pik-20d wing spar web bonding - etusivu | traficom

PIK-20D Wing Spar Web Bonding Erkki Soinne

Traficom Research Reports

26/2019

Traficom Research Reports 26/2019

1

Date of publication

November 15th

2019

Title of publication

PIK-20D Wing Spar Web Bonding

Author(s)

Erkki Soinne

Commissioned by, date

Publication series and number


ISSN (online) 2669-8781

ISBN (online) 978-952-311-358-9

URN http://urn.fi/URN:ISBN: 978-952-311-358-9

Keywords

Sailplane, composites, dimensioning, fatigue

Abstract

This document studies the bonding of the wing spar web of the PIK-20D sailplane. Analytical expressions for the shear

stress and strain distributions in the bonding adhesive are derived in the elastic range. Corrective formulas for the

corrections of the shear stress and strain distributions are derived due to plasticity. Effects of web vertical compression

on bonding line shear combined loading are investigated. Estimations of the bonding fatigue characteristics are made

based on past fatigue tests. The effects of various factors on the bonding adhesive shear stress and strain distributions

and fatigue are discussed.

Contact person

Erkki Soinne Language

English

Confidence status

Public

Pages, total

44

Distributed by Published by Traficom


2

FOREWORD

This report is focused on the wing spar web bonding shear stresses and strains on

the PIK-20D sailplane, which are important factors in the dimensioning of a

composite wing structure. The impact of starting this investigation was received

when publishing the Benalla OSTIV Congress paper “PIK-20D Glider Fatigue

Review” in Technical Soaring. The present report is a complementary analysis to

the Trafi Research Report 7/2015 "PIK-20D Fatigue Evaluation”.

Helsinki, 15.11.2019

Erkki Soinne

Chief Adviser, Aeronautics

Finnish Transport and Communications Agency Traficom


3

Table of Contents

Nomenclature …………………………………………………………………..………………………….....4

1 Introduction ......................................................................................................... 5

2 Lap joint in edgewise shear .................................................................................. 7

2.1 Elastic distributions ...................................................................................... 7

2.2 Effects of plasticity ..................................................................................... 10

3 Wing spar web distributions ............................................................................... 13

3.1 Web bonding configuration .......................................................................... 13

3.2 Measured shear strains ............................................................................... 15

3.3 Bonding adhesive elastic distributions .......................................................... 19

3.4 Adhesive elastic–plastic model..................................................................... 24

3.5 Bonding adhesive plastic distributions .......................................................... 26

3.6 Vertical compression loads .......................................................................... 28

4 Bonding adhesive dimensioning ......................................................................... 31

4.1 Static dimensioning .................................................................................... 31

4.2 Fatigue ..................................................................................................... 32

5 Diverse effects .................................................................................................... 37

6 Conclusions ........................................................................................................ 42

References ................................................................................................................. 43


4

Nomenclature

b distance

c width of plastic zone

C1, C2 integration constants

D1, D2 integration constants

G adhesive shear modulus

G1 adherend 1 shear modulus

G2 adherend 2 shear modulus

h structural height

l lap joint bonding adhesive width; width

M bending moment

n load factor; redundancy factor

py spanwise load intensity

P point load

Py spar load

pz vertical load intensity

Pz vertical load

q shear flow intensity

q1 adherend 1 shear flow intensity

q2 adherend 2 shear flow intensity

t adhesive thickness

t1 adherend 1 thickness

t2 adherend 2 thickness

v displacement

v1 adherend 1 displacement

v2 adherend 2 displacement

x Cartesian coordinate

β angle

γ shear strain

γe elastic shear strain

γp plastic shear strain

γu ultimate shear strain

ε strain

εu ultimate strain

λ parameter

ξ Cartesian coordinate

σ stress

σu ultimate strength

τ shear stress τav average shear stress

τe elastic shear stress τILSS allowable inter laminar shear stress

τkl,Br ultimate bonding shear stress

τp plastic shear stress

τu ultimate shear strength


5

1 Introduction

The airworthiness requirements for sailplanes, such as the OSTIV requirements

ref. [1] used for the original certification of the PIK-20 sailplane, have traditionally

not required fatigue analysis for composite structures. The same version of the

OSTIV requirements was used for the certification of PIK-20D. The powered

sailplane PIK-20E was certified to meet the OSTIV Airworthiness Requirements for

Sailplanes, September 1976, Utility Category, Powered Sailplanes and the

German Airworthiness Requirements, Lufttüchtigkeitsforderungen für

Segelflugzeuge und Motorsegler (LFSM), October 1975, Utility Category, Powered

Sailplanes.

In the 1980s the German airworthiness authority, Luftfahrt Bundesamt, developed

preliminary instructions for the fatigue testing of sailplanes, such as those in ref.

[2]. However, the certification of PIK-20 series sailplanes and powered sailplanes

was done in the 1970s without a requirement of fatigue analysis. Consequently

there is no lifetime prescribed in the airplane flight or service manuals. The

present European airworthiness requirements for sailplanes (CS-22 ref. [3]) do

not require fatigue analysis or testing. Paragraph CS 22.627 only says that: “The

structure must be designed, as far as practicable, to avoid points of stress

concentration where variable stresses above the fatigue limit are likely to occur in

normal service.” This is the same phrasing as in the past OSTIV requirements.

On commercial and military aircraft there are requirements of damage tolerance

to tolerate Barely Visible Impact Damage BVID, for example of dropping tools on

the wing surface. Sailplane wing spar is protected inside the wing and most of the

skin structures on the wing and fuselage are buckling critical tolerating large

damage. For sailplanes there is no requirement for damage tolerance analysis. As

fatigue and damage tolerance calculations are not required for sailplanes, the

philosophy of dimensioning bonding lines has been to use low allowables in static

dimensioning. This does not warrant too sophisticated analysis methods, such as

FEM calculations, in the analysis. Analytical methods have the advantage of giving

an understanding about the entire physical problem, whereas numerical methods

only give a numerical result. An example of this is presented in the Hitchhikers

Guide to the Galaxy (ref. [4]), in which the enormous supercomputer Deep

Thought gave the answer “42” to the Ultimate Question of Life, the Universe, and

Everything after a computation time of 7,5 million years. Numerical methods are

useful in complicated detail studies, but as Andrei Tupolev formulated it “Do only

what is necessary”.

The wing spar web bonding has traditionally been treated on composite sailplanes

by using low average values for the bonding adhesive shear stress and the

bonding has been considered as lightly loaded. For example in the fatigue testing,

made for the fatigue life extension of sailplanes (ref. [5]), only the stub wing spar

was simulated in the test, not the wing spar web bonding on the other side of the

root rib. Recently a question was raised about the bonding line fatigue in the

connection of the publication of the Benalla OSTIV Congress paper on “PIK-20D

Glider Fatigue Review”. That paper does not include the bonding line fatigue as

there is no fatigue data on the bonding adhesive. The present report intends to

investigate the bonding adhesive shear stress and strain more in detail and to

give an indication of the bonding line fatigue based on comparisons on full scale

fatigue tests.

The elastic stress and strain distributions in a lap joint have been studied in the

past by Volkersen ref. [6], Hart-Smith ref. [7] and Eppler ref. [8]. The analytical

elastic shear stress distribution is of cosh type with the highest stresses and

strains at the ends of the adhesive. Often the adhesive yield stress is reached at

ultimate load. Hart-Smith has studied the effect of plasticity on the stress and

strain distributions. He has also investigated the bonding adhesive fatigue, see

ref. [9]. In the present report the analytical equations for an edgewise shear


6

loaded lap joint are derived. The elastic and plastic shear stress and strain

distributions are calculated for the critical section of thePIK-20D wing spar web.

Effects of combined loading including web compression due to wing bending are

treated. Estimation of web bonding fatigue is based on comparison data on full

scale fatigue tests.


