Fracture toughness of adhesively bonded joints

Engineering Fracture Mechanics Printed in the U.S.A.

Vol. 21, No. 5, pp. 997-1004.

FRACTURE

0013-7944/85 $3.00 + .OO 0 1985 Pergamon Press Ltd.

1985

TOUGHNESS OF ADHESIVELY JOINTS

BONDED

F. FLASHNER, S. KENIG,? I. G. ZEWI and H. DODIUK Ministry of Defence, P.O. Box 2250, Haifa, Israel Abstract-The fracture toughness of an epoxy-based film adhesive has been investigated using Mode I and combined Mode 1 + Mode II loadings. The opening Mode, Mode I, was realized by employing the Tapered Double Cantilever Beam (TDCB) specimen, while the mixed opening and shear modes, Mode I + Mode II, resulted from utilizing the Cracked Lap Shear (CLS) specimen. Fracture toughness was studied under conditions of constant elongation rate as well as sustained load. Furthermore, the environmental effects of both temperature (up to 70°C) and water were investigated in the sustained load case. Experimental results showed that the resistance to crack growth decreased in both the uniaxial and biaxial loading cases when sustained loads were applied, compared to the case of constant elongation rate. Higher temperatures (up to 70°C) in air did not cause any significant decrease in fracture toughness. However, the combination of water and temperature resulted in a significant decrease in the resistance to crack growth. Finally, mixed mode loading showed the most pronounced effect on the critical energy release rate parameter, GI,, as compared to a uniaxial, opening mode loading. The combined effect of biaxial load, temperature (up to 70°C) and water resulted in a drastic decrease in fracture toughness of the studied film adhesive in comparison to uniaxial loading ambient conditions. This result is of practical importance when fracture characteristics are entered in the design considerations for an adhesively bonded structure.

INTRODUCTION bonding has been used as a joining technique for secondary parts in aircraft and missiles for several decades. It offers the potential advantages of extended fatigue life, improved fail-safe capability and reduced manufacturing costs. With the development of improved adhesive systems and adherend surface treatments, adhesive bonding has reached the stage at which it can be utilized to replace mechanical fasteners in primary airborne structures. When designing primary structures, it is of great importance to consider the growth of initial flaws in the bond line. Such an analysis will determine the durability of the bonded component and may be used as a design parameter. Aerospace and aircraft structures are subjected to primary multiaxial stresses. However, fracture mechanics parameters like the stress intensity and energy release rate factors are measured by means of uniaxially loaded specimens. For purely linear elastic materials, multidirectional loading in the crack plane does not affect the stress intensity near the crack tip, thus the uniaxially derived parameters are valid also for the multiaxially loaded structure. For plastic deformable materials, and especially for viscoelastic materials, this is not the case as a result of yielding and relaxation. Hence, multiaxial loads affect the crack opening stresses. The question then arises whether the uniaxially derived parameters are relevant for adhesively bonded structures under real multidirectional loading. To explore this issue, the fracture toughness of an epoxy film adhesive was determined. Both uniaxial loading of Mode I type and biaxial loading of combined Mode I and Mode II were applied for appropriate adhesively bonded joint specimens, under conditions of both ambient as well as elevated temperature and high humidity. The relevance of the stress intensity factor (K) and the energy release rate (G) to polymers and viscoelastic materials, have been the subject for discussions. Experimental results have indicated that the toughness parameters depend on the mode and rate of loading, specimen geometry and dimensions and, in the case of adhesives, on the thickness. Consequently, the present publication explores the fracture toughness of adhesives, bearing in mind the above-mentioned limitations, hence the toughness parameters are considered to be the “effective” ones for the adhesive, geometry and loadings chosen. However, even under these constraints, the study of crack propagation using the energy release rate (G) parameter, is of great importance. ADHESIVE

iTo whom correspondence

should be addressed. 997

998

F. FLASHNER

ef al.

