)
Fig 9 Narrow band random loading at mean stress -- 225(140) MN/m 2. Bushes unpassivated
®
"11
l ,
¢.O

1%1
70-
A
120 -
6O - ~ tO0
7
:~ 50 ~ 80
in
in ; 60
c- t--
in 30 "K
E
~0
e-
e--
ilJ
20 -
~ 2O
10-
w
Bushed lug 0.2/,% interference
25./, mm dia pin
Frequency = 27Hz
Stress scale is rms. For peak
amptitude mu[tiply by v~"
unpassivated
O- 0
I I I I
103 10/. 105
Log mean endurance (cycles)
106
10 7
Fig 10 Effect of passivating bushes on constant amplitude performance at
mean stress = 153(95) MN/m2
/
"11
I o
O

E
Z
I J1
L..
e-
E
L.-
.m
e'-
m
(--
70-
E
120
60 - ~z10( -
U3
¢$1
50 - ~ BC -
40 -~
f..
¢-
30 ~
20 - ~
c
6c -
m
~/.0 -
~20 -
10 -=
0 0
10 a
Bushed lug 0.27%
Unbushed mean stress = 155(96)MN/m 2 interference
~ B u 25.4mm dia pin
Frequency = 2?Hz
Stress scale is rms.
2 For peak amplitude
shed mean stress = 225 (140) MN/m muttipiy by~
%
mean stress =153(95} MN/m 2
I I I I
104 105 106 107
Log mean endurance (cyctes)
Fig 11 Comparison of the performance of bushed and unbushed lugs under
constant amplitude loading
"11
m,

70-
120
60 - 100
E ~
m
Z ~
x 50 - ~ 80 -
U3
i1~ r-
N~0-~
¢" r
,n 30-
. 6o -
e~
E m
E 40 -
t"-
~ 20_ o~
~ r--
~- 20 -

?0
6O
E
z 50
U3
u3
E
t..
I-
40
30
N 30
e-
<
10
120 -
EEI00
ETJ
.o
e-
r"
<
80
60
40 -
20 -
0 103
Unbushed mean stress =277 (172) MN/m 2
Bushed lug 0.27%
25./, mm dia pin
Frequency = 2? Hz
interference
\\ Bushed mean stress=225(140)NN/m 2
"~,f~Bushed 2 " mean stress =153 (95) MN/m
Unbushed mean stress=155196)MN/m 2 ~ _ _ ~
I I
10 ~ 105
Endurance (cyctes)
Fig 13 Comparison of the effect of mean stress on bushed and unbushed lugs under NBR loading
I I
106 10 ?
"11
¢Q

E
?O-A
120 -
E
~I00 -
60-:E
Z m
~. 50 - ~ 80 -
Lq
~'P O3
t..
c"
&..
40- .3
~ 60-
t-
~.
E30- ul
c. E
_= " 40
-=-' ¢~
m , ~ 20 =
(.-
=20
10 -<
O- 0
103
Bushes passivated
10 ~
Log
Bushed lug 0.27%
25.4 mm dia pin
Frequency = 2?Hz
/--..
Miner's rule predition""
I I
105 106
mean endurance (cycles)
Achieved /
Fig 14 Accuracy of Miner's rule for NBR loading at mean stress = 153(95) MN/m 2
interference
performance
I
I0 ~
"1"1
m,
4==

E
Z
I[
¢-
(Jl
E
L_
.E
e-
70
120 -
04
EIO0
GO - "--
2
50 - ~80
,.=..
E~
40 - .E
6o-
G:
30 - ~-
20 - r-
.m
U1
E ~.oI
L.
n~
10 ~..$ 20
0 0 10 3
Miner s
Bushed lug 0.27%
25.4mm dia pin
Frequency = 27Hz
~ Achieved performance
I I I
10 ~ 1 05 106
Log mean endurance (cycles)
Fig 15 Accuracy of Miner's rule for NBR loading at mean stress = 225(140) MN/m 2
interference
I
10 ?
=11
i°
¢¢2
O1

(~
E
Z
~E
i...
Is)
6+1
E
En
C
.w
n~
¢-
t..
<
30
20
10
('M
E
ul
ul
~a
L.
E~
C
o~
qa
JE~
i-
o~
trl
E
i._
r-
r--
50
40
30
20
10 -
0 0
m
Mean
Mean
I
stress=225 (140) MN/m 2
bushes unpassivatedx / J ~ ' -
I ~ + J Mean stress=153 (95)MN/m 2
Jl *
stress=153 (951 MN/m 2
bushes unpassivated
I
I
I t I I
1 2 n 3 4
zW
n
Fig 16 Z Ki values for lugs with interference fit bushes at two mean
stresses under NBR loading
"11
mo
O1

