Wood-adhesive bond loaded in mode II: experimental and numerical analysis using elasto-plastic and fracture mechanics models

2.1 Test specimens

Test specimens were cut from a defect-free board of European beech by cutting with standard band and circular saws. For the 3ENF test, the specimens were prepared with dimensions of 17 × 20 × 500 mm³ in radial (R), tangential (T) and longitudinal (L) directions, respectively, according to Yoshihara (2001) as orthotropic blocks and with the necessary span-to-height ratio to induce stable crack propagation and insignificant plastic deformation due to contact with supports and loading head (Figure 1). An artificial crack of length ≈ 182 mm was introduced in L direction at the end of the specimen across the whole width of the specimen. All the specimens were weighed and dimensionally measured prior to the mechanical testing and without crack introduced. Test groups were defined as follows: (i) bond with EPI adhesive (Advantage EP-915 FS); (ii) bond with MUF adhesive (Prefere 4535); (iii) bond with PRF adhesive (Cascosinol 1711 with hardener 2520); and (iv) bond with PUR adhesive (PURBOND PR 3105). Lamellas were bonded using the recommended amount, pressure, time and temperature (20 °C) for particular adhesive as follows: EPI – 400 g/m², 1.4 MPa, 120 min; MUF – 460 g/m², 1.4 MPa, 270 min; PRF – 535 g/m², 1.0 MPa, 240 min; PUR – 790 g/m², 1.2 MPa, 120 min.

Figure 1:

(a) Scheme of sample geometry for 3ENF test with marked AoI for DIC analysis and two points (u⁺, u⁻) for obtaining displacement slip; L = 230 mm, L′ = 20 mm, a₀ = 182 mm, b = 17 mm, h = 10 mm, α is fiber angle, R and T denote radial and tangential directions, respectively. The solid line represents crack, the dashed line represents adhesive bond. (b) Experimental setup at universal testing machine including stereovision set accompanied with lights.

2.2 Physical testing

3ENF tests were performed on a universal testing machine (UTM) Zwick/Roell Z050 equipped with a 50 kN load cell; the load rate was set to 3 mmmin⁻¹ (Figure 1b). A deflection of the specimen was measured using cross-head of the UTM. The 3ENF provided force-deflection data that were further processed using CBBM and ECLA to obtain fracture properties. Before testing, Teflon paper was inserted into the crack to reduce friction between lamellas. At the side of the samples, a stochastic black-and-white speckle pattern was applied before testing to create the area of interest (AoI) for later computation of displacement slip using DIC (Figure 1a). All 3ENF tests were recorded at a 2 Hz acquisition rate by means of an optical stereo-vision system consisting of two 9MPx CCD cameras focusing on one side of the AoI. The optical system was synchronized with the UTM. The images were further processed in 3D-DIC software Aramis 2016 (GOM Inc.) to obtain the full-field displacements and compute the strains over the AoI. The analysis used a subset size of 27 × 27 px² and a step size of 3 px. Postprocessing of the DIC results provided the displacement slip (w) that was obtained from two points at the introduced crack tip, one above and one below the assumed neutral axis (Figure 1a). The displacement slip is calculated from w_II = |u⁺ − u⁻|, where u⁺ is for the upper component, u⁻ is for the lower component and both are in horizontal directions. After removing invalid measurements, such as for weakly bonded specimens, the total count was 17, 19, 16 and 20 specimens for EPI, MUF, PRF and PUR adhesive, respectively.

2.3 Calculation of strain energy release rate

The theoretical derivation of the strain energy release rate (G_II) by 3ENF and equivalent crack length (a_eqv) has been described by Yoshihara (2010), and Fernandes et al. (2013), so it is omitted here only for principal steps. The ECLA procedure does not require crack length monitoring during the test and leads to direct derivation of G_II respecting Irwin–Kies equation, which is for strain energy release rate as follows:

where P is force (N), a_eqv is equivalent crack length (m), b and h are specimen width and height (m) respectively, E_f is flexural elastic modulus. The main advantage of such a data reduction scheme is that the R-curve, i.e., G_II = f(a_eqv), can be obtained solely from the force-deflection (P/δ) curve. To obtain the G_II-w_II curve, the procedure shown in Xavier et al. (2014) was followed. To derive the cohesive law, the G_II-w_II curve was truncated at the beginning of the steady-state crack propagation (i.e., at maximal force). The truncated G_II-w_II curve was then differentiated to obtain the cohesive law in mode II. For this purpose, a continuous logistic function Q(t) (Eq. (2)) was used to approximate the data points in the reconstruction of the fracture cohesive law. The logistic fit (Q) searched for parameters t, R and α with lowest residuals according to:

