PSI - Issue 19

Christian Schneider et al. / Procedia Structural Integrity 19 (2019) 370–379 Ch. Schneider et al / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction

For continuous fiber composite laminates, the stress-based "Wöhler" approach with experimental S/N curves (stress amplitude vs. number of cycles) is a widely used method for predicting the service life of components (Radaj 2003; Talreja 2003; Haibach 2006). However, S-N curves only describe the final failure of the specimens in a fatigue test but do not describe any changes in stiffness. For a real definition of the end-of-fatigue-life it is important to identify the type of failure mechanism and the corresponding sequence effects correctly (Ye 1989; Curtis 1991). Many fiber composite laminates exhibit a decrease in stiffness after a short dynamic load, followed by a plateau. Due to a highly hierarchical, multi-level structure of fiber composite laminates the initial (micro-) cracks are arrested at fibers or neighboring ply interfaces. Consequently, the failure behavior of samples with multidirectional stacking sequences is a combination of the failure behavior of the individual layers. When a layer is embedded in a laminate, the initiation of a first crack in many cases does not lead to failure of the entire laminate. Rather, matrix cracks are retained in the neighboring layers and additional cracks accumulate to a saturation state before the crack grows again (Curtis 1991; Gamstedt and Talreja 1999; Reifsnider and Talug 1980; Ye 1989). 3D Finite Element (FEM) simulations were carried out to find the optimal configuration of the tabs that minimize the risk of failure outside the gauge section. For this, FEM models of a rectangular specimen with layers of carbon fibre reinforced polymers (CFRP) and a layup of [0° (1) /90° (4) /symm.] were analyzed using the FEM software Abaqus (Abaqus 2014). The effect of tab material and taper angle on the risk of failure in the first two plies in the laminate and on the stress concentration in the adhesive layer between tab and laminate was studied. For the tab material aluminum and glass fibre reinforced polymers (GFRP) woven fabric and for each material the two most extreme ta per angles α = 90° and α = 14° we re compared. Due to the symmetry of the specimen, a quarter model with symmetry boundary conditions was used. The geometry of the model is shown schematically in Fig. 1 and the geometry data is listed in Table 1. The model was discretized with hexahedral elements of quadratic order (C3D20) with a general meshsize of 0.25 mm and a refinement to 0.1 mm within the transition area from gauge section to the tabs ( X = 0 mm). Three elements were used over the height of each ply and one over the height of the adhesive layer. 2. Modelling of Tabs

Fig. 1: Schematic representation of the specimen geometry with the area of the quarter model marked by the red dashed line (left) and detail view with paths defined for output extraction (right). In addition to the symmetry boundary conditions, the clamping forces of the testing rig were modelled. A schematic representation of the clamping is shown in Fig. 2. The clamping force F C in Z-direction is a result of the force F from the testing machine and was computed as = sin( ) cos⁡( ) (1)