Experimental estimation of the mechanical and fracture properties of a new epoxy adhesive

The automotive industry is currently increasing its use of high performance structural adhesives in order to reduce vehicle weight and increase the crash resistance of automotive structures. To achieve these goals, the high performance adhesives employed in the automotive industry must not only have high mechanical strength but also large ductility, enabling them to sustain severe dynamic loads. Due to this complex behaviour, the design process necessary to engineering structures with these materials requires a complete knowledge of their mechanical properties. In this work, the mechanical properties of a structural epoxy, Sikapower® 4720, were determined. Tensile tests were performed to determine the Young’s modulus (E) and tensile strength (σf). Shear tests were performed to determine the shear modulus (G) and the shear strength (τf). Tests were also performed to assess the toughness of the adhesive. For mode I toughness determination (GIc), the double-cantilever beam (DCB) test was employed. For determination of toughness under mode II (GIIc), the end-notched flexure (ENF) test was performed. The data obtained from the DCB and ENF tests was analysed with the compliance calibration method (CCM), corrected beam theory (CBT) and compliance-based beam method (CBBM) techniques. The test results were able to fully mechanically characterize the adhesive and demonstrate that the adhesive has not only high mechanical strength but combines this with a high degree of ductility, which makes it adequate for use in the automotive industry.

as crash resistant adhesives due to their ability to plastically deform but still maintain the structure firmly bonded under significantly large loads, therefore ensuring that the structure has a large degree of energy absorption. Modern automotive structures combine multiple bonded materials and use adhesive layers with complex geometry. To efficiently design such structures, the use of finite element method (FEM) techniques is fundamental. One of the most accurate methods to model adhesive layers are cohesive zone models (CZM) to simulate adhesive failure and associated debonding. CZM are a very powerful tool for studying the behavior of adhesive joints. Cohesive elements can be easily added to FEM models. Needleman [2], Tvergaard et al. [3] and Camacho et al. [4] were among the first to adapt this technique for use in adhesive joints. A CZM improves on classical continuum mechanics modelling and can describe the fracture process and location. By using both strength and energy parameters to simulate the nucleation and advance of a fracture crack [5], these elements can fully simulate the crack progression in adhesive layers. The relationship between the stresses and displacements is governed by a traction separation law.
The experimental campaign described in this work enabled the estimation of E, G, σ f , τ f , G Ic and G IIc . The tensile properties of the specimen (E and σ f ) were determined using the bulk tensile testing of "dog bone" specimens. This almost universal test is standardized under ISO 527:1997 [6] and its ASTM equivalent D638-03 [7]. To measure the shear properties of the adhesive (G and τ f ), the thick adherend shear test (TAST) was employed. This test follows the standard ISO 11003-2:1993 [8]. Another method commonly employed to assess τ f of adhesives is the torsion test, standardized under ASTM E143-02 [9]. The determination of G Ic is usually performed with the DCB specimen [10], although other common specimen geometries exist such as the tapered double-cantilever beam (TDCB) or the single edge notch bend (SENB) specimens. The DCB test is widely used because it requires relatively simple specimens and it has well defined testing procedures. Several methodologies exist that allow the derivation of G Ic from this testing data, resulting from a linear elastic fracture mechanics analysis. During a DCB test it is assumed that a crack will stably propagate when the tensile strain energy release rate (G I ) equals G Ic . The CCM is based on the Irwin-Kies [11] equation and requires the calculation of the compliance (C) relatively to the crack length (a). The compliance is given by C = δ/P, where δ is the displacement and P is the applied load. As an alternative, the DBT uses the classical beam theory equations to assess the compliance [12] and the CBT improves on it by taking account the effects of crack tip rotation and deflection [13]. All these methods require the constant measurement of the crack location, which might be difficult or yield imprecise results. As an alternative, the CBBM uses the concept of the crack equivalent [14]. This means that it derives the crack location solely from C at any given moment, negating the need to visually monitor the crack progression as required by other methods [15]. The determination of G IIc can be performed using three different tests by the theoretically steady-state value of shear strain energy release rate (G II ) that is attained during crack propagation. The ENF test, the end-loaded split (ELS) and the four point end-notched flexure (4ENF) test. Among these alternatives, the ENF is the most commonly used, as it does not exhibit the friction problems found in the 4ENF test and avoids the excessively large displacements found in the ELS test. The ENF has also the advantage of using a specimen mostly similar to the one used in the DCB tests, differing only in the loading direction. The ENF test is simply a three-point flexure test on a pre-cracked specimen. During the ENF test the relative displacement of the upper and lower specimens introduces a shearing load in a pre-cracked adhesive layer. The data from these tests can be analyzed using the same methods used for the analysis of the DCB test results.
Saldanha et al. [16] have used similar methods to perform a characterization procedure on a high elongation, high toughness epoxy adhesive. They found that such adhesive combined the high tensile strength and shear strength typical of epoxy adhesives with the high toughness of polyurethane adhesives. Similarly, García et al. [17] characterized a toughened epoxy adhesive to use in the FEM. Their experimental procedure used only tensile and shear tests to build a continuum damage model that was able to accurately simulate the mechanical behavior of complete joints. Much of the work on characterizing toughened, high elongation epoxy adhesives focuses on the study of the fracture properties, where there are significant improvements to be found. A variety of specimen types are used in these tests. Jin et al. [18] studied the mode I fracture behavior of a self-healing toughened adhesive by the TDCB test. Kim et al. [19] performed a similar characterization for a nanoparticle reinforced epoxy but used the simpler single SENB specimens for this purpose. All these tests found improvements in toughness over standard epoxy formulations.
In this work, the mechanical properties of a structural epoxy, Sikapower ® 4720, were determined. Tensile tests were performed to determine E and σ f . Shear tests were performed to determine G and τ f . Tests were also performed to assess the toughness of the adhesive. For G Ic characterization, the DCB test was employed. For determination of G IIc , the ENF test was performed. The data obtained from the DCB and ENF tests was analysed with the CCM, CBT and CBBM techniques. Comparison of the Sikapower ® 4720 with another epoxy adhesive was also undertaken. The Araldite ® 2015 was chosen for this purpose because of being a direct competitor in terms of applications and being established in the market. With this work, complete data for the numerical design of bonded structures with this novel adhesive is provided, enabling the optimization of the joints and the subsequent cost and weight reduction of the structures. Figure 1 shows the specimen dimensions for the bulk specimens with dogbone shape for tensile testing, which were fabricated according to the French Standard NF T 76-142 [20]. Curing of the specimens was carried out in a steel mold [21] that permits the simultaneous production of 6 specimens (Fig. 2). The top and bottom plates of the mold were machined by computer numerical control (CNC), and then grinded (to improve the surface finish) and hard chrome plated (to increase the abrasion resistance and facilitate demolding). The mold plate, to be placed between the top and bottom plates to produce the adhesive cavities, was laser cut. Before application of the adhesive, the mold was cleaned with acetone and demolding agent was applied. The adhesive was applied in the mold cavities by the application gun and manually spread, before being left for cure during 1 week. The tensile tests were performed in an Instron ® 3367 testing machine with a 30 kN load cell, at room temperature and under displacement control (2 mm/min).

