Issue 39

M. Romano et alii, Frattura ed Integrità Strutturale, 39 (2016) 226-247; DOI: 10.3221/IGF-ESIS.39.22 236 Figure 4 : Different element formulations in the region of the zero-crossing: PLANE42 with enabled first keyoption KEYOPT(1) in the region of the ondulated warp yarn causing the element coordinate systems to follow the sine-shaped ondulation and PLANE182 in the region of the fill yarns and the matrix with the element coordinate systems aligned to the global coordinate system. Boundary conditions and application of selected deformations A clamped edge is defined on one vertical edge. On the opposite vertical edge a free edge is defined where the selected displacements are applied. Both definitions on the boundaries allow a transversal deformation of the cross-section due to Poisson effects, as the translational displacements in the vertical y -direction as well as the rotational degree of freedom to the z -direction perpendicular to the x - y -plane are defined free. On the nodes of the defined free vertical edge selected longitudinal deformations as strains x l u l L 0 F     (17) are applied in two intervals. For verification and comparison issues they are the same as used in the analytical model for u rel (7), i. e. the large one is x 3 3 1 10 1 10          in steps of 4 1 10   and the small one is x 4 4 1 10 1 10          in steps of 5 1 10   , resulting in 39 and 21 substeps. Regarding the boundary conditions on the horizontal edges, i. e. on the top and bottom side of the model, two basically different conditions exist. Fabric reinforced composites usually consist of more than one layer, mostly an even number of plies. Thus the single layers can be considered as elastically supported on both sides, when located as an inner ply, and elastically supported on one side, when located as an outer ply. Therefore, a case-by-case analysis is considered further. The calculation of the value of the elastic support k el is done by means of a weighted average of the plane stiffnesses based on the areas of the different regions. The similar calculation is carried out by Barbero 2011 [35], 2006 [10] and 1995 [36] as well as by Byun 2000 [4]. Structural mechanic material properties of the single components The two exemplarily considered single components are HT-carbon fibers as reinforcement fibers and epoxy resin as a polymeric matrix system. Because of its characteristic structural mechanic material properties this combination is commonly used in mechanically highly loaded structures. Tab. 1 contains the structural mechanic material properties the two components, taken from [30-33]. The densities of the single components as a physical material property are indicated for the HT-carbon fibers 3 HT Carbon 1.74 g/cm    and for the epoxy resin as matrix system 3 m 1.20 g/cm   . In detail the structural mechanic material properties correspond to the values indicated in the data sheets of the three sets of comparable specimens of HT-carbon fiber reinforced epoxy, used in the experimental investigations described in Romano et al. 2014 [24, 25] and Romano 2016 [26].