where Q is the logistic function, Q_inf is curve maximum, t is quasi-time, R is symmetric inflection point, α is time decay constant. Once the continuous function of G_II(w_II) was obtained, the G_II was differentiated to obtain cohesive law as follows:

where σ_II is stress (Pa) and w_II is displacement slip (m). Above mentioned calculations were made on an averaged force-deflection (P/δ) curve. The average P/δ curve was obtained by calculating arithmetic mean P/δ curve from all specimens in the group. Average curve was subsequently fitted by polynomial of 6th degree, which resulted in representative P/δ curve for each group. These curves were further processed to calculate G_II and critical strain-energy release rate (G_IIc). To examine the differences between studied group mean values, single and multiple one-way analysis of variance test (one-way ANOVA) was used, assuming significance level of 0.05. The multiple 1way ANOVA was made using ‘multcompare’ function. This test provided answers whether adhesive groups differ in terms of P_max and δ. Postprocessing, statistical analyses and other calculations were performed in Matlab 2014b (Mathworks Inc.).

2.4 Numerical modeling

The physical test carried out at UTM was modeled using finite element method (FEM) implemented in software Ansys 19.1 R1 (ANSYS Inc., USA). The 3D sample and boundary conditions reflected the physical test at UTM, so the geometry included the sample, steel supports and loading head (Figure 2). The wood material was modeled using quadratic finite element SOLID95, and the adhesive bond was modeled using cohesive zone model (CZM) and finite element INTER204. The traction-separation behavior in CZM was modeled using bilinear function, and the G_II for this function was taken as a mean value from the measurement for given adhesive. Lamellas below and above the introduced crack were covered by quadratic contact elements (CONTA170 and TARGE174) to simulate their interaction during the bending test. This contact pair was modeled as flexible-to-flexible. The contact of wood with steel supports and loading head was modeled as rigid-to-flexible, so deformation of steel parts was neglected. The element size was set to 3 mm in longitudinal direction, but around supports and load head, the FE mesh was refined. Element size of 2 mm was set thickness-wise, so each lamella consisted of five elements in thickness. The total number of elements/nodes, including contact and cohesive ones, was 18000/55366. After validation of the FE model based on the comparison with experimentally obtained data, FE sensitivity analyses were performed to analyze an influence of: (i) friction coefficient between wooden lamellas (μ_WW) by varying it from 0 to 1; (ii) fiber angle with respect to the longitudinal axis of the specimen (α) from 0° to 18°; (iii) fiber angle with respect to the cross-section axes from 0° to 90°. The sensitivity analysis was performed to examine the impact of these three parameters on resulting P/δ curves, namely stiffness and P_max.

Figure 2:

Geometrical and finite element model of the 3ENF test.

Within the FE analyses, three material models of beech wood (Table 1) were employed: (i) orthotropic elastic model (Elas); (ii) orthotropic elasto-plastic model with the same compression and tension yield stresses (EP) and (iii) orthotropic elasto-plastic model with different compression and tension yield values (EP+). The first two models were taken from Milch et al. (2016). The third one was developed based on the second model using a procedure that aimed to extend the difference between compression and tension yield values while preserving Hill plasticity conditions (Hill 1983). The coefficient of friction between steel supports, loading head and wood was set constant to μ_sw = 0.33, and the same value was used for wood-wood interaction between wooden lamellas (μ_ww), except for analysis of impact of μ_ww on resulting P/δ response.

