Adhesive thickness effects of a ductile adhesive by opticalmeasurement techniques

R.D.S.G. Campilho a,n, D.C. Moura b, M.D. Banea c,d, L.F.M. da Silva c

a Departamento de Engenharia Mecânica, Instituto Superior de Engenharia do Porto, Instituto Politécnico do Porto, Rua Dr. António Bernardino de Almeida,431, 4200-072 Porto, Portugalb Instituto de Telecomunicações, Departamento de Engenharia Electrotecnica e de Computadores, Faculdade de Engenharia, Universidade do Porto, Porto,Portugalc Departamento de Engenharia Mecânica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugald IDMEC, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

a r t i c l e i n f o

Article history:Accepted 30 November 2014Available online 8 December 2014

Keywords:PolyurethaneAluminium and alloysFracture toughnessFractureJoint design

a b s t r a c t

Adhesive bonding is an excellent alternative to traditional joining techniques such as welding,mechanical fastening or riveting. However, there are many factors that have to be accounted for duringjoint design to accurately predict the joint strength. One of these is the adhesive layer thickness (tA).Most of the results are for epoxy structural adhesives, tailored to perform best with small values of tA,and these show that the lap joint strength decreases with increase of tA (the optimum joint strength isusually obtained with tA values between 0.1 and 0.2 mm). Recently, polyurethane adhesives were madeavailable in the market, designed to perform with larger tA values, and whose fracture behaviour is stillnot studied. In this work, the effect of tA on the tensile fracture toughness (Gc

n) of a bonded joint isstudied, considering a novel high strength and ductile polyurethane adhesive for the automotiveindustry. This work consists on the fracture characterization of the bond by a conventional and theJ-integral techniques, which accurately account for root rotation effects. An optical measurementmethod is used for the evaluation of crack tip opening (δn) and adherends rotation at the crack tip(θo) during the test, supported by a Matlabs sub-routine for the automated extraction of theseparameters. As output of this work, fracture data is provided in traction for the selected adhesive,enabling the subsequent strength prediction of bonded joints.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Adhesive bonding is an excellent alternative to traditional joiningtechniques such as welding, mechanical fastening or riveting. Actually,the developments in recent commercial structural adhesives enabledtheir use for adhesive bonding in many fields of engineering, such asautomotive and aeronautical. Many of the industrial adhesives usednowadays, such as epoxies and polyurethanes, have high strength andductility [1,2]. There are many other advantages such as more uniformstress fields, capability of fluid sealing, high fatigue resistance, and thepossibility to join different materials. On the other hand, length-wisestress concentrations owing to the gradual transfer of load betweenthe adherends and the adherends rotation in the presence of asy-mmetric loads act as disadvantages [3]. Many works, such as that ofCampilho et al. [4], detail the critical factors affecting the integrity of

adhesive joints, such as the value of adhesive layer thickness (tA),bonding length and geometric modifications that reduce stressconcentrations. These factors have to be accounted for in joint designand to accurately predict the joint strength.

The effect of tA on single-lap joints is well documented in theliterature. Most of the results are for typical structural adhesives andshow that the lap joint strength decreases as tA increases. For epoxyadhesives, as stated by Adams and Peppiatt [5], the optimum joi-nt strength is obtained with a small value of tA, in the range of0.1–0.2 mm. However, analytical models like those of Volkersen [6] orGoland and Reissner [7] predict the opposite. There are many theoriesthat attempt to explain this fact and this subject is still controversial.Adams and Peppiatt [5] claimed that an increase in tA increases theodds of having internal imperfections in the joint (voids and micro-cracks), which will lead to premature failure of the joints. Crocombe[8] shows that thicker single-lap joints have a lower strength byconsidering the plasticity of the adhesive. Gleich et al. [9] showed witha finite element analysis on single-lap joints that the increase ofinterface stresses (peel and shear) as tA increases causes the failure

Contents lists available at ScienceDirect

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International Journal of Adhesion & Adhesives

http://dx.doi.org/10.1016/j.ijadhadh.2014.12.0040143-7496/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author. Tel.: þ351 939526892; fax: þ351 228321159.E-mail address: raulcampilho@gmail.com (R.D.S.G. Campilho).