EXPERIMENTAL

A specimen that is quite commonly used for toughness characterization of adhesive bonds is the Tapered Double Cantilever Beam (TDCB), proposed by Mostovoy et al. [ 11. Strain energy release rate in TDCB is computed from eqn (1) [I]: G, = &

&

m (J/M*),

wherep is load (N), bq is adhesive width (m), E is adherend Young’s modulus (Pa), h is adherend width (m) and m is geometrical constant (1.13 . lo4 - l/m in this work). Crack length (a,) in a TDCB specimen is computed from eqn (2): 6 ar = - . 1.06 . 10e4(m), P

where 6 is crack opening displacement (COD) - (m), p is load (N) and 1.06 . 10e4 is a constant related to the geometry and adherend material (l/N). A relatively simple specimen, which allows the study of an adhesive under bimodal loading was proposed by Brussat et al. [2]. In this so-called cracked lap shear (CLS) specimen, Mode I and Mode II loadings are applied simultaneously. The specimen is shown in Fig. 1. In principle, it consists of a long beam bonded to a shorter beam. Tension is applied through a pin to both beams at one end and to the longer beam at the opposite end. This geometry and the way of loading make the CLS a constant strain energy release rate specimen and introduce a significant Mode I component at the crack tip. The strain energy release rate, G, is computed from eqns (3) and (4):

p2

G=

2b,(EAL

(3)

[l-s].

where G is total strain energy release rate (Gi + Gii), P is load, (EA)2 is tensile stiffness of a single beam, (EAh is tensile stiffness of a two-layer beam and b, is width of the adhesive layer. CLS

SPECIMEN

ADHERENDS

INITIAL

ADHESIVE

CRACK

LAYER

ADHE’SIVE

Fig.

1, Schematic

description

of the CLS specimen.

999

Fracture toughness of adhesively bonded joints

2 P2 (y2 - &J* Gr

-

=

7b,(~z)2{~[(~z)oI(~z)21

+

(4)

I)* '

where L2 is location of the centroid of a two-layer beam, Lo is location of the centroid of a single beam, (EZ)o is bending stiffness of a two-layer beam and (EZ)z is bending stiffness of a single beam. Though the CLS specimen exhibits a constant strain energy release rate, so that crack length does not enter the calculations, it is important, from a practical point of view, to know the crack length. This is given by eqn (5): d

=

62 h

_ 2

70) h A0 [ew(-A24 0

+

h2a

-

11,

where d is the separation of the two adherends at the end of the short beam, ho = [P/(EZ)o]“2, AZ = [Pl(EZ)2]“2 and a is the crack length. Brussat et al. [2] did not calculate the stresses developed in the adhesive layer during loading. However, in actual structures the known parameters are loads rather than strain energy release rates, and thus calculation of stresses becomes necessary. Such an analysis was performed using a finite elements scheme. The assumptions underlying this analysis were plane stress and elastic behavior of the components. The adhesive layer was first divided into two horizontal parts, and further subdivision was carried out in a plane normal to the adhesive. In the regions subject to the highest stresses, i.e. in the vicinity of the crack tip and the loading point, smaller elements were chosen. The adherends were made of aluminum 2024 T351 and treated according to Boeing Specification BAC-5514 [3] where a sulfuric acid-sodium dichromate etch (FPL) is prescribed. The adhesive was American Cyanamid’s FM73, processed as recommended by the manufacturer. The dimensions of the specimens are given in Fig. 1, and in Table 1. Application of wider adhesive layers was not attempted, since the applied loads were already close to the maximum capacity of the tensile machine used. The elastic constants of the adherend material and the adhesive are shown in Table 2. Two types of experiments were carried out with the CLS specimens: (1) Extension of the specimen at a constant rate of 0.05 cm/min in an Instron machine 1185. The load was recorded automatically and continuously, while the relative motion of the two adherends was indicated by a micrometer and recorded with a marker on the load chart. Table 1. Dimensions of the different types of CLS specimens b

Specimen type

GIJ

(m)

1

3s 45 55 75

22 32 42 62

2 3 4

bn

hz

110

(mm)

(mm)

(mm)

3 3 3 3

12.7 12.7 12.7 12.7, 9.5 7.6, 6.35

12.7 12.7 12.7 12.7

ho is height of the short beam. hz is height of the long beam. d = 50 mm. c = 70 mm.

Table 2. Elastic constants of aluminum 2024 and FM-73 film adhesive AI Young’s modulus, E (GPa) Poisson’s ratio

69 0.3

FM-73 10 0.3

1000

F. FLASHNER CONSTANT

LOAD

et al.

SET-

UP

ENVIRONMENTAL CHAMBER

l-l llOl

I

Fig. 2. Sustained load of set-up for CLS specimen.