7

2 Lap joint in edgewise shear

2.1 Elastic distributions

The spar web lap joint is primarily loaded in the bonding line (tangential) direction

by an edgewise shear loading. The analytic solution equations for the elastic case

are derived here following the references by Hart-Smith [7] and Eppler [8]. Study

a lap joint shown in Figure 1. q is a shear flow intensity [N/mm] acting on the lap

joint adherends. Force balance on an element on adherend 1 gives

q� + �� dx − q� − τdx = 0 (1)

�� − τ = 0 (2)

where τ is the local adhesive shear stress, which is assumed to be constant in the

thickness direction. Similarly

q� + �� dx − q� + τdx = 0 (3)

�� + τ = 0 (4)

The shear strains in the adherends are

γ� = �� = �� ⁄

�� (5)

γ� = �� = �� ⁄

�� (6)

Figure 1. Lap joint notation.

t1, G1

t2, G2

t, G

q q

q q+(dq/dx)dx

dx dv

l

x


8

The shear stress in the adhesive is caused by the different displacements in the

adherends τ = G ��

� (7)

Combining equations (2), (4), (5), (6) and (7) gives

�� G�t� ��

�� − G �� = 0 (8)

�� G�t� ��

�� + G �� = 0 (9)

and further

�� − �

�� (v� − v�) = 0 (10)

�� + �

�� (v� − v�) = 0 (11)

Subtracting the equations gives a second order homogeneous differential equation

�� (v� − v�) − �

� ( �� + �

��)(v� − v�) = 0 (12)

which can be written as

�� − λ�v = 0 (13)

where v=v1-v2 and parameter λ is given by

λ� = �� ( �

�� + ��) (14)

The solution of the differential equation is

v(x) = C�e!� + C�e�!� (15)

The boundary conditions are

x =0

q1=0

q2=q

x=b

q1=q

q2=0

As dv/dx is

�� = ��

�� − �� (16)

the boundary conditions give at x=0

�� = 0 − �

��

and at x=b

�� = "

#�$� − 0

Solving for the integration constants gives

�� = C�λe!� + C�(−λ)e�!� (17)


9

C�λe% + C�(−λ)e% = − qt�G�

C�λe!& + C�(−λ)e�!& = qt�G�

yielding

C� = �!'()*�(+)*, - �

��$� + .+)*��$�/ (18)

C� = �!'()*�(+)*, - �

�� + ()*��/ (19)

This is the solution for elastic deformations without consideration for adherend

bending, which is negligible due to the external load acting in the direction of the

long shear lap joint. The obtained shear stress and strains distributions are of

cosh type with peak values at the adhesive ends. When the adherends are not

similar the distributions are asymmetric with the critical stress and strain values at

the end from which the softer adherend extends (ref. [7] page 23).


10

2.2 Effects of plasticity

When the adhesive shear stress exceeds the adhesive yield value there is local

yield and the shear strain is increased. The adhesive plasticity can be modeled

with an elastic-plastic formulation with an example shown in Figure 2. Within the

plastic zone the differential equation is not equation (13) but somewhat different

and is derived in the following. The shear strain is obtained from equation (7)

γ = �� (20)

Taking the derivative and using equations (5) and (6)

�0�� = �

��(��)

�� = ��

�� − �� (21)

Derivating further

��0�� = �

� � ��

�� − �

�� (22)

and using equations (2) and (4)

��0�� = �

� � 1�� − �1

�� (23)

��0�� = �

� � �� + �

�� τ=��

�� + �� τ2 = !�

� τ2 = constant (24)

where τp is the shear stress in the plastic zone, assumed constant in the elastic-

plastic model. So in the plastic zone the second order differential equation is non

homogeneous.

Use coordinate ξ starting at the inner edge of the plastic zone with width c,

situated at the right end of the bonding line. Consequently:

Figure 2. Example of elastic-plastic modeling of adhesive characteristics

(ref. [10] page 6-32).


11

dξ = dx

x = l-c => ξ = 0

x = l => ξ = c

The differential equation can be solved by straight forward integration

��0�3� = !�

� τ2 (25)

�0�3 = !�

� τ2ξ + D� (26)

γ(ξ) = !�� τ2ξ� + D�ξ + D� (27)

where D1 and D2 are integration constants.

Plasticity also changes the elastic zone solution so that at the interface of the

elastic and plastic zones the shear stress has the adhesive yield value τp and the

shear strain the corresponding elastic value τp/G. The elastic zone shear strain

solution is

γ(x) = �# 'C�e!� + C�e�!�, (28)

The integration constants of the elastic and plastic zone solutions are determined

from the boundary conditions. When there is a plasticity zone only at the right

end of the bonding line the boundary conditions are

γ = 16� at x=l-c and ξ=0

�0�� = �0

�3 at x=l-c ξ=0

�0�� = − 178&

�� at x=0

�0�3 = 178&

�� at ξ=c

The second condition ensures continuity in the adherend stresses. The boundary

conditions give the following equations for determining the integration constants

C1, C2, D1 and D2

�� 'C�e!(&�9) + C�e�!(&�9), = 16

� (29)

D� = 16

� (30)

�� 'C�e!(&�9) + C�e�!(&�9), = D� (31)

�� 'C�λe!% − C�λe�!%, = − 178&

�� = − �� (32)

Constants C1 and C2 for the elastic solution are solved for using equations (29)

and (32), which give

C� =):6;

< � =;�<�(+)(*+>)

!'()(*+>)�(+)(*+>), (33)

C� =):6;

< � =;�<�()(*+>)

!'()(*+>)�(+)(*+>), (34)


12

Constants D1and D2 for the plastic solution are directly obtained from equations

(30) and (31).

Based on the boundary conditions Hart-Smith ref. [7] has derived after some

manipulation the following relation (Appendix equation (A.35)) for a normal

loaded lap joint

1 + �!9� � @tanh -λ �&�9

� �/ + ��DEF-!�*+>

� �/G = tanh -λ �&�9� �/ H178

16 �!9� � ��IJK(�)

�LIJK(�)� − CTHERM(1)R

+�

�DEF-!�*+>� �/ H178

16 �!9� �R (35)

where CTHERM(1) is a term depending on different thermal expansion coefficients

on the adherends. As the layups are now the same in the adherends the term

CTHERM(1)=0. The term ETR(1) is now on a shear loaded lap joint the ratio

ETR(1) = t�G�t�G�

For long overlaps

tanh Hλ Sl − c2 WR → 1

Inserting these into relation (35) and simplifying the following equation is

obtained for the plastic zone width at one end of the bonding line

c = �16

��L�� − �

! (36)


13

3 Wing spar web distributions

3.1 Web bonding configuration

The wing spar web is laminated to the lower wing shell and the final bonding

takes place to the upper wing shell, see Figure 3. The L-shaped profiles are

supported with foam core during the bonding. The sandwich web and the L-

shaped profiles at the bonding have the form shown in Figure 4.

Figure 3. PIK-20D wing spar structure.

Figure 4. Wing spar web bonding configuration.

30

40

20

4 weaves 92125

2 weaves 92125 bonding adhesive

web


14

The spar web is laminated to the root rib with four weaves of Interglas 92125

with the configuration shown in Figure 5. The connection laminates are inside the

web bonding adhesive and the connection laminates and the L-shaped profiles for

web bonding overlap. The figure shows the configuration used in the initial static

tests of PIK-20D. A third weave of 92125 was added into the type design

configuration on each web skin at the root area y=0 to 250 mm, see ref. [11]

page 27. The root rib is shown in Figure 6.

Figure 5. Wing spar web connection to the root rib.

Figure 6. Root rib structure.

web

60

20

root rib

4 weaves 92125


15

3.2 Measured shear strains

The measured shear strain values of the PIK-20D wing spar web are shown at

limit load +20% in Figure 7. The values are for the maximum takeoff weight of

450 kg with the water ballast in the wings, which gives the maximum bending

moment. A lower take-off weight of 350 kg without water ballast gives the

maximum shear force for the wing, but it is only 2,5% higher than with water

ballast, ref. [12] Nyström page 8. As the difference is so small, it has been

ignored here. The total shear load is due to the air loads minus mass loads

integrated from the wing tip to the section in question and consequently shows an

increasing value. This is shown in the strain gage values of shear strain along the

neutral axis in Table 1. Wing torsion contributes to the different values at the

forward and aft sides of the web. The load case is not always the same so the

values are envelope values.

