Issue 48

J.P.S.M.B. Ribeiro et alii, Frattura ed Integrità Strutturale, 48 (2019) 332-347; DOI: 10.3221/IGF-ESIS.48.32 334 Several tensile fracture characterization tests to evaluate G IC are available, such as the Double-Cantilever Beam (DCB), the Tapered Double-Cantilever Beam (TDCB), the Compact Tension (CT) and the Single-Edge Notched Bending (SENB). The DCB test became the most used, being supported by the BSI 7991:20001 [13], ASTM D3433 [14] and ISO 25217 [15] standards, providing guiding processes for the experiments and data reduction. This test requires an initial crack introduced during the fabrication process at the adhesive-free edge of the specimen, which will propagate by applying an opening load at the specimen’s edge. The R -curve plots the G I against the crack length ( a ). In theory, this curve provides a perfectly horizontal G I - a curve during damage growth, whose steady-state value gives the measurement of G IC . Shear fracture testing is considerably more complex and is yet to be standardized [16]. Nonetheless, several different tests have been proposed: End-Notched Flexure (ENF), 4-Point End-Notched Flexure (4ENF) and End-Loaded Split (ELS). Among those, the most commonly used is the ENF, which presents a simple three-point bending setup and reliable data reduction methods. It requires a pre-cracked specimen and a constant measurement of P ,  and a . Since adhesive joints are typically subjected to mixed-mode, few tests are also available to evaluate the mixed-mode strain energy release rate ( G ), such as the Asymmetric Double-Cantilever Beam (ADCB), the Mixed-Mode Flexure (MMF), the Mixed-Mode Bending (MMB) and the Single-Leg Bending (SLB). The MMB test is the only standardized test available to estimate G of composites, referred in ASTM D6671 [17]. A combination of the DCB and ENF is the basis of the MMB test [18], and allows to change the mixed-mode ratio almost without limit between the pure mode I and pure mode II loading conditions [19]. Hence, it provides a complete understanding of the joints’ fracture behaviour under different loadings, known as fracture envelope. The SLB test is simpler than the MMB as it does not require special jigs. However, is more limited with respect to the change of the mixed-mode ratio. Jung Lee et al. [9] suggested a systematic procedure to evaluate the CZM parameters of an adhesive bond, using SLB tests for the extrapolation of the pure-mode laws, hence simplifying the inverse fitting method. Co-cured specimens were made of steel and unidirectional carbon fibre reinforced material. Measurement of G was carried out from the test data, and the mixed-mode was defined from the classical beam theory. A mixed-mode CZM was applied to reproduce the experiments, including a triangular law shape, the quadratic nominal stress criterion for damage initiation and the linear power law criterion for damage growth. The missing cohesive parameters (stiffness in tension, K nn , stiffness in shear, K ss , t n 0 and t s 0 ) were assessed by the design of experiments (DoE) and kriging metamodel (KM) techniques. The authors concluded that the proposed procedure accurately described the fracture behaviour of mixed-mode joints, attaining predictions within 15% of the experimental data. Moreover, it had the advantage of non-requirement of two separate tests (e.g., DCB for tensile and ENF for shear characterization). Rodrigues et al. [20] determined the fracture envelope of an aluminium adhesive bonded joint in dry and wet conditions, enabling to predict the humidity effect on G . After assessing the adhesive moisture absorption capability, DCB and ENF fracture tests were performed for mode I and II, respectively. For the mixed-mode test, an apparatus described in reference [21] was used that allows to test within a range of mode combinations between pure-modes I and II. The dry and wet fracture envelopes showed the ageing effect on the P m and P -  curves. Moreover, the applied methodology enabled obtaining the full fracture envelope with a linear correlation between the pure and mixed- mode data points. Nunes and Campilho [22] estimated the fracture envelope of joints bonded with three adhesives with different ductility using the Asymmetric Tapered Double-Cantilever Beam (ATDCB) mixed-mode test. Pure-mode TDCB tests and the Corrected Beam Theory (CBT) were used to assess G IC , and the ENF test together with the Compliance-Based Beam Method (CBBM) served to estimate G IIC . CZM laws were built based on a triangular law and the power law mixed- mode growth criterion, and the respective numerical results were compared with the experiments. This enabled to validate the CZM laws and the mixed-mode propagation criterion of each adhesive. Some inconsistencies were detected in the stiffness and P m of the most ductile adhesive, since the triangular law was not suitable to capture the plasticity inherent to theses adhesives [23]. However, the authors manage to prove that the data reduction method used for the ATDCB specimens is accurate and quick. The main objective of this work is to verify, by CZM, which is the  value that best suits the energetic crack propagation criterion for CZM modelling, using SLJ and DLJ with aluminium adherends and bonded with three different adhesives. With this purpose, numerical simulations of the SLJ and DLJ are carried out, and P m is compared with experiments. E XPERIMENTAL WORK Joint materials (fracture tests and lap joints) he DCB, ENF and SLB adherends, used to build the fracture envelopes of the adhesives, were manufactured from CFRP plates. The composite plates were fabricated using 20 plies with 0.15 mm thickness each, stacked by hand- lay-up using unidirectional layers. The SEAL ® Texipreg HS 160 RM pre-preg was used in this process. The curing T