International Journal of Adhesion & Adhesives 57 (2015) 125–132

load of a bonded joint to decrease with increasing tA. Grant et al. [10]found a reduction in joint strength with increasing tA when testingsingle-lap joints for the automotive industry with an epoxy adhesive.The strength reductionwas attributed to the higher bending momentsfor the lap joints with large tA values due to the increase in the loadingoffset. When composites are used, a decrease in tA increases the peelstress at the ends of the overlap and might trigger compositedelamination. Therefore, the benefits of using a small value of tAmight be reduced. Other studies dealt with the influence of tA on thecohesive strength (t0n for tension and ts

0 for shear) and fracturetoughness (Gc

n for tensile and Gsc for shear, or generically Gc). The

consensus in this matter, as discussed in the work of Leffler et al. [11],is that adhesives in the form of thin bonds behave differently than as abulk material, because of the strain constraining effects of theadherends and the respective typical mixed mode crack propagation.Different studies reported the dependence of Gc

n of adhesive bondswith tA, e.g. the work of Lee et al. [12]. The value of Gc

n of epoxyadhesive bonds was previously studied mostly by the Double-Canti-lever Beam (DCB) test. Typically, Gc

n increases with tA up to a peakvalue, bigger than the bulk quantity. After, Gc

n decreases with tA to asteady-state value, corresponding to Gc

n of the bulk adhesive (the workof Duan et al. [13] is a clear example of this effect). Biel [14]emphasized on the bigger values of Gc

n near the optimal value of tAthan as a bulk. This was due to the predominantly state of prescribeddeformation at the region where the crack could propagate, whichenlarged the damage zone. Actually, with tough engineering adhe-sives, near the optimal value of tA, the damage zone typically extendsseveral times larger than the value of tA, and substantially longer thanin bulk adhesives, resulting on bigger values of Gc

n. Kinloch and Shaw[15] argued that Gc

n is directly related to the plastic zone size that, inturn, is controlled by the surrounding constraints (i.e., adherends).Equivalent studies, such that of Carlberger and Stigh [16], are availablefor Gs

c, mainly by the End-Notched Flexure (ENF) test. Recently,polyurethane adhesives appeared in the market, designed to performwith larger tA values, and whose fracture behaviour is still not studied.

Since the values of strength and toughness of adhesive layers varyas discussed, it is mandatory that they are estimated with accuracy.The DCB test is the most suitable to measure Gc

n due to the testsimplicity and accuracy. The conventional and standardized Gc

nestimation methods are based on Linear-Elastic Fracture Mechanics(LEFM) and rely on the measurement of the crack length (a) duringthe test. However, it is known that Gc

n of ductile adhesives is notaccurately characterized by LEFM methods [17]. In recent years,methods that do not need measurement of a have been developed,such that considered in the work of Campilho et al. [18], additionallyincluding the plasticity effects around the crack tip. As an alternative,in the presence of large-scale plasticity, J-integral solutions arerecommended. Carlberger and Stigh [16] computed the cohesive lawsof adhesive layers in tension and shear by the J-integral using the DCBand ENF tests, respectively, considering 0.1rtAr1.6 mm. The rotationof the adherends was measured by an incremental shaft encoder andthe crack tip opening (δn) by two Linear Variable Differential Trans-ducers (LVDT). The analysis of Ji et al. [19] used a J-integral techniqueapplied to the DCB specimen to study the influence of tA on t0n and Gc

nfor a brittle epoxy adhesive (Loctites Hysol 9460). The analysismethodology relied on the measurement of Gc

n by an analytical J-integral method, requiring the measurement of the adherends rota-tion at the specimen free ends. For the measurement of rotation, twodigital inclinometers with a 0.011 precision were attached at the freeend of each adherend. A charge-coupled device (CCD) camera with aresolution of 3.7�3.7 μm2/pixel was also used during the experi-ments to measure δn, necessary for correlation with the load androtation for the definition of the tensile strain energy (Gn).

In this work, the tA effect on the value of Gcn of a bonded joint is

studied, considering a novel high strength and ductile polyurethaneadhesive for the automotive industry. The experimental work consists

on the fracture characterization of the bond by a conventional and theJ-integral techniques. An optical measurement method is used for theevaluation of δn and adherends rotation at the crack tip (θo) during thetest, supported by a Matlabs sub-routine for the automated extractionof these parameters.