One would also expect the shear strain values to be about the same at the neutral

axis and just under the spar cap. The latter values are systematically lower, only

about half of the neutral axis values. In an I-beam one would expect almost

constant shear stress and strain in the web. A reason for the different values may

be that the strain gages just under the spar cap are bonded to the L-shaped

profiles for the web bonding. The additional thickness of the profile flange

increases the local web stiffness thus reducing the shear deformation. Check now

this hypothesis by calculating the shear flow intensity, which is constant at a wing

station.

As the exact vertical positions of the strain gages under the spar cap are not

known, it is assumed that they are placed at the middle of the 30 mm wide

flange. Also it is assumed that the flange has no effect at the outer edge, full

effect at the inner end and 50% effect at the strain gage positions. The shear flow

intensity is

q = Gγt&Y9D& (37)

At wing stations y=855 mm and 255 mm there are two weaves of Interglas

92125 at each web skin. The L-shaped profile is here made of four weaves of

92125, of which two are assumed to be effective at the strange gage positions.

The thickness of one 92125 laminate is 0,290 mm and the shear modulus for a

±45o laminate is 9400 N/mm2, see ref. [13] page 8. These values give the shear

flow values presented in Table 2. The hypothesis of half of the flange thickness

being effective seems to give reasonably accurate results, within 23% at station

y=855 mm and within 8% at station 255 mm.

Table 1. PIK-20D wing spar web shear strains at limit load (n=6,62) +20%,

see Figure 7.

Wing station

[mm]

Forward side Aft side

Gage nr γγγγxy

[%]

Gage nr γγγγxy

[%]

4735

3610

1955

855

255

21

17

13

11

7

0,210

0,233

0,294

0,336

0,555

22

18

14

12

8

-0,126

-0,285

-0,347

-0,371

-0,512


16

Fig

ure 7

. P

IK-2

0D

win

g s

par

web s

hear

str

ain

s γ

yz a

t lim

it load (

n=

6,6

2)

+20%

. Rig

ht

win

g,

vie

w lookin

g a

ft.

The n

um

bers

in t

he c

ircle

s identify

:

t

op

–

dis

tance y

fro

m r

oot

rib r

efe

rence s

tation

m

iddle

– s

train

gage n

um

ber

b

ott

om

– n

um

ber

of

sta

tic t

est

The d

ashed lin

e indic

ate

s t

hat

the s

train

gage is o

n t

he a

ft s

ide o

f th

e w

eb

Ref.

Nystr

öm

[13],

Appendix

13a,

16a.

Wing station y=255

Root rib wing station y=0


17

The shear strains at station y=34 mm do not follow the pattern of the other two

stations. The values would better fit the pattern of the previous stations if the

gage numbers were swapped by a mishap. This is unlikely due to the systematic

numbering of the forward and aft side gages. The measurements are very likely

correct and the reason for the odd looking values is probably the reaction from

the opposite wing spar end on the root rib just forward of the web (see Figure 6).

The reaction of the spar end gives a complicated load distribution on the root rib

with disturbances escalating to the wing spar root. Gerhard Waibel ref. [14]

commented that they have also seen a same type of disturbance at the wing root.

The higher strains at gage number 1 at the wing spar neutral axis are transferred

to the root rib and do not pass over the web bonding line.

The wing loading tests were performed on a test wing differing from the type

design wing at the web root. At the root area y=0 to 250 mm there was only two

weaves of 92125 on each side of the web core. The measured shear flow

intensities are valid for the type design configuration, but the shear strains and

stresses will be reduced due to the locally added web skin thicknesses.

The shear flow from one web skin must pass over the 30 mm wide bonding line

shown in Figure 4. At wing station y=255 mm the shear flow intensity is (more

reliable value at the neutral axis, see Table 2)

q = 30,3/1,2

= 25,3 N/mm limit load, n=6,62

At wing station y=34 mm the shear flow intensity passing over from the web to

the wing shell can be calculated using expression q = Gγt&Y9D& (37) and strain

gage nr 4 value of Figure 7

q = 9400*(0,00678/1,2)*(2+2+2)*0,290

= 92,4 N/mm limit load, n=6,62

The number of 92125 weaves is 2 in the web skin, 2 weaves taken effective at the

connection to the wing shell and 2 weaves taken effective in the connection to the

root rib, see Figure 4 and Figure 5. This is the local shear flow intensity, based on

strain gage measurement at the corner of the web on top of the laminated

connections to the root rib and the web. This shear flow intensity acts on the web

lower side whereas the web bonding is on the web upper side. There is no strain

gage measurement available close to the bonding line. The connection to the root

rib via the laminated weaves is stiffer than the load path over the bonding line.

Based on equation (7) the displacement over bonding load path is proportional to

Table 2. PIK-20D wing spar web shear flow intensities at limit load (n=6,62)

+20%.

Wing station

[mm]

Side Neutral axis Under spar cap

Gage nr q

[N/mm]

Gage nr q

[N/mm]

855

855

255

255

fwd

aft

fwd

aft

11

12

7

8

18,3

20,2

30,3

27,9

9

10

5

6

21,5

15,6

31,1

25,7


18

v ≈ 1� tl (38)

where the bonding adhesive entities are: τ is shear stress, t thickness, l width and

G shear modulus. The adhesive shear stress is proportional to the external shear

flow intensity (equations (7), (15), (18) and (19))

v ≈ q �&� (39)

This means that the load path stiffness is proportional to G/(tl). For a 30 mm wide

and 1,5 mm thick bonding adhesive with Eccospheres glass micro balloons this

gives a value (ref. [13] page 15)

2200/(1,5*30) = 48,9

Load transfer in inter laminar shear over a layer of resin to a 60 mm wide

laminated connection represents an elasticity comparable to a bonding line

elasticity. Assuming the resin layer thickness to one half of the 92125 weave

thickness the stiffness value is

1250/(0,5*0,290*60) = 143,7

The bonding line would transfer a fraction of

48,9/(48,9+143,7) = 0,254

the total load. This is about 25% of the total shear flow intensity and the

laminated connection transfers about 75%. If the shear flow intensity q=92,4

N/mm would act in the web upper corner the bonding line would experience a

shear flow intensity

q = 0,254*92,4 = 23,5 N/mm limit load, n=6,62

which is less than at wing station y=255 mm. However, there are no strain gage

results in the web upper corner. The load distribution at the wing root is complex

with disturbances escalating to the web root. The local shear flow intensity could

in theory be higher than at the web lower corner. If the web bonding line could

not locally take the higher load, the connection laminate can bear it alone as it is

dimensioned for the even higher shear flow intensity at the neutral axis.


19

3.3 Bonding adhesive elastic distributions

The elastic bonding line shear stress distributions are checked at wing station

y=255 mm. The additional reinforcement weave begins inboard of this station at

y=250 mm. Outboard of this station there are two weaves of 92125 on one web

skin and inboard three weaves. The outboard area is more critical due to the

larger unbalance of the adherend properties. The elastic distributions are

calculated with the expressions of chapter 2.1 and the following initial data (ref.

[13] page 35).

Adherend 1, web skin, 2*92125 ±45o

t1 = 2*0,290 = 0,580 mm

G1 = 9400 N/mm2

Adherend 2, L-profile, 4*92125 ±45o

t1 = 4*0,290 = 1,160 mm

G1 = 9400 N/mm2

Bonding adhesive, Rütapox L02 resin filled with Eccospheres micro balloons

l=30 mm

t = 1,0, 1,5 and 2,0 mm

G = 1250 N/mm2 and 2200 N/mm2

The thickness values were chosen based on bonding thicknesses observed in cut

wing sections. The lower shear modulus is that of pure resin. The higher shear

modulus was based on a calculation of a unidirectional glass fiber laminate with

37,5% of resin (volume). It was reasoned that the unidirectional glass fibers

would fill the compound in the same way as the glass micro balloons and a

significant deformation would be only in the resin.