SPRING

-r \

1W TDM

SPECIMEN

Fig. 3. Sustained load set-up for TDCB specimen.

(2) Application of a constant load to the specimen. Figure 2 shows the test set-up, including the specially constructed jacket that served as an environmental chamber. The relative motion of the adherends was read as in the constant rate experiments. The load was changed when further crack propagation was not observed. In all cases the crack length was obtained from eqn (5). The procedure consisted of solving the equation for the crack length, a, by application of a non-linear least-squares program. As mentioned earlier, Mode I loading was carried out using the TDCB specimen. Continuously increasing load was applied at rate of 0.1 cm/min. The load was recorded automatically and continuously. Application of constant load was performed by a system of weights, springs and beams (Fig. 3). The load was changed by 1 N/day. The COD was measured by a micrometer. RESULTS A. Numerical analysis for CLS Finite element analysis showed that the crack length in a CLS specimen influenced significantly the stresses developed at the crack tip (Table 3). While the shear stress remains approximately constant with a slight tendency to increase, the normal stress clearly increases but seems to reach a constant value for large crack lengths. No effect of specimen length was found. The ratio of shear stress to normal stress (~yz/cr=) in a single lap joint specimen, made of the same materials as the CLS specimen, was compared to 0.64 when using the method of Guess et al. [4]. This value differs greatly from those found for CLS specimens (Table 3). The CLS specimen appears to be a significant improvement over the more common SLJ and TDCB specimens. Furthermore, this developed stresses which change when the geometry Table 3. Stresses developed in a CLS specimen (external load of I

Pa) Crack length

(mm) 5

IO IS

t \ (Pa)

mv,, (Pa)

0.0403 0.0408 0.043

0.005 0.009 0.010

8.06 4.53 4.3

1001

Fracture toughness of adhesively bonded joints

is altered and can be calculated. This can be done to simulate stresses occurring in actual structures. Hence the specimen not only gives stress and strength data for mixed mode loading, but also the toughness of the adhesive joint. As mentioned, stress analysis carried out in the present study assumed elastic behavior and plane stresses. However, an organic adhesive cannot be completely elastic, and thus the first assumption may not be accurate. Neglecting end effects, especially in the thin and narrow adhesive layer, also constitutes an approximation. The influence of specimen length on the results suggests a significant contribution of these effects. B. Tensile experiments with CLS Brussat et al. [2] suggested the use of long specimens to prevent possible end effects. The infhtence of specimen length on the strain energy release rate and on the load needed to increase the crack length was determined in preliminary tensile experiments. A typical crack length vs load curve is shown in Fig. 4. Pi is a representative load in the region where the slope changes rapidly, co~esponding to the initiation phase. The graph shows some crack development at smaller loads, but growth is negligible relative to the final crack length. Another fact is the poor agreement with eqn (5) in this region. P, is the final load, measured at the moment of catastrophic failure. The region between Pi and P,. can be assumed to constitute the propagation phase. The change of the slope is not sharp and, consequently, Pi is not represented by a definite point but rather by a range of values. The numerical results are shown in Table 4. It can be seen that the maximum load increased by 30% when the total specimen length is increased from 0.35 m to 0.75 m. However, the final crack length remains nearly constant. The strain energy release rates change accordingly. To eliminate length effects as far as possible, the largest specimen that could be accommodated by the tensile testing machine was chosen for the experiments under constant load. A typical curve of load vs crack growth rate is shown in Fig. 5. As can be noticed the crack growth rate decreases at a constant external load, until it becomes practically zero. Increasing kN

T

100

LOAD-CRACK

4

2

LENGTH

3

4

5

Fig. 4. Crack length development

LG(dA/dt m/h

7

cm

1 ._ CRACK

-4

6

with Ioad-CLS.

,_

LOAD -2

,.

-3

__

48

PROPAGATION

VELOCITY

20

IN

UNDER

STATIC

CLS

22

24

26

28

kN

Fig. 5. Crack propagation velocity under sustained load in CLS.