2. Experimental work

2.1. Materials

The material selected for the adherends is a laminated highstrength aluminium alloy sheet (AA6082 T651) cut by precision disccutting into specimens of 140�25�3mm3. The mechanical proper-ties of this material are available in the literature in the refere-nce of Campilho et al. [20], giving the following bulk values:Young's modulus (E) of 70.0770.83 GPa, tensile yield stress (σy) of261.6777.65 MPa, tensile failure strength (σf) of 32470.16 MPa andtensile failure strain (εf) of 21.7074.24%. A novel polyurethanestructural adhesive, SikaForces 7752-L60, was selected for this work.This is a two-part adhesive, and it consists of a filled polyol based resinand an isocyanate based hardener. It is characterized by a roomtemperature cure, high impact resistance and flexibility at lowtemperatures. This adhesive was previously characterized in bulktension in the work of Faneco [21], giving the following properties:E¼493.81789.60 MPa, σy¼3.2470.48 MPa, σf¼11.4970.25 MPaand εf¼19.1871.40%. Fig. 1 shows the experimental σ–ε curves ofthe adhesive Sikaforces 7752 obtained in the above mentioned work,emphasizing the ductile behaviour of the adhesive.

2.2. Joint geometries

Fig. 2 presents the geometry of the DCB specimens. Thedimensions of the specimens are total length L¼140 mm, initialcrack length a0E55 mm, adherend thickness h¼3 mm, widthB¼25 mm and tA¼0.1, 0.2, 0.5, 1 and 2 mm. The fabrication ofthe specimens involved grit blasting the bonding surfaces withcorundum sand, cleaning with acetone and assembly in a steelmould. To achieve the different values of tA uniformly throughoutthe adhesive layer, calibrated spacers of 1 mm were insertedbetween the adherends at the adhesive layer edges. A sharp pre-crack at the specimens' free edge was induced by a spacercomposed of a 0.1 mm thick razor blade between 0.45 mmcalibrated bars. These were stacked and glued together, making atotal thickness of 1 mm. The cutting edge of the blade was offsetfrom the sheets and positioned facing the adhesive layer beforeapplication of the adhesive such that, after curing of the adhesive,a sharp pre-crack was produced at the adhesive layer edge.Application of demoulding agent to the spacers enabled theirextraction after curing of the adhesive. Curing was performed atroom temperature. The spacers were removed and one of the

0

2

4

6

8

10

12

14

0 5 10 15 20 25

[MPa

]

ε [%]

Fig. 1. Experimental σ–ε curves of the adhesive Sikaforces 7752.

R.D.S.G. Campilho et al. / International Journal of Adhesion & Adhesives 57 (2015) 125–132126

specimens' sides was sprayed with white brittle paint, to allow aneasy identification of a, and a printed scale was glued in thatspecimen side to aid the a measurement or input data for thedigital correlation technique. Thirty specimens were tested (six foreach configuration) at room temperature in an electro-mechanicaltesting machine (Shimadzu AG-X 100) with a load cell of 100 kN.To prevent strain-rate-induced variations in the Gc

n measurements,the test velocity was defined to ensure a constant strain-rate for allvalues of tA [22]. Each test was fully documented using an 18MPixel digital camera with no zoom and fixed focal distance toapproximately 100 mm. This procedure allowed obtaining thevalues of δn and θo, necessary for the J-integral method. Thecorrelation of the mentioned parameters with the load-displacement (P–δ) data was achieved by the time elapsed fromthe beginning of each test.

3. Methods to determine Gcn

Giovanola and Finnie [23] claimed that LEFM methods areinaccurate to estimate Gc when the adhesives are ductile, althoughsome expressions consider correction factors to account for plasticity(e.g. the methods depicted in the standards ASTM D3433-99:2005and BS 7991:2001). The Compliance-Based Beam Method (CBBM),which accounts for the damage zone ahead of the crack tip (alsoknown as fracture process zone), and the J-integral were consideredfor the present study to consider plasticity effects. By these methods,the effects of root rotation caused by the expected long plastic zonebeyond the crack tip are taken into account.

3.1. Compliance-Based Beam Method

The CBBM is a relatively straightforward but a robust method,based on an equivalent crack, and it only depends on the speci-men's compliance during the test. Applied to the DCB test speci-men, it gives

Gcn ¼

6P2

B2h

2a2eqh2Ef

þ 15Gxy

!: ð1Þ

Detailed explanations of the method can be found in the workof Campilho et al. [18]. In the expression, aeq is an equivalent crack

length estimated from the current specimen compliance andtaking into consideration the damage zone, Ef is a correctedflexural modulus to account for stress concentrations at the cracktip and stiffness variability between specimens, and Gxy is theshear modulus of the adherends in the plane xy (Fig. 2).

