Microsoft Word - numero_31_art_1 R.D.S.G. Campilho et alii, Frattura ed Integrità Strutturale, 31 (2015) 1-12; DOI: 10.3221/IGF-ESIS.31.01 1 Advanced techniques for estimation of the tensile fracture toughness of adhesive joints R.D.S.G. Campilho Departamento de Engenharia Mecânica, Instituto Superior de Engenharia do Porto, Instituto Politécnico do Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal raulcampilho@gmail.com M.D. Banea, L.F.M. da Silva Departamento de Engenharia Mecânica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal ABSTRACT. Adhesive bonding has become more efficient in the last few decades due to the adhesives developments, granting higher strength and ductility. As a result, adhesives are being increasingly used in industries such as the automotive, aerospace and construction. Thus, it is highly important to predict the strength of bonded joints to assess the feasibility of joining during the fabrication process of components (e.g. due to complex geometries) or for repairing purposes. When using the Finite Element Method with advanced propagation laws, the tensile (Gnc) and shear (Gsc) fracture toughness of adhesive joints must be determined with accuracy. Several conventional methods to obtain Gnc and Gsc exist in the literature, mainly based on Linear Elastic Fracture Mechanics (LEFM). The J-integral technique is accurate to measure these parameters for adhesives with high ductility. In this work, the J-integral is used to obtain Gnc by the Double-Cantilever Beam (DCB) test. An optical measurement method is developed for the evaluation of the crack tip opening and adherends rotation at the crack tip during the test, supported by a Matlab® sub-routine for the automated extraction of these quantities. As output of this work, an optical method that allows an easier and quicker extraction of the parameters to obtain Gnc than the available methods is proposed (by the J-integral technique) and some results are presented regarding joints with different geometry and adherend material. KEYWORDS. Fibres; Fracture toughness; Damage mechanics; Joining. INTRODUCTION he developments in adhesives technology made possible the use of adhesive bonding in many fields of engineering, such as automotive and aeronautical [1]. However, stress concentrations exist in bonded joints along the bond length owing to the gradual transfer of load between adherends and also the adherends rotation in the presence of asymmetric loads [2]. A large amount of works addresses the critical factors affecting the integrity of adhesive joints, such as the parent structure thickness, adhesive thickness, bonding length and geometric modifications that reduce stress concentrations [3-5]. A large number of predictive techniques for bonded joints are currently available, ranging from analytical to numerical, using different criteria to infer the onset of material degradation, damage or even complete failure. Initially, the prediction was performed by theoretical studies as those of Volkersen [6], which had a lot of embedded simplifying assumptions, by T R.D.S.G. Campilho et alii, Frattura ed Integrità Strutturale, 31 (2015) 1-12; DOI: 10.3221/IGF-ESIS.31.01 2 comparing current stresses with the allowable material strengths. Many improvements were then introduced, but these analyses usually suffered from the non-consideration of the material ductility. Fracture mechanics-based methods took the fracture toughness of materials as the leading parameter. These methods included more simple energetic or stress-intensity fracture techniques that required the existence of an initial flaw in the materials [7]. More recent numerical techniques, such as Cohesive Zone Models (CZM), combine stress criteria to account for damage initiation with energetic, e.g. fracture toughness, data to estimate damage propagation [8]. This allows to consider the distinct ductility of adhesives and to gain accuracy in the predictions. All of these fracture toughness-dependent analyses rely on an accurate measurement of Gnc and Gsc. CZM in particular can accurately predict damage growth if the fracture laws are correctly estimated [9]. These laws are based on the values of cohesive strength in tension and shear, tn0 and ts0, respectively, and also Gnc and Gsc. These parameters that cannot be directly related with the material properties measured as bulk, since they account for constraint effects (for adhesive joints, caused by the adherends). The estimation of these fracture parameters is generally accomplished by performing pure tension or shear tests. Regarding Gnc, the DCB test is the most suitable, due to the test simplicity and accuracy [10]. As described by Suo et al. [11], in the presence of large-scale