significance of rivet flexibility for load transfer in lap joints

63

��

� �� !�"#��"$#" %#"$�"&��'��#�()�*�+"#, %(#��# "� �"& �!"��$�)-%�.�/)0��"&12(.�%�3�4�$!� &��3�

��

��5$�%6��-��+0��) �2�(6��7��8

�)�"&%6 9-��+0��)�&�2-��:��

�

�*�� ;�:�� <�� 0 =��

��

�� !�� "�� "� �� "�� "�� #�� !�� #�� $�� %�� "�� #�&� �� !�� #�� $ � "�� "�� "�'� �� "�� "�� (�� "� �� "�� $ � �� "��

��)� �� '� �� '� �#�&� ��'� �� '� ��

*+�,*-+$-� �./�!+.0,$� +$!12� 2� !��+�3-�*-� .4,$56-+$�� 2� �.75,*-+$�,8� *�97�/9.2�,8

�&�� "�� "��:�� ;"� �� <�� ;"� ��&� �� =>�� &&� ��&�&�;�� &?�� ;"� "� &�(:@��:�"�� @=�&�� "�� :�� :�� &�� 4�� &� � �� /AB,&�!2� @=�&�� &��&?�� ;"� &�:�"�� &� �"�� ;>�� @�� "��&�� &�� @�� &�� =>�� (�� <�� ;"� ��&"��@�� ;"�� :<�� >� �&��<�� ;>�� :� ��'� "� �� ";�� (�� &�� &��"�� &&� �� ;" � 9��&�� :<�� <�� ;"� ��"� ��@��&��@��=�� "� ��&�&�;�� &:�� &�&�� @=�&�� "�&��&�� &�� >�� ;"� ��(�"�� *�� "�@�"� ��@�� &�:�"�� =>�� &&� ��&�&�;�� &?�� ;"� ��&� �� <C�� ;"� �� ;>�� "�@�<�� &�?�&��"�� @=�&�� "��&�� &=� �� <C� �� ;""� <��:�"�� &?�&�� @=�&�� "� ��;"�� &� &?�� :�� ,��>� "� �� :�� &?�� <�� ;"� ��@�� :�� '� �� =>�� &&� :�>�� &� �� @� �� 2��:�� =�'� >� &"�:�� "�� (�� &��"� �&��>��=�� =>�� :�� <�� ;"� ��"��&�C� ��=� �� &��@�&�("�� "��:;"

�� )� �� "�� @=�&�� &�:@��:�"'� &�?�&�� @�'� ��@�� &�:�"��'� �� =>��'� � ��

��

The knowledge of the stress distribution within a rivetedjoint is a fundamental step in estimating its fatigue life anddamage tolerance characteristics. In order to approach theproblem of stress conditions at the rivet holes the distribu-tion of loads acting in the joint must be known. The role ofa rivet is to transfer the load from one sheet to the othersheet in the overlap region. For a configuration with morethan one row of the rivets the applied force P is split at thefirst row into the bypass load (TBP) which remains in thesheet and the transfer load (TTR) transmitted to the othersheet, as schematically shown in Figure 1. The TTR-load is

comprised of the bearing force (TBR) resulting from thebearing pressure exerted by the rivet shank on the hole sur-face and the friction force (TFR) induced by friction betweenthe mating sheets. Friction is localized mainly beneath therivet heads where the maximum clamping occurs.

As shown in Figure 2 for an overlap of two sheets withthree rivet rows, the internal axial forces in the sheets can becomputed by considering the displacement compatibilitybetween the sheets and rivets, Eq. (1), and the equilibriumcondition for each transverse section of the overlap, Eq. (2).The elongations of the sheets (Δ) and the rivet deflectionsbetween the sheets (δ) can be expressed in terms of the in-ternal axial forces in the sheets (T) through Eq. (3) and (4).