3.1 End-notched flexural tests

The analytical calculation of strain energy release rate (G_II) follows the equivalent crack length approach (ECLA) for determination of the resistance curve (R-curve) that is explicitly determined from the experimental force-displacement (P/δ) curves (Figure 3). Figure 3 shows that slopes of the elastic zone for all samples is more or less within the same range no matter what adhesive was used; the scatter in stiffnesses may be explained by natural variability of wood properties rather than the type of adhesive. Mean values and standard deviations (in brackets) for flexural stiffnesses (E_f), as calculated according to Eq. (3) in Silva et al. (2014), are 16.1 GPa (251 MPa), 15.6 GPa (563 MPa), 19.0 GPa (434 MPa) and 16.9 GPa (327 MPa) for EPI, MUF, PRF, and PUR adhesive, respectively. Multiple one-way ANOVA test for E_f revealed that all groups do not have significantly different means (at α = 0.05). The moisture content (MC) level of all groups was also proved as statistically equal using an ANOVA test and was in a range of 10.5–11.0%; the same holds true for the density having mean values between 705 and 728 kg/m³. These results imply that adhesive type did not influence mean E_f for the groups. Further, the highest maximal force (P_max) and maximal deflection at P_max (δ_max) was achieved for PUR adhesive that also possesses significant plastic region between yield point and P_max. This fact implies that PUR group has the highest apparent fracture toughness (i.e., area under the P/δ curve), which can be attributed to adhesive properties having a larger range of elastic and plastic deformation compared to other studied adhesives. On the other hand, EPI and PRF adhesives showed the most brittle-like behavior because deflection at P_max is lowest, so they would likely have the lowest apparent fracture toughness among studied adhesives.

Figure 3:

Experimental and numerical P/δ curves for tested adhesives.

Variability of P_max and δ_max for all adhesive groups is shown in the box plots in Figure 4. As seen in the EPI, MUF and PRF are more alike, contrary to PUR that has a significantly higher median value (red line in box plot). A one-way ANOVA test for adhesive groups revealed the same findings for both P_max and δ_max. For both physical quantities, significant differences between mean values were found only between PUR and all other adhesives (α = 0.05). This phenomenon can be attributed to both higher elastic and plastic capacity of adhesive and plastic deformation that occurred in wood due to bending. PUR adhesive belongs with the elastomeric adhesives that show rigidity comparable to other used adhesives, but it also shows higher flexibility due to the aliphatic portions of the polymer, which could contribute to this behavior (Troughton 2009). Martins et al. (2019) examined the same groups of adhesives as in the presented study, but they did so only in terms of shear strength according to EN 14080. Their results showed very similar shear strengths and force vs. deflection diagrams in terms of both elastic and plastic ranges of strain for all adhesives, which is slightly different from findings of this study where PUR group had the highest P_max. However, PUR group results may be partially attributed to significant plastic strains developed in wood due to bending. It is also necessary to mention Martins et al. (2019) used a different test, with higher strain rate (failure till 20 s) and different wood species (Maritime pine), so the comparison with this case is only partially valid. The effect of the bonding pressure on P_max was not studied in this work, but Santos et al. (2019) found no differences in shear strength of Maritime pine elements glued with PUR adhesive in this respect. Despite the pressure applied to the analyzed adhesives being slightly different, due to their specific technical recommendations, it is assumed it did not influence the test to a great extent, so it will not be discussed further. Mean relative difference between deflections at P_max obtained by cross-head and DIC was 2.57%.

Figure 4:

Box plots showing variability for tested adhesives in terms of P_max (left) and δ_max (right). The red line denotes median value, plus denotes outliers.

3.2 DIC analysis

Optical image series were processed with 3D-DIC software (Aramis), which provided displacements in three directions with respect to fiber direction (L, R, T), normal strains in two directions (ε_LL, ε_RR) and shear strain (ε_LR). Since mode II is shear mode, ε_LR is the best to show strain concentration at the bondline (Figure 5a). Figure 5a clearly shows the shear opening and deformation at the adhesive bondline and, further, two points below and above the crack tip (green dots) that enabled obtaining displacement slip (w_II). The typical experimental horizontal displacements (u⁺ and u⁻) for these two points are plotted in Figure 5b. It shows that the horizontal displacement below and above the sample’s ideal neutral axis (NA) follows different paths which, consequently, creates the w_II; it may also identify linear zones and a moment of P_max where the specimen failed. The position of these points is crucial for further correct calculations of G_II. These points should be located as close as possible to a crack tip that is ideally located at the NA. However, to achieve this for bonded wood lamellas is very difficult due to variability of wood properties, their geometry and possible different elastic moduli in tension and compression as found for various species, for instance for beech at MC below 13% (Ozyhar et al. 2013) or for cherry and walnut (Bachtiar et al. 2017). In addition to the unknown position of the NA, these uncertainties contribute to the fact that it is very difficult to obtain true fracture toughness in mode II for wood-bonded specimens. Figure 5c shows three pairs of points above and below NA and their horizontal displacements vs. relative time (pseudo-time of analysis) obtained from FE model that has symmetry of both material properties and geometry with respect to the NA. Curves are paired from outer to inner, and they demonstrate that the closer the pair of points is to the NA, the greater the displacement slip (w_II) is, in this case, w_II is 2, 4 and 6 mm. The w_II is important for deriving a track-separation model, as seen below.

