Issue 39

M. Romano et alii, Frattura ed Integrità Strutturale, 39 (2016) 226-247; DOI: 10.3221/IGF-ESIS.39.22 229  the two fill yarns with predominant direction perpendicular to the cross-section and so E E 2 3  in the investigated plain model and  the matrix region that is not reinforced at all with E m . There are significant differences in the values of the stiffnesses of the different regions. Thereby the stiffness E 1 of the unidirectionally reinforced yarns is significantly higher in the direction of the reinforcement compared to the stiffness E 2 in direction perpendicular to the reinforcement and the stiffness E m of the matrix region. The relations can mathematically be related by E E E 1 2 m   (1) Common homogenization theories yield E E E 1 2 m 150 GPa 11.5 GPa 3.3 GPa      in case of a unidirectionally reinforced single layer with high tenacity (HT) carbon fibers with a presumed fiber volume content of f 60 %   as absolute values for the stiffnesses. Two different effects in the model can be identified, when positive and negative longitudinal deformations are considered. In both cases the unidirectionally reinforced ondulated yarn is subjected to a purely elastic deformation. Additionally at the same time in case of positive longitudinal deformations a smoothing or flattening, and in case of negative deformations an upsetting of the unidirectionally reinforced ondulated yarn is induced due to its ondulated shape. In both cases the variation of the amplitude is a superposition of transversal deformation due to Poisson effects as a purely elastic response and a purely kinematic response due to geometric constraints in the mesomechanic scale. In contrast longitudinal deformations applied on a unidirectionally reinforced single layer in direction of the reinforcement leads to a lengthening and shortening in longitudinal direction and a transversal contraction directly coupled due to Poisson effects only. The repeated acting of this mesomechanic kinematic due to geometric constraints is presumed to enhance the damping properties of fabric reinforced single layers compared to unidirectionally reinforced ones. For an evaluation the free decay behavior of flat beamlike specimens with fabric and unidirectionally reinforced single layers can be considered. Thereby the fixed-free boundary condition has been identified as adequate. During the free decay the structure undergoes the kinematic in a number of cycles equal to the fundamental frequency. The basic concept and the identification of the acting mechanism has been validated basically in Ottawa et al. 2012 [23] for one set of comparable specimens of basalt fiber reinforced epoxy (0° unidirectionally and 0° twill fabric 2/2 reinforced in warp direction) and more detailed in Romano et al. 2014 [24, 25] and Romano 2016 [26] for three sets of comparable specimens of carbon fiber reinforced epoxy (0° unidirectionally and 0° plain and twill fabric 2/2 reinforced in warp direction). Thereby, the term comparable is defined by the property and the quality of the composite material of the respective set of specimens. One set of specimens is considered comparable when its single layers consist of the same kind of reinforcement fiber, 0° unidirectionally reinforced on the one hand and 0° fabric reinforced single layers (i. e. in warp direction) on the other hand, with the same polymeric matrix system and additionally at approximately same fiber volume contents f 60 %   and overall thicknesses of the laminate t . M ESOSCOPIC APPROACH he phenomena of ondulation in fabric reinforced composites are examined on the mesoscopic scale. It is an effect in fabrics as textile semi-finished products. The warp yarns are perpendicularly crossed by the fill yarns alternating at its top and at its bottom. In the following investigations the relatively simple and at the same time easily describable geometry of a balanced plain weave fabric is considered further. The aim of the carried out investigations is the identification of the previously described acting mesomechanic kinematic correlations. In the carried out analytical and numerical investigations based on plain representative sequences the variable characteristic geometric parameters are the amplitude A and the length of the ondulation in the fabric L F and the length of the cross-section of a roving as a fill yarn L R , respectively. The parametric variation of the geometric dimensions in realistic steps provides the analysis of the sensitivity of the acting mesomechanic kinematic to the differently shaped ondulations. First a one-dimensional analytic approach is carried out. A kinematic is derived analytically and investigated parametrically. For a first approach strongly simplifying presumptions are necessary, so the elastic parts are neglected in this case. T