Tensile fracture characterization of adhesive joints by standard and optical techniques
Introduction
The developments in adhesives technology made possible the use of adhesive bonding in many fields of engineering, such as automotive and aeronautical, because of higher peel and shear strengths, and ductility. As a result, bonded joints are replacing fastening or riveting [1]. More uniform stress fields, capability of fluid sealing, high fatigue resistance and the possibility to join different materials are other advantages of this technology. 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], [4], [5].
A large number of predictive techniques for bonded joints is currently available, ranging from analytical to numerical, using different criteria to infer the onset of material degradation, damage or even complete failure. Initially, stresses were estimated by analytical expressions as those of Volkersen [6], which had a lot of embedded simplifying assumptions, and the current stresses were compared 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 factor techniques that required the existence of an initial flaw in the materials [7], [8]. More recent numerical techniques, such as CZM, combine stress criteria to account for damage initiation with energetic, e.g. fracture toughness, data to estimate damage propagation [9], [10]. 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 GIC and the shear critical strain energy release rate (GIIC). CZM in particular can accurately predict damage growth disregarding the bonded structures’ geometry if the fracture laws are correctly estimated [11]. These laws are based on the values of cohesive strength in tension and shear, tn0 and ts0, respectively, and also GIC and GIIC. These parameters 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 GIC, the DCB test is the most suitable, due to the test simplicity and accuracy [12]. As described by Suo et al. [13], 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 GIC or GIIC. 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.
Since the values of strength and toughness of adhesive layers vary as discussed, it is mandatory that they are estimated with accuracy. These parameters that cannot be directly related with the material properties measured as bulk, since constraint effects must be accounted for. The DCB test is the most suitable to measure GIC due to the test simplicity and accuracy. The conventional and standardized GIC estimation methods are based on Linear-Elastic Fracture Mechanics (LEFM) and rely on the continuous measurement of the crack length (a) during the test. However, it is known that GIC of ductile adhesives is not accurately characterized by LEFM methods, as discussed in the work of Kafkalidis and Thouless [14]. In recent years, methods that do not need measurement of a were developed [15], [16], additionally including the plasticity effects around the crack tip. As an alternative, in the presence of large-scale plasticity, J-integral solutions are recommended [17]. For tensile loading, J-integral solutions are available for the DCB test, either for loading by pure bending moments or the standardized and moment-free tensile pulling. With this technique, it is also possible to estimate the cohesive law of the adhesive layer. Carlberger and Stigh [18] computed the cohesive laws of adhesive layers (epoxy adhesive Dow Betamate® XW1044-3) in tension and shear using the DCB and End-Notched Flexure (ENF) tests, respectively, considering 0.1 ⩽ tA ⩽ 1.6 mm, tA being the adhesive thickness. The value of θo was measured by an incremental shaft encoder and δn by two Linear Variable Differential Transducers (LVDT). The analysis of Ji et al. [19] used a J-integral technique applied to the DCB specimen to study the influence of tA on tn0 and GIC for a brittle epoxy adhesive (Loctite® Hysol 9460). The analysis methodology relied on the measurement of GIC by an analytical J–integral method, requiring the measurement of the adherends rotation at the specimen free ends (θp). For the measurement of rotation, two digital inclinometers with a 0.01° precision were attached at the free end of each adherend. A charge-coupled device (CCD) camera with a resolution of 3.7 × 3.7 μm/pixel was also used during the experiments to measure δn, necessary for correlation with the load (P) and θp for the definition of the tensile strain energy release rate (GI). The current tensile traction (tn) vs. δn laws (or CZM laws) were obtained by differentiation of the GI–δn data. The obtained results showed that the value of GIC increases with tA up to the maximum considered value (1 mm). On the contrary, for tA = 0.09 mm, tn0 is approximately 3 times the bulk tensile strength of the adhesive, while the increase of tA leads to a reduction of tn0 up to near the bulk adhesive strength (for tA = 1 mm). A study regarding the tA effect on the interfacial value of GIC of laminated composites was presented by the same authors [20], considering the same experimental analysis procedure. The same tA effect on GIC was found, although tn0 increased with tA, oppositely to the previous study. This difference was justified by the different external constraints. Ouyang et al. [21] derived a concise form of the J-integral for the pure tensile fracture behaviour of DCB specimens with dissimilar adherends, considering the inclinometer method to estimate θp. A different study was published [22] regarding the mixed-mode fracture behaviour of the Single-Leg Bending test using an identical procedure to measure θp and digital image correlation to measure the crack-tip displacements. Campilho et al. [16] developed a methodology for the DCB test geometry that enables obtaining GIC and the CZM law by a J-integral methodology. The procedure consisted on an automated image processing technique that estimated the required parameters during the test. The GIC measurements of the adhesive Sikaforce® 7888 were consistent with the literature data and the CZM law confirmed the ductile characteristics of the adhesive.
The objective of this work is the estimation of GIC of adhesive joints between aluminium adherends by the DCB test, considering adhesives with different degrees of ductility. The J-integral is used to estimate GIC since it takes into account the plasticity of the adhesives. To calculate the J-integral, an optical measuring method is used, developed for assessing δn and θo during the tests, since these parameters are necessary to calculate GIC. This procedure is supported by a Matlab® subroutine for the automatic extraction of these values. On the other hand, the cohesive laws of the adhesives are obtained by the direct method. The J-integral results are also compared with traditional methods for evaluating GIC (methods that require the measurement of the crack length and methods based on an equivalent crack) and the corresponding conclusions are drawn.
Section snippets
Materials
The material selected for the adherends is a laminated high-strength aluminium alloy sheet (AA6082 T651) cut by precision disc cutting into specimens of 140 × 25 × 3 mm3. The mechanical properties of this material are available in the literature in the reference of Campilho et al. [23], giving the following bulk values: Young’s modulus (E) of 70.07 ± 0.83 GPa, tensile yield stress (σy) of 261.67 ± 7.65 MPa, tensile failure strength (σf) of 324 ± 0.16 MPa and tensile failure strain (εf) of 21.70 ± 4.24%. Three
Methods to determine GIC
In the work of Giovanola and Finnie [27] it is claimed that LEFM methods are inaccurate to estimate the critical strain energy release rate (GC) in presence of ductile adhesives, although some expressions consider correction factors to account for plasticity (e.g. the methods depicted in the standards ASTM D3433-99:2005 and BS 7991:2001). In this work, four methods were considered to consider plasticity effects: the Compliance Calibration Method (CCM), the Corrected Beam Theory (CBT), the
Results
The DCB tests were accomplished by the mentioned testing procedure. By visual inspection of the failed specimens all failures were cohesive in the adhesive layer with no signs of plasticity in the adherends.
Conclusions
This work presented the estimation of GIC of adhesive joints between aluminium adherends by the DCB test, considering adhesives with different degrees of ductility. The J-integral was used to estimate GIC and to obtain the CZM law of the adhesives in tension. GIC was also compared with standard characterization techniques. All tested methods are suited to capture GIC for ductile adhesives by considering root rotation effects that are large on account of the adhesive characteristics. The GIC
Acknowledgments
The authors would like to thank Sika® Portugal for supplying the adhesive Sikaforce® 7888.
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