International Journal of Fracture 80: R69-R76, 1996. (~) 1996 Kluwer Academic Publishers. Printed in the Netherlands. R69

EFFECT OF ADHESIVE LAYER THICKNESS ON FATIGUE STRENGTH OF ADHESIVELY BONDED BUTT, SCARF AND BUTTERFLY TYPE BUTT JOINTS

Makoto Imanaka Osaka University of Education, Asahigaoka Kashiwara City Osaka 582, Japan Tel: +81-729-78-3444

Takashi lwata Technical Research and Development Department Toyoda Gosei Co., Ltd., Kitajima Inasawa City, Aichi 492, Japan

Recently, adhesive bonding methods have been applied for joining of several structural members. To extend the application of adhesively bonded joints, it is necessary to define fracture criteria for the joints. In particular, fatigue failure criteria are crucial for adhesive joints as mechanical parts in cyclic loads via vibration and transmission of power. Furthermore, most of the bonded joints have complex multiaxial stresses in the adhesive layer; hence fatigue fracture criteria for the joints should be based on the fatigue strength under multiaxial stress conditions.

In a previous study [1], we proposed a method for evaluating the fatigue strength under multiaxial stress condition using adhesively bonded butt, scarf and butterfly type butt joints, where the stress multiaxiality in the adhesive layer was varied in a wide range. These joints with thin adhesive layer thickness have considerable uniform stress distributions except at the free end of the adhesive layer. However, an increase in the adhesive layer thickness enlarges the range having nonuniform stress distributions, resulting in lowering of the adhesive strength. To obtain critical fatigue strength of the joints under multiaxial stress conditions, the effect of adhesive layer thickness on the fatigue strength must be quantified.

Some studies have been published on the effect on the static and fatigue strength of the butt joint [2-5]; however, there are few studies on the scarf and butterfly type joints [6,7]. Furthermore, the effect of adhesive layer thickness on the fatigue strength of these joints has not been investigated. In the present study, fatigue tests under multiaxial stress conditions were conducted for the three types of butt, scarf and butterfly type butt joints in a variety of scarf angle and adhesive layer thickness.

Int ~urn o¢ Fracture 80 (1996)

R70

An 0.5% C Carbon steel (JIS.S55C) was used as the adherend for butt, scarf and butterfly type butt joints, and the adhesive was a thermosetting epoxy adhesive (Toyoda Gosei: EA9432NA).

The shape and sizes of the butt and scarf joints used in this study are shown in Fig. 1, where the scarf angle 0 was of four values: 300,450,60 ° and 90 ° (butt joint). As shown in this figure, the width of the adherend was varied in accordance with the scarf angle 0 so as to maintain a constant adhesive area of 190 mmh Figure 2 illustrates the details of the butterfly type butt joint together with its loading frame. This basic geometry was proposed by Arcan et al. [8]; the adhesive area was also the same as that of the scarf joints. The butterfly type butt joint was assembled into the loading frame by six pins. Then, the assembled loading frame was fixed with two pins into a fatigue testing machine. In this study, the fatigue tests were conducted under conditions where the center of the adhesive layer was located on the loading line (0---0°).

The adhesively bonded joints were prepared as follows: the bonding surfaces of the adherends were polished with emery paper of grade 180 mesh under a dry condition. Then, the adherends were degreased by acetone in an ultrasonic bath. The adhesive layer thickness of the joints was set up to 0.05 mm, 0.1 mm and 0.5 mm using an adhesion jig incorporated with a micrometer-head. The joints were cured at 140 ° C for 1.5hr and cooled in a furnace. Then, these joints were kept for a day at room temperature and submitted to the fatigue test.

Cyclic tensile fatigue tests were conducted with an electro-hydraulic type fatigue testing machine under conditions where the stress ratio R(maximum load/minimum load)--0.1 and loading frequency H=30 Hz.

Endurance limits of the butt, scarf and butterfly type butt joints used are shown in Table 1. In this table, the averaged axial stress range of the adherend, o,, and the averaged shear stress range in the adhesive layer, '¢M, are used for the butt and scarf joints, and the butterfly type butt joints, respectively. As Table 1 shows, the endurance limits of all the joints decrease with increasing adhesive layer thickness.

To make use of the data in Table 1 for evaluating endurance limits of another type of adhesively bonded joints, it is necessary to convert the axial stresses in the adherend of the scarf joints to the stress values in the adhesive layer.

Although having a complex stress situation at the free end of the adhesive layer, both scarf and butterfly type joints have comparatively uniform stress distributions in the adhesive layer. As described in the previous paper [1], assuming that the adherend is a rigid body under the axial stress conditions of oo as shown in Fig. 3, the normal stress, o , and shear stress, '¢,, in the uniform stress region of the adhesive layer of the scarf joints are given by [9,10]

o, = o= sin20 (1)

'~,~ = oo sinOcosO (2)

Int Journ of Fracture 80 (1996)

R71

Furthermore, when the plane strain is assumed with respect to the z direction and e. (strain for the s direction)=0, the tensile stresses in the z and s directions, ~ and t~, are given as:

V a

-- - - ~Pl (3)

where v is Poisson's ratio of the adhesive layer.