The acting shear flow over the bonding line is

q = 1,5*25,3 = 37,9 N/mm at ultimate load, n=6,62, ref. page 17

The results are collected into Table 3 and Table 4. The integration of the shear

flow intensity from the shear stress distribution of the case G=2200 N/mm2 and

t=1,5 mm gave a value q=40,3 N/mm. This is 6,3% higher than the external

shear flow intensity q=37,9 N/mm. Regarding the concave shear stress

distribution the result shows the expected trend and confirms a good accuracy in

the calculations.

The shear stress distributions are presented in Figure 8 and Figure 9. the

distributions are asymmetric due to the factor two different adherend properties

with very low shear stresses in a wide area in the middle of the lap joint. It is

seen that the shear stress peak value at one end of the adhesive is a factor 2

higher than at the other end. This is due to the adherend at the web face having a

factor 2 higher flexibility than at the L-profile. At the wing root y=0 to 250 mm

there is a third weave of 92125 at the web skin. With this stiffer adherend the

joint is more balanced and with the nominal adhesive thickness t=1,5 mm and

shear modulus G=2200 N/mm2 the peak shear stresses at the adhesive ends are

τ=12,1 N/mm2 and 9,09 N/mm2 compared with the corresponding values τ=16,04

N/mm2 and 8,02 N/mm2 of Table 3. A more balanced lap joint gives a more even

shear stress distribution with a lower peak value.

The peak shear stress values appear at the end from which the softer adherend

extends. This is the end which is visible inside the wing and possible to inspect.

Figure 10 shows the peak shear stress values as function of adhesive thickness t

and shear modulus G. The peak values increase with increasing joint stiffness,

that is with increasing shear modulus value and decreasing adhesive thickness.

The peak shear stress value τ=16,04 N/mm2 at ultimate load corresponds to a


20

peak value of τ=10,69 N/mm2 at limit load indicating a slight plasticity at limit

load. The analytical solution of the elastic shear stress distribution is based on the

assumption that the shear stress is constant across the adhesive thickness. This

assumption leads to the non-zero shear stress at the adhesive end (ref. [7] page

8). This is of course unphysical at a free surface and the analytical equations

represent an idealized solution.

Table 3. PIK-20D wing spar web bonding line shear stress distributions at y=255

mm at ultimate load n=6,62 with bonding adhesive shear modulus

G=2200 N/mm2.

x

[mm]

ττττ

[N/mm2]

t=1,0 mm t=1,5 mm t=2,0 mm

0

1

2

3

4

5

10

15

20

25

26

27

28

29

30

9,82

4,51

2,07

0,95

0,44

0,20

0,0041

0,0025

0,0082

0,40

0,87

1,90

4,14

9,02

19,64

8,02

4,25

2,25

1,19

0,63

0,33

0,0140

0,0018

0,0280

0,67

1,26

2,39

4,50

8,50

16,04

6,95

4,01

2,31

1,33

0,77

0,44

0,0286

0,0054

0,0568

0,89

1,54

2,67

4,62

8,01

13,89


21


mm at ultimate load n=6,62 with bonding adhesive shear modulus

G=1250 N/mm2.

x

[mm]

ττττ

[N/mm2]

t=1,0 mm t=1,5 mm t=2,0 mm

0

1

2

3

4

5

10

15

20

25

26

27

28

29

30

7,40

4,12

2,29

1,27

0,71

0,39

0,0211

0,0033

0,0421

0,79

1,42

2,55

4,58

8,24

14,81

6,05

3,75

2,32

1,44

0,89

0,55

0,0512

0,0138

0,1011

1,10

1,78

2,87

4,64

7,49

12,09

5,24

3,46

2,28

1,51

1,00

0,66

0,0854

0,0312

0,1669

1,32

1,99

3,02

4,57

6,92

10,47


22

Figure 8. Bonding adhesive elastic shear stress distribution at y=255 mm at

ultimate load n=6,62.

Figure 9. Bonding adhesive elastic shear stress distribution at y=255 mm at

ultimate load n=6,62.

0

5

10

15

20

0 5 10 15 20 25 30

ττττ[N/mm2]

x [mm]

G = 2200 N/mm2

t=1,0 mm

t=1,5 mm

t=2,0 mm

0

5

10

15

20

0 5 10 15 20 25 30

ττττ[N/mm2]

x [mm]

G = 1250 N/mm2

t=1,0 mm

t=1,5 mm

t=2,0 mm


23

Figure 10. Bonding adhesive maximum elastic shear stresses at y=255 mm at

ultmate load n=6,62 as function of adhesive thickness t and shear

modulus G.

0,00

5,00

10,00

15,00

20,00

0 1 2 3 4 5

ττττ[N/mm2]

t [mm]

Peak shear stresses

G=1250 N/mm2

G=2200 N/mm2


24

3.4 Adhesive elastic–plastic model

To take into account the adhesive plasticity it is needed a model for the adhesive

characteristics. An elastic-plastic model, as shown in Figure 2, is utilized here for

the compound of Rütapox L02 resin filled with Eccospheres glass micro balloons,

used on the PIK-20D sailplane. The plastic shear stress should be chosen so that

it gives equal strain energy to rupture compared with the true adhesive

characteristics. The exact characteristics of the adhesive compound are unknown,

but there are ultimate shear stress values, determined with strength tests. The

tests were performed with tension loaded lap joints with a specimen size of about

1 times 1 inch. Depending on the adhesive thickness the scatter reduced shear

strength values were the following (ref. [13] page 19)

τu = 10,0 N/mm2 t=1,0…1,5 mm

τ u = 9,0 N/mm2 t=1,5…2,5 mm

τ u = 7,0 N/mm2 t=2,5…3,5 mm

The values are average shear stresses based on ultimate force per specimen

shear area. It is acknowledged that measuring adhesive material values contains

many pitfalls and and the results are dependent on the coupon type, see ref. [15]

Hart-Smith page 19…25. For the nominal adhesive thickness of 1,5 mm the shear

stress value of τ = 9,0 N/mm2 on the low side is selected. The nominal shear

modulus for the compound was derived as G=2200 N/mm2 (see page 19).

Consequently the maximum elastic shear strain is (equation (7))

γ = τ/G = 9/2200 = 0,00409

Rütapox L02 resin has an ultimate strain εu exceeding the value 0,03, which was

registered in material tests when the strain gages ruptured. Torsion specimen of

the cured resin were used to determine the shear strain from measured strain

values in +45o and -45o directions using formula (Perälä ref. [16] page 55)

γ = [\]^�[+\]^��'[\]^L[+\]^,L� (40)

which in pure shear becomes

γ = εà^ − ε�à^ = 2εà^ (41)

If this would apply up to rupture the shear strain at rupture would be

γ u = 2*0,03 = 0,06

However, the 0,375 volume fraction of glass would reduce the ultimate strain by

factor (1-0,375) assuming no elongation of glass micro balloons. This would give

γ u = (1-0,375)*0,06 = 0,0375

For more details see ref. [13] page 42 and 43. The elastic-plastic model for the

adhesive compound can now be constructed and is presented in Figure 11.


25

Figure 11. Elastic-plastic modeling of adhesive characteristics with Rütapox L02

resin and Eccospheres glass micro balloons compound.

γ 0 0,01 0,05

0

10

ττττ [N/mm2]


26

3.5 Bonding adhesive plastic distributions

The effects of plasticity in the adhesive shear stress and strain distributions are

calculated using the equations of chapter 2.2 and the elastic-plastic model of

chapter 3.4. The amount of plasticity is determined from equation (36) which

gave a plastic zone width c=1,231 mm. In the idealized distribution the shear

stress is limited to the adhesive yield value 9,0 N/mm2 within the plastic zone. In

the idealized distribution the value τ=9,0 N/mm2 extends to the edge x=30 mm.