3.2. J-integral method

The technique described in this section is called the directmethod, and it allows obtaining Gc

n and the cohesive law of theadhesive by the simultaneous measurement of the J-integral andδn, as reported by Ji et al. [19]. The scope of the J-integral fallswithin the non-linear elastic behaviour of materials, but it is suitedto the measurement of Gc

n because it remains valid in the presenceof a plastic but monotonically-applied loading, as it occurs duringa DCB fracture characterization test. However, by this formulationit is assumed that the adherends behave elastically during theloading process. Using the generic J-expression defined by Rice[24], it is possible to derive a closed-form solution for Gn from theconcept of energetic force and also the beam theory for the DCBspecimen, as defined by Ji et al. [19]

Gn ¼ 12Puað Þ2Eah

3 þPuθo or Gn ¼ Puθp; ð2Þ

where Pu represents the applied load per unit width at theadherends edges, Ea the Young's modulus of the adherends andθp the relative rotation of the adherends at the loading line (Fig. 3).Between the two expressions of (2), the authors opted for usingthe first expression, considering θo instead of θp, because ofprevious evidence of stability and accuracy in the measurementsand test simplicity [18]. In this equation, the first term is the LEFMsolution (without root rotation corrections) and the second term isthe correction for root rotation. It should be noted that thisformulation relies on the classical beam theory, which does notaccount for shear effects. These effects in particular may have alarge influence on the results regarding the measurement ofGcn under specific conditions. However, as tested by Ji et al. [19],

for DCB bonded joints having adherends with a small value of h,the influence of the shear deformation was under 2% on theGcn measurements. Thus, this formulation is considered valid.

A further validation of this methodology was previously presented[25] by estimating Gc

n using the DCB specimen and the respectivetensile Cohesive Zone Model (CZM) law. Validation was achievedby replicating the experimental tests in CZM simulations with highaccuracy. If the J-integral is taken along an arbitrary path encir-cling the start of the adhesive layer, Ji et al. [19] defined that

Gn ¼Z δnc

0tn δnð Þdδn: ð3Þ

δnc is the crack-tip end-opening at failure of the cohesive law andtn is the current normal traction. When the specimen is loaded,Gn increases up to attaining Gc

n, corresponding to the onset of crackpropagation. Gc

n is thus obtained by the steady-state value of Gn in theFig. 2. Geometry of the DCB specimens.

Fig. 3. DCB specimen under loading, with description of the analysis parameters.

R.D.S.G. Campilho et al. / International Journal of Adhesion & Adhesives 57 (2015) 125–132 127

Gn–δn plot. The tn(δn) plot or cohesive law of the adhesive layer isobtained by fitting of the Gn–δn plot and differentiationwith respect toδn [19]

tn δnð Þ ¼ ∂Gn

∂δn: ð4Þ

3.2.1. Continuous measurement of δn and θo by the optical methodA numerical algorithm was developed in a previous work by

Campilho et al. [26] to study the influence of h on Gcn, based on

digital image processing and tracking reference points by thesoftware to give estimated measurements of θo and δn. The opticalmethod requires the identification of 8 points (Fig. 4): points p3and p4 enable measuring the current tA value at the crack tip (tACT)during loading in image units (pixels), points p7 and p8 identify astraight line in the image for which the length (d) is known in realworld units (mm), and finally points p1 and p5 on the top specimenand points p2 and p6 on the bottom specimen will enable theestimation of θo. The details of the point tracking algorithm used toautomatically track the 8 points of each picture of a given test,after the points in the first figure of the test are manuallyidentified, are presented in Appendix A.

3.2.1.1. θo calculation. The value of θo is obtained by the angle betweenthe tangents to the horizontal curves of the 2 scales closest to theadhesive, measured at the crack tip (Fig. 5). The curvature of the topadherend is first computed by fitting a quadratic function to points p1,p3 and p5. The first derivative of the quadratic function at p3 yields theslope of the top curve (mtop) at the crack tip, which is then used todefine a direction vector v!top¼(1,mtop). The same process is repeatedfor points p2, p4 and p6, yielding the slope of the tangent to the bottomcurve at the crack tip (mbottom) and its direction vector v!bottom ¼1;mbottomð Þ. Finally, θo is obtained bymeasuring the angle between thetwo vectors

