On Experimental Methods to Investigate the Effect of

Layer Thickness on the Fracture Behaviour of

Adhesively Bonded Joints

Stephan Marzia, Anders Bielb, Ulf Stighb

aFraunhofer IFAM, Wiener Str. 12, D-28359 Bremen, GermanybUniversity of Skovde, Hogskolevagen, SE-541 28 Skovde, Sweden

Abstract

A number of different experimental methods are used at two independentlaboratories to evaluate the influence of layer thickness on the fracture prop-erties of one batch of a crash resistant epoxy adhesive. Both mode I and IIare considered. Novel, as well as state of the art methods are used. In mode I,the Double Cantilever Beam (DCB) and two versions of the Tapered DoubleCantilever Beam (TDCB) specimens are utilized; in mode II, two versionsof the End Notch Flexure (ENF) and the End-Loaded Shear Joint (ELSJ)specimens are used. Good agreement between the test results is achieved forthin layers in both fracture modes. For thicker layers the variation is larger.

Keywords: adhesive bonding, fracture mechanics, energy release rate,(Tapered) Double Cantilever Beam (TDCB/DCB) test, End Notch Flexure(ENF) test, End-Loaded Shear Joint (ELSJ) test

Preprint submitted to International Journal of Adhesion and Adhesives July 6, 2011

1. Introduction

Adhesive joining is considered as one of the key technologies for the devel-opment of light-weight cars for a future with limited resources and increasingenvironmental concerns. The potential to use multimaterial joints is regardedlarger for this joining technology than for most other techniques. This givesnew design possibilities and a larger degree of freedom in an optimizationprocess leading to lighter and more competitive vehicles. Adhesive joiningalso decreases the demands of tolerances in the manufacturing process; theadhesive can be used with the variation of layer thicknesses that result fromcost-efficient manufacturing processes.

In modern product development, virtual testing is an essential ingredient.With adhesively joined structures, the strength should be predictable froma virtual model. This put high demands on the quality of the models of theadhesive joints. Historically, three types of models can be identified. Thestart of strength prediction of adhesive joints is often attributed to Volkersen[1]. Here, fracture is assumed to occur when when the maximum stress in theadhesive is reached. Later, the criterium and stress analysis developed withnotable contributions from Goland and Reissner [2] and Hart-Smith[3]. Athorough introduction is given in [4]. The second fracture criterion is devel-oped from the concepts of fracture mechanics with pioneering contributionsfrom Ripling and coworkers, [5]. Fracture is now assumed to occur when theenergy release rate G equals the fracture energy Gc, considered a materialproperty. The energy release rate equals the release of energy stored in thestructure and the work performed by the acting loads per unit created cracksurface during crack propagation. Three modes of loading are considered.Mode I corresponds to a state at the crack tip where the adherends sepa-rate in the normal direction relative the normal of the adhesive layer. Thisis sometimes denoted peel deformation. In mode II and III, the adherendsseparates along the adhesive layer. This is often denoted shear loading. Anintroduction is given in [6]. Compared to the stress criterium, the predictivecapability increases for many situations. However, a major drawback is thatwe must assume the existence of a crack to use the method. An awkwardproblem to deal with in the design process. With the third model, cohesivemodels, this is no longer necessary. With this model, the adhesive layer ismodeled as a cohesive surface with properties given by a cohesive law. Thatis, the cohesive law is a representation of the constitutive properties of theadhesive layer, thus a material volume. Sometimes this result in unfortunate

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confusion. From a physical point of view, the parameters of a cohesive lawreflecting the separation of atomic surfaces should correspond to a stresslevel of about 1 GPa and a fracture energy of about 1 J/m2, [7]. However,for a cohesive model of the material volume in an adhesive layer, the param-eters are very different. The maximum stress is often in the range of tensof MPa and the fracture energy is normally in the range of several hundredsto ten thousands J/m2, cf. [8]. The reason for the large differences is thatthe cohesive model of an adhesive layer models the mechanical behaviour ofa material volume and not an atomic surface.

Methods to measure the fracture energy GIc of adhesives in mode I is oftenconsidered a mature topic. This is reflected in the development of standard-ized methods using the Double Cantilever Beam (DCB) and the TaperedDCB (TDCB) specimens, e.g. ASTM D3433-99 [9] and BS 7991:2001 [10].An ambitious round-robin shows consistent results in the sense that rea-sonably similar values of the fracture energy are derived using the differentmethods, cf. [11]. However, a theoretical study show that the methods cangive large errors. Based on simulations of experiments using experimentallymotivated cohesive models, two of the authors show that most of the meth-ods result in large errors in the evaluated fracture energy, cf. [12] and [13].The reason can be attributed to the considerable toughness of modern crashresistant adhesives. In this case, the evaluation procedures appears to beunable to handle the situation where a large inelastic process zone heads thecrack tip. Evaluation methods that give considerably better accuracy aregiven in [14, 15]. Common to these methods is that the expressions for thefracture energy are not explicitly dependent of the crack length. The appar-ent tradeoff is that other parameters of the experiment has to be measured.In [14], the rotation of the loading point is measured; in [15], the separationof the loading points is measured. For the present authors this appears ad-vantageous compared to the standardized methods where the crack lengthis necessary to measure. Experimentally, it is often difficult to identify theposition of the crack tip since the fracture process often is associated withnucleation and growth of micro cracks heading the crack tip. Thus, the cracklength is often harder to measure than the separation of the loading pointsor their rotation.