This is of course unphysical and in reality the shear stress goes to zero on a free

surface. The shear stress distribution is affected within a distance from the

adhesive ends, of a few times the adhesive layer thickness (ref. [7] page 8). Due

to the adhesive spreading out from the space between the web skin and the L-

profile (see Figure 4) and increasing the bonding line length the idealized solution

may represent the situation quite well. The shear strain at the beginning of the

plastic zone is

γ p = τp/G = 9/2200 = 0,00409

From this value the additional plastic shear strain γp increases the shear strain

with a parabolic distribution. The distributions are presented in Table 5 and Figure

12.

Figure 12. Distributions of adhesive shear stress and strain at wing station

y=255 mm at ultimate load n=6,62.

0,000

0,005

0,010

0,015

0,020

0

5

10

15

20

25 26 27 28 29 30

ττττ[N/mm2]

x [mm]

Shear stress, elastic

Shear stress,

plasticity included

Shear strain, elastic

Shear strain, plasticity

included


27


mm at ultimate load n=6,62.

x

[mm]

Elastic Plasticity included

ττττe

[N/mm2]

γγγγe ττττp

[N/mm2]

γγγγp γγγγtot

25,0

25,5

26,0

26,5

27,0

27,5

28,0

28,5

28,769

29,0

29,5

30,0

0,82

1,13

1,55

2,13

2,93

4.02

5,52

7,59

9,00

0,00037

0,00051

0,00070

0,00097

0,00133

0,00183

0,00251

0,00345

0,00409

9,00

9,00

9,00

9,00

0

0,00064

0,00234

0,00445

0,00409

0,00473

0,00643

0,00854


28

3.6 Vertical compression loads

Due to wing bending one spar cap is elongated and the other one is compressed

causing a vertical side load as shown in Figure 13 (see ref. [17]). Spar cap load Py

induces a vertical side load

Pc = Pddβ (42)

Elongations in the upper and lower spar caps give

εdx − (−εdx) = hdβ

yielding

2εdx = hdβ (43)

and by substitution

Pc = fF

�[��F (44)

where M is the bending moment corresponding to the spar cap loads Py at a

distance h. The vertical normal load intensity is

pc = hi�� = �f[

F� (45)

This acts as a compression load on the wing spar web. Estimate the load at wing

station y=255 mm from the root rib, where

M = 2825 kpm limit load, W=450 kg

ε = 0,0037 limit load, W=450 kg

h = 127 mm ref. [13] page 58

These values give for one web skin a compressive normal load intensity of

Figure 13. Vertical side loads.

dββββ

h

−ε−ε−ε−ε

εεεε

Py

Py

Py

Py dββββ

Py Py

Pz


29

pz = 7,4 N/mm ultimate load

to be compared with the acting shear flow intensity

q = 37,9 N/mm ultimate load

Besides these load intensities there is also a spanwise load intensity py, acting

over the wing spar web and the web bonding as shown in Figure 14. However,

this load does not pass over the web bonding adhesive but is a bypass load.

The vertical normal load intensity pz acts over the bonding line and the joint is

loaded as a double-lap joint under compression. This creates in the bonding

adhesive a shear stress and strain in the vertical direction, perpendicular to the

deformation due to the edgewise shear of the shear flow intensity q. The shear

distribution due to the normal load intensity can be derived analogous to the

edgewise shear in chapter 3.3. In the equations the shear flow intensity q is

replaced by the normal load intensity pz and the adherend terms Giti by Eiti. The

material values are then with the nominal adhesive thickness and shear modulus

Adherend 1, web skin, 2*92125 ±45o

t1 = 2*0,290 = 0,580 mm

E1 = 9800 N/mm2

Adherend 2, L-profile, 4*92125 ±45o

t1 = 4*0,290 = 1,160 mm

E1 = 9800 N/mm2

Bonding adhesive, Rütapox L02 resin filled with Eccospheres micro balloons

l=30 mm

t = 1,5 mm

G = 2200 N/mm2

Figure 14. Web loading notation.

q

q

pz

pz

py

py


30

At ultimate load pz=7,4 N/mm the peak shear stress at x=30 mm is τ=3,07

N/mm2 and the corresponding shear strain is

γ=0,00140

The resultant shear strain due to the vertical normal load and edgewise shear

load intensities is

j0,00140� + 0,00854� = 0,00865

and the increase due to the vertical normal load intensity is less than 2%. Failure

will occur when the resultant exceeds the adhesive ultimate shear strain value

(ref. [7] Hart-Smith page 40)

pγd� + γc� ≥ γr (46)

The adhesive compound ultimate shear strain was conservatively estimated,

based on material tests of Perälä ref. [16], as γu=0,0375. The Margin of Safety is

MS≥100% and the bonding adhesive is lightly loaded.

The level of the bypass load intensity py may have an effect on the bonding

adhesive fracture under the resulting shear strain. The acting compression due to

py was

ε=0,00555 ultimate load

The Rütapox L02 resin has an ultimate compression strain ε>0,03 (ref. [16]

Perälä page 43). Assuming conservatively a volume fraction of 0,375 of

Eccospheres glass micro balloons (a normal value for wet layup) and the micro

balloons to be infinitely stiff, the ultimate compression strain for the adhesive

compound is estimated as

ε=(1-0,375)*0,03=0,01875 >> 0,00555

The bonding line adhesive is lightly loaded in spanwise compression and this

effect is ignored in the combined fracture.


31

4 Bonding adhesive dimensioning

4.1 Static dimensioning

There are bonding shear stress allowables, approved by Luftfahrt Bundesamt LBA

for sailplane structures, Vorläufige Dimensionierungswerten für Holme von

Segelflugzeugen und Motorseglern ref. [18]. There is a value for new production

τkl,Br = 7 N/mm2

where kl refers to bonding (Klebe) and Br to ultimate static value (Bruch). So this

is a static dimensioning value based on average shear stress. However, LBA has

lost the connection to the original report and cannot say if the values are backed

up by fatigue tests also (ref. [19]). There is no specification of the bonding

material, such as resin or micro balloons, but it says that the value is valid in new

production of glass, carbon and synthetic fiber structures. Obviously the value

covers all common resins used in the 1980s, also the Epikote 162/C260.

Static strength tests, made at Helsinki University of Technology on Rütapox

L02/H91/SL66 + Eccospheres glass micro balloons, showed the following ultimate

shear strength values at varying bonding thicknesses

τ u = 10,0 N/mm2 t = 1,0…1,5 mm

τ u = 9,0 N/mm2 t = 1,5…2,5 mm

τ u = 7,0 N/mm2 t = 2,5…3,5 mm

The dimensioning values are based on average shear stress over the bonding line.

There is also a recommendation to use a safety factor n=2,0 in all bondings.

These values are somewhat higher than the LBA approved values, which can be

explained by the better resin. The recommended safety factor is explained by

general conservatism with a joint which is not analyzed in detail.

The average shear stress at wing station y=255 mm is at ultimate load

τ = �& = �,a∗t%,t/�.�

t% = 1,26 N/mm�

Based on visual observations of cut wing sections the bonding adhesive thickness

has been typically 1,0…2,0 mm with emphasis towards the lower value.

Howeverm on a 7 m long bonding line it is not possible to hold strict values and

based on a typical thickness of 1,5 mm the lower allowable of 7,0 N/mm2 is

selected. The redundancy factor is then

n = y,%�,�z = 5,6

So the margin of safety greatly exceeds MS > 100% fulfilling the recommendation

of having at least a redundancy factor of n=2,0.

There is no mention about the influence of environment in the LBA or Helsinki

University of Technology documents. The environmental factors (temperature and

humidity) should be considered in dimensioning (ref. [15] Hart-Smith page 7).

Normally the hot-wet conditions are dimensioning for composite structures. In the

Helsinki University of Technology values the recommended additional safety factor

may also cover the environmental uncertainty.