Tensile tests
During the tests, the longitudinal strains (ε) were measured with a mechanical extensometer with a base length of 25 mm.
For the determination of the bulk tensile mechanical properties of the adhesive, the standard EN ISO 527-2 [6] was considered. E was measured between values of ε of 0.05 and 0.25 % as where Δσ and Δε are the variations of tensile stress and strain, respectively. The yield stress (σ y ) was obtained for ε = 0.2 %, by the intercept between the tensile stress (σ)ε curve and a parallel line to the initial part of this curve. σ f is calculated by the ratio between the maximum load and the initial cross section of the sample. During the test, the tensile failure strain (ε f ) was also registered, corresponding to the maximum displacement sustained by the specimen.

Shear tests
The TAST was selected to perform the shear tests, using the adherends and machine gripping tools developed by Morais [22] in DIN C45E steel. All aspects related to the tests (e.g. geometry and dimensions) followed the ISO 11003-2 standard [8]. Surface preparation of the steel adherends consisted of grit blasting and cleaning with acetone. The adherends were cured in a jig ( Fig. 3) that ensures the precise alignment of the adherends and correct overlap length. The specimens were assembled using 1 mm spacers between adherends to attain the correct value of overlap length. These spacers and all the mounting jig surfaces potentially in contact with the adhesive were coated with demolding agent to facilitate extraction of the specimens after curing. Application of the adhesive was done manually (Fig. 4a), followed by manual positioning of the adherends with application of pressure on the joints (Fig. 4b). The limiting bars were then fastened to the jig to assure the correct overlap length and the specimens left to cure for 1 week at room temperature. The longitudinal strains during the test were measured with a mechanical extensometer. Figure 5 represents the test setup. The considered test speed was 0.5 mm/min (ISO 11003-2 standard [8]). The ISO 11003-2 standard [8] was considered to determine the shear mechanical properties of the adhesive by TAST tests. The shear stress (τ) was calculated using the following equation where l is the bond length and B is the specimens' width. The expression used to calculate the shear strain (γ) is given by where t A is the adhesive thickness. Subsequently, the value of G was determined in the elastic portion of the τ-γ curve as