64

��5$�%6�� -��+0�) �2�(6 ��7��8) �"&%6 9 -��+0�) �&�2 -��:��

�*�� ;�:�� < �� 0 =��

� ��! 2 ��!% %#, �%�/��39�#"��%�! ��23��#�"��>#��%� (#"�! (! �(

� ��>#��%� (#"(! �(��/�?�� %��39�#"�

In Eq. 3, (EA)j is the longitudinal rigidity of sheet j while fiin Eq. (4) is the parameter representing the flexibility ofrivets in row „i”. The interest in fastener flexibility mea-surements has been caused by the desire to calculate theload transfer distribution in joints with multiple fastenerrows using the above procedure. The literature evidence in-dicates that the rivet flexibility depends on the sheet andrivet material, the joint geometry and can be affected by theriveting process, e.g. (Morris 2004, Jarfall 1986).

1, 1 2, ;i i i i i il l++ Δ + δ = + Δ + δ i = 1, 2, 3; j = 1, 2 (1)

1, 2,i iT T P+ = with T1,0 = T2,3= P and T2,0 = T1,3 = 0 (2)

,, ( )

j i ij i

j

T l

EAΔ = (3)

( )1, 1 1,i i i iT T f−δ = − (4)

Presented in this paper are measurement results on therivet flexibility and load transmission for a simple lap jointof two sheets of equal thickness representative for theaircraft fuselage. An attempt has been made to account forthe effect of sheet bending on the measurement data. Varia-tions of the rivet flexibility during the fatigue loading aswell as the dependence of the rivet flexibility and loadtransmission on the rivet squeeze force have been investi-

gated. Because literature data on the rivet flexibility showa very large spread, as evidenced by comparisons betweenempirical formulas on rivet flexibility produced in (Morris2004, Jarfall 1986), several methods of rivet flexibilitymeasurements have been applied and evaluated in thepresent investigation, including the novel optical tech-niques proposed in this paper. The axial forces in the sheetsobserved in the experiments have been compared with thosecomputed according to the procedure given in Figure 2.

��

The rivet flexibility and load transfer were measured duringconstant amplitude fatigue loading (Smin=12 MPa,Smax=120 MPa) on riveted lap joint specimens assembledfrom two D16 Alclad 2 mm thick sheets using 5 mm diaround head AD rivets. For each of two specimens tested, therivets were squeezed with a different force to obtain theD/Do ratio of 1.3 and 1.5, where D and Do is the diameter ofthe rivet driven head and rivet shank respectively. The over-lap configuration and the location of the extensometer andthe strain gauges are shown in Figures 3a and b.

Besides the riveted specimens a monolithic specimen ofthe same Al alloy and dimensions shown in Figure 3c wasalso used in some methods of the rivet flexibility measure-ments, as detailed in the next section.

65

��

� ��3 �#2 "(��%%#, �� >#'#�#��"&��&�%�"(� %2 �(�% 2 "�(@�A%#, � &(3 �#2 "1

'A >� "(�2 � %�"&(�%�#"$��$ ��#�"(1�A&�22�(3 �#2 "

�A 'A �A

��

The rivet flexibility measurements should ensure as far aspossible that the measured results are not influenced by thesheet bending because this effect is not accounted for in thecomputation of the rivet flexibility from the measurementdata (cf. Fig. 2). The specimen extension between theclamping edges and then the average rivet flexibility valuefor the joint can be derived from records of the machinedisplacement gauge (LVDT transducer), Figure 4a, provi-ded that the component resulting from the compliance ofmachine elements is subtracted from the measured displace-ment value (Δl). The middle rivet rows may show a diffe-rent deflection response than the fatigue critical end rowsbecause the middle rows undergo much more uniform bear-ing pressure than the end rows where the maximum momentdue to sheet bending occurs. In order to measure the flexi-bility for the end rivet rows the extensometer can be posi-tioned as shown in Figure 3b. At that short gauge length,however, the sheet curvature due to the bending should beaccounted for because the difference between the displace-ments measured at the outer surface and those occurring atthe faying surface can be of the same order of magnitude asthe rivet deflection. Figs 4b and c show the principle ofoptical measurements of the rivet flexibility, not affected bysecondary bending, proposed by the present authors. Thetechnique further referred to as the edge method (Fig. 4b),enables to determine the deflection of a rivet in the end rowfrom the measured relative displacement between the mat-ing sheets at the overlap edge: Δy = ymax – ymin, where thedistances ymax and ymin correspond to the Smax and Smin

stress of the fatigue cycle. Because Δy is in the order of10–2 mm, a high accuracy measurement system is required.