32

4.2 Fatigue

Because there is not available fatigue data for the adhesive compound in an

edgewise shear loaded lap joint, the estimates are based on PIK-20D fatigue

tests. These were started with an unreinforced wing performing first about 30

static loadings at high load levels, see ref. [11] Trafi Research Reports 7/2015

page 31. 9 of the loadings were at limit load +20% at n=7,944. The 6000 FLH

Kossira-Reinke spectrum, with 12,5% aerobatic flight added, contains 10 cycles at

limit load, ref. [11] Trafi Research Reports 7/2015 page 69. Because only the

highest load cycles contribute to the cumulative fatigue sum the static loads

represent

9*6000/10 = 5400 FLH

of Kossira-Reinke spectrum including aerobatics at 20% elevated level. The effect

of the elevated level test can be estimated with the load enhancement factor

presented in Figure 15. Use the gradient of the NAVY database as it has the

highest scatter, as wet layup tends to have a higher scatter than prepreg

production. A load enhancement factor of 1,2 corresponds to a life factor of about

14 in testing time based on equal statistical confidence. Consequently the testing

time of 5400 FLH corresponds to 75600 FLH with life factor 1. Using a life factor of

4 the testing covers a flying time of 18900 FLH of aerobatic flight in excess of the

elevated level fatigue test of 4000 FLH normal flight including a life factor of 4.

Based on the NAVY curve the 4000 FLH at 20% elevated level corresponds to

56000 FLH at nominal level. Altogether the testing amounts to

Figure 15. Influence of test duration on B-basis Load Enhancement Factors (LEF)

for different materials data bases, ref. [20] Tomblin & Seneviratne

page 80.


33

18900 + 56000 = 74900 FLH

which the wing web bonding line has endured.

The testing was made at takeoff weight W=450 kg simulating water ballast

whereas the maximum wing shear load takes place without water ballast at

takeoff weight W=350 kg. The wing shear load is 2,5 % higher in the latter case,

ref. [12] Nyström page 8. Based on the Navy curve this corresponds to a change

of test factor 1,473 in flight time amounting to

50800 FLH

The wing spar web bonding line is covered by this amount of testing including a

life factor of 4.

Another indication of bonding line life time can be obtained based on the fatigue

tests on the Janus wing performed at the Royal Melbourne Institute of

Technology, see Patching & Wood ref. [21]. The wing was tested with a so called

Dorning spectrum including aerobatic maneuvers up to n=5,3. The spectrum

consisted of 6000 FLH and static loading up to design limit loads n=6,0 and

n=-2,5 was performed manually at every 6000 FLH. The wing endured 35482 FLH

of loading until the testing was stopped. During the testing there were fractures in

the root rib around the metal spigot bearings that were repaired, but not on the

wing spar or the spar web bonding. The two-seater Janus sailplane has a bigger

wing than the PIK-20D, but the shear flow intensities are roughly the same due to

similar wing planforms. The wing root airfoils are the same so the structural

heights are proportionally the same. As the bonding line dimensions and materials

are similar the Janus fatigue gives an indication for the PIK-20D wing web

bonding fatigue life. The Janus wing is made of Epikote C162/C260 resin/hardener

combination that has more than factor 100 shorter fatigue life than the Rütapox

L02/SL resin system, see table Table 6. Another factor contributing to the good

fatigue properties of the PIK-20D sailplane is that the composite structure was

post cured overnight at elevated temperature (70o C for colored and 54o C for

white surfaces) giving a stable resin matrix during the service life. This is

demonstrated in the wing surfaces of PIK-20D and LS-4 sailplanes in Figure 16

and Figure 17. The dimpling pattern of the wing skin, bonded to the foam core, is

visible on the LS 4 whereas on PIK-20D there is no pattern. The bonding line

adhesive fatigue life can be scaled up indicating a fatigue life of

1000000*35482/7900/4 = 1,123*106 FLH

including a life factor or 4.

Hart-Smith (ref. [9]) has studied creep fatigue of bonded aircraft fuselages. On a

balanced lap joint, based on practical engineering experience, the Hart-Smith

Table 6. Effect of resin system on composite laminate fatigue properties,

based on Luftfahrt Bundesamt material acceptance fatigue tests

(L20/SL 19.8.1975 and GE162/C260 performed at DFVLR 4.6.1974),

ref. [22] Lumppio page 131.

Number of cycles to fracture

Probability of fracture

(Bruchwahrscheinlichkeit)

Epikote 162

& Laromin C

260

Rütapox L20

& SL

Rütapox L20

& H91

90 % 7900 106 1,2*106


34

Figure 16. Wing surface of a 40 year old PIK-20D sailplane.

Figure 17. Wing surface of a 30 year old LS-4 sailplane.

Dimples


35

criterion for avoidance of failure in fatigue requires that at ultimate load the

minimum of adhesive shear stress along the bond length is no-greater than one

tenth of the yield-stress. The criterion is illustrated in Figure 18. Hart-Smith

studied creep fatigue as one flight (of a length from a few minutes to a few hours)

gives one loading cycle when the fuselage is pressurized during the flight. Creep

fatigue is more critical than high frequency fatigue as shown by MIL-HDBK-17-3F

ref. [10] which quotes that when a specimen could endure 30 cycles in creep

fatigue it could take 1000 cycles in high frequency fatigue. So a lap joint, fulfilling

the Hart-Smith criterion, would be even less critical in high frequency fatigue.

For a balanced lap joint (equal adherends) an analytical equation can be derived

for the hart-Smith criterion. The shear stress distribution is symmetric

τ = Acosh(λx) (47)

with the coordinate x starting in the middle of the lap joint. At the beginning of

the plastic zone at x=d/2

Acosh �λ �� = τ2

yielding

A = 169Y~F�!�

�� (48)

At the middle of the elastic zone at x=0

169Y~F�!�

�� cosh(λ ∗ 0) = 0,1 ∗ τ2

yielding

cosh (λ ��) = 10

Figure 18. Hart-Smith criterion for avoidance of failure in fatigue, ref. [9]

page 14.


36

and further

hyp�� cos h �λ �� = λ �

� = 2,993 ≈ 3 (49)

which sets a requirement on the elastic zone width d. The requirement was

derived for a tension loaded lap joint, but when using expression(14) for

parameter λ the requirement is valid for a shear loaded balanced joint with equal

adherends.

Conservatively calculate the value of λ using the higher thickness of 1.16 mm for

both adherends giving a low value for the parameter λ=0,51867/mm.

Consequently the minimum length of the elastic zone is

d = 2*2,993/0,51867 = 11,5 mm

and the maximum total length of the plastic zones is

l-d = 30 – 11,5 = 18,5 mm

which is fulfilled by a large margin, see Figure 12.

It is obvious that the bonding line in the lap joint is so wide that the Hart-Smith

criterion is fulfilled and there should be no fatigue problems. The same indication

is given by the PIK-20D and the Janus wing fatigue tests, but should there be

bonding line fatigue problems one would expect those first on a sailplane with

Epikote 162/C260 resin system.


37

5 Diverse effects

The following issues are treated here:

- peel stresses

- thermal expansion

- L-profile corner bending

- L-profile inter laminar shear stress

- solution accuracy at the adhesive ends

- joint adhesive thickness

- lap-joint unbalance

- joint adhesive width

- fatigue

For normal force loaded lap joints with thick adherends there is a bending loading

due to load eccentricity causing adherend cracking starting at the adhesive end

region. For thin adherends this is less of a problem. However, there is a bending

load due to the eccentricity even in a normal force loaded double-lap joints, see

ref. [7] Hart-Smith page 27…32. A double-lap joint is shown in Figure 18. The

vertical normal load intensity has the eccentricity, but the web sandwich core

supports the bonding minimizing the peel stresses due to bending. On an

edgewise shear loaded lap joint the external force is in the direction of the long

bonding line and the eccentricity bends the whole package, supported by the

sandwich core and the L-profile. Consequently the peel stresses are not

considered a problem.

Different thermal expansion in the adherends would create thermal stresses as

shown in ref. [7] Hart-Smith chapter 4. Now the layups are the same ±45o

weaves in the web skin and the L-profiles so there is no thermal mismatch. The

wing spar in unidirectional carbon fiber has though a different thermal expansion

coefficient. Between the L-profile (including the wing inner skin with

reinforcement weaves) and the spar cap there is a difference in thermal

expansion coefficients creating thermal loads. To a lesser extent these loads can

propagate further over the bonding line, but as secondary these loads are not

investigated.