plasticity, J-integral solutions can also be employed for accurate results, in contrast to LEFM-based solutions. The J-integral is a relatively straight-forward technique, provided that the analytical solution for a given test specimen exists for the determination of Gnc or Gsc. The most prominent example is the DCB specimen, for which J-integral solutions are available. It is also possible to estimate the tensile CZM law. A few methods are available to estimate the cohesive parameters and the respective laws: the property identification and inverse methods consist on assuming a simplified shape (bilinear or trilinear) for the fracture laws and defining the respective parameters by standardized procedures, while the direct method estimates the precise law shape by computing it based on fracture characterization data [12]. This is accomplished by the differentiation of the strain energy release rate in tension (Gn) or shear (Gs) with respect to the relative opening (n for tension or s for shear). A few works addressed the J-integral method. Carlberger and Stigh [13] computed the CZM laws of adhesive layers in tension and shear using the DCB and End-Notched Flexure (ENF) tests, respectively, considering 0.1≤tA≤1.6 mm (tA is the adhesive thickness). The J-integral methodology and the direct method were used for measurement. The rotation of the adherends was measured by an incremental shaft encoder and the crack tip opening by two Linear Variable Differential Transducers (LVDT). The aforementioned techniques were considered accurate and enabled extracting the parameters with little noise during the full range of the tests. Nonetheless, added difficulties were found because of the complicated test setup. The value of Gnc revealed a monotonic increase from tA=0.1 to 1.0 mm. Above this value, a slight reduction was found. Under shear, the dependence of Gsc with tA is not so significant, but an identical increasing trend is clear under tA=0.2 mm. In both cases, the observed behavior was explained in light of the increasing plastic zone size with the corresponding increase of tA. Ji et al. [14] studied by the J-integral the influence of tA in DCB joints on tn0 and Gnc for a brittle epoxy adhesive. Gnc was measured by a direct technique. For the measurement of the adherends rotation, two digital inclinometers with a 0.01º precision were attached at the free end of each adherend. The normal displacement at the crack tip was measured by a charge-coupled device (CCD) camera. Regarding the test setup, a step forward in terms of procedure was achieved by replacing the opening measurement system by a non-contact system. Regarding the influence of tA on Gnc, an increasing trend was found from 0.09≤tA≤1.0 mm, which was related to increasing plastic dissipations with the increase of tA. This work evaluates Gnc of adhesive joints for different conditions: adhesive bonding for adhesive joints with natural fibre composite as adherends, adhesive bonding between aluminium adherends to study the effect of the adherends thickness (h) on Gnc, and finally adhesive bonding between aluminium adherends considering varying values of tA. The J-integral is selected to measure Gnc to account for the plasticity effects, together with the direct method to define the cohesive laws. An optical measurement method is used for the evaluation of crack tip opening and adherends rotation at the crack tip, supported by a Matlab® routine for the automated extraction of these parameters. This technique provides a step forward in the available methods to extract the adherends rotation and crack opening at the crack tip, enabling a much easier test setup, without compromising the accuracy of the results. The data analysis is also automated to ease the data reduction process. EXPERIMENTAL WORK Characterization of the materials hree joint configurations were tested in this work, presented in Tab. 1, considering the DCB test geometry. For configuration 1, typical properties of jute are as follows: density of 1.3-1.4 g/cm3, elongation at failure (f) of 1.5- 1.8%, tensile strength (f) of 400-800 MPa and Young’s modulus (E) of 15-30 GPa [15, 16]. Epoxy was chosen T R.D.S.G. Campilho et alii, Frattura ed Integrità Strutturale, 31 (2015) 1-12; DOI: 10.3221/IGF-ESIS.31.01 3 for the matrix material on account of the good mechanical (strength and stiffness) and toughness properties, and also because of the superior wetting characteristics on natural fibres [17]. The epoxy resin type SR 1500 and SD 2505 hardener from Sicomin Epoxy Systems were used. The matrix properties, as specified by the manufacturer, are as follows: E=3.1 GPa, f=74 MPa, strain at maximum load m=4.4% and f=6.0%. The jute-epoxy composite was composed by 30% of jute fabric (by weight) and gave the following properties in tensile testing: E=5.7 GPa and f=124.3 MPa. For configurations 2 and 3, the aluminium adherends were cut from a high strength aluminium alloy sheet (AA6082 T651). Configuration Adherends Adhesive 1 Jute-epoxy composite SikaForce® 7888 2 Aluminium SikaForce® 7888 3 Aluminium SikaForce® 7752-L60 Table 1: Configurations tested to measure Gnc. This material was characterized in bulk tension in previous works by the authors [18] using dogbone specimens and the following mechanical properties were obtained: E=70.07±0.83 GPa, tensile yield stress (y) of 261.67±7.65 MPa, ultimate tensile stress (f) of 324±0.16 MPa and elongation (f) of 21.70±4.24%. Configurations 1 and 2 used the polyurethane adhesive SikaForce® 7888, which was characterized in the work of Neto et al. [19] by bulk tensile tests for the determination of E, f and f, and DCB and ENF tests to define the values of Gnc and Gsc, respectively. The bulk characterization was performed as specified in the EN ISO 527-2 standard [20]. The obtained results gave E=1.89±0.81 GPa, f=28.60±2.0 MPa, f=43.0±0.6 %, Gnc=0.7023±0.1233 N/mm and Gsc=8.721±0.792 N/mm. Configuration 3 used a novel polyurethane structural adhesive, SikaForce® 7752-L60. This is a two-part adhesive, and it consists of a filled Polyol based resin and an Isocyanate based hardener. It is characterized by a room temperature cure, high impact resistance and flexibility at low temperatures, having a tensile strength of approximately 10 MPa and tensile failure strain of 25% (manufacturer’s values). Figure 1: Geometry and characteristic dimensions of the DCB specimens. Configuration L (mm) a0 (mm) h (mm) B (mm) tA (mm) 1 160 50 5 15 1 2 160 40 1, 2, 3 and 4 25 1 3 160 55 3 25 0.1, 0.2, 0.5, 1.0 and 2.0 Table 2: Dimensions of the three joint configurations. Joint geometries The geometry of the DCB specimens is shown in Fig. 1. The characteristic dimensions are the total length (L), initial crack length (a0), h, width (B) and tA. The chosen values for each joint configuration are presented in Tab. 2. Some dimensions differ between configurations, but these do not affect the Gnc measurement. The joints for configuration 1 considered jute-epoxy composites as adherends, consisting of 8 stacked weave plies with a fibre volume fraction of approximately R.D.S.G. Campilho et alii, Frattura ed Integrità Strutturale, 31 (2015) 1-12; DOI: 10.3221/IGF-ESIS.31.01 4 30%. The plates were fabricated by hand lay-up and cured at room temperature in a vacuum bag. For the three joint configurations, for a uniform value of tA, calibrated spacers were inserted between the adherends. These spacers were inserted at both bonding edges between the adherends to control the value of tA. For the calibrated spacer at the crack tip, 3 plies were stacked and glued together, composed of a 0.1 mm thick razor blade between steel spacers to achieve the desired value of thickness, to create a pre-crack. For all specimens, stainless steel piano hinges were glued to both faces of the specimens at the cracked edge with a ductile adhesive, to provide a loading means in the testing machine grips. Also, a metric scale was glued with cyanoacrylate in both adherends to allow measurement of the crack length (a) and of the input data for the extraction of the J-integral. Six specimens of each configuration were tested at room temperature (≈20ºC), relative humidity of ≈40% and 2 mm/min in an electro-mechanical testing machine (Shimadzu AG-X 100) with a load cell of 100 kN. Data recording was carried out at 5 Hz for the load (P) and testing machine grips displacement (), registered during the test as a function of the time elapsed since its initiation. Pictures were recorded during the specimens testing with 5 s intervals using a 15 MPixel digital camera with no zoom and fixed focal distance to approximately 100 mm. J-INTEGRAL TECHNIQUE TO MEASURE Gn c n the proposed method, the CZM law is measured by the direct method. Under this scope, the path-independence of the J-integral can be used to extract relations between the specimen loads and the cohesive law of the crack path [21]. Based on the fundamental expression for J defined by Rice [22], it is possible to derive an expression for the value of Gn applied to the DCB specimen from the concept of energetic force and also the beam theory for this particular geometry, as follows [23]:  u n u o n u p 2 3 12 or P a G P G P Eh     (1) where Pu represents the applied load per unit width at the adherends edges, o the relative rotation of the adherends at the crack tip andp the relative rotation of the adherends at the loading line (Fig. 2). Figure 2: DCB specimen under loading, with description of the analysis parameters. In