PSI - Issue 51

Hugo Vidinha et al. / Procedia Structural Integrity 51 (2023) 9–16

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H. Vidinha et al./ Structural Integrity Procedia 00 (2022) 000–000

Nomenclature 3D

three dimensional First principal strain

 I

DIC Digital image correlation EWM Element weakening method FF Fibre fracture FRP Fibre-reinforced polymer IFF Inter fibre fracture

industries. In order to improve structural design and predict failure and the mechanical behaviour of composite structures, different failure theories have been created over the years. Most of the damage happening in composite structures occurs at the microscopic level, however, the heterogeneous microstructure of composite materials makes it difficult to predict microscopic damage events, becoming micromechanics analysis rather complex and time consuming. Therefore, if a macromechanics approach is considered using an accurate three-dimensional failure criterion, precise simulation results can be achieved with an acceptable computational effort. One of the first failure theories for anisotropic materials was developed by Hill in 1950. In order to work properly, this theory requires difficult experimental parameters. Later, in 1968, Tsai adapted Hill's theory by introducing a new concept based on the von Mises distortional energy yield (Tsai, 1968). In this theory, failure is assumed to occur whenever the distortional yield energy surpasses a value related to the lamina’s strength. A few years later, in 1971, Tsai and Wu proposed a theory based on the total strain energy density valid for anisotropic materials (Tsai and Wu, 1971). A very appealing characteristic of Tsai-Hill theory is the fact that this theory predicts the lamina failure under general loading conditions using a single equation. However, for non-transversely isotropic materials, the model requires the determination of a high number of experimental parameters, which makes the process quite expensive and laborious. A more complex failure criterion for transversely isotropic composites was developed by Hashin in 1980 (Hashin, 1980). In this criterion, fibre and matrix failures under tension or compression are distinguished. In recent years, much more complex theories have been developed, such as LarC03 (Dávila et al., 2005) and Puck (Puck and Schürmann, 1998). LarC03 developed six phenomenological failure criteria, and both fibre and matrix failures under compression are based on a Mohr-Coulomb interaction of the fracture plane stresses. On the other hand, Puck used the Hashin’s criterion and developed a physically-based failure criterion. The above-mentioned models have been widely used in finite element analysis (Dávila et al., 2005; Shokrieh and Lessard, 2000; Warren et al., 2016; Lee et al., 2015; Gonilha et al., 2021). Furthermore, progressive damage models grounded on these failure criteria have also been implemented in commercial FEM software (Maimí et al., 2007), for instance, a three-dimensional damage model (Miamí et al., 2008), a micromechanical damage model (Zhang and Zhao, 2011), and Puck’s failure criterion combined with the Element Weakening Method (Lee et al., 2015). These works demonstrated that such models could predict the initiation and growth of internal defects on composite structures. Nevertheless, detailed analyses of initiation and growth of internal defects emanating from severe geometric discontinuities rarely have been addressed in the literature. Hence, in the present work, Puck’s failure criterion along with the Element Weakening Method were implemented for predicting the initiation and progression of the damage of a notched laminate subjected to tensile loading. The numerical simulations were validated from tensile stress-strain tests and the analysis of the strain fields near the geometric discontinuities measured by Digital Image Correlation. 2. Materials and Methods The material used in this study was a glass-fibre-reinforced epoxy composite, which was prepared via autoclave/vacuum-bag moulding. The plates were produced with 12 layers, arranged in a sacking sequence of (0º, 45º, 90º, 45º, 0º, 90º)s, and had an overall dimension of 330×330×2.3 mm 3 . The specimen geometry is exhibited in Fig. 1. As can be seen, it consists of a rectangular cross-section with a central hole measuring 5 mm in diameter. The hole was drilled using a twist drill bit operated at a suitable cutting speed to prevent delamination. Three tensile tests were performed using a Shimadzu Autograph AGS-X machine, according to ASTM D3039 standard, at room temperature