Figure 5:

(a) Shear strain (ε_xy) computed using DIC with the two points used for calculation of displacement slip highlighted (w). (b) Graph showing displacements in horizontal direction vs. time for the two green points at crack tip; (c) horizontal displacements from FE simulation for 3 pairs of points with various vertical distance from the crack tip.

The w versus deflection for all specimens, including the averages for all adhesive groups, is presented in Figure 6. For the EPI, MUF and PRF adhesives, it shows mild increase with loading, and at the point of reaching elastic limit, the curves start progressing steeply. PUR group does not have such rapid change of steepness at the elastic limit. As visible, scatter of the w is very high, especially after reaching the elastic limit. The scatter is caused by progression of the crack at the bondline that often has a tooth-like effect on a curve. Progression of the crack was not studied for individual specimens, so it is not possible to say whether it happened in the wood or adhesive for a given tooth-like step. Looking at the PUR, it may also be noticed that the polynomial curve experiences an inflection point at a deflection of about 25 mm. This is caused by w data and could be removed by limiting to a certain maximal deflection. However, because the P_max was achieved for several specimens after deflection of 25 mm, it would not be consistent to do this within the group and, therefore, it was left it as it is. The question that arises from results of PUR (Figures 3 and 6) is whether the methodology used is convenient for testing wood-adhesive bonds made with PUR or PUR-like adhesives, i.e., adhesives with large elastic and plastic strain capacity. Furthermore, using 3D-DIC cannot fully assist in exploration of microcracking at adhesive bond loaded in mode II at such a level of observation. Wood-adhesive bond is a very different situation compared to the adhesive bonds in man-made composites (e.g., carbon-adhesive) where identification of differences for adhesives of various toughness is possible, including the pattern of microcracking because the crack predominantly propagates through adhesive (Bradley 1991). Therefore, displaying raw data is important and useful for wood-adhesive bondline because it may reveal common phenomena within individual specimen’s behavior.

Figure 6:

Displacement slip (w) vs. deflection for tested adhesives. Raw data are plotted as grey. The black dashed line represents arithmetic average of curves, and the blue solid line is polynomial fit of 6th degree.

3.3 Strain energy release rate and cohesive model

The procedure of ECLA and Eq. (1) for average P/δ curves and average w enabled to obtain a relationship between G_II and equivalent crack length (a_eq). The result of this procedure is shown in Figure 7a as four average curves for particular adhesive groups. The curves include mean critical strain energy release rate G_IIc (denoted as red asterisk), which attributes for P_max. The mean G_IIc is 1.80, 2.33, 1.59 and 5.40 Nmm⁻¹ for EPI, MUF, PRF and PUR, respectively. PUR has the highest G_IIc because the P_max was achieved much later after reaching the elastic limit for other groups of adhesives. All obtained mean values of G_IIc are higher than the value for clear beech wood (1.41 Nmm⁻¹) at similar MC presented by Sebera et al. (2019). However, with respect to wood variability, it can be claimed that only EPI, MUF and PUR have likely significantly higher G_IIc than mentioned value of clear wood due to a presence of adhesive bond. The increase of shear stiffness and shear strength due to a presence of adhesive bondline may happen; for instance, it was reported for balsa wood tested in pure shear using Iosipescu specimens (Osei-Antwi et al. 2013). Such increase is attributed to higher rigidity and shear strength of adhesive compared to wood at loaded plane. From a practical perspective, it is important to know that adhesive bond enhances stiffness and strength of beam elements which might be used to an advantage when designing timber construction elements.

Figure 7:

(a) Average strain energy release rate (G_II) vs. average equivalent crack length (a_eq). Red asterisk denotes average critical strain energy release rate at P_max (G_IIc). (b) Average G_II vs. average displacement slip (w_II). Red lines represent data up to G_IIc and blue lines represent logistic function fitted to the averaged curves. (c) Cohesive model computed by differentiating logistic functions (blue part of the curves) shown in Figure 7b and extrapolated cohesive model using Gaussian fit from Table 1 (red dashed parts of curves).