θ0 ¼ arccosv!top U v!bottom

v!top

��� ��� v!bottom

��� ���0B@

1CA: ð5Þ

3.2.1.2. δn calculation. Initially, tACT is calculated in real world units(mm) by the following expression:

tACT ¼ dp3�p4�� ��p7�p8�� ��: ð6Þ

The value of d/|p7�p8| enables the conversion of |p3�p4| fromlength in pixels to length in mm. A length of d¼15 mm was usedfor all trials (length between points p7 and p8 in Fig. 4). The pixelsize was on average 0.021 mm and, thus, the estimated maximumerror of the image acquisition process is 70.011 mm. Finally, δncan be defined as

δn ¼ tCTA �tiA; ð7Þwhere tA

i is the initial value of tA.

4. Results

All DCB tests were carried out by the previously mentionedprocedure, considering six specimens for each tA value. By visualinspection of the failed specimens, no signs of plasticity werefound in the adherends. Failure was cohesive in all specimens.

4.1. Gcn calculation by the CBBM

The CBBM enables plotting the R-curve for each specimen, relatingGn with aeq. The R-curve ideally gives a constant value of Gn over theentire propagation phase, although experimentally some fluctuationsoccur due to different adhesive mixing, adhesion issues, defects andcrack arrest phenomena. Fig. 6 compares representative R-curves foreach of the tested tA values (i.e., selected curves that show the typicalaverage behaviour for each condition). These curves show the crackpropagation with a steady-state value of Gn. The initial phase of thecurves relates to the increase of Gn up to the onset of crackpropagation and allows the visualization of aeq before damage, whichis slightly bigger than a0 because aeq accounts for the damage zone[18]. For example, for the representative specimen with tA¼0.2 mm,and a0¼48.6 mm, while the corresponding value of aeq is 54.7 mm(calculated directly from the P–δ data by the first drop of P in the P–δcurve). Fig. 7 shows the evolution of Gc

n (N/mm) with tA and standarddeviation of each testing group. There is a clear tendency of Gc

nincrease with tA from 0.1 to 2.0 mm, with an apparently bigger

Fig. 4. Points taken by the optical method to measure δn and θo.

Fig. 5. Calculation of θo. Quadratic functions were fitted to points p1, p3, p5 and p2, p4, p6, representing the curvature of the top and bottom specimen, respectively, while thestraight lines show the tangents to the curves at the crack tip (corresponding to 10 mm in the scales).

R.D.S.G. Campilho et al. / International Journal of Adhesion & Adhesives 57 (2015) 125–132128

increase for the smaller tA values. For tA¼0.1 mm, a value ofGcn¼1.85870.264 N/mm was found. From this point, the improve-

ments were 13.2% for tA¼0.2 mm, 50.4% for tA¼0.5 mm, 102.9% fortA¼1.0 mm and 179.9% for tA¼2.0 mm. This tendency is responsiblefor the increased load capacity of the joints as tA becomes thicker, as itwas discussed in a previous work by Ji et al. [19].

4.2. Gcn calculation by the J-integral

Following the method described in Section 3.2, Gcn was calcu-

lated by the first equation of (2), which considered θo instead ofθp, to obtain Gn. The procedure to obtain θo is presented inSection 3.2.1.1 and enabled plotting the curve θo–testing time withone data point every 5 s. Fig. 8 shows a θo–testing time curve for aspecimen with tA¼0.2 mm, with emphasis to the raw curve, the6th degree fitting law and the adjusted law, considering θo(testing

time¼0)¼0. The adjustment removes the experimental measure-ment noise and cancels any misalignment between the measure-ment scales. Throughout the data analysis, different orderpolynomials were considered by achieving the best correlationfactor, R (this also applies to the forthcoming fitting data). Theδn–testing time data was also plotted to build the Gn–δn curve andthe cohesive law by Eq. (4). Fig. 9 presents this curve for the samespecimen of Fig. 8. In this figure, the adjusted curve was shiftedupwards by 0.02 mm for clarity. Equally to the work of Ji et al. [19],the value of Gc

n is obtained at the beginning of crack propagation(peak value in the P–δ curve) and is defined by the steady-state Gn

value in the Gn–δn curve.Fig. 10 shows a representative Gn–δn curve for each tA value