E
Z
30 - E
Z
:E
ul
Ltl
,ol
(,'1
=20-5
~. rt
Ul
._ 10-c.
C ,*-,
O-
60-
50-
Z.0 -
30 -
20 -
10-
0
i
Mean
Fig 17
I
I
I
I
stress = 155
!
I
(96) MN/m 2
Mean stress - 277 (172)
I I I ,I
2 n 3 /. 5
n
2; ~ values for unbushed lugs at two mean stresses under NBR loading
MN/m 2
"11
n .
tQ

Material: BSZL65
Nominal dimensions in mm
Hole
Hole
I i i
1
i
!
' I
!
!
1 !
I
i i i
25-40 d~a ~5train gauges-~
A- to accommodate bush
B-for clearance fit pin
165-I 44 "5
254-0
Fig 18 Lug used in companion specimen testing
;
//--28-58 dia

Bush is split olong-~
this line so that
each half can be
inserted into the
lug from opposite
sides
Scale: 2:1
Material: SBO steel
t
Nominal dimensions in mm
25.40
28-65
Fig 19 Interference fit bush
6.4 dia window
for strain gouge
t
¢%1
Chamfe r 450
x 0.6
Bush to be inserted
into hole A in Figl8
Fig 19

i
Scale: 314
M~terial: BS 2L65
Nominal dimensions in mffl
For use vith specimen in Fig18
i I
S
D
3 i.7 rQd
Fig 20 Plain specimen
Strain gauges
L
139-7
114 "3
82"6
;l
=11
mo
¢Q

2values of prestress applied in constant amplitude
%
z t, O0
/ . / ~ ~ _ A47l*(29/~) MN/mz
== 300
200
1oo
o ~
n 0
Sequence progression
Peaks applied in random fatigue tests at
,oo
~6(28.5)MN/m 2 rms respectively
300
200
100
m
32(20) and
fatigue tests
Peaks applied inrandom fatigue tests at 16(10), 32(20) and
/~8 ( 3 0 ~ ~ e c t ively
Fig 21a-c Sequences applied to lugs in Companion Specimen tests
Fig 21 a- c
a
c

Fig 22
E
z
C
°~
.0
C
,w
~L.
500
z, O0
300
200
100
0 5000 10000 15000
Local strain (pc)
Fig 22 Pin bearing stress vs local strain diagram for lug with interference fit bush.
Sequence (a)

500 -
400
300
ZOO
!00
0
- I00 I
- ZOO L
/ 7f I0 000
Local strain (p¢~)
Fig 23 Companion plain specimen reproduction of local stress and local strain in a lug
with an interference fit bush. Sequence (a)
r
"11
~ °
¢=0

+
Fig 24
E
Z
~E
e.-
°--
CL
500
1,00
300
200
100
I
0 5000 10000
Local strain (IJ.¢)
I I I I I
15000
Fig 24 Pin bearing stress vs local strain diagram for lug with clearance fit pin.
Sequence (a)

N
E
z
I/I
f~
¢1
0
..I
500 r-
400
300
200
i00
-I00
0
-200
l I I I
5000
'Local strain OJ¢)
Fig 25 Companion plain specimen reproduction of local stress and local
strain in a lug with a clearance fit pin. Sequence (a)
I
!0 000
=11
mo
01

Fig 26
E
500
i, O0
300
Z
x 200
U~
I,,,,,
U
o
--J
100
-1001-
-200 L
ol J m
20 ~0 60 80
rms pin bearing stress (MN/m 2
0
Bushed
Unbushed
I I
100 II 120 I/.0 160
Fig 26 Comparison of Iocai'stress excursions in a bushed and an unbushed lug under
constant amplitude loading at mean stress = 153(95) MN/m2

¢W
E
500
z,00
300
z 200
I/1
I/I
w
(J
o
..-I
100
0
-100
-200
I
2O
D
Bushed
Unbushed
f
I I I I~,
0 60 80 100
rms pin bearing stress (MN/m 2
Fig 27 Comparison of local stress excursions in a bushed and an unbushed lug under
constant amplitude loading at mean stress = 225(140) MN/m2
120
Fig 27
I
160

700[ Bushed Unbushed Bushed Unbushed
300
600 / ~
!
constant amplitude
load ing at
~E S00]-- ~E rms stress = 64.4 (40) HN/m z
~: /
-~
="
Heart stress = 153 (95) HN/m z
4001- ~ 200
x x---.---x E
,oo[ 1
OI I I i I I I I I I J J
0 403 483 0 403 483 0 403 483 0 403 483
(?SO) (300) (ZSO) (300) (2SO) (300) (ZSO) (300)
Prestress NN/m 2 Prestress HN/m z
Fig 28 Effect of prestress on local stress histories during constant amplitude loading
"11
0O