The method presented in Figure 4c is applicable to rivets inboth the outer and the inner rows. The effect of sheet bendingis compensated by using a piece of wire bonded to the sheetsurface near the rivet head. The rivet deflection is deter-mined from the measurements of the rivet head displace-ment on both sides of the overlap, Δy1 and Δy2, and thedisplacement of the tip of the bonded piece of wire, Δy3, as

2 1 32 ,y y yδ = Δ − Δ − Δ with max min( ) ( ).i i iy y S y SΔ = −All above mentioned techniques have been applied in

the present experiments. As shown in Figure 3a, the exten-someter was mounted at locations EXT-1 and EXT-2 inorder to measure the end row rivet flexibility along the rivetcolumn and midway between the columns. Both these loca-tions were also considered when the optical edge method(Fig. 4b), was used.

As said above, with the technique utilizing the protrud-ing wire element the rivet deflection can be directly derived.When other techniques were used two approaches wereapplied in an attempt to extract the rivet deflection from themeasured data. One of these referred to as the analyticalcompensation involved subtracting from the measuredextension appropriate sheet elongations computed from theHook law (cf. Eq.(c), Fig. 2). In the case of the LVDT trans-ducer records this analytical compensation can only elimi-nate the sheet extension between the specimen clampingedges but it is not capable of eliminating the deformation ofthe machine components included in the measured Δl data.With the other approach referred to as the experimentalcompensation and applicable only in the case of the exten-someter measurements and the LVDT transducer recordsextensions measured for the monolithic dummy specimenshown in Figure 3c were subtracted from those acquired forthe riveted specimens. It was believed that this concept

66

��5$�%6�� -��+0�) �2�(6 ��7��8) �"&%6 9 -��+0�) �&�2 -��:��

�*�� ;�:�� < �� 0 =��

should enable to eliminate also the contribution of themachine elements compliance included in the LVDT trans-ducer records.

The axial forces in the sheets needed to compute thesheet elongations and the rivet flexibility using Eqs. (c) and(d) respectively (cf. Fig. 2) were determined from straingauge measurements, as detailed in the next section.

The results on both the rivet flexibility (except for theoptical techniques) and the axial loads were derived fromaveraged measurement data on strains, extensions or dis-placements recorded during three consecutive load cycles.The data acquisition was repeatedly performed at some cy-cle intervals throughout the fatigue tests.

Comparisons between some results on the rivet flexibil-ity derived for the D/Do = 1.3 specimen are presented inFigure 5. For clarity, only the data captured along a singlerivet column are shown in the case of the extensometermeasurements and the edge method. Slightly higher f-va-lues midway between the columns compared to those alongthe columns were only detected using the edge method andsolely for the D/Do = 1.3 specimen. The measurements indi-cated a good repeatability of results obtained for variousrivets in a given row and symmetry of the flexibility valuesfor both end rows. It can be seen in Figure 5 that the opticalmethods and the extensometer measurements coupled

with the analytical compensation yield similar results forthe rivets in the end rows. Altogether, the measurement datafor both the D/Do = 1.3 and D/Do = 1.5 specimen have indi-cated that the scatter of the f-values measured using the con-sidered three methods for the rivets in the end rows is within±10%. Behind the differences between the results fromthese three techniques can be simplifications involved incomputing the sheet extension, like neglecting the stressconcentration and, in the case of the extensometer measure-ments, ignoring the sheet curvature due to the bending.Note also that the accuracy of the optical measurementsetup used in this investigation (±2 μm) equals several percent of the measured deflection values. Especially in thecase of the method employing the bonded wire elementwhich involves measurements of three small quantitiesa somewhat higher resolution of the optical system wouldbe desired. Only the latter method enables to measure f forthe middle row. The corresponding data reveal a lowerflexibility parameter of rivets in that row compared to theflexibility measured for the outer rows, as evidenced in Fi-gure 5 by the results for rivet no. 4 consistently lower thanthose for rivets no. 1 and 7.