With the Tapered DCB (TDCB) specimen, the geometry of the specimenis designed to provide an expression for the energy release rate that is inde-pendent of the crack-length. The basic analysis employed in the evaluationschemes of all of these methods, with the exception of the method in [14], is

3

the Irwin-Kees equation of linear elastic fracture mechanics (LEFM). Thatis, the energy release rate, G, is given by

G =F 2

2b

dC

da(1)

where F , b, C, and a denote the applied force, the out-of-plane width,the compliance and the crack length, respectively.

The method in [14] is based on the path independent J-integral. It isgiven by

J =

∫C

(Wdy − Ti

∂ui

∂xdC

)(2)

where W , Ti, ui, and C are the strain energy density, the i-th componentof the displacement vector, the i-th component of the traction vector, and anintegration path starting at the lower crack face and circumscribing the cracktip, ending at the upper crack face, respectively. Moreover, subscripts i = 1, 2corresponds to the x- and y-components of the vector, respectively; repeatedindexes indicates summation. The coordinate system is oriented with thex-axis along the crack and pointing in the direction of crack propagation. IfW exists, or at least can be identified for a mathematically equivalent elasticmaterial mimicking the properties of the material at loading, and if W is notexplicitly dependent of the x-coordinate, C can be chosen freely. By usingalternative integration paths, an expression for J can be derived. It is notedthat J = G if the material is linearly elastic.

Several studies of the fracture properties of adhesives are based on thesetest geometries and evaluation methods. Blackman et al. [11, 16, 17, 18, 19]measure GIc using DCB- and TDCB-specimens with dimensions accordingto ASTM D3433-99 [9] and BS 7991:2001 [10]. The evaluation of GIc isbased on the Irwin-Kies equation. Marzi et al. [20] determined GIc from alinear regression between the generated crack growth length after one cycleof loading and unloading and the corresponding dissipated energy.

The measurement of the fracture energy in mode II, GIIc, of an adhe-sively bonded joint is a much less developed topic. It often leads to practicalproblems when investigating strong, crash-optimized adhesives. Commontechniques are based on the End Notch Flexure (ENF), the Tapered EndNotch Flexure (TENF) or the End-Loaded Split (ELS) specimens. Russeland Street [21] firstly presented an analytical expression to determine GIIc

4

in an ENF test with elastically deforming adherends. This expression is ex-tended by Alfredsson [22] and Leffler et al. [23], who consider the complianceof an adhesive layer. This extension represents the current state of the artfor testing adhesively bonded ENF specimens. Recently, Stigh et al. [24]present a new evaluation method for the ENF test based on the path in-dependence of the J-integral. This method does not require the adherendsto behave purely elastically and allows for much smaller specimens. Besidesthe force, the specimen rotations at the points of loading and supports aremeasured. The fracture energy is calculated by an analytical expression forthe J-integral. Daghyani et al. [25] investigate the mode II fracture energyof adhesive joints with the Compact Pure Shear (CPS) specimen firstly in-troduced by Ripling et al. [5]. In the CPS test, the adhesive layer is assumedto be loaded in pure shear and the fracture energy is evaluated from themaximum force and geometrical parameters. The evaluation method of theCPS test is quite sensitive to the mechanical properties of the investigatedadhesive, since the expression for GIIc considers the shear stress distributioninside the adhesive layer. Marzi et al. [26] propose the End-Loaded ShearJoint (ELSJ) test in which the adhesive layer is loaded in pure shear. Alinear regression between crack growth length and the dissipated energy isused to evaluate the fracture energy. This makes the method suitable fortesting thick adhesive layers. However, the method is limited to adhesiveswith stable crack propagation to allow for the test to be stopped to unloadthe specimen.

In the present paper, we investigate the fracture behaviour of adhesivelybonded joints with the crash-optimized structural adhesive SikaPower 498TM.The adhesive layer thickness ranges from 0.20 to 4.00 mm. The specimenpreparation and the tests are carried out at two different laboratories usingthe same batch of the adhesive. A number of different methods are usedto evaluate the fracture energy in mode I and II. In mode I, both DCB-and TDCB-specimens are used. These are evaluated according to the meth-ods developed in [14] (DCB) and [20] (TDCB) as described below. TDCB-experiments are also evaluated with the Irwin-Kies equation. Furthermore,TDCB bulk-experiments are performed and evaluated using the integrationmethod by Marzi et al. [20]. These should represent the performance of theadhesive in the limit of an infinitely thick layer. In mode II, both ELSJ-and ENF-specimens are used. The ELSJ experiments are evaluated with themethod presented in [26]. Two different ENF-geometries are used. One isbased on the use of elastically deforming adherends, i.e. a modification of

5

the method presented in [23]. The modification is due to the high toughnessof the present adhesive. With the other method, we allow for plastically de-forming adherends and evaluate according to the method presented in [24].Even if neither the ELSJ test nor the ENF test with plastically deformingadherends represent the state of the art, an agreement of the results achievedwith both methods would give a first indication of the validity of these tests.It should be remembered that the specimen fabrication and the tests havebeen carried out at two independent laboratories using the same batch ofadhesive in all investigations.