Using Eq. (2) enabled to find parameters to fit the relationships of G_II vs. w_II with a logistic function. This functional fit, together with average curves ending at G_IIc, is plotted in Figure 7b. The use of logistic function decreased the value of G_IIc, which is the value logistic function asymptotically converges to on a given range.

It may also be noticed that those fits do not start at zero of the y-axis, which is due to the fact that the best logistic fit to the G_II vs. w_II data was used. Differentiation of the logistic curves following Eq. (3) led to a cohesive model for studied adhesives (Figure 7c). The fact that logistic curves do not have a zero tangent at position of x = 0 resulted in cohesive models that do not start at zero y-axis (stress) positions (see blue sections of the curves in Figure 7c). Such cohesive models are not complete; i.e., the area under the curves is not equal to the G_IIc, so they need to be extrapolated up to y = 0. For this, the Gaussian model of 2nd order (GM2) was used, and the result of the fit is listed in Table 1 and plotted as red dashes on the cohesive model in Figure 7c. The GM2 has a form of a₁ × e(−((x − b₁)/c₁)ˆ2) + a₂ × e(−((x − b₂)/c₂)ˆ2), where x is variable and e is Euler’s number. It is also necessary to mention a certain error affecting the derivation of G_II stemming from the fact that residual stresses in specimens were neglected. This also implies that obtained toughness is apparent and not true. However, assessing this issue is out of the scope of this study; a method to address this problem was published for double cantilever beams loaded in mode I (Nairn 2000).

3.4 FE model

Cohesive models for all adhesives in the form of 2nd order Gaussian function in Table 2 can be easily transformed into the bilinear cohesive model (BCM) because the Gaussian fit is an evenly symmetric function. The BCM presented in Table 2 was used in FE simulations of the physical test for all adhesives. The results of the simulations are shown in Figure 3 as three solid lines (black for Elas, green for EP and red for EP+). FE prediction of force-displacement response in the elastic part of the test is sufficient compared to polynomial fit (blue line); only the PRF group shows a certain bump in the middle of the elastic part due to using arithmetic average as the base for polynomial fit. An agreement of FE model with the experiments regarding stiffness is determined by an orthotropic material model taken from the literature (Milch et al. 2016). This implies that wood used in this work had very similar properties as one in the Milch et al. (2016), despite the fact that both woods came from different growing positions within the region of Central Europe.

The prediction of FE models in terms of relative difference (RD) regarding the maximal force (P_max) is shown in Table 3. It shows that using the elastic model with cohesive zone predicts P_max very accurately for EPI, MUF and PRF groups (RD <5%), but for the PUR adhesive it reaches RD about 13.5%. The EP material model predicts P_max within the same accuracy as the elastic one (RD <5.2%), except for the PUR, which has RD of about 15%. This is due to the fact that wood in PUR group started to plasticize parallel to the fiber before reaching stress needed to open the crack. The crack in PUR group opened later at higher load levels and propagated less than for other adhesive groups. This is clearly visible from the green line in Figure 3 that shows the scenario of beech wood with the same tensile and compressive yield stresses. The FE model with EP+ material predicts P_max with the lowest RD’s (<3.4%); although for EPI, MUF and PRF adhesive, it sometimes exceeds RD compared to Elas and EP material models. The biggest improvement in using EP+ was achieved for PUR adhesive, whose RD decreased to −3.35%. This means the material model with different tensile and compressive yield stresses is the most suitable for modeling PUR-like adhesives for this test. Illustration of this phenomenon when using EP+ material model for the 3ENF test is depicted in Figure 8. It shows that when using elastic material only (Figure 8a), the maximal deflection, and also maximal compressive strain (3rd principal strain ≈ 0.013), occur in the middle of the specimen; meanwhile, when using EP+ material (Figure 8b), the maximal deflection and compressive strain (3rd principal strain ≈ 0.037) occur away from the specimen center near the introduced crack tip due to reaching yield stress in compression parallel to fiber in the upper part of lamellas. This phenomenon was also observed within the experiments with the PUR group that showed the highest deflection and failure at the crack tip (Figure 8c).

Figure 8:

(a) Computed 3rd principal strain at max. deflection for PUR adhesive with Elas material. (b) Computed 3rd principal plastic strain for PUR at δ_max with EP+ material. (c) Typical specimen from PUR group with denoted specimen center (grey line) and the δ_max at crack tip (red ellipse), photographed after the test.