(polynomial approximation of the real curves). The shape of thecurve is invariant to tA and it is constituted by three distinctregions: initially, the increase of Gn with δn is slow (very smallregion and not visible in the figure), secondly, a region ofapproximate linear increase of Gn appears and finally the curvetends to a steady-state value of Gn. The shape of these curves issimilar to the ones reported in the literature (e.g. Campilho et al.[18] and Ji et al. [19]), although in brittle to moderately ductileadhesives the three mentioned regions are more similar in exten-sion. It is visible that the initial slope of the Gn–δn curves (beforethe softening leading to the steady-state value of Gn) increases byincreasing tA. This behaviour is related to a faster propagation ofthe plastic zone with the applied loading for bigger values of tA.Since the tn–δn curves, to be presented further in this work, areobtained by differentiation of the Gn–δn curves, the aforemen-tioned slope effect will result on increasing values of t0n byincreasing tA. The Gn–δn curves were plotted for all specimensand the average Gc

n results for each tA value and respective

0.0

1.0

2.0

3.0

4.0

5.0

6.0

40 60 80 100 120

Gn

[N/m

m]

aeq [mm]

0.1 mm 0.2 mm 0.5 mm 1.0 mm 2.0 mm

Fig. 6. Comparison of representative R-curves for each of the selected tA values.

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5

Gnc

[N/m

m]

tA [mm]

Fig. 7. Average values and deviation of Gcn as a function of tA by the CBBM.

-0.02

0

0.02

0.04

0.06

0 50 100 150 200 250 300

θ o[r

ad]

testing time [s]

Raw curve Adjusted curve Polynomial (Raw curve)

Fig. 8. Plot of θo testing time for a specimen with tA¼0.2 mm: raw curve,polynomial approximation and adjusted polynomial curve.

0.00

0.10

0.20

0.30

0 50 100 150 200 250 300

δ n[m

m]

testing time [s]

Raw curve Adjusted curve Polynomial (Raw curve)

Fig. 9. Plot of δn–testing time for a specimen with tA¼0.2 mm: raw curve,polynomial approximation and adjusted polynomial curve.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Gn

[N/m

m]

δn [mm]

0.1 mm 0.2 mm 0.5 mm 1.0 mm 2.0 mm

Fig. 10. Representative Gn–δn laws for each value of tA.

R.D.S.G. Campilho et al. / International Journal of Adhesion & Adhesives 57 (2015) 125–132 129

deviation are presented in Fig. 11. The results are consistent with theCBBM of Fig. 7 regarding the absolute values and tendency with tA.For the specimens with tA¼0.1 mm, the obtained results gaveGcn¼1.83470.237 N/mm. The increase of Gc

n from this point was of14.6% (tA¼0.2 mm), 57.8% (tA¼0.5 mm), 105.6% (tA¼1.0 mm) and195.8% (tA¼2.0 mm). Differentiation of the Gn–δn curves, accordingto Eq. (4), gives the tn(δn) or CZM laws of the adhesive layer.

Fig. 12 shows selected CZM laws for each tA value. The markedductility of the adhesive can be testified by shape of the curves, inwhich cohesive stresses extend up to a large value of δn (although thecurves are cropped to enable a clear view of the most pertinentregions). Comparing with typical laws of ductile epoxy adhesives (e.g.the work of Carlberger and Stigh [16]), in which a clear and significantsteady-state region of tn appears at the onset of plasticization, followedby quick failure, for this adhesive this region is almost inexistent but,in contrast, the cohesive stresses are cancelled over a much biggerspan of δn. This behaviour could be anticipated by the shape of theGn–δn plots of Fig. 10, in which the third region (of Gn stabilization) ispreponderant, in opposition to epoxy adhesives. In view of thisbehaviour, the trapezoidal laws that usually mimic very well thebehaviour of ductile epoxy adhesives (e.g. Campilho et al. [26,27]) arenot the most appropriate to model this particular adhesive. In thissituation, the triangular law would fit better. A linear-exponential law(composed of linear behaviour up to the peak strength, but followedby exponential degradation up to failure) is surely the most appro-priate to reproduce the experimentally degradation trend [28].Another feature that contrasts to the typical behaviour of epoxyadhesives is the increase of t0n with tA. In epoxy adhesives, the inversetendency is found, i.e., the value of t0n is highest for small values of tAand gradually diminishes with the increase of this parameter up to thebulk value of t0n [19].

