Issue 31

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 G n c and G s c . 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, t n 0 and t s 0 , respectively, and also G n c and G s c . 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 G n c , 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 G n c or G s c . 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 ( G n ) or shear ( G s ) 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≤ t A ≤1.6 mm ( t A 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 G n c revealed a monotonic increase from t A =0.1 to 1.0 mm. Above this value, a slight reduction was found. Under shear, the dependence of G s c with t A is not so significant, but an identical increasing trend is clear under t A =0.2 mm. In both cases, the observed behavior was explained in light of the increasing plastic zone size with the corresponding increase of t A . Ji et al. [14] studied by the J -integral the influence of t A in DCB joints on t n 0 and G n c for a brittle epoxy adhesive. G n c 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 t A on G n c , an increasing trend was found from 0.09≤ t A ≤1.0 mm, which was related to increasing plastic dissipations with the increase of t A . This work evaluates G n c 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 G n c , and finally adhesive bonding between aluminium adherends considering varying values of t A . The J -integral is selected to measure G n c 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. E XPERIMENTAL 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/cm 3 , 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