Issue 48

F.A.L. Viana et alii, Frattura ed Integrità Strutturale, 48 (2019) 286-303; DOI: 10.3221/IGF-ESIS.48.29 288 determined by DCB and ENF tests, respectively, are initially used in the respective CZM law. Concurrently, approximate bulk values can be used for t n 0 or t n 0 for the initiation of the trial and error iterative process. Examples of experimental data for the iterative fitting procedure are the R -curve, the crack opening profile and the P -  curve [12]. Xu et al. [13] developed an improved interpolation-based CZM model to capture the tensile behaviour of different fracture scenarios in composite adhesive joints, using the DCB specimen. Simultaneously, an inverse method was developed to assess the tensile CZM parameters. This inverse analysis relies upon both experimental P -  curves and displacement distribution in the neutral layer of bending beam. The numerical CZM simulations, and an optimization algorithm capable to approach the simulations to the experimental results, enabled obtaining the optimal tensile CZM parameters. Throughout experimental data, the model was validated, showing the reliability of the proposed solution. Azevedo et al. [14] estimated the CZM laws of adhesively-bonded joints subjected to shear loading through the inverse method based on a curve fitting procedure. Three adhesives with different ductility grades were used to bond aluminium adherends. To estimate the shear CZM laws, ENF tests were carried out. G IIC was used to build a triangular CZM law to begin the iterative process and then iterations were performed, by fitting the experimental and numerical P -  curves, to estimate t s 0 . During the fitting process, it was shown that the Young’s modulus ( E ) affects the elastic part of the curve, G IIC affects the maximum load ( P m ), while t s 0 changes P m and highly affects the specimen’ stiffness up to the P m , leading to a more sudden post peak load reduction with the increase of t s 0 [23]. After application of this process to all specimens, the authors concluded that a unique shear CZM law could be found for each specimen. Moreover, the triangular CZM managed to capture with accuracy the adhesive layer behaviour for all adhesives tested. In the study of Bouhala et al. [15], an inverse method has been also applied to unidirectional carbon fibre-reinforced/epoxy matrix composite failure, showing a trustworthy determination of the tensile failure parameters. In this work, the cohesive laws of three adhesives, Araldite ® AV138, Araldite ® 2015 and Sikaforce ® 7752, were obtained by the application of an inverse adjustment method between the numerical and experimental P -  curves of DCB tests for tensile characterization and ENF tests for shear characterization. Next, these laws were validated with experimental data of SLJ and DLJ, using Abaqus ® . W ORK METHODOLOGY iming to define the tensile and shear CZM laws of the three studied adhesives, enabling their subsequent use for strength prediction of adhesively-bonded joints, the following methodology was followed:  G IC and G IIC of the three adhesives were experimentally estimated by robust fracture tests such as the DCB and ENF, respectively, and the Compliance-Based Beam Method (CBBM);  A numerical data fitting process was undertaken, in which individual DCB and ENF models were constructed, with the input G IC and G IIC of each specimen and reference values of the other CZM parameters. The CZM law of each test (either tensile or shear) was individually found by iteratively adjusting, using a trial and error procedure, the reference CZM parameters until the best match is found between the experimental and numerical P -  curves of the fracture tests;  Validation of the obtained CZM laws, which is an essential step to enable the design of bonded joints by this process, is divided into three steps: (1) joint stress analysis, which is used to provide a discussion on the P m differences between joint types, geometry and adhesive type, (2) performing experimental tests and provide the respective discussion, to enable further comparison with numerical models for validation of the CZM laws, and (3) experimental and numerical P m comparison for all tested conditions which, if positively accomplished, will give the basis for subsequent design of joints bonded with the three adhesives. E XPERIMENTAL WORK Adherends and adhesives he aluminium alloy AA6082 T651 is the material chosen for the DCB, ENF, SLJ and DLJ adherends. This material is a high strength and ductile aluminium alloy, which enables measurement of the CZM laws by the respective fracture tests without evidence of plasticization, which otherwise would result in errors of property estimation. The relevant mechanical properties of this alloy were established in the work of Campilho et al. [16]: E of 70.07  0.83 GPa, tensile yield stress (  y ) of 261.67  7.65 MPa, ultimate tensile strength (  f ) of 324  0.16 MPa and tensile failure strain (  f ) of A T