4.3. Analysis of the results

By comparing Fig. 7 and Fig. 11, which give the CBBM andJ-integral results, respectively, results agree in absolute values andincreasing trend of Gc

n with tA. Table 1 shows the summary ofaverage values and deviation of Gc

n [N/mm] for both data reductionmethods and all tA values, together with the percentile deviationbetween the CBBM and the J-integral (%Δ). The % deviation foreach tested condition (i.e., tA value) is generally under 10%, whilstthe %Δ between methods has a maximum of 4.31% for tA¼2 mm.Regarding the available studies (for epoxy adhesives), Yan et al.[29] studied the influence of tA on the fracture properties (Gc

n) ofDCB and Compact Tension (CT) joints with a rubber-modifiedepoxy adhesive. A Gc

n increase was found up to tA¼1 mm and adecrease afterwards. An identical conclusion was found by Khooand Kim [30] for an epoxy adhesive between 0.2≤tA≤1.5 mm, withthe maximum Gc

n being found for tA¼1 mm. Azari et al. [31]experimentally studied the influence of tA on Gc

n for a single parttoughened epoxy adhesive, considering 130≤tA≤790 μm, showingan increasing trend, but suggesting the attainment of a steadystate value of Gc

n near the biggest value of tA. This dependence wasattributed to the large plastic zone size at the crack tip, because ofusing a highly-toughened epoxy adhesive. The cohesive zoneanalysis of Ji et al. [19] addressed the influence of tA on t0n andGcn for a ductile epoxy adhesive (Loctites Hysol 9460) by the DCB

specimen. Results showed the previously mentioned increase ofGcn with tA, although without reduction, which was considered to

be due to the marked ductility of the adhesive. A value oftn0¼88 MPa found for tA¼0.09 mm, much higher than the bulkstrength of 30.3 MPa. However, by increasing the values of tA, thet0n values quickly approached the bulk strength of the adhesive.Different authors addressed the cause for this increase of Gc

n withtA. The explanation of this behaviour was previously discussed.

The increasing trend obtained in this work of Gcn with tA is linear

up to tA¼2.0 mm, and this result is consistent with previous studies inthis matter, except from a reduction of Gc

n for big values of tA that iscommon with less ductile epoxy adhesives. Another exception is thework of Marzi et al. [32], which attained a maximum Gc

n betweentA¼1 and 2mm for the polyurethane SikaPowers 498TM, a moderncrash resistant epoxy adhesive, without a reduction tendency of Gc

n upto tA¼2mm, due to its large ductility. An identical trend to this workregarding the Gc

n–tA law was found by Banea et al. [22] with the highelongation polyurethane Sikaforces 7888, characterized with conven-tional fracture methods in the range of 0.2rtAr2mm. For thisparticular adhesive, Gc

n increased almost linearly up to tA¼1 mm,showing a lesser improvement from this value up to tA¼2mm. Inboth this and the present work, the peak value of Gc

n is attained for atA value bigger than 2 mm, but in this range of values the joints aremore likely to have fabrication defects and are more difficult tofabricate, which justifies their limited industrial applicability. Thisbehaviour is related to the generation of plastic zones of increasing

0

20

40

60

80

100

0 0.02 0.04 0.06 0.08 0.1

t n[N

/mm

]

δn [mm]

0.1 mm 0.2 mm 0.5 mm 1.0 mm 2.0 mm

Fig. 12. Representative CZM laws for each value of tA.

Table 1Average values and deviation of Gc

n [N/mm] for both data reduction methods.

tA (mm)

0.1 0.2 0.5 1 2

CBBM Average Gcn (N/mm) 1.858 2.102 2.794 3.770 5.200

St. deviation (N/mm) 0.264 0.166 0.215 0.424 0.493% deviation 14.2 7.9 7.7 11.3 9.5

J-integral Average Gnc (N/mm) 1.834 2.102 2.893 3.770 5.425

St. deviation (N/mm) 0.237 0.103 0.238 0.278 0.363% deviation 12.9 4.9 8.2 7.4 6.7

%Δ between methods �1.29 0.01 3.54 0.00 4.310

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5

Gnc

[N/m

m]

tA [mm]

Fig. 11. Average values and deviation of Gcn as a function of tA by the J-integral.

R.D.S.G. Campilho et al. / International Journal of Adhesion & Adhesives 57 (2015) 125–132130

dimensions with tA prior to crack propagation [22], enabled by thereduction of the adherend constraining effects concurrently to themarked adhesive ductility that allowed the enlargement of the plasticzone up to tA¼2mm.