From (1)-(3), we obtain the maximum, medium and minimum principal stresses, (~, o2 and (r 3 as follows:

m + Or, + N/(m _0.)2 + r,c2

~1- 2 (4)

m + o~ - N/(m - m) 2 + 4"c 2

~3- 2

(~2-- (~s

(5)

(6)

In this study, detailed stress distributions in the adhesive layer were also analyzed for these butt, scarf and butterfly type butt joints by a two dimensional finite element method. The results show that for the butt and scarf joints the values ~i, ~2 and (~3 in the uniform stress region agree almost exactly with values calculated by (4)-(6) irrespective of adhesive layer thickness. For a butterfly type butt joint, it was also confirmed from the results of FEM analysis that nearly pure shear stress condition is obtained in the uniform stress region, though there is a little normal stress component.

In general, stress multiaxiality affects the ductility of most polymeric materials, see for example [11]. This suggests that the stress multiaxiality in the adhesive layer is a significant parameter indicating the strength characteristics of the adhesive layer. The stress multiaxiality can be defined by the principal stress ratios, that is, o~/~ 1 and G3/(r r Hence, to investigate the stress multiaxiality in the adhesive layer of the butt, scarf and butterfly type butt joints, Fig. 4 shows the relation between cJ~l and (~Jo~ in a uniform stress range, where these principal stress ratios were calculated by using the values obtained from the FEM analysis. This figure indicates that o3/(~ ~ increases with increasing scarf angle 0, moreover, (~J(r, increase linearly with increasing (~J~l. This indicates that the stress multiaxiality in the adhesive layer increases with increasing o / o r Hence, we use the principal stress ratio ~/(~1 as a parameter indicating stress multiaxiality in the adhesive layer.

Int Journ oF Fracture 80 (1996)

R72

Then, to investigate the effect oLthe stress multiaxiality on the endurance limit, we have attempted to correlate the endurance limits of the scarf and butterfly type butt joints with a parameter, a ] o r Figures 5(a)-(c) show the relationship between the endurance limit and the principal stress ratio in the adhesive layer, t~3/(~ ~, where the repective ordinates indicate using the maximum principal stress, (a~),,, Mises equivalent stress ( ~ ) , , , and the maximum shear stress (xm),,, in the adhesive layer at the endurance limits. All the data points in Fig. 5 were taken in the uniform stress range of the adhesive layer, using the stress distributions obtained from FEM analysis and the values in Table 1 as well as the values in the previous study [1] for the adhesive layer thickness t=0.1 mm. As can be seen in the figure, the endurance limits decrease with increasing t~3/a ~ irrespective of the adhesive layer thickness. It is also observed that the difference in the endurance limits is small between t--0.1 mm and t=0.05 mm and these joints have almost the same stress gradient, whereas there is a distinct difference between t--0.1 mm and t=0.5 mm. Furthermore, the gradient of (a~),, is more gentle than those of ( t~.) , and (xm),,. This indicates that the stress multiaxiality affects the minimum for (~),,.

As a result, the maximum principal stress is considered to be a suitable stress parameter and these regression lines obtained for thinner adhesive layer (t---0.05 mm or t---O.1 ram) are available for evaluating the strength of another type of adhesive joints.

Acknowledgements: The authors wish to express deep appreciation to Professor Kunio for his helpful advice on our work. This work was partly supported by a Grant-in-Aid for Scientific Research C(No. 04650086) from the Ministry of Education, Science and Culture, Japan.

REFERENCES

[1] M. Imanaka and T. Iwata, Journal of Adhesion, in press. [2] A.N. Gent, Journal of Polymer Science, Part A-2, 9 (1971) 283-294. [3] T. Tanaka and K. Taniyama, Proceedings of the 19th Japan Congress on Material Research (1976) 179-184. [4] H. Nakayama, K. Tozawa, A. Hirano and O. Okubo, Journal of Adhesion Society of Japan 13 (1977) 4-11, in Japanese. [5] M. Imanaka, W. Kishimoto, K. Okita and H. Nakayama, Journal of Composite Materials 18 (1984) 412-419. [6] Y. Suzuki, Japan Society of Mechanical Engineering, International Journal 30 (1984) 1042-1051. [[7] G.P. Anderson and K.L. DeVries, Journal of Adhesion 23 (1987) 289-302. [8] V. Weissberg and M. Arcan, ASTM STP 981 (1988) 28-38. [9] J.L. Lubkin, Transactions ASME, Journal of Applied Mechanics 24 (1957) 255 -260. [ 10] Y. Suzuki, Japan Society of Mechanical Engineering, International Journal

Int Journ of Fracture 80 (1996)

R73

28 (1985) 2575-2584. [11] Y. Narisawa, Strength Characteristics of Polymeric Materials, Oumu-sya (1982), in Japanese.