The effect of the fatigue loading on the flexibility beha-viour was found to depend on the squeeze force level. In thecase of the D/Do = 1.3 specimen an insignificant decrease of

� ��%#��(2 �!�&(��%%#, �� >#'#�#��2 �(�% 2 "�(@�A�� %�"(&�� %% ��%&(1

'A &$ 2 �!�&1�A3%��%�&#"$/#% 2 �!�&

�A 'A

�A

67

��

� ��> 23��%�% (��(�"%#, �� >#'#�#��%�2( , %��2 �(�% 2 "�� !"#B� (

�� !��

� �(�% &%#, �� >#'#�#�# (�"&��23�� &��&�%�"(� %%��#�(��%�� %�"&2#&&� %#, �%�/

D/Do outerf (mm/MN) middlef (mm/MN) ,TR outT P ,TR midT P

1.3 26.7 16.4 0.293 0.414

1.5 18.1 12.8 0.314 0.327

the flexibility during the fatigue loading was observed onlyfor rivets in the middle row. For the D/Do = 1.5 specimena moderate decrease in f occurred also for the outer rows.After 100 kcycles the rivet flexibility for the latter specimenbecame reduced by 20%. A decrease in the joint flexibilityduring both constant amplitude and variable amplitude fa-tigue loading has also been reported by Jarfall (1986). Thisbehaviour can be understood if it is recalled that the rivetdeflection is controlled by the bearing force rather than bythe total transfer force. Load transfer measurements demon-strate that whilst the load transfer ratio (TTR/P) remainsessentially invariable during the fatigue loading, the frictioncontribution (TFR) can significantly increase with the num-ber of cycles causing the bearing component to decrease(Jarfall 1986, Terada 1985).

Whilst the extensometer measurements and both opticalmethods provide the flexibility for a specific rivet, the re-sults derived from the LVDT transducer records representthe average rivet flexibility of the joint. Figure 5 demon-strates that compared to other measurement techniques thelatter method coupled with the analytical compensationwhich does not cover the deformation of the machine partsyields an over threefold overestimate of the rivet flexibility.Thus the present results offer the explanation for the overlyhigh f-values according to the Morris (2004) formula basedon the same measurement technique. On the other hand,the data in Figure 5 imply that the experimental compensa-tion leads to an underestimate of the flexibility because theaverage results on f obtained from the LVDT transducerdata and, especially, the extensometer measurement resultsfor the outer rows are even below the flexibilities measured

for the middle row. Evidently the deformation of the dum-my specimen cannot properly represent the deformation ofthe sheets in the riveted specimen. Altogether the presentwork suggests that due to difficulties with allowing for thecompliance of the machine parts reliable f-values cannot bederived from the LVDT transducer records.

In Table 1 the measured rivet flexibility parameters aver-aged over the initial 75 000 load cycles for either specimenand the corresponding load transfer ratios computed for themeasured f-values according to the procedure from Figure 2are given. It is seen that due to the lower difference betweenthe flexibility for the outer and middle rivet row in the caseof the D/Do = 1.5 specimen the computed load transmissionthrough the joint is for that specimen more levelled of thanfor the D/Do = 1.3 specimen. The computed TTR/P ratiohigher for the middle row than for outer rows is reflective ofthe lower f-value for the middle row. These results cannotbe, however, considered reliable because the sheet bendingwhich contributes to the differences between the rivet flexi-bility for the outer and inner row is neglected in the loadtransfer computations.