6

2. Experiments

The influence of the thickness of the adhesive layer on the fracture en-ergy is determined experimentally for a tough crash-resistant epoxy adhesive.Two research laboratories perform the experiments and evaluate the resultsindependently of each other. To ensure the comparability of the results,the investigated adhesive SikaPower 498TM is taken from the same batch.Different test geometries and evaluation methods are employed by the twolaboratories.

In the case of mode I fracture, TDCB experiments are evaluated accordingto the state of the art using the Irwin-Kies equation (TDCB(i-k)). Theresults of these experiments are compared to the results of DCB- and TDCB-experiments evaluated by basically different and recently published methods.One method is based on analytical approaches (DCB), the second one on acorrelation between crack growth length and dissipated energy (TDCB(int)).

In the case of mode II fracture, ENF experiments are performed and eval-uated by a modified method according to the state of the art. In this case,the adherends are deforming elastically during the tests (ENF(el)). Further-more, ENF experiments with different, smaller dimensions are performed.Here, a recently published evaluation method is employed. This methodallows for plastic deformation of the adherends. However, it requires addi-tional measurements of rotation (ENF(pl)). The results of the different ENFexperiments are compared to each other as well as to the results of ELSJexperiments. While the ENF experiments are performed for thin adhesivelayers only, the ELSJ tests are used for thicker layers as well. In total fiveadhesive layer thicknesses are considered. The investigations of mode II frac-ture give two basic results: Firstly, the recently published ENF method aswell as the recently published ELSJ method are benchmarked against an ex-perimental setup representing the state of the art. Secondly, the dependenceof the fracture energy on the thickness of the adhesive layer is determinedexperimentally.

The adherends of the tested DCB and ENF specimens consist of toolsteel; the TDCB and the ELSJ specimens are fabricated from steel 1.6358.The surfaces are cleaned with methyl ethyl ketone (MEK). Then the surfacesare blasted with corundum and finally cleaned once again with MEK. Theadhesive is cured according to its technical data sheet in 20minutes at thetemperature 175 ◦C.

7

2.1. Mode I fracture

For the DCB and TDCB experiments, the nominal specimen width b =5 mm is chosen for all specimens. It is noted that the relevant standards[9, 10], recommend a width four to five times larger to ensure plane strainconditions at the adhesive layer. However, considering the considerable dif-ference in stiffness between the adhesive and the adherends and the largedifference between the transversal and peel strain it is still safe to assumethat the adhesive is in a state of uniaxial strain, cf. [14] for a discussion.Moreover, with the present width, the adherends behave more like beamsthan plates as is the consequence of the standards.

8

2.1.1. DCB experiments

The specimen with notation is shown in figure 1. Due to the symmetryof the specimen and the anti-symmetry of the loading, pure mode I loadingis achieved for the adhesive.

Figure 1: Deformed DCB-specimen with geometry and used notation

Several methods have been developed to evaluate the experimental re-sults, cf. e.g. [11]. The accuracy of these methods varies largely, cf. [13].The methods can be divided into two main categories; methods based onlinear elastic fracture mechanics (LEFM) [27, 28] and methods based on theJ-integral [29, 7].

Methods based on LEFM extended with corrections for nonlinearities arethe basis for the industrial standards to measure the fracture energy [9, 10].The J-integral methods are however preferable since they do not rest on theassumption of linearity. Moreover, they can be used both to achieve thefracture energy and the cohesive properties of the adhesive layer. Cohesiveproperties are ideally suited for FE-analysis of adhesively bonded structures,cf. e.g. [30]. Cohesive properties have been analysed for several adhesives,cf. e.g. [31, 32]. For a DCB-specimen loaded symmetrically with two forcesthe energy release rate is given by,

JI (w) =2F (w) θ (w)

b(3)

where, F is the applied force, θ the rotation of the loading points and b

9

the width of the specimen, respectively. The cohesive stress is derived bydifferentiating JI with respect to the deformation of the adhesive layer, w, atthe crack tip, cf. figure 1. That is

σ (w) =dJI (w)

dw(4)

Among other things, cohesive properties are dependent on temperature,strain rate and thickness of the adhesive layer, cf. [20, 33, 6, 34, 35].

The experimental setup is shown in figure 2. The machine is speciallydesigned for DCB-specimens. The specimen is vertically oriented and theload is applied by low friction bearings. The deformation of the adhesivelayer w is measured at the outside of the adherends by the use of two LVDTs.This is possible since the adhesive is many times more compliant than theadherends. The rotation is measured with an incremental shaft encoder.Two phase shifted digital outputs provide 2×105 pulses per revolution. Thisgives a resolution of π × 10−5 rad/pulse.