Fracture tests
DCB tests were considered to calculate G Ic , and ENF tests to obtain G IIc . Both test methods used AA6082 T651 aluminum alloy adherends with the dimensions of 140 × 25 × 3 mm 3 (DCB tests) and 230 × 25 × 3 mm 3 (ENF tests). Previous characterization of this material in bulk tension [23] resulted in the following mechanical properties: E = 70.07 ± 0.83 GPa, σ y = 261.67 ± 7.65 MPa, σ f = 324 ± 0. 16 MPa and ε f = 21.70 ± 4.24 %. Figure 6 depicts the geometry and relevant dimensions of the DCB (a) and ENF specimens (b). The dimensions for the DCB joint are: total length L = 140 mm, initial crack length a 0 ≈ 55 mm, adherend thickness t P = 3 mm, B = 25 mm and t A = 0.2 mm. The dimensions of the ENF specimens are: mid-span L = 100 mm, a 0 ≈ 60 mm, t P = 3 mm, B = 25 mm and t A = 0.2 mm. The specimens were fabricated in a laboratory with controlled temperature and humidity. The bonding faces were prepared by grit blasting with corundum sand, cleaned with acetone and assembled in a steel mould for bonding. To obtain a constant value of t A throughout the bonded portion of the specimens, calibrated steel spacers were inserted between the adherends, after proper preparation with demoulding agent. Moreover, at the crack tip, a sharp pre-crack was induced by a 0.1 mm thick razor blade between the calibrated steel spacers. After applying the adhesive, the specimens were closed following the best practices to avoid air entrapment and appearance of air bubbles within the adhesive layer. Curing was performed at room temperature. Preparation for testing consisted of removing the steel spacers, spraying the adherends' sides with brittle white paint to enable a clear identification of a, and gluing a black numbered scale in both adherends to aid the a measurement. The testing programme involved testing six DCB and eight ENF specimens at room temperature using an Instron ® 3367 electro-mechanical testing machine equipped with a 30 kN load cell. Images were captured during the tests using an 18 MPixel digital camera with no zoom and fixed focal distance to approximately 100 mm, which enabled obtaining the values of a with accuracy. The values of a were then correlated with the Pδ data by the time elapsed since the beginning of each test. The value of G Ic was evaluated by three data reduction schemes: the CCM, the CBT and the CBBM. The classical reduction schemes to estimate G Ic are usually based on compliance calibration or the beam theory. The CCM is based on the Irwin-Kies equation [11] where C = δ/P. Cubic polynomials (C = C 3 a 3 + C 2 a 2 + C 1 a + C 0 ) were used to fit the C = f(a) curves, leading to Beam theories were also used to measure G Ic . Using the CBT, G Ic is obtained using [24] where Δ is a crack length correction for crack tip rotation and deflection, obtained as specified in the standard ISO 15024 [25]. The CBBM is a relatively straightforward but robust method, based on an equivalent crack length (a eq ), and it only depends on the specimen's compliance during the test. Applied to the DCB test specimen, it gives Detailed explanations of the method can be found in the work of Campilho et al. [26]. The value of a eq is estimated from the current specimen compliance and taking into 3C 3 a 2 + 2C 2 a + C 1 . consideration the damage zone, E f is a corrected flexural modulus to account for stress concentrations at the crack tip and stiffness variability between specimens, and G AD is the shear modulus of the adherends.
The following techniques were tested for the ENF specimen: CCM, CBT and CBBM [27]. The classical data reduction schemes to obtain G IIc are usually based on compliance calibration or beam theories. The CCM is based on the Irwin-Kies equation [28] Cubic polynomials (C = C 1 a 3 + C 0 ) were used to fit the C = f(a) curves, resulting into Beam theories were also used to measure G IIc . The CBT, which accounts for crack length corrections to consider the effects of shear deformation, was proposed by Wang and Williams [29] and is written as where E x is the adherends E value in the length direction and Δ 1 is a crack length correction to account for shear deformation [27] in which G xy is the in-plane shear modulus of the adherends and Γ is given by where E y is the value of E of the adherends in the thickness direction. The CBBM was also developed for the ENF specimen [27], enabling the estimation of G IIc only using the experimental compliance. This technique relies on a eq , which is computed based on the current specimen's compliance and accounts for the fracture process zone (FPZ) effects at the crack tip (not taken into account when the real value of a is considered). G IIc can be obtained by the following expression Detailed explanations of the method can be found in Ref. [27]. Equally to the DCB tests, E f is an equivalent flexural modulus obtained from the specimen's initial compliance and value of a 0 .