��

��"��"��

In order to measure the axial loads in the sheets the rivetedspecimens were instrumented with twelve 2 mm base lengthstrain gauges A1, A2 to F1, F2, Figures 3a and b. For jointswith eccentricities, like the lap joints, the measured axialstresses indicate a combined effect of the axial loads andbending moments. The stresses contributed by the axial

68

��5$�%6�� -��+0�) �2�(6 ��7��8) �"&%6 9 -��+0�) �&�2 -��:��

�*�� ;�:�� < �� 0 =��

� ��#�� %�"(� %��&2 �(�% 2 "�% (��(@�A(�! 2��#6��#�"��! (�% ((&#(�%#'��#�"(#"�! �%�"(, %( ( ��#�"(

' �/ "�! %#, �%�/(1'A��&�%�"(� %%��#�(��%�! ��39�#"�

forces were obtained as the average of the stresses mea-sured by the gauges bonded at the same location at the outerand faying surface of the sheet adjacent to the manufacturedrivet heads, as shown for gauges A1 and A2 in Figure 3b.It is seen that bonding the gauges at the faying surfacerequired that a 0.3 mm deep recess for each gauge had to bemachined in the mating sheet. Also, about 0.3 mm deep slotswere milled in that sheet to lead out the gauge wiring. Ineither of the two transverse sections considered in the mea-surements the gauge located midway between the rivet co-lumns indicated nearly the same stress as the gauge locatedat a distance of 6.25 mm from the column, i.e. the stressmeasured at location B equalled that measured at location E,and the stress at location D was the same as that at location F.Considering above, the axial loads in the sheets have beencomputed by integrating the stress distributions schematizedas shown in Figure 6a, where the measured stresses are spec-ified as a percentage of the tensile stress applied on the joint.It is seen in Figure 6a that compared to the D/Do-ratio of 1.3the stress distribution corresponding to D/Do = 1.5 is morelevelled off as in the latter case the differences between thestress value at the rivet column and between the columns aresmaller in either of the two sections. This observation is con-sistent with the experimental results of Terada (1985) ob-tained using a thermo-elastic analyser.

Integrating the measured stress field presented in Figu-re 6a yields the distribution of the load transfer ratiothrough the joint shown in Figure 6b. Here, a most strikingfeature is the non-symmetrical load transmission by the endrivet rows. For both the D/Do = 1.3 and D/D = 1.5 specimenload T1–3 transferred from the sheet adjacent to the rivetmanufactured head to the sheet adjacent to the driven headis lower than load T7–9 transmitted at the other end row, i.e.from the sheet next to the driven head to the sheet underthe manufactured head. The difference in the load transferdistribution by the outer rows is more pronounced for theD/Do = 1.3 than for the D/Do = 1.5 specimen for which theload transmission through all three rows is more homo-geneous.

The non-symmetrical load transfer observed experimen-tally is not reflected by the rivet flexibility measurementswhich for either of the two specimens provide identical re-sults on f for both outer rivet rows. The differences in theload transmission by these rows are, presumably, associatedwith large differences between the hole expansion in thesheet adjacent to the driven head and in the sheet next tothe manufactured head revealed in experimental (Skorupaet al. 2009, Skorupa et al. 2010) and numerical (Rans 2007,Müller 1995) studies.

��

Rivet deflections in lap joints of Al-alloy sheets with threerivet rows have been observed using several methods in-cluding new techniques developed by the authors. Axialforces in the sheets needed to compute the rivet flexibilitywere determined from strain gauge measurements per-formed in the way to account for the effect of sheet bending.The major conclusions are the following:

�A ! "�, ��3�#�� !"#B� (��%%#, �� >#'#�#��2 �(�?

% 2 "�( 3%�3�( & #" �!#(/�%. �% (�3 %#�% �� >3 %#?