E
700
600
500
z
x 400
c
c~
L-
300
-- 200
o
O
..J
!00
0
- Bushed
P
o ®
- E?_~ c
_ b
o ®
1
Before
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I x
I
I
I
I
i
I
1 I I
After Before
Before or after
peak in sequence
Unbushed
P
X X
x d x
O
X X
b
G
X
X
1
After
E
L.
e.-
o
E
o
u
o
400 -
30O
200
100
0
Bushed Unbushed
X
X
c b
X ×
P
I I I I
Before AFter Before After
Before or after
peak in sequence
Fig 29 Effect of peak stress on local stress histories during subsequent
smaller net stress cycles
Simulated NBR loading
at:
rms stress =32.2 (20) MN/m z
Mean stress = 153 (95) HN/m 2
Xn/N bushed=l.8
Pin bearing stress
121 -- 185 a
89- 217 b
56 - 250 c
24-- 282 d
ii - 295 p
( peak )
range
"n
w,
¢0

(%1
E
Z
¢I
£,.
¢,.
m
o
¢.}
o
-J
700 -
600 -
500 -
400 -
300
200
I00
0
P
C> C)
a
Bushed
I 1
Before After
Before
peak in
P
X X
e
x ~ X
X ~
x ~
d .-....x
b ~x
×
×
E
Z
~r
f,,#=l
l,=.
e-
E
u
o
,.=i
400 -
300 -
200
I00-
m
X
x- T-
Unbushed Bushed Unbushed
I I I I 1 I
Before After Before After Before After
or after Before or after
sequence peak in sequence
Fig 30 Effect of peak stress on local stress histories during subsequent
smaller net stress cycles
Simulated NBR loading
at:
rms stress =45.9(28.5)MN/m 2
Mean stress = 153 (95) MN/m z
~E a/N bushed = 3.6
Hn bearing
MN/m z
121-185 a
8g--217 b
56- 250 c
24 -- 282 d
0-314 e
O-- 355 p
( pea k ]
stress range
"11
m,
gO
C~

E
z
IE
_ 200-
¢-
[..
¢¢1
{--
o
o
_J
700 --
600 -
500 -
400 -
300 -
I00 -
0
Bushed Unbushed
P
Q Q
cp._ a..__..Q
I I I
Before After Before
Before or after
peak in sequence
X
X
x
P
b
a
X
--X
, X
z
E
u~
400
300
t--
" 200
c-
a
E
o
-J
I00
Bushed Unbushed
,J I I I I
After Before After Before After
Before or after
peak in sequence
Fig 31 Effect of peak stress on local stress histories during subsequent
smaller net stress ranges
Simulated N B R loading
at:
rms stress =16.1 (10) MN/m z
Mean stress=Z25.4 (140) MN/m z
]rn/M bushed = 3.2
Pin bearing stress range
HN/m z
193- 258 a
161 -290 b
14 - 309 p
( peak }
"11
~o
(A1

E
z
c
o
L.
o
..,I
700
600
500
400
300
200 -- b_._ E)
_ IOC
i
P
Q 0
-- C
E> 0
Bushed
0 t !
Before After
Before
peak
P
X ~ X
C
X X
b --.---,X
X....~--~
a
X.-~-----.._. x
E
O
..J
400
300
200
IOC
b a
Unbushed > Bushed Unbushed
I I 0 < I I I I
Before After Before After Before After
or after Before or after
in sequence peak in sequence
Fig 32 Effect of peak stress on local stress histories during subsequent
smaller net stress cycles
C
X
'i~ a Simulated N BR loading
at:
rms stress=32.2 (20) MNlm z
Mean stress=225.4 (140)HN/m 2
~n/N bushed = 2.2
d
Pin bearinq stress range
MN/m z
193-258 a
16| =290 b
129- 322 c
97 -354 d
74 - 377 p
(peak)
"11

E
700-
600 -
500-
Z
z400 -
(P
e,-
0
L
300 -
- - 2(i)0
o
o
I00
Q
P
f IQ
e
b...~
Cp__a----¢
Bushed
P
X X
x_.-L--x
x_~e x
C
X X
I I I I
Before After Before After
Before or after
peak in sequence
Unbushed
E
Z
x
L
c
o
¢B
E
m
¢.1
o
.J
400
300
200
I00
Bushed
! I I !
I
~efore After Before After
Before
peak in
I
I
!
I
!
!
X
I
!
i
i
I
I
I
I
!
I
i
I
i *
I
I
I
I
I Unbushed
or after
sequence
Fig 33 Effect of peak stress on local stress histories during subsequent
smaller net stress cycles
Simulated NBR loading
at:
rms stress=48.3 (30)MN/m z
Hean stress=225.4 (140)HN/m z
Zn/N bushed = 2.25
Pin bearing
MN/m 2
193-258 a
161 - 290 b
129 - 322 c
97 - 354 d
64 - 386 e
32 - 419 f
20 -- 431 p
(peak)
stress range
"!1
mo
¢Q