Results and discussion
Tensile tests Figure 7 shows the σ-ε curves of the six bulk tensile tests, revealing the high repeatability of the results, apart from some deviations in the value of ε f . All failures were smooth without voids or porosities. Table 1 summarizes the tensile mechanical properties of the bulk tests to the adhesive Sikapower ® 4720 (P max and δ max are the maximum load and the maximum displacement, respectively).
In the present work, σ f = 27.519 ± 0.845 MPa was found for the Sikapower ® 4720, slightly higher than the manufacturer's value of 24 MPa. However, the percentile standard deviation of only 3.1 % clearly shows the repeatability of the results obtained. Possible causes for this discrepancy are different curing parameters (time and/or temperature) or test protocol. The value of ε f (1.973 ± 0.343 %) was smaller than that postulated by the manufacturer (3 %). This difference can be related to small fabrication defects that would prevent the full plasticity of the adhesive to develop in the bulk tests. On the other hand, E was higher that the reference value (2052.477 ± 84.818 MPa against 1900 MPa, respectively). The curing conditions, testing temperature and humidity, and also method used to estimate E may be on the origin of this difference. σ y is not available for comparison.   Table 2 evaluates the tensile mechanical properties of the Sikapower ® 4720 with another epoxy adhesive, the Araldite ® 2015 [30]. Comparing the two adhesives, the Sikapower ® 4720 excels in σ f , E and σ y , while the Araldite ® 2015 has a higher value of ε f . Figure 8 presents the τ-γ curves of the adhesive Sikapower ® 4720. Identically to the previous analysis, a high repeatability between specimens is found regarding the elastic stiffness, shear strength and ductility (except for specimen 1, which showed a significantly smaller value of maximum shear strain, γ f , possibly due to fabrication related issues). The values of γ f were calculated from the sharp drop of the load sustained by the specimens immediately before complete failure. Figure 9 represents the followed procedure to calculate the shear yield stress (τ y ), using the intercept between the τ-γ curve and a line parallel with the same initial slope of the τ-γ curve but offset by γ = 0.2 %. All failures were cohesive in the adhesive layer. Table 3 presents the collected shear mechanical properties from the TAST tests to the adhesive Sikapower ® 4720. There is generally a good correspondence between specimens for each measured property, with a standard deviation below 10 %. Only for δ max (37.1 %) and γ f (34.0 %) this was not observed. The deviations between specimens regarding δ max are related to premature failures, possibly induced by fabrication defects, or t A variations to the expected design value induced during fabrication. The scatter in the values of γ f is directly related to the δ max variations.  The TAST tests revealed a higher average value of τ f than that provided by the manufacturer's sheet. Actually, the obtained value was 24.341 ± 0.941 MPa against an expected value of 14 MPa. However, the percentile standard deviation (3.9 %) is extremely low and all failures were cohesive, which validates the obtained results. It was not possible to compare γ f because of absence of reference data. The obtained results revealed some scatter between specimens (23.150 ± 7.859 %), which is due to the difference in specimen 1. This value of γ f clearly corresponds to a highly ductile adhesive. G measurements resulted in a value of 750.738 ± 46.356 MPa (percentile deviation of 6.2 %). Due to the isotropic nature of the adhesive, E and G can be used to obtain the Poisson's ratio (ν), which gave 0.367 and is in agreement with typical values for these adhesives. It was not possible to compare τ y because of the lack of information. Table 4 evaluates the shear mechanical properties of the adhesive Sikapower ® 4720 against the Araldite ® 2015 [30]. All values of the Sikapower ® 4720 overshoot those of the Araldite ® 2015 except γ f . Moreover, τ y is much similar between both adhesives.