2 "��2 �!�&( % 3�%� & #" �! �#� %��% #" �!�� ! �

"�'� ��!�"&� �! #"�� "� ��(! �' "&#"$�"&��

& � %2#" �! �� >#'#�#��%�(3 �#�#�%#, �%�/��%%�?

" ��( % (��( �" �! �, %�$ %#, � �� >#'#�#�� "(�

/! " �! ��#$� 2��!#" &#(3�� 2 "� $��$ C��

�%�"(&�� %A% ��%&(�% 23�� &��& %#, �! %#, �& ?

�� #�"()�(3%��#( &��%��"$ %�, %��3(/#�!2��#3�

%#, �%�/(�

�A ! !#$! %(B� 6 ��%� �# �&(��/ %,�� (��! %#?

, � �� >#'#�#�� 3�%�2 � % �"& �2�% � , �� & �� &

�%�"(2#((#�"�!%��$!�! 9�#"��

DA � & �% �( �� ! %#, � �� >#'#�#�� 3�%�2 � % /#�! �!

"�2' % �� ( #( 2�% (#$"#�#��"� �� ! !#$! %

(B� 6 ��%� � , ��

EA ! %#, � �� >#'#�#�� 3�%�2 � % ��% �! #"" % %#, � %�/

#( ��/ % �!�" ��% �! �� % %�/( &� �� ! &#�� % "�

�2��"�(��(! �' "&#"$�� #�! %��! ( ��#�"(�

�A 'A

69

��

FA ! "�"?(�22 �%#�� & �%�"(� % �'( %, & >3 %#?

2 "��#("��% �� &'��! %#, �� >#'#�#��2 �(�?

% 2 "�(/!#�! ��% � $#, " (3 �#2 "3%�,#& #& "�#��

% (��( ��% '��! �� % %#, � %�/(� � 2�(� 3%�'�'�

% �(�" ��% �!#( ' !�,#��% �% &#�� % "� ( #" �! !��

>3�"(#�" �"& % �! 2�"��% & �"& &%#, " %#, �

! �&�

GA ! 3% ( "�/�%.% , ��(�!��! %#, �� >#'#�#��#("��

�! �"��%/!#�!�� (�! ��&�%�"(2#�� &'��!

%#, �� !#(#23�# (�!��! 3%�� &�% ��3#��( &��

��23�� ! ��&�%�"(� %�!%��$!�! 9�#"��"&��#�#6#"$

��"&#�#�"( �� ! &#(3�� 2 "� ��23��#'#�#�� ' �/ "

(! �( �"& %#, �(2��3%�,#& B��"�#��#, �� "& , "

B��#��#, ��#"��%% ��% (��(�

Acknowledgements

The authors acknowledge the financial support from thegovernmental research funds within the years 2009–2012.

�!$!%!&'!(

=�%��HG)�� "��=�� !#�� (#$")

,��I)33�DDIJDI�

��%%#(*��E)/�� (� �� (�� 0!��#(( %��#�") +� ��) ! � �! %��"&(�

�K�� %��0�*��F)�� !�� #�&��'��DEDF(!G��H��G�0!��#(( %��#�") +� ��) ! � �! %��"&(�

��"(��I)!�� (� �� 0!��#(( %��#�")��%� ��"+"#, %(#��)��/�)��"�&��

.�%�3��).�%�3��)��!"# /#�6 �)-�%' ��)��( �� L#"@M��=�:�(C�&�A):%#&$#"$�! *�3' �/ " ! �%��"&�3 %��#�?

"��0%��#� ),��H)�� %&�2)33�EE�JEID�

.�%�3��).�%�3��)��!"# /#�6 �)-�%' ��)-�� (�� "?� %"��#�"��=��%"��#$� ),��D�)��I)33��GJ��D�

%�&��HF)�� (�� I��J�K�� ALMN�3�� ) �� %&�$�" C�&�A)� � 0 ��) ,�� F) 0!#��& �?

3!#�)33�FFIJFI��

Documents

significance of rivet flexibility for load transfer in lap joints