The loads transferred over the bonding adhesive pass to the flange of the L-profile

and then further to the under structure, to which the L-profile other flange is

laminated. The shear load transfer is unproblematic but the secondary

compressive normal load can be thought of causing local bending on the L-profile

flange. The L-profile resembles a classical L-fitting which is connected to the

under structure with a fastener. Bending of the clamped flange is critical on the L-

fitting. On the bonded L-profile there is however no fastener and consequently no

stress concentration around the fastener head. Even if there is no radius specified

for the L-profile corner there will be some rounding in the corner. The space

between the rounded corner and the under structure is filled with the adhesive

compound or resin. Consequently there will be no significant bending of the L-

profile corner, if the adhesive compound and resin can transfer the flatwise

compressive load to the under structure. Some bending may be present due to

different elasticities and combined deformation of the structure. The acting

normal load intensity due to web compression was calculated in chapter 3.6 as


38

pz=7,4 N/mm. On a 1,16 mm thick flange this gives nominally a compressive

stress

σ = 6,4 N/mm2 ultimate load

The resin ultimate strength was estimated as

σu = 25,1 N/mm2 ref. [13] Soinne page 73

and consequently the Margin of Safety exceeds 100% and the structure is lightly

loaded. In practice the flange load will spread out in about 45o angle and the

acting stress is reduced to one third. This is based on analytical plate theory

solutions. Figure 19 shows the stress distributions of an infinite plate where a

point load P is acting in the plane of the plate normal to the boundary. At a

distance b from the edge the peak normal stress is

σ = 0,637 h�� (50)

where t is the plate thickness. Assuming a constant stress over a width l it can be

written as

σ = h&� (51)

Setting the constant stress equal to the actual peak value the effective width and

half angle can be determined. It turns out that the half angle becomes a value

38o. The same result is obtained at any distance from the point load.

The L-profiles are directly laminated to the wing spar flange and wing inner skin.

This interface is not subject to the shear loading as the web bonding line, where

the shear load passes from one adhesive end to the other. The shear load from

the L-profile is transferred to the wing spar flange as in an ordinary I-Beam

without noticeable stress concentrations. The acting shear flow intensity q=37,9

N/mm2 at wing station y=255 mm at ultimate load on one L-profile is transferred

on an effective width of 19,4 mm to the wing spar flange giving a nominal shear

stress of

τ=2,0 N/mm2 ultimate load, ref. [13] page 74

Figure 19. Stress distribution on an infinitely wide plate due to a point load P

acting in the plane of the plate normal to the boundary, ref. [23]

Girkmann page 63.


39

The allowable inter laminar shear stress, referred to the limit load, is estimated as

τILSS=59 N/mm2 ref. [13] page 74

The Margin of Safety MS>100% and the detail is lightly loaded. The allowable

ILSS value is considerably higher than the corresponding value for the adhesive

compound, because of the much smaller inter laminar layer thickness and the

weave layers touching each other.

The analytical solutions of the adhesive elastic shear stress and strain

distributions are based on the assumption of the shear stress being constant

across the adhesive thickness. This assumption leads to the non-zero shear stress

and strain at the adhesive ends, ref. [7] Hart-Smith page 8. This is of course not

possible on a free end surface. The estimated effect of plasticity also shows a

non-zero shear stress and strain at the adhesive end, see Figure 12. In practice

these will be equal to zero on a free surface and the distributions will be

smoothed out in some way. Due to the adhesive spreading out from the space

between the web skin and the L-profile (see Figure 4) and increasing the bonding

line length the idealized solution may represent the situation quite well.

The effect of the bonding adhesive thickness t was studied by varying the

thickness from 1 mm and 1,5 mm to 2 mm. With decreasing thickness the elastic

peak shear stress value was increasing as shown in Table 3 and Table 4.

However, the amount of plasticity would not be much increased due to the

steeper shear stress rise. The effect is also somewhat compensated by the

increase of adhesive ultimate shear strength with decreasing adhesive thickness,

see Chapter 4.1.

The lap-joint is called balanced when the adherends have the same properties. On

a balanced joint the shear distributions are symmetric and the peak shear

stresses at the adhesive ends are equal. The peak shear stresses are shown in

Table 7 indicating the effect of the lap-joint unbalance. Inboard of wing station

y=250 mm there is an additional third 92125 weave on the web skin and the peak

shear stress is reduced 25%. The higher peak values appear at the adhesive end

where the thinner adherend continues (End 1). On the PIK-20D wing spar web the

web skin is the thinner adherend. Thus the critical adherend end is visible inside

the wing and it is possible to inspect the critical adhesive end.

The bonding adhesive width l was varied for the nominal lap joint configuration

t=1,5 mm and G=2200 N/mm2 and with 2 weaves on the web skin and 4 on the

L-profile. The results are shown in Table 8. It is seen that the peak shear stress is

almost constant. In the middle of the bonding adhesive the shear stress values

Table 7. PIK-20D wing spar web adhesive elastic peak shear stress values at

ultimate load n=6,62 q=38,9 N/mm, depending on the edgewise shear

loaded lap-joint unbalance. Adhesive thickness t=1,5 mm and shear

modulus G=2200 N/mm2.

ττττ [N/mm2] Number of 92125 weaves on web skin/

L-profile

2/4 3/4 4/4

End 1 16,04 12,13 9,82

End 2 8,02 9,09 9,82


40

are low. Only the shortest l=10 mm configuration misses the Hart-Smith criterion

for fatigue as the mid position shear stress slightly exceeds the requirement of

10% yield stress. The 20 and 30 mm wide lap joint configurations fulfill the

criterion with a large margin giving lots of redundancy for possible bonding

defects, such as voids and air bubbles.

The fatigue life indications of Chapter 4.2 were based on the Kossira-Reinke

spectrum including aerobatics (ref. [24]) and the Dorning spectrum (ref. [21])

also containing aerobatic flight. The Kossira-Reinke spectrum contains the

following steps:

- 750 FLH of aerobatic flight was added into the basic 6000 FL spectrum without

taking anything out.

- A life factor of 3 is applied on the 6000 FLH spectrum. However, the limit load

spectrum is extrapolated to 18000 FLH giving double effect.

- The aerobatic flight maximum load factor is extrapolated from the flight test

measured n=5,52 to 6,62 at limit load. The ten load cycles at n=6,62,

exceeding the Utility class design limit load factor n=5,3, were included into

the spectrum in contradiction to the FAA principles. Ref. [25] instructs to

discard all cycles above Design Limit Load or high load sequencies with max

10 cycles.

For these reasons the Kossira-Reinke spectrum including aerobatics is

theoretically questionable. It is also considered to be “very much to the

conservative side”, ref. [26] Gerhard Waibel page 57. The Dorning spectrum

includes aerobatic maneuvers up to n=5,3. The spectrum consisted of 6000 FLH

and static loadings up to design limit loads n=6,0 and n=-2,5 were performed

manually at every 6000 FLH. Performing loading to design limit load creates an

extreme spectrum for the testing. In both the Kossira-Reinke spectrum including

aerobatics and the Dorning spectrum including static loadings there are very high

loads. The same is true for the fatigue test of the PIK-20D wing, which was

started with a number of high level static loadings.

One could imagine that this makes the spectra conservative. On one hand adding

high loads into a spectrum makes it more severe, but also more uncertain as

determining or extrapolating a few high loads is very uncertain. On the other

hand high loads may have a non-conservative effect on the structure. This is

known since the testing of the Comet jet aircraft. On a metal component a single

high load causes plastic yield at a stress concentration or at a tip area of a

forming fatigue crack. This creates a compressive residual stress that causes a

too positive effect on fatigue risking the fatigue test. On composite structures,

Table 8. PIK-20D wing spar web adhesive elastic shear stress values at adhesive

end 1 and mid position at ultimate load n=6,62 q=38,9 N/mm,

depending on the adhesive width. Adhesive thickness t=1,5 mm and

shear modulus G=2200 N/mm2.