Figure 2: Experimental setup for the DCB-experiments with t = 4.0 mm

In this study, 31 specimens with five different adhesive thicknesses are ex-perimentally analysed. Nominal thicknesses are t = 0.2, 0.5, 1, 2 and 4 mm;

10

the actual thickness is measured individually. The length of the specimensis l = 200 mm, the width is b = 5.0 mm, the height of the adherends ish = 8.0 mm, and the unbounded length is a = 80 mm. All experiments areperformed quasi-statically with a nominally constant cross head displace-ment speed, u = 1.7×10−2 mm/s. All experiments are analysed according toequation (3). The energy release rate, JI, vs. the deformation of the adhesivelayer is shown in figure 3. A curve can be divided into three characteristicparts. The first parabolically increasing part of the curve corresponds to thelinear elastic behaviour of the adhesive layer. The second part of the curve isalmost linearly increasing which corresponds to the region where the adhesivestarts to damage and the maximum stress is reached. In the third part, theslope decreases and when a crack starts to propagate, the curves should behorizontal provided crack propagation commences with constant fracture en-ergy. This behaviour is shown for the two thinner layers, t = 0.2 and 0.5 mm,cf. figure 3. The fracture energy is almost constant during crack propagationindicating crack propagation with constant fracture energy. For the thickerlayer t = 1 mm, JI decreases markedly after the maximum is reached. Crackpropagation for all the experiments with t = 4 mm is unstable. The curvesare therefore cut at the first sign of instability. Thus, the otherwise stableDCB-specimen gives unstable crack growth with the most flexible adhesivelayer. This also indicates that the cracks propagate before all fracture energyis consumed at the crack tip. Thus, the recorded fracture energy is somewhatlower than what would be recorded in a stable experiment. The difference ishowever not expected to be large. For the specimens with t = 1 mm, the de-creasing fracture energy might be an effect of the creation of a sharper cracktip during crack propagation. The present authors argue that the propertiesrelated to initiation of crack propagation is of larger engineering value thanthe properties related to propagation of a crack. This is the reason for usinga blunted start of the adhesive layer and not a thin teflon insert as describedin [9, 10]. For t = 2 mm, the fracture energy increases during crack propaga-tion. A study of the fracture surfaces shows that all cracks start near one ofthe interfaces. Some of these experiments show a rotating crack front. Thatis, the visible crack at one of the sides of the specimen is close to one of theinterfaces and at the other side, it propagates from the same interface to theother. This results in a larger crack surface and increasing fracture energy.For all experiments the fracture energy, GIc is taken as JI (w) when the stresshas decreased to 5% of the maximum value σmax, cf. [34].

Figure 4 shows the cohesive stress for all the experiments. The results are

11

Figure 3: Energy release rate vs. the deformation of the adhesive layer

achieved by adapting a Prony series and differentiating according to equation(4), cf. e.g. [36]. As shown, the scatter is small. The peak stress is aboutthe same for all layer thicknesses. The major influence of increasing the layerthickness is to increase the maximum deformation of the layer, from about0.1 mm for t = 0.2 mm to about 0.3 mm for t = 4 mm.

Figure 4: The cohesive stress vs. the deformation of the adhesive layer

The dependence of the fracture energy on the adhesive layer thickness isgiven in the next section, cf. figure 18.

12

2.1.2. TDCB experiments

Two different methods are used to evaluate the TDCB experiments.Besides the classical evaluation method based on the Irwin-Kies equation,TDCB experiments have been performed with specimen unloading after crackpropagation. The fracture energy is then obtained from a linear regressionbetween the crack growth length ∆a and the corresponding dissipated en-ergy Wtot. Figure 5 shows the dimensions of the used TDCB specimens.While the TDCB(i-k) experiments are evaluated according to the state of

32

.00

0.3

0

258.00

73.20

80.0048.00

6.0

0

2.00

14.50

8.00

15.00

14.50

30

.00

0.3

0

100.00

26.00

2.00

6.0

0

5.00

110.00

5.0

0

[mm]

Figure 5: Dimensions of TDCB(i-k) (left) and TDCB(int) (right) specimens

the art using the Irwin-Kies equation, cf. Eq. (5), the TDCB(int) tests areevaluated by the integration method, cf. [26]. Furthermore, TDCB bulkspecimens to represent an adhesive joint of infinite thickness, are fabricatedwith the dimensions of the TDCB(int) specimen and evaluated by the inte-gration method.

The TDCB(i-k) experiments are evaluated by the Irwin-Kies equation,

GIC =F 2

plat

2b

dC

da, (5)

where Fplat denotes a plateau force. The specimen width is b = 5mm. Thechange of compliance with crack growth dC/da = 3.56 × 10−5N−1. Thespecimens are fabricated with five different adhesive layer thicknesses tadh,cf. table 1. Figure 6 shows the measured force-displacement curves of allexperiments. When the crack starts to propagate, the measured force reachesits plateau value Fplat. Four specimens are tested in each test series. Theplateau force Fplat has been evaluated by averaging the measured force F inthe range between the two cross head displacements u1 and u2. Constantvalues are chosen for u1 and u2 and individually for each test series. Thedetailed test evaluation is given in table 1.

13

Figure 6: Results of TDCB(i-k) tests

Table 1: Evaluation of TDCB(i-k) tests acc. to Irwin-Kies equationtadh [mm] u1 [mm] u2 [mm] Fplat [N] GIc [kJ/m2]

0.27± 0.01 2.0 5.0 942.9± 16.9 3.17± 0.130.58± 0.04 3.0 6.0 1106.3± 52.7 4.23± 0.421.09± 0.07 3.0 6.0 1329.3± 42.1 6.29± 0.402.04± 0.02 3.0 7.0 1405.9± 76.4 7.04± 0.773.97± 0.01 3.5 6.5 1256.1± 52.1 5.62± 0.47

14

In the TDCB experiments, the fracture energy increases with the adhesivelayer thickness and seems to reach a plateau value GIc ≈ 5.5− 7.0 kJ/m2 foradhesive thicknesses larger than 1mm, cf. figure 18.