1002

F. FLAS~NE~

et uf.

the load induces crack propagation, the rate of which subsequently decreases. This phenomenon repeats itself until a critical load is reached. Thereafter, the growth rate slows down temporarily and finally increases rapidly until failure occurs. The loading method has a crucial effect on the results. In monotonously increasing tension, the load at failure was about 62 kN for the longest 4 specimens (Table 4). A much smaller load was required to increase crack length under constant load, typically 31 kN at 25°C. In this case, there seems to be a threshold value of the load below which no crack growth is observed. A plausible explanation for the difference between sustained load and monotonously increasing loads stems from the viscoelasticity of the adhesive. These effects may be responsible for the decrease in crack growth rate under sustained load. The flow of the polymer causes stress relaxation and a subsequent reduction in the growth rate. experimental support for this explanation is given by the results of the long specimens, with different heights of the short beam. This change of the dimensions induces different ratios of Gi/G and Gri/G. The results, as shown in Fig. 6, indicate that the strain energy release rate increases when the tensile component (Mode I) of stress increases, i.e. G is not constant, as assumed by the usual elastic theory. Data on constant load experiments under different environmental conditions are presented in Table 5. There is practically no difference between the results of experiments performed in air at room temperature and at higher temperatures, up to 70°C. Water at room temperature has likewise only a limited effect on the test results. The simultaneous action of high temperature, mechanical load and water changes the situation drastically. The load needed to induce catastrophic crack growth in water at 50°C is half that at room temperature, and the final crack length shows about threefold increase. The conditions at 70°C appear to be somewhat milder. Plasticization and relaxation of stresses in hot water may contribute to the observed behavior. C. Tensile experiments with TDCB The results of tensile expe~ments under constant load are summarized in Table 6. The critical load P,. is lower in water than at room temperature. This may be a consequence of plasticization and of interphase damage, as can be concluded from the failure character. The drastic decrease in P,. and Gic in specimens tested in water at 40°C is possibly a result of severe damage of the interphase. Plasticization of the adhesive contributes to lower P,.. Crack velocity in the experiments (Fig. 7) with TDCB remains constant on average.

Table 4. Tension experiments,

(m)

Pmax (kN)

NCTl:,X (ml

0.35 0.45 0.M 0.75

45.22 47.11 54.46 61.92

0.08 0.081 0.096 0.081

Specimen length

CLS specimens

GC

GK

Pi

Gi

(kJ/m’f

(kJ/m’)

(kN)

fkJ/m’)

1.56

6.05 6.55 6.71 1I .73

37.6 39.2 41.8 45.6

I .08

I .69 2.27 2.67

I.18

1.34 1.59

Glii

tkJ/m’) 4.19 4.58 5.20 6.17

In all cases 100% cohesive failure.

Table 5. Sustained load experiments.

CLS

Pmax (kN)

ClmZlx

Environment

(m)

(kJlm*)

(kJ/m’)

Air, 25°C Air, 50°C Air, 70°C Water. 25°C Water, 50°C Water, 70°C

31.17 34.15 33.4 29.95 15.63 18.73

0.23 0.21 0.17 0.18 0.66 0.52

0.743 0.908 0.853 0.686 0.187 0.268

2.88 3.52 3.31 2.66 0.725 1.04

GC

GIIC

Failure mode (% cohesive) IO0 90 90 70 50 50

1003

Fracture toughness of adhesively bonded joints

GI/G

LOAD

Fig. 6. Total energy release rate (G) as fraction of the GI/G ratio.

Fig. 7. Crack propagation velocity under static load- rDCB specimen.

(NI

DISCUSSION TDCB experiments exhibit the destructive influence of water on adhesive joints. The interphase is damaged and the failure mechanism changes significantly from fully cohesive to partially adhesive. P, and Glc decrease by 20-30%. The temperature causes further damage of the interphase, and plasticization of the adhesive, and consequently, P, and Glc decrease. Grc, as measured in the sustained load experiments, is lower than that from continuously increasing load experiments (Tables 6, and 7). Viscoelastic effects that take place in sustained load experiments may be responsible for these differences. The changes in crack velocity seem to be the consequence of local changes in the interphase of the adhesive. Constant crack velocity can be assumed as an overall result. The CLS experiments give similar results. Exposure to air at different temperatures does not decrease the final load and does not change the failure mechanism in sustained load experiments. It means that co-operation of mechanical load and high temperature has a little influence on the joint, compared to air at room temperature. Adding water changes the failure mechanism to more adhesive, but the P, and the Glc remain essentially unchanged. Elevation of water temperature changes the failure mechanism to be more adhesive. This change, and possibly plasticization of the adhesive, lower drastically the properties’ levels to about half of that in air at room temperature. Comparison of G1 and of Gr + Gn (= G) from the single mode and combined mode experiments, indicate that the determined value of Gr using the TDCB specimen is different from those calculated from the CLS specimen. In the former case, the toughness parameter is much higher and furthermore it changes with the total energy release rate G in the latter case. Extrapolation of the CLS derived values to G1/G does not yield the G1 value obtained from the TDCB specimen. The problem encountered here is similar to that in metals [5]; when mixed Table 6. Sustained load experiments,