Tensile fracture tests
The P-δ curves of the six DCB tests are presented in Fig. 10. P initially increases linearly, as the energy stored in the specimen increases. When G I reaches its critical value,  Table 3 TAST mechanical properties in shear of the adhesive Sikapower ® 4720 G Ic , the crack starts to grow, and a reduction of P takes place because of the increasing bending moment induced by bigger a values. The curves of the several specimens showed a good correspondence, although with minor variations in the initial stiffness on account of different values of a 0 . The R-curves were built from the P-δ curves following the previously mentioned data reduction methods, allowing to relate G I with a or a eq during the crack growth phase of each test [31]. Ideally, the R-curves are horizontal lines, although experimentally fluctuations may occur due to issues such as poor adhesive mixture, adhesion problems, defects and unstable crack growth. Figure 11 shows the R-curves by the different methods for a representative specimen of the DCB tests. It should be mentioned that, for the CCM, it is necessary to derive the C = f(a) curve and to differentiate it. The C = f(a) curve should span from the beginning of crack propagation up to the specimen's failure. For the particular specimen of Fig. 11, the R-curves are practically overlapped, resulting in consistent measurements of G Ic . The CBBM has the advantage of not requiring the measurement of a, unlike happens with the CCM and CBT, which highly reduces the time required in the analysis and prevents errors in the measurement of a. The CCM still adds another source of error in the data analysis, because of the approximation taken in the calculation of dC/da, which is performed by taking the derivative of the C = f(a) curve after fitting cubic polynomials [24]. After performing all the tests, fully cohesive failures were obtained for all DCB specimens. Table 5 summarizes the values of G Ic by the different methods for all specimens, and also P max and δ max for each specimen. The G Ic data is highly consistent for each specimen between methods, and between specimens of each method (small values of standard deviation). However, the G Ic values of the CBBM were slightly higher than for the other methods. Nonetheless, this is regarded as the most robust method since it fully accounts for the FPZ and it is not affected by possible measurement errors of a.
After the analysis of all DCB specimens, no significant differences were found in the R-curves when comparing all considered data reduction methods. The measured values of G Ic for each specimen were close between data reduction methods. No data is available from the manufacturer regarding this parameter. Evaluated against the CBBM, which is regarded as the most reliable method by not requiring measurement of a and including the FPZ effects in the results, the observed differences to the other methods were 7.2 % (CCM) and 1.2 % (CBT). Between specimens of the same method, the percentile deviations were 11.5 % (CCM), 10.3 % (CBT) and 14.1 % (CBBM). The current adhesive has G Ic = 1.294 ± 0.182 N/mm (CBBM values) compared to G Ic = 0.43 ± 0.02 N/mm of the Araldite ® 2015 [30], which corresponds to an excess of nearly three times.   Figure 12 compares the P-δ curves obtained in the eight ENF tests. For this particular test, eight specimens were considered to safeguard possible unstable crack propagations in some specimens, prone to occur in the ENF test. The general shape of the curves is in agreement between specimens, although one of these has a smaller elastic stiffness induced by a higher value of a 0 . After P max is attained, the load starts to decrease, which corresponds to the interest part of the ENF tests, in which G IIc is measured. Afterwards, the load increases again when the FPZ reaches the vicinity of the loading cylinder. This portion of the curves was truncated because it is no longer valid for the measurement of G IIc . Figure 13 compares the R-curves of a single specimen by the CCM, CBT and CBBM. In an identical manner to the DCB specimens, these R-curves correlate G II with a or a eq and their steady-state value during the crack propagation phase provides an estimation of G IIc . For the specimen depicted in the figure, the valid crack propagation region ranged between 84 ≤ a eq ≤ 92 mm (CBBM curve). After this region, a gradual increase of G II was found related to the FPZ reaching the loading cylinder and biasing the measured value of G IIc . The full set of G IIc values obtained by the three methods is shown in Table 6, together with the P max and δ max values for all specimens. The results for specimen 6 were discarded from the analysis due to a significant offset to the typical values obtained for the other specimens. Equally to the DCB results and owing to previous evidence regarding these methods [27], the CBBM is considered the most reliable.

Shear fracture tests
In accordance with the previous tests, the ENF tests also revealed a high repeatability. The G IIc results of each test agreed well between methods. Equally to G Ic , comparison with reference values cannot be carried out. The percentile differences to the CBBM, once again considered the most robust method, are 3.3 % for the CCM and 22.9 % for the CBT. The discrepancy for the CBT is linked to the energy dissipated in

Conclusions
The main objective of this work was the complete mechanical and fracture characterization of a new epoxy adhesive (Sikapower ® 4720). Bulk tensile and TAST tests were performed to obtain the tensile and shear mechanical properties, respectively. The bulk tensile tests gave the following values: E = 2052.477 ± 84.818 MPa,   (14 MPa), which corresponds to a significant difference to the obtained value in this work. However, the manufacturer's value was empirically defined by the von Mises criterion which, as it is known, does not apply to toughened adhesives. The availability of E and G permits the calculation of ν for isotropic materials as 0.367, which is within the interval of expected values for structural adhesives, i.e., between 0.3 and 0.5 [1]. The