ττττ [N/mm2] Bonding adhesive width

[mm]

10 20 30

End 1 16,07 16,04 16,04

mid position 1,01 0,0419 0,0018


41

especially carbon fibers, the character of deformation is linear up to fracture. A

single high load in a mild stress concentration area would conservatively cause

initial damage. However, in a bolted joint there are high stress concentrations and

a crushing of fibers around the bolt holes both at low and at high level loads. This

leads to a smoothing out of the stress concentration. The crushing due to a small

number of uncertain high loads may cause a too beneficial effect on fatigue

risking the fatigue test. For these reasons it would be wise to follow the FAA

recommendations about the test spectrum.

Hart-Smith (ref. [9]) has studied creep fatigue of bonded aircraft fuselages. Hart-

Smith studied creep fatigue as one flight (of a length from a few minutes to a few

hours) gives one loading cycle when the fuselage is pressurized during the flight.

In hot-wet conditions bonded joints are subject to creep fatigue. It is more critical

than high frequency fatigue as shown by MIL-HDBK-17-3F ref. [10], which quotes

that when a specimen could endure 30 cycles at 1 cycle per hour it could take 10

million loading cycles in high frequency fatigue at 30 Hz. So a lap joint, fulfilling

the Hart-Smith criterion, would be even less critical in high frequency fatigue.


42

6 Conclusions

The dimensioning of wing spar web bonding line has traditionally been based on

simple analysis and low allowables on average shear stress. Fatigue has been

confirmed in fatigue tests of an entire wing. However, it is to be noted, that the

critical loading cases for the web shear appear normally for the sailplane wing

without water ballast, complicating the fatigue testing of the spar web. It is also

to be noted, that a fatigue spectrum should not contain high load sequencies with

a maximum of 10 cycles to avoid plasticity in metal components and a crushing of

fibers due to uncertain high loads.

Analytical expressions were derived for the bonding adhesive elastic and plastic

shear stress and strain distributions. The adhesive compound elastic plastic

model, including the Eccospheres glass micro balloons, was based on material

tests of the adhesive compound and the resin. The calculations show that on PIK-

20D wing spar web the elastic shear stress and strain distributions are of cosh

type with an asymmetry due to different adherend properties. At ultimate load

there is plasticity at one end of the bonding adhesive with constant shear stress

and a parabolic distribution of shear strain. The effect of vertical compression

loads on the web due to wing bending is small compared with the web shear. The

effect was less than 2% on the adhesive shear strain.

Sensitivity analysis on the bonding line width showed, that reducing the width

from 30 mm to 20 mm brought virtually no increase in the adhesive mid or end

position shear stresses. Consequently the 30 mm bonding line is so wide that the

through in the shear distribution gives a good protection against fatigue and

redundancy for possible flaws in the adhesive. Due to the asymmetric adherends

the critical adhesive end is the one at the point where the web skin continues.

Thus the adhesive critical end is visible inside the wing and possible to inspect.

The static dimensioning of PIK-20D wing spar web bonding was based on low

allowable values and an additional safety factor of 2,0, which makes the bonding

adhesive lightly loaded. Fatigue calculations were not performed, but estimates

based on fatigue tests of PIK-20D wing, Janus wing and Hart-Smith fatigue

criterion indicate that there is a long fatigue life. Due to the superior fatigue

properties of the Rütapox L02/SL resin system one would expect fatigue problems

first with sailplanes made of Epikote 162/C260 resin system, if there would be

any.


43

References

[1] OSTIV Airworthiness Requirements for Sailplanes, Organisation Scientifique et Technique

Internationale du Vol a Voile, September 1971, 68 p.

[2] Vorläufige Richtlinien zur Führung des Festigketnachweises für Bauteile aus glasfaser- und

kohlenstoffaserverstärkten Kunsstoffen von Segelflugzeugen un Motorseglern, Luftfahrt-

Bundesamt, Abt. Technick - I/3, Ausgabe Januar 1981, 9 p.

[3] Certification Specifications for Sailplanes and Powered Sailplanes CS-22, European

Aviation Safety Agency, Amendment 2, 5 March 2009.

[4] Adams D., The Hitchhikers Guide to the Galaxy, Pan Books Ltd, 1979.

[5] Kensche C. W., Proposal for a certification procedure of extended sailplane lifetime,

Technical Soaring, April 2002, p. 32...43.

[6] Volkersen O., Die Nietkraftverteilung in Zugbeanspruchten Nietverbindungen mit

Konstanten Laschen-Querschnitte, Luftfahrtforschung 15, 1938, p. 4...47.

[7] Hart-Smith L.J., Adhesive-Bonded Double-Lap Joints, NASA CR-112235, 1973, 106 p.

[8] Eppler R., Heavily Loaded Glued Joints, Technical Soaring, Volume XXII, No 3, 1998, p.

87...90.

[9] Hart-Smith L.J., Further Developments in the Design and Analysis of Adhesive-Bonded

Structural Joints, Douglas Papaer 6922, ASTM Symposium on Joining of Composite

Materials, Minneapolis, 1980, 26 p.

[10] Department of Defence Handbook, Composite Material Handbook, MIL-HDBK-17-3F, 17

June 2002.

[11] Soinne E., PIK-20D fatigue evaluation, Trafi Research Reports 7/2015 Amendment A1,

93 p.

[12] Nyström S., A static and dynamic strength test of a sailplane wing, Helsinki University of

Technology MSc Thesis, 1977, 148 p., (in Swedish).

[13] Soinne E., PIK-20D Wing spar web bonding work notes, Traficom, 20190827, 75 p + App.

[14] Waibel G., Personal communication with Gerhard Waibel at the XXXIII OSTIV Congress in

Benalla, January 2017.

[15] Hart-Smith L.J., Differences Between Adhesive Behavior in Test Coupons and Structural

Joints, Douglas Paper 7066, ASTM Aadhesives Committee D-14 Meeting, Phoenix, Arizona

March 11-13, 1981, 27 p.

[16] Perälä H., Theoretical and experimental determination of the elasticity coefficents of glass

fiber reinforced plastics, Helsinki University of Technology, MSc Thesis, 1975 (in Finnish).

[17] Dimensionieren von Bauteilen aus GFK (Glasfaservverstärkte Kunststoffe), Verein

Deutscher Ingenieure, VDI 2013 Blatt 1, Januar 1970, 20 p.

[18] Vorläufige Dimesionierungswerten für Holme von Segelflugzeugen und Motorseglern,

Luftfahrt-Bundesamt, Stand: 20.August 1981, 10 p.

[19] LBA email 5.6.2019 by Adrian Schwitalla.

[20] Tomblin J., Seneviratne W., Determining the fatigue life of composite aircraft structures

using life and load-enhancement factors, DOT/FAA/AR-10/6, 2011, 115 p.

[21] Patching C.A., Wood L.A., Further fatigue testing of a glass fiber reinforced plastic glider

wing, Technical Soaring Vol. XXI, No. 1, 1998, p. 11...16.

[22] Lumppio K., Life time and usability of a composite aircraft, Helsinki University of

Technology, MSc Thesis, 1997, 149 p. (in Finnish).

[23] Girkmann K., Flächentragwerke, Wien, Springer-Verlag, 1963, 632 p.

[24] Kossira H., Reinke W., Festigkeit von modernen GFK-Konstruktionen für Segelflugzeuge -

Bestimmung eines Belastungskollektives, IFL-IB 84-01 Technische Universität

Braunschweig, 1984, 234 pages.


44

[25] AFS-120-73-2, Fatigue evaluation of wing and associated structure on small airplanes,

Engineering and Manufacturing Division, Airframe Branch, FAA, May 1973, 20 p.

[26] Waibel G., Safe life substantiation for a FRP-sailplane, Technical Soaring, Volume XXVI,

April 2002, page 56...61.

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