1 November 1996

Table i. Endurance limited of butt, scarf and butterfly type butt joints

wh~re the value of endurance limit is defined as a fatigue strength at

i0 stress cycles

Type of joint Angle between loading axis and adhesive/adherend

interface 8( ° )

90

60

45

30

Butt joint

Scarf joint

Butterfly type butt

joint

Adhesive layer

thickness

t(mm)

Endurance limit

0"~. r~ (MPa)

0.05 35.90

0.i 32.91

0.5 26.92

0.05 37.89

0.I 34.45

0.5 33.07

0.05 46.31

0.i 42.10

0.5 42.10

0.05 71.80

0.i 71.80

0.5 59.83

0.05 44.87

0.i 44.87

0.5 32.90

Int Journ o~ Fracture 80.(1996)

R74

I" I I

Adhes ive l aye r t h i c k n e s s

t=O.05, 0 .1, 0 .5

~ / 0 I , I I ~ I I

90+2 .5 /s I n e 9 0 - 2 . 5 / s I n 0

I i I I I I

: Y/f38s I n 0 ~

Figure i. Shape and sizes of the scarf joints.

6-~8 1141

• 1- i 5

J Z z i t

J _ l

t h i ck hess t=O.05, 0 .1 , 0 .5

(a) Butt .erf ]y type j o i n t • . . -11, ,~r,-, 8= 0", e =

; - - " 25-

, 0 0 I I I

' ,o o

o S

v~ I - - (b ) L o a d i n g f r a l e

4 - ~ 1 0

Figure 2. Shape and sizes of the butterfly type joint and loading frame.

Int Journ of Fracture 80 (1996)

R75

Adhesive layer n

Rig id body Rig id body

i w

da

Figure 3, Simplification of stresses in adhesive layer~

a2/a l l r

Scarf joint.......__

8 =3N° ~' ~ °l~O -45° Butterfly type joint 8 ~

°'~ ~ '~' . . . . . . . 0

- 1 -

- Butt joint :~ _ = o 8 = 9 0 °

I I I I

I G3/G 1

Figure 4. Principal stress ratios in the adhesive layer~

Int Journ of FractTAre 80 (199G)

R76

100 . . . . . . . . ,

'~" 90 O. o t=O.OSrnm

Q t=O.5mm 70

(0" ~ ).=40.18-10.49( o" ,10" ~ ) 60 .Of~am)

b ~ t = O (0 ~ )~=37.68-10.88( 0 =lo ~ ) -- 50 ~..../. - - ..... ~.:::::::: " - . - = ~ (t=O,Irnm)

4Or- .... ~ "::::~=:::::: :-o ..... | o .......... ~ ........................ ".~::: "-:::~::::~- ...........

o" 3o i- \ ........ " .......... ::: . . . . .

]_ ,,.O.,mm " '° ..... .~ 20

I ,,c 10 I

01-0'.8:0.6-0'.4-0=.2 0 012 014 016 018 1 0 '3 /0 ' 1

(a)Maximum principal stress

"~" 90 O.

80:

70

60

50

40

30 c:

20

lO f, JJ

100 . . . . . . . . .

0 t=O.O~.n "~ & t=O.lmm

".. "-,. D t=o.Smm '...

~"'i:i"." 0..).=37.27..,4(L1~3(0" ,10 i )

"'"-.~.'. ~ , ' / ~ o OSmm) ........ . . "~z~ / . (o f . , .),--35.~-44.S7(~Io ,)

"--. , (OAmm)

t = O . S m m / ...... iii~ii : "

%,. .% I I I I l I I " " , I

-0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 0 "3 /0 " 1

(b)Mises equivalent stress

5O

o. ~" 40

: 30 t

k,

~ 2o

o* 10

o.~

i i i i i i E , i

..... i: .... • ..¢... ~, t=O. 1 tmrn

~' " ' ; ' . Q tffiO.Smm -~, "..2>.

....... ".~,~ ('r .m).=20.64.27.91(o , I o ,) ....... • ....I (o.os,,n)

..... ""~ "Q::b J.lr ~1,,,=t9.84-26.00(a, I o ......... :a : :<" <o.~.,,,,)

l~l "..b ... ".:;.

~OSm. / e:~.; • ../::..

\ I I I I I I "11

-0.S-0.6-0.4-0.2 (} 0'.2 0.4 0.6 0.8 O'3/O" 1

(c)Maximum shear stress

Figure 5. The maximum principal, the Mises equivalent and the maximum shear stresses at the endurance limit with several adhesive layer thickness.

Int Journ of Fracture 30 (1996)