5. Conclusions

The present work aimed to assess the effect of tA on Gcn of a largely

ductile adhesive, the Sikaforces 7752 FRW-L60.With this purpose, theDCB test was considered to be the most suited. For the measurementof Gc

n, the CBBM and the J-integral were used. Comparing bothmethods in which regards time requirements, the J-integral is moretime consuming because of the necessity to measure θo and δn at thecrack tip during the test. Actually, if only Gc

n is requested, the methodonly requires measurement of θo. However, the measurement of δngives the possibility to obtain the cohesive law of the adhesive layer bydifferentiation of the tn¼ f(δn) curve, which is a clear advantage forsubsequent strength predictions by advanced methods such as CZMmodelling. Both methods are suited to capture Gc

n for ductile adhesivesby considering root rotation effects that are large on account of theadhesive characteristics. The obtained results by both methods werecomparable, with a maximum deviation of 4.31% for tA¼2.0 mm.An increasing linear trend was found between Gc

n and tA up totA¼2.0 mm. The Gc

n increase is due to the predominantly state ofprescribed deformation at the region where the crack can propagate,which enlarges the damage zone and consequently Gc

n. This result isconsistent with previous literature studies, although epoxy adhesivestypically experience a Gc

n decrease up to the bulk Gcn. However, due to

the ductility of the selected adhesive, such behaviour was not foundup to tA¼2.0 mm. The study of bigger values of tA was not consideredrelevant since fabrication of the joints and resulting characteristics(e.g. stiffness) become inappropriate. The tensile CZM laws of theadhesive, enabled by the J-integral technique, showed the ductilecharacteristics of the adhesive. These CZM laws can subsequently beused as input in numerical simulations for the strength prediction ofbonded joints.

Acknowledgements

The authors would like to thank Sikas Portugal for supplyingthe adhesive.

Appendix A. Point tracking algorithm

Initially, the eight points are identified manually in the first pictureof a test. To be noticed that points p1 to p6 are printed with a distinctcolour (although this is not perceptible in Fig. 4), which helps findingtheir correct locations. Since the points of the first image are manuallyidentified, in order to minimize variations on the measuring processdue to user errors, the location of the points is first optimized using aMatlabs algorithm that takes into account colour information of theruler. Then, starting from the optimized points of the first picture, thepoints of the following pictures are automatically tracked with analgorithm in Matlabs. For each point pi, a rectangular region centredin pi is extracted from the first image forming a template (t). Thistemplate describes the image pattern that surrounds the point and isused for locating the point in the next image. This is done by findingthe position (u,v) in the next image (I) that has the highest normalizedcross-correlation with the template. The normalized cross-correlationis a measure of similarity between two images. To take advantage ofthe colour information, the colour space of the images (and conse-quently, of the templates) was transformed to the CIELAB colourspace. The CIELAB system represents the value of a pixel by three

components, L, a and b, where L represents luminosity and a and bdefine colour. Since points p1 to p6 are differentiated by their colour,only the a and b components are used when detecting points. Thenormalized cross-correlation (γ) of template t with image I at theposition (u,v) of image I for the colour component c is defined asfollows [33]:

γ u; v; cð Þ ¼ ∑x;y I x; y; cð Þ� Iu;v;c� �

t x�u; y�v; cð Þ�tc� �

∑x;y I x; y; cð Þ� Iu;v;c� �2

∑x;y t x�u; y�v; cð Þ�tc� �2n o0:5;

ðA:1Þ

where I(x,y,c) is the intensity of the colour component c of the pixel(x,y) of image I, t(x,y,c) is the intensity of the colour component c of thepixel (x,y) of the template t, Iu;v;c is the average intensity of thecolour component c of the region of image I centred at pixel (u,v)and with the same size as t, and tc is the average intensity of thecolour component c for the template t. Finally, the normalized cross-correlation for a single pixel taking into account the colour componentsa and b is defined as follows:

γ u; vð Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiγ u; v; að Þ2þγ u; v; bð Þ2

qðA:2Þ

Calculating γ for all the pixels of I results in a matrix where themaximum absolute value yields the location of the region in I that hasthe highest correlationwith t and, thus, themost likely location of pi inthe next image. This is done for every one of the eight points identifiedin the first image. After successfully identifying all the points of thesecond image, new templates are computed from the second image tosearch for the eight points in the third image, and so on untilprocessing all images.

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