E
Z
~E
120 -
100 -
~n 80
el
Oa
u';
.c_ 60
t--
n
¢-
o-/* 0
el
E
L..
20
f/
0 40
..~3
////
x~ ?xl 4
X ~ X
3x106 x
5x 106
~ X
~ x
~ x
"=-="=='=--=-x
I I I I I I I
80 120 160 200 2/.0 280 320
Mean stress (MN/m 2)
Fig 34 Alternating-mean stress diagram for unbushed lugs
X
X
Constant life lines
=11
4~

Z
E
ol
¢-
r~
L.
ul
I/I
U
o
.J
600-
500
400
300
200
100
Constant life [ines
I I I
100 200 300
Locat mean stress (MN/m 2)
x
x S./,/o~
3 x 10 s
x ~ ~ . _ x
x-- 1.6 x 106 --X
Fig 35 Local mean-local alternating stress diagram for unbushed lugs
Fig 35
I
,~00

70
6O
E
z 50
~E
Ul
I/1
E
30
C
"~ 20
fll
e-
10
0
- Z
IN
120
I/1
I/1
-~80-
m
I/1
O!
t--
5-.
.JO
60 -
I/1
E ~0 -
o ~
c-
¢::
~,20-
- 0
103
Unbushed achieved
\
Bushed predicted performance from local stress measurements
performance ~ , ~ . ~ - achieved per formance
I I I J
104 105 106 10 ?
Log mean endurance (cycles)
Fig 36 Estimation of endurance of bushed lugs using local stress
history measurements. Mean stress = 153(95) MN/m2
"il
m o

A
I/I
70
60
50
40
f..
u~ 30
E
¢...
o - -
~ 20
C
m
10 -
120
C~
w-
°m
,bJ
t~
e-
+.~ 20 -
0- 0 103
- \
~ X Bushed predicted
- J
_ \
_/_,,
Unbushed estimated achieved per ormance~ ,,
- from fatigue test results ~ ~
perform ante
Bushed
J
from local stress measurements
achieved performance
I I I I
10 ~ 105 106 10 ?
Log mean endurance (cycles)
Fig 37 Estimation of endurance of bushed lugs using local stress
history measurements. Mean stress = 225(140) MN/m2
_-q.
¢Q
¢0

Fig 38
N
E
Z
i/1
ul
P

A
Tensile stre ss-~ ~ _ ~
spring
Lug
-Spring
inside
Fig 39 Simulation of bush by a spring in compression
in compression
hole
Fig 39

m
u
o
.,.I
Sin1
StuB
0
Local stress due to external toad
÷
Local stress due to
bush
Time
Time T
m
m
Sm 2
Fig 40 Effect of bush on local stress history in a lug
0
Local stress in interference fit lug
Sm 2=Sml+Sm B (Mean stress)
Saz=Sat-SaB (Alternating
Time T
stress)
v
=11
m o
4==
O

IJ.
141
.E
u
x
0
, m
0 ~
m
o
a~
IO_ 0 0
-~
10 -1
10 .2
I 0 "3
1 0 -4
lO-5
io-6
45.9
\
10
(F/o rms) 2
/
(28.5) MN/m 2
32.2
/
(20)
/
/
20
MN/m 2
Fig 41 Measured load spectra at mean stress = 153(95) MN/m 2 at various rms
alternating stress levels
Fig41

Fig 42
U.
LU
e-
~P
X
O
.D
nl
.O
O
Q.
( F/o rms) 2
0 10 20
10 -0 ~ ~ ]
10-1
1 0 -2
10 -3
10 -t,
10-5
10-6
48.3 (30) MN/m 2
32 2 (20) MN/m 2
16.1 (10) MN/m 2
Fig 42 Measured load spectra at mean stress = 225(140) MN/m 2 at various rms
alternating stress levels

E
800
700
600
Z
~E 500
c-
m
ul
~00
- 300
r~
(D
....I
200
100
0
I
100
Constant life lines
I I I
200 300 400
Local mean stress MN/m 2
Bushes passivated
Locus of results at mean stress =153 (95) MN/m 2
Locus of results at mean stress = 225 (1/~0)MN/m 2
I I
5OO 600
Fig 43 Local mean-local alternating stress diagram for bushed lugs "I1
m °
4~

© Crown copyright 1979
First published 1979
HER MA3ESTY'S STATIONERY OFFICE
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Government Publications are also available
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R &M No.3835
ISBN Of] 471168 2