An alternative evaluation method is proposed by Marzi et al. [20]. Thisallows for a smaller TDCB(int) specimen. Another advantage is that thechange of compliance with crack length, dC/da is not necessary to knowin advance. Furthermore, information on the crack initiation energy, Winit,I

is obtained. On the other hand, different crack growth lengths are usedby unloading the specimen and the crack has to be visible on the specimensurface. Moreover, the displacement of the loading point has to be measured.A larger number of experiments is necessary to evaluate GIc.

The load is applied at the pin holes. A certain decrease ∆F of the appliedforce F triggers the start of the unloading. By choosing different values of∆F , different crack growth lengths ∆a can be achieved in the experiments.The total energy per specimen width Wtot/b during the test is given by

Wtot/b =1

b

∫Fdu. (6)

It can be calculated by integrating the measured force displacement curve,where u denotes the cross head displacement measured in the line of loadintroduction. When correlating the crack growth length ∆a to Wtot/b bylinear regression, the slope of the regression line is interpreted as the fractureenergy, GIc. The intercept with the energy axis is denoted the crack initiationenergy under mode I, Winit,I. All experiments are carried out at a constantcross head displacement rate u = 1.7 × 10−2 mm/s. The rate of unloadingin the TDCB(int) and TDCB bulk tests are u = 8.3 × 10−2 mm/s. Cohe-sive fracture occurred in all tests. Five nominal adhesive layer thicknessesranging between 0.25 and 4.0mm are investigated and 10 to 14 single testsare evaluated in each test series, cf. table 2. Figure 7 shows the test resultsgraphically. A linear regression line is adapted for each test series.

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Figure 7: Dissipated energy Wtot vs. crack growth length ∆a (TDCB(int))

Table 2 gives the results of the single test series. The fracture energy GIC

and Winit,I are obtained as the parameters of the linear regression lines. Thevalues are given with their corresponding standard deviation. The influenceof layer thickness on fracture energy is given in figure 18.

Table 2: Evaluation of TDCB(int) tests with integration methodtadh [mm] GIc [kJ/m2] Winit,I [J/m]

0.28± 0.09 2.80± 0.28 22.3± 9.70.48± 0.02 3.41± 0.20 24.2± 4.91.33± 0.14 4.95± 0.89 66.4± 24.72.03± 0.06 4.20± 0.60 59.9± 23.64.08± 0.05 4.21± 0.72 64.0± 23.3

The TDCB bulk specimens are milled out of adhesive bulk plates of ap-proximately 4.6mm thickness. Figure 8 shows the nominal dimensions ofthe specimen. These dimensions correspond to the ones of the TDCB(int)specimen. Additionally, two notches are milled into the specimens’ faces toenforce the crack to propagate straight along these notches. The notch depthis dnotch,1,2 ≈ 0.8mm.

16

Figure 8: Dimensions of TDCB bulk specimen

Opposite to the tests of TDCB specimens with adherends of steel, thecrack tip of the TDCB bulk specimen was shaped with a saw before testingthe specimen. However, as in the other experiments, no initial mode I crackwas introduced into the specimen. Figure 9 shows the crack propagation ina TDCB bulk specimen.

Figure 9: Crack propagation in TDCB bulk specimen

The TDCB bulk specimens are evaluated in the same way as the TDCB(int)experiments: A constant cross head displacement rate u = 1.7×10−2 mm/s ischosen to load the specimen. Unloading is performed with the cross head dis-placement rate u = 8.3× 10−2 mm/s. Different crack growth lengths ∆a areenforced by choosing different target cross head displacements. No significant

17

decrease in the measured force is detected during crack growth. The dissi-pated energy is obtained by integration of the measured force-displacementcurves, cf. figure 10.

Figure 10: Measured force-displacement-curves in TDCB bulk tests

The specimen width bfrac at the fracture surface is smaller than the nom-inal specimen bnom. Thus,

bfrac = bnom − dnotch,1 − dnotch,2. (7)

Thus, bfrac and the crack growth length ∆a is measured for every specimenafter the test.

18

Figure 11: TDCB bulk tests: Wtot vs. ∆a

Figure 11 shows the experimental results of the TDCB bulk tests. Alinear regression is fitted to the measured data. The regression parametersare GIc = 7.39± 0.30 kJ/m2 (slope) and Winit,I = 22.35± 6.06 J/m (interceptwith energy-axis).

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2.2. Mode II fracture

The fracture energy of adhesively bonded joints under shear loading isinvestigated using the ENF- and ELSJ-specimens. The classical evaluationmethods for ENF experiments are based on a purely elastic adherend defor-mation. With strong crash resistant adhesives, this requires large and heavyadherends to avoid plastic deformation. Hence, an alternative method forthe ENF-experiment has recently been developed. This allows for plasticdeformation of the adherends and by this, smaller specimens. However, itrequires additional measurements of rotations of the specimen at the load-ing and support points. Furthermore, the ELSJ has recently been proposedfor the determination of the fracture energy under shear loading of high-strength adhesives. In the following, the results of the ENF-experiments aswell as the results of the ELSJ-experiments are presented and compared tothe results of the ENF-experiments evaluated according to a modification ofthe state of the art method. It should be mentioned that the comparison ofENF- and ELSJ-experiments is performed for thin adhesive layers only, whileELSJ-experiments are performed for five nominal adhesive layer thicknesses.