this work, the first expression of (1) is considered, using o instead of p, due to a simpler extraction of the parameter by the optical method. The J-integral can be calculated along an arbitrary path encircling the start of the adhesive layer, giving [21]:   nc n n n n 0 dG t     (2) where nc is the end-opening at failure of the cohesive law (measured at the initial crack tip) and tn is the current normal traction. Gnc can be considered the value of Gn at the beginning of crack growth. Thus, Gnc is given by the steady-state value of Gn, at a n value of nc [13]. The tn(n) curve can be easily obtained by differentiation of Eq. (1) with respect to n   nn n n G t      (3) I R.D.S.G. Campilho et alii, Frattura ed Integrità Strutturale, 31 (2015) 1-12; DOI: 10.3221/IGF-ESIS.31.01 5 As a result, the procedure of an experiment is to measure the history of P, a, n and o. The cohesive law in tension can then be estimated by plotting Gn in Eq. (1) as a function of n, polynomial fitting of the obtained curve and differentiation [21]. Optical method for the parameter measurement For calculating n and o for a given image, the optical method requires the identification of eight points (Fig. 3): two points (p1, p2) for measuring the current tA value at the crack tip (tACT) during loading in image units (pixels), two points (p3, p4) identifying a line segment in the image for which the length (d) is known in real world units (mm), two points (p5, p6) on the top specimen and two points (p7, p8) on the bottom specimen. Figure 3: Points taken by the optical method for measuring o and Gn c. Points Identification All eight points are manually identified in the first picture of a trial using an in-house software tool. The identification of the points is aided by the ruler attached to the specimens. Using the location of the points in the first picture, the points of the following pictures are automatically identified using a computer algorithm implemented in Matlab®. Basically, for each point pi, a rectangular region centred in pi is extracted from the first image forming a template (t). This template describes the image pattern that surrounds the point and is used for locating the point in the next image. This is done by finding the position (u,v) in the next image (I) that has the highest normalized cross-correlation with the template. The normalized cross-correlation is a measure of similarity between two grayscale images that is invariant to linear changes in illumination and that quantifies the correlation between the grayscale levels of two images/regions. The normalized cross-correlation () of template t with image I at the position (u,v) of image I is defined as:           , , 0.522 , ,, , . , , , . ,                            x y u v x y x yu v f x y f t x u y v t u v f x y f t x u y v t (4) R.D.S.G. Campilho et alii, Frattura ed Integrità Strutturale, 31 (2015) 1-12; DOI: 10.3221/IGF-ESIS.31.01 6 where f is the region of the image I with the same size as t centred in the position (u,v). Calculating  for all the pixels of I results in a matrix, where the maximum absolute value yields the location of the region in I that has the highest correlation with t and, thus, the most likely location of pi in the next image. This is done for every one of the eight points identified in the first image. After successfully identifying all the points of the second image, new templates are computed from the second image to search for the eight points in the third image, and so on until processing all the images. Computation of n The value of tACT in real world units (mm) is calculated as follows 1 2CTA 3 4    p p t d p p (5) For all trials, a region of length d=45 mm was used (Fig. 3). The pixel size was on average 0.024 mm and, thus, the estimated maximum error of the image acquisition process is ±0.012 mm. Finally, n can be defined as CTn A A  t t (6) where tA is the theoretical design value of 1 mm. Since tA can show small variations due to the fabrication process, an adjustment to n is also applied to make n=0 at the beginning of the test. Fig. 4 gives an example of the evolution of n for a selected test specimen of configuration 2 (with h=4 mm). Shown in the graphic are the raw curve, the 6th degree fitting curve and the corrected polynomial and final curve, adjusted to make n (testing time=0)=0. This polynomial adjustment is required to smooth the raw data and remove experimental measurement scatter, but also to cancel any eventual misalignment between glued scales in both adherends. n = -4.2482E-17t6 + 3.5246E-13t5 - 1.5875E-10t4 + 2.3802E-08t3 - 7.1272E-07t2 + 1.3125E-04t - 1.2653E-04 R² = 9.9307E-01 0.00 0.04 0.08 0.12 0.16 0 50 100 150 200 250 300  n [m m ] testing time, t [s] Raw curve