To evaluate the most precise material model of wood for all adhesive bonds altogether, the summation of absolute values of RD’s for a given material model can be used (see ΣRD in Table 3). Then, the EP+ performs the best, followed by Elas and EP. However, for a quick, simple, valid and sound prediction of P_max, the orthotropic elastic material model is a high-quality choice for EPI, MUF and PRF adhesive bonds. To model adhesive bonds made with PUR, this work suggests using orthotropic elasto-plastic material models of wood with different tensile and compressive yield stresses. This holds true especially for Mode II-dominating problems or problems of bending where induced stresses might get higher yield than stress parallel to fiber of wood. This work implies that used geometrical configuration needs to be modified for testing PUR adhesive bond to achieve deformations only at adhesive bond, i.e., without having plastic strains at surface fibers of specimen. It has been shown that using orthotropic elasto-plastic material models to analyze phenomena occurring when wooden elements are mechanically loaded has become a valid approach leading to more precise predictions. This was demonstrated for clear pine wood (Pěnčík 2015), spruce and beech wood (Milch et al. 2017), and glulam beams made from softwoods with various connection surfaces (Uzel et al. 2018).

3.5 Friction

In the experiment, Teflon paper to reduce the friction between non-glued lamellas was used since it affects the measurement of force and displacement and, consequently, the obtained G_II values. The FE model enabled analysis of the impact of friction coefficient between lamellas (μ_WW) on stiffness and P_max of the specimen. The friction between specimen and steel grips was kept at constant value of μ_SW = 0.33. Varying μ_WW from 0 to 1 resulted in an increase in P_max of ∼4.3% and increase of stiffness (P/δ) of ∼2.5%. The impact μ_WW on both is depicted in Figure 9a; only a scenario with EPI adhesive was computed to illustrate this effect. This means that it is physically justified to insert Teflon paper into the crack to obtain more precise results. The Teflon paper should be located right above the support where the highest contact pressure occurs (Figure 9b). Visual comparison of the two most typical failures that occurred is shown in Figure 9c. It shows that the failure of adhesive bond with PUR adhesive occurred primarily in wood (Figure 9c left); meanwhile, for EPI adhesive (Figure 9c right), it showed brittle-like failure at adhesive-wood interface, which was found to be a typical failure of PRF and MUF groups, too.

Figure 9:

(a) FE analysis of impact of μ_WW on stiffness and P_max. (b) FE computed friction stress (Pa) at introduced crack (red zone is located right above the support, top view). (c) Typical failure for PUR (left) and EPI & PRF (right). (d) FE analysis of impact of α on stiffness and P_max using EP+ material. (e) FE analysis of impact of α on stiffness and P_max using Elas material.

3.6 Fiber angle

The specimens for 3ENF test are relatively long (0.5 m) and, therefore, there is higher probability that fiber direction will not be precisely aligned with specimen main axis. Therefore, the impact of fiber angle distortion on P_max and stiffness response with respect to longitudinal axis was analyzed using Elas and EP+ material models because these two were shown to be the best to simulate the 3ENF test for given adhesives. Results of these 80 simulations are displayed in Figure 9d and 9e. Figure 9e shows scenarios with Elas material, and it reveals the P_max is more impacted by angle distortion than stiffness on average, e.g., at 6° angle distortion, P_max is reduced by 5%; meanwhile, stiffness is reduced the same at an angle of 9°. It is clear that by using Elas material, all the adhesive groups behave very alike. On the contrary, using EP+ material shows that the more brittle the adhesive bond is, the less impact the fiber angle has on P_max. For instance, for PUR, the 5% or RD is reached at 6°, but for EPI, this RD is achieved at 9°. The impact of grain angle on stiffness using EP+ is similar when Elas material is used. This concludes in a finding that adhesive bonds made by various adhesives react differently to grain angle distortion. If angle distortion below 4° is kept, the impact will be maximally 2.5% in RD for all the adhesives in terms of P_max and even lower in terms of stiffness. FE analysis of the effect of fiber angle distortion at specimen cross section (RT plane) on stiffness and P_max is not shown since it does not influence the behavior as much; changing the angle at RT plane from 0 to 90° impacted resulting P_max until 2% and stiffness below 1%.