20

2.2.1. ENF tests

The End Notch Flexure specimen (ENF), shown in figure 12, is commonlyused to measure the fracture energy of adhesively bonded joint loaded inshear. However, certain design aspects have to be accounted when preparing

Figure 12: ENF-specimen, deformed geometry with current notation

the experiments. The shear is non-uniformly distributed along the adhesivelayer; it varies from a large value at the start of the adhesive layer to alower value. Moreover, it switches its direction at the loading point. In[22], a method is derived to extract the cohesive law from measurements ofthe applied load F and the shear deformation at the start for the adhesivelayer v. This method is based on three requirements, the adherends have todeform elastically, the distance between the start of the adhesive layer and theloading point has to be large enough to capture the zone of inelastic behaviourof the adhesive layer, and the specimen has to be stable cf. [22, 37, 23]. Ifthis is the case, the energy release rate is given by

JII =F (v)

bah

[9

16

F (v) a2

Ebh2+

3

8v

], (8)

with the load F applied centrally between the supports (β = 12). a and h are

geometrical dimensions, v is the shear deformation of the adhesive layer atthe start of the layer, and ba is the width of the adhesive layer; here allowed

21

to differ from the width of the specimen, b. From this, the cohesive law inshear is given by

τ (v) =dJII (v)

dv(9)

As for the evaluation of the DCB-experiments, a Prony series is first adaptedto the J-data before differentiation according to equation (9). In order forthe adherends to remain elastic during the experiment, the adherends haveto be high enough. That is, h > hallowed which is mainly determined by thefracture energy and the yield strength of the adherends. With the presenthigh strength adhesive, the width of the adhesive layer has to be smaller thanthe total width of the specimen in order for the specimens to be of realisticdimensions. Thus, only a part of the width of the specimen is adhesivelyjoined, i.e. ba < b. Moreover, if the unbounded length of the specimen is tooshort the experiment will terminate unstably, cf. e.g. [37]. With β = 1/2, acriterion based on linear elastic fracture mechanics is a > 0.35L for stability,cf. [38, 39]. These criteria tend to result in large specimens. The methodhas been used successfully in a number of studies, cf. [34, 35, 37, 23]. Thismethod is denoted ENF(el) in the sequel.

Recently a new method has been derived that allow the specimens todeform plastically and thereby reducing the specimen size substantially, cf.[24]. By this method the energy release rate is given by

JII =F

ba

[βθA − θB + (1− β) θC] , (10)

where θi is the clockwise rotation for the three points i = A, B and C, respec-tively, cf. figure 12. This method is dependent on certain criteria to provideaccurate results. Crack growth appears always to occur after the maximumload is reached in an experiment and the crack starts to grow when F hasstarted to decrease. This means that the adherends are unloading and theJ-integral is not strictly path independent, cf. [24]. Moreover, with a thickand thereby more flexible adhesive layer, it appears as the high load belowthe loading point compress the adhesive layer and obstructs crack growth.This method is denoted ENF(pl) in the sequel.

Both methods are used in order to determine the fracture energy and thecohesive shear stress. All experiments are performed with a prescribed dis-placement rate. Figure 13 shows the experimental setup for the experimentsbased on equation (8). The specimens are designed to be stable and notallowing for inelastic deformation of the adherends. Nominal dimensions are

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given by L = 1.00 m, a = 0.35 m, h = 16.4 mm, b = 32.6 mm, ba = 10 mm,t = 0.3 mm, and β = 1/2. Each specimen is measured individually. Theloading rate is u = 1.7× 10−2 mm/s.

Figure 13: Tensile testing machine used for ENF experiments. An ENF specimen ismounted in the machine

The experimental setup for the experiments based on equation (10) isshown in figure 14. The three rotations θi are measured with an opticalmeasurement system. At each point of interest, a ruler is glued to the spec-imen.The rulers are photographed at regular time intervals during the ex-periment. The photos are analysed and the angle is calculated, cf. [40].Nominal dimensions are given by L = 0.20 m, a = 70 mm, h = 10.6 mm,b = 6 mm, t = 0.3 mm, and β = 0.30. Each specimen is measured individ-ually. The specimens are loaded at a constant cross head displacement rateu = 1.0 mm/min.

Four experiments with two different methods and one adhesive thicknessare performed. Figure 15 shows the energy release rate and the cohesivestress vs. the shear deformation for all experiments, It is noted that theresults appear very similar. However, at the end of the curves there is a sig-nificant difference. For the specimens with elastically deforming adherends,the fracture energy is still slightly increasing when the crack starts to prop-

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Figure 14: Experimentally set up for the specimens with plastically deforming adherends.Left: The measure system with an LVDT used for measure the shear deformation. Right:The rulers used by the optical measurement system in order to capture the angles at thethree points there load are applied

agate. A study of the fracture surfaces show that the crack growth starts asadhesive failure. After about 2 mm crack growth, the crack deviates into theadhesive layer and becomes cohesive.