Adjusted curve Polinomial (Raw curve)Polynomial (Raw curve) Figure 4: Evolution of n for one test specimen: raw curve obtained from the optical method, polynomial fitting curve and corrected polynomial curve. Computation of o o is calculated as the angle between lines l1 and l2 (Fig. 5). These lines could be directly calculated from points (p5, p6) and (p7, p8) respectively. However, for increasing robustness to small fluctuations of the point detection process, an image processing algorithm was used to extract the midline of the edge of the ruler that contains the pair of points in hand. In particular, a Difference of Gaussian filters was applied for enhancing the edges of the ruler, resulting in an image where pixels belonging to edges have high intensity values, while the remaining ones have low intensity (Fig. 5). R.D.S.G. Campilho et alii, Frattura ed Integrità Strutturale, 31 (2015) 1-12; DOI: 10.3221/IGF-ESIS.31.01 7 Figure 5: Image after applying the Difference of Gaussian filters and the extracted lines (l1 and l2) that are used for measuring o. Then, for the rows of the image between p5 and p6, the midpoint of the edge at each row is computed. The midpoint is first extracted for the row of p5 by (1) collecting all the pixels to the left and to the right of p5 that can be reached from p5 without dropping the pixel intensity bellow a given threshold (10% for all experiments), and (2) by averaging the position of all the collected pixels weighted by the pixels intensity value (so that pixels with higher intensities, i.e. pixels belonging to the edge, have a higher impact in the row’s midpoint calculation). This makes the process robust to blur in the images and to the point identification process because points p5 and p6 do not need to be identified exactly in the midline of the edge. This process is repeated for all the following rows until reaching p6, resulting in one point per row of the image between p5 and p6 that define the midline of the edge of the ruler. Since these points are not necessarily collinear, a linear regression is used for obtaining l1. The same process is repeated with points (p7, p8) for obtaining l2 and, finally, o may be calculated as the angle between the two lines 1 20 1 2 arccos v v v v              (7) where 1v  and 2v  are the direction vectors of lines l1 and l2, respectively. Fig. 6 shows the o-testing time plot for a specimen, more specifically the three curves of Fig. 4. Due to scaling difficulties, the raw curve in the figure is already translated such that o(testing time=0)=0. o = 1.0646E-11t4 - 4.6515E-09t3 + 8.0223E-07t2 + 7.7256E-05t + 8.6406E-03 R² = 9.9726E-01 0 0.02 0.04 0.06 0 50 100 150 200 250 300  o [r ad ] testing time, t [s] Raw curve Adjusted curve Polinomial (Raw curve) 0.06 0.04 0.02 0  o [r ad ] Polynomial (Raw curve) Figure 6: Evolution of o for one test specimen: raw curve obtained from the optical method, polynomial fitting curve and corrected polynomial curve. R.D.S.G. Campilho et alii, Frattura ed Integrità Strutturale, 31 (2015) 1-12; DOI: 10.3221/IGF-ESIS.31.01 8 RESULTS Configuration 1 or the bonded specimens with jute-epoxy adherends, n and o were defined as specified previously. The values of Gnc for the bonded joints were defined by plotting the Gn-n curves, considering Gnc as the steady-state value of Gn in the Gn-n curve [13]. Fig. 7 plots the experimental Gn-n law and the corresponding 6th degree polynomial fitting curve for a given specimen. At the beginning of the test, Gn slowly increases with n, but the growth rate of Gn rapidly increases up to nearly n=0.02-0.04 mm, and a steady-state value of Gn is attained at approximately n = 0.09 mm. For this specimen, the measured value of Gnc is 1.429 N/mm. For the six bonded specimens, the obtained data gave Gnc=1.182±0.215 N/mm. Fig. 8 shows the obtained experimental tn-n law, showing the ductile characteristics of the adhesive after the peak value of tn is attained. For this specimen, the following values were found: tn0=20.73 MPa and nc=0.0935 mm. For the complete batch of tested specimens, average values and deviations were as follows: tn0=23.18±3.57 MPa and nc=0.0843±0.156 mm. Proposed triangular and trapezoidal simplified CZM laws are also presented, allowing concluding that for the adhesive SikaForce® 7888 a trapezoidal law is particularly suited, since it accounts the best for the adhesive ductility. Gn = 7.1158E+06n6 - 2.8985E+06n5 + 4.3017E+05n4 - 3.1299E+04n3 + 1.1496E+03n2 + 2.9621E-01n - 6.2813E-04 R² = 9.9999E-01 0 0.4 0.8 1.2 1.6 2 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 G n [N /m m ] n [mm] Experimental law Polinomial (Experimental law) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 2 1.6 1.2 0.8 0.4 0 Polynomial (Experimental law) Figure 7: Experimental Gn-n law for one test specimen and polynomial fitting curve (configuration 1). 