TDCB

Environment

P,. Critical load (N)

GIG (kJ/m’)

Failure mode (% cohesive)

RTiair RT/air 40”C/water 60”Uwater

1025 878 535 640

1.89 1.38 0.84 I .34

85 30 10 45

Table 7. Results for GI and GII -

Environment Air 25°C (tension) Air 25°C (sustained load) Water 25°C (sustained load) Water 50°C (sustained load) Water 60°C (sustained load)

CLS vs TDCB

GI CLS (kJ/m2)

GI

Gc + Gnc

TDCB (kJ/m’)

(CLS) (kJ/m’)

2.67 0.74 0.69 0.19 -

4.41 1.89 I .89 1.34

14.4 3.62 3.35 0.91 -

1004

F. FLASHIER

et al.

mode loading is applied, the values for GIs obtained from experiments in uniaxial mode, are not useful, when one considers multiaxial loading, and they have to be determined according to the state of stresses in the joint. The criterion for failure is not clear (G,. = Glc + Gllc is not valid any longer), and has to be determined after considering the character of the adhesive (elastic, viscoelastic, etc.) and of the stresses in the real joints. The crack velocity is different in the two cases. In TDCB the average crack velocity is constant, and the crack propagates under every load. This must not be the case always, because under a small enough load, the crack will not propagate [6]. However, after initiation, it will grow because of the increase of the moment in the crack tip. In CLS, the behaviour is different. The crack velocity decreases under every load, except under the final critical one. In practice it means that not every damaged component must be changed, and the loads and crack length should be determined when replacement is considered. CONCLUSION 1. The resistance to crack growth in adhesively bonded structures decreases by a calibration of temperature and humidity for both uniaxial and biaxial loading. 2. Increased temperature alone is not harmful up to 70°C for crack growth. 3. Under similar environmental conditions biaxial loads (80/20) decrease significantly the resistance for crack growth compared for the uniaxial case superposition of temperature-humidity-multiaxial loading reduce the toughness of adhesives by almost an order of magnitude for the 80~~0 case. 4. There is a need for an improved numericat analysis to account for plasticity and end effects. The cracked lap shear specimen has considerable potential for the evaluation of adhesive joints in a manner simulating stresses in real airborne structures. Joints with FM 73 structural adhesive can sustain appreciable loads for prolonged times without failure in the absence of a hostile environment. Bond strength is strongly affected by the co-operative action of mechanical load, temperature and water. Acknowledgements-The authors wish to thank Mr A. Dorban and Mr F. Weinstein for the finite element analysis and Mr Y. Miller for performing the mechanical tests.

REFERENCES [II S. Mostovoy, P. B. Crosley and E. J. Ripling, Use of crack-lined-loaded

specimens for measuring plane-strain fracture toughness, J. Mater. 2, 661-681 (1968). 121T. R. Brussat, S. T. Chiu and S. Mostovoy, Fracture mechanics for structural bonds. Final rep.. AFML-TR-77163 (1977). 131 Boeing Aircraft Co., BAC 5514: Common Bonding Requirements for Structural Adhesives. _. _ * _ ,.‘ 141 _ _ T. R. Guess, R. E. Allred and F. P. Gerstle, Jr., ~om~rison of lap shear test specrmens. J. restmg ~vat. 3, 6493 (1977).

[5] D. Aurich, W. Brooks, R. Jordan, J. Olschewski, H. Veith and J. Ziebs, The influence of multiaxial stress on characteristic parameters for cleavage fracture in elastic-plastic range. Int. Conf. Applications of Fracture Mechanics to Materials and Structures, Freiburg, Germany, 20-24, June (1983). [6] A. C. Carg, Environmental stress cracking behavior of glass fiber reinforced epoxy resins. Engng Fract. Mech. 17, 575-577 (1983).