Figure 15: Energy release rate (left) and cohesive stress (right) vs. shear deformation ofthe adhesive layer. Experiments with elastically deforming adherends: results evaluated byequations (8) and (9), experiments with plastically deforming adherends: results evaluatedby equations (9) and (10)

Table 3 gives a detailed overview of the individually measured specimen

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dimensions and the results. The ENF(el) experiments with purely elasticallydeformed adherends have been evaluated with equation (8), while equation(10) is used for the ENF(pl) tests with plastic adherend deformation. Thefracture energy GIIc is evaluated as JII , when the cohesive stress has de-creased to 5% of the maximum value τmax.

Table 3: Specimen dimensions and results of ENF tests: 2 ENF tests with elasticallydeforming adherends (el.) and 2 tests with plastically deforming adherends (pl.)

L a h b ba tadh β GIIc τmax

[mm] [mm] [mm] [mm] [mm] [mm] [kJ/m2] [MPa]

el. 1000 350 16.4 32.6 10.0 0.33 0.50 13.2 35.5el. 1000 350 16.4 32.5 10.7 0.32 0.50 12.8 37.3pl. 200 70 10.6 5.9 5.9 0.27 0.30 12.1 37.9pl. 200 70 10.6 5.1 5.1 0.36 0.30 13.3 38.2

No significant differences between the results obtained from the ENF(el)and ENF(pl) experiments are found. When merging all ENF results, GIIc =12.9 ± 0.5 kJ/m2 and τmax = 37.2 ± 1.2 MPa have been determined for anadhesive layer thickness tadh = 0.32± 0.04 mm.

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2.2.2. ELSJ experiments

The End-Loaded Shear Joint (ELSJ) is proposed by Marzi et al. [26] todetermine the fracture energy in shear loading. Figure 16 shows the dimen-sions of the ELSJ specimen. The adherends consist of steel 1.6358 with thewidth of b = 5mm.

Figure 16: Dimensions of the ELSJ specimen

The ELSJ experimental series is performed with five nominal adhesivelayer thicknesses ranging from 0.25 to 4.0mm. A constant cross head dis-placement rate u = 1.7 × 10−2 mm/s is used. Cohesive failure occurs in allexperiments. To enforce different crack growth lengths ∆a in the adhesivelayer during one test series, different decreases ∆F of the force F are usedto trigger the start of specimen unloading. This stops the crack propagation.When the remaining, uncracked adhesive layer is cracked after the test withmode I loading, the mode II crack area is visible on the fracture surface ismeasured. When correlating the crack growth length ∆a to the total workper specimen width, Wtot/b,

Wtot/b =1

b

∫Fdu, (11)

by a linear regression line, the fracture energy under shear loading, GIIC, isgiven by the slope of the regression line. The intercept with the energy axisrepresents the corresponding crack initiation energy, Winit,II. Figure 17 showsthe results for all five investigated adhesive layer thicknesses and the adaptedlinear regression lines. Firstly it can be noticed that a linear regression fits

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the measured data well for each experimental series. Secondly, the slope GIIc

as well as the axis intercept Winit,II increase with the adhesive layer thicknessup to a certain plateau value. The experimentally obtained dependence ofGIIc and Winit,II from the adhesive layer thickness is given in the followingsection in figure 20.

Figure 17: ELSJ test results: Wtot vs. ∆a

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3. Experimental Results and Discussion

In this section, the experimental results achieved with different specimentypes and evaluation methods are summarized and discussed.

3.1. Mode I Fracture

The fracture energies, GIc, obtained with the DCB- and the TDCB-specimens are plotted together in figure 18. As shown, GIc depends stronglyon the thickness of the adhesive layer. When the thickness of the adhesivelayers exceeds some certain value, above approximately 1.0mm , GIc reachesa plateau value. Earlier studies with the DCB-specimen show similar results,cf. [35, 41]. Both of these studies give a maximum fracture energy for a layerthickness between t = 1.0 and 1.5 mm. In this study, the maximum fractureenergy is achieved between t = 1.0 and 2.0 mm.

A comparison of the results from the different experimental techniquesshow that the fracture energies agree well in the case of thin adhesive layersonly. When discussing the observed data it should be remembered, thatthick layers of crash-optimized structural adhesives are not of relevance inpractical application today. A typical adhesive layer thickness of such joints isapproximately 0.3 mm. With respect to industrial application, it can thus beconcluded that all of the investigated methods give satisfying and agreeingresults. For thicker layers, which are currently of scientific interest only,the results differ. More detailed investigations should follow to identify thereasons for that discrepancies. As shown, the results achieved from the Irwin-Kies equation give slightly larger values than the other methods for thicklayers. It is reasonable to assume that this is due to the lack of recognition ofthe flexibility of the adhesive layer using this evaluation method. It shouldbe noted that the evaluation method is based on the assumption of a rigidadhesive layer. As the layer thickness increases, this assumption is more andmore inadequate.

The fracture energy determined in the TDCB bulk tests, which is per-formed to mimic an adhesive layer of infinite thickness, is about a factor 1.5larger than the values of joint specimens with a thick adhesive layer. Atfirst this result is unexpected. However, the adhesive in the other DCB- andTDCB-specimens are almost in a state of plane strain while the bulk test isin a state of plane stress. This is probably the reason for the unexpectedlylarge value.