0 5 10 15 20 25 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 t n [M P a] n [mm] Exp erimental CZM law Triangular aprox. Trap ezoidal ap rox. 25 20 15 10 5 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Figure 8: Experimental tn-n law for one test specimen. Configuration 2 Gnc was calculated by Eq. (1). The experimental Gn-n laws were identical in shape to Fig. 7, and an example for h=3 mm is presented in Fig. 9. The Gnc results by applying this procedure for all tested specimens are shown in Fig. 10 as a F R.D.S.G. Campilho et alii, Frattura ed Integrità Strutturale, 31 (2015) 1-12; DOI: 10.3221/IGF-ESIS.31.01 9 function of h. The deviation is somehow large, and whose justification lies on the experimental process to obtain Gnc, which relies on a number of measured parameters and approximation functions, which are difficult to adjust to the experimental data [24]. While for the specimens with h=1 mm, a value of Gnc=0.781±0.146 N/mm was obtained, improvements of 12.6, 37.7 and 40.2% were attained by increasing h up to 4 mm. These results show the stabilization of Gnc for a given value of h (in this case between Gnc=1.075±0.226 N/mm for h=3 mm and Gnc=1.095±0.195 N/mm for h=4 mm a stabilization of Gnc was found). y = 4.6496E+07x6 - 1.1350E+07x5 + 1.0422E+06x4 - 5.1126E+04x3 + 1.5765E+03x2 - 5.6343E+00x + 4.8466E-03 R² = 9.9994E-01 0 0.4 0.8 1.2 1.6 0 0.02 0.04 0.06 0.08 G I [N /m m ] n [mm] Experimental law Polinomial (Experimental law) 0 0.02 0.04 0.06 0.08 1.6 1.2 0.8 0.4 0 Polynomial (Experimental law) Figure 9: Experimental Gn-n law for one test specimen with h=3 mm and polynomial fitting curve (configuration 2). 0 0,4 0,8 1,2 1,6 0 1 2 3 4 G nc [N /m m ] h [mm] 1.6 1.2 0.8 0.4 0 Figure 10: Average values and deviation of Gnc as a function of h by the J-integral. This increase of Gnc is reported in the literature because of the stress field variations ahead of the crack tip being dependent on the joint geometry, which highly influences the shape and size of the damage zone, and the local yield stress as well [25]. As it was discussed in previous works [26], thicker adherends provide an elevation of peel stresses further within the joint, shifting the loading conditions from peeling to cleavage, and giving a larger length for the damage zone. These findings are corroborated in the work of Azari et al. [27], regarding the adherend stiffness influence on the fatigue failure of bonded joints, which proved by Finite Elements that the plastic zone in adhesive joints between steel adherends was consistently higher than identical joints between aluminium adherends during the entire damage uptake process up to crack initiation. Mangalgiri et al. [28] justified this tendency with the plastic zone and stress distributions ahead of the debond tip. Actually, the plastic zone was bigger in length across the adhesive layer with increasing number of composite plies (and thus, increasing h). Also, thicker adherends used a larger amount of the input energy to the specimen to develop a lengthier plastic zone, thus leaving less available energy for damage growth [29]. On account of this, higher values of Gnc can be expected for joints with higher degrees of restraint (i.e., stiffer or thicker adherends). R.D.S.G. Campilho et alii, Frattura ed Integrità Strutturale, 31 (2015) 1-12; DOI: 10.3221/IGF-ESIS.31.01 10 Configuration 3 Following the method described in J-integral technique to measure Gnc section, Gnc was calculated identically to the previous cases, which considered o instead of p to obtain Gn. The aforementioned method was applied to all tested specimens and the Gnc results for each tA value and respective deviation are presented in Fig. 11. For the specimens with tA=0.1 mm, the obtained results gave Gnc=1.83±0.24 N/mm. The increase of Gnc from this point was of 14.5% (tA=0.2 mm), 57.8% (tA=0.5 mm), 105.6% (tA=1.0 mm) and 195.9% (tA=2.0 mm). 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 G nc [N /m m ] tA [mm] Figure 11: Average values and deviation of Gnc as a function of tA by the J-integral. Regarding the available studies (for epoxy adhesives), Yan et al. [30] studied the influence of tA on the fracture properties (Gnc) of DCB and Compact Tension (CT) joints with aluminium adherends and a rubber-modified epoxy adhesive. Using a large deformation Finite Element technique and the peak loads measured in the experiments, the critical value of the J- integral was calculated for different values of tA. A Gnc increase was found up to tA=1 mm and a decrease afterwards. An identical conclusion was found by Khoo and Kim [31] for an epoxy adhesive between 0.2