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Figure 18: fracture energy GIC vs. adhesive layer thickness tadh

When evaluating the TDCB experiments with the integration method,information on the crack initiation energy Winit,I is obtained. The dependenceof Winit,I on the adhesive layer thickness is shown in figure 19. For the crackinitiation energy Winit,I there are two plateau values detected: the first onefor thin adhesive layers with layer thicknesses below 0.5mm and the TDCBbulk test; and a second one for thicker adhesive layers. However, since Winit,I

may depend strongly on the shape of the initial crack tip in the adhesivelayer, any correlation between Winit,I and the adhesive layer thickness mayoccur coincidentally. Furthermore it has to be stated that the aim of thepresented test method is the evaluation of the fracture energy, GIc. Whenapplying the integration method, Winit,I is obtained as an additional resultof the experiments. Even when its relevance to the fracture behaviour ofthe joint is not yet finally clarified, the determined values of Winit,I for eachadhesive layer thickness are given for reasons of completeness.

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Figure 19: Crack initiation energy in mode I Winit,I vs. adhesive layer thickness tadh

3.2. Mode II Fracture

The fracture energies of adhesively bonded joints under shear loading areevaluated in ENF- and ELSJ-experiments. The ENF experiments are per-formed in two ways. Firstly, ENF experiments with large adherends and areduced adhesive layer width are performed to ensure purely elastic defor-mation of the adherends. Secondly, smaller ENF specimens have been fabri-cated and tested. Here, a recently developed evaluation method is employedthat allows plastic deformation of the adherends. The ELSJ experiments areperformed for five nominal adhesive layer thicknesses, while the ENF exper-iments are performed for the layer thickness 0.3 mm only. Evaluating theENF experiments with the two methods, no differences between the exper-imental results with respect to the can be detected. A direct comparisonbetween ENF and ELSJ experiments is difficult since the thicknesses of theadhesive layers measured after specimen fabrication differ slightly betweenboth specimen types. However, the results of all investigated specimen typesand analysis methods are in good agreement.

This agreement between the results can be seen as a first validation of therecently developed evaluation method of ENF experiments. It is furthermorea first validation of the ELSJ experiments. For a complete and satisfyingvalidation of the presented evaluation methods, further experimental and

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theoretical studies have to be done.Figure 20 shows the fracture energy GIIc and the crack initiation energies

Winit,II, form all experiments in mode II vs. the adhesive layer thickness. Itillustrates that the ENF experiments are in agreement with the results of theELSJ experiments.

Figure 20: Fracture energy GIIC vs. adhesive layer thickness tadh: Comparison betweenENF and ELSJ experiments

Even when the experimental scatter increases with increasing adhesivelayer thickness, a plateau of both values GIIC and Winit,II is detected foradhesive layers thicker than approximately 1mm. For thin layers, GIIc aswell as Winit,II increase with increasing adhesive layer thickness. It should beremembered that any evaluated value of Winit,II and its regression with theadhesive layer thickness may occur coincidentally for the reasons reported incase of the mode I loading. Furthermore, the plateau value of GIIc appearsin the range 30− 40 kJ/m2 for thick layers and is about a factor of 3.5 largerthan the values obtained for a thin layer of 0.3 mm thickness. This increaseseems reasonable since the corresponding increase of GIc with adhesive layerthickness is in the same order of magnitude; a factor of approximately 3between thin at thick adhesive layers.

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4. Conclusions

The influence of the adhesive layer thickness on the fracture energy of thecrash-optimized high-strength adhesive SikaPower498TMis evaluated at twoindependent laboratories using the same batch of adhesive.

Three different methods (DCB, TDCB(int), and TDCB(i-k)) are used tomeasure the mode I fracture energy. One of these (TDCB(i-k)) is consideredas state of the art. Another method provides the cohesive law as well as thefracture energy (DCB). All methods give virtually the same fracture energyfor small layer thicknesses. Here, the fracture energy increases with increasinglayer thickness. This is in accordance with the results of other studies. Forlarger thicknesses, the results from the different methods deviate. It is arguedthat the larger flexibility of the adhesive layer is the major reason for this asthe TDCB methods are based on the assumptions of a rigid adhesive layer.This assumption is more correct for a thin layer.

In mode II, the fracture energy is measured with three methods (ENF(el),ENP(pl), and ELSJ). One of these (ENF(el)) is a modification of the oneconsidered as state of the art. Two of the methods (ENF(el) and ENF(pl))also provide the cohesive law of the adhesive. Virtually the same fractureenergy is measured for thin layers. Here, the fracture energy increases withincreasing thickness. This is in accordance with previous studies.

In summary, an increase of the fracture energy with increasing adhesivelayer thickness is detected for the adhesive SikaPower498TM at quasi-staticloading conditions in both mode I and II. The results show that furtherstudies are necessary to improve the methods to measure mode I fractureenergy for thick layers. For thin layer, all methods studied here give con-sistent results; the choice of method is more of an open question. However,the DCB-method also provide the cohesive law for the adhesive. In mode II,the newly proposed ENF(pl) method shows promising results. However, forthick layers further studies are necessary to gain confidence in the methods.

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Acknowledgement. The authors acknowledge the partial financial support ofthe presented work through the project FUTURA-IP by the European Union.

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