Issue 39

M. Romano et alii, Frattura ed Integrità Strutturale, 39 (2016) 226-247; DOI: 10.3221/IGF-ESIS.39.22 228 ondulated rovings is done by the weighted average of the experimentally determined global fiber volume content, based on the relative part of the areas of the different regions. Ballhause 2007 [11] investigates the structural mechanics of dry fabrics on the mesomechanic scale under one- and two- dimensional loading. A failure model is formulated based on the increase of contact forces and simultaneously the reduction of the curvatures at the crossings under increasing loads. Matsuda et al. 2007 [12] besides the elastic behavior investigate the viscoplastic parts in plain weave fabrics. A homogenization theory is developed numerically considering the in-phase and out-of-phase arrangement. Nakanishi et al. 2007 [13] investigate the damping properties of fabric reinforced composites. Thereby glass fibers as a plain weave fabric in a polymeric matrix system are considered in numerical investigations. Based on the determined mesomechanic properties flat beam-like specimens have been modeled by means of FE-analyses and investigated up to the third bending mode in vibration. Badel, Vidal-Sallé and Boisse 2007 [14] as well as Hivet and Boisse 2008 [15] identify a mesoscopic mechanical behavior for woven composites. Therefore dry fabrics under biaxial tension are investigated numerically. A strong nonlinearity is reported especially at the beginning of the loading. El Mahi et al. 2008 [16] present an analytical description of structural mechanic material damping mechanisms in fabrics. The carried out FE-calculations are validated. The strain energy under the presumption of plane stress is considered. The validation is carried out by the decay of vibrating flat beam-like specimens at the first three natural frequencies. The 0°- unidirectionally reinforced specimens show smaller structural material damping as the fabric reinforced ones, whereat the plain-weave reinforced specimens showed distinctly higher damping values than the twill-fabric reinforced ones. The effect, however, is lead back to friction, what is rather improbable when the specimens originally are neither prestressed nor damaged. Szablewski 2009 [17] treats representative sequences of plain-weave reinforced single layers under the simplifying presumption of sine-shaped ondulations of the rovings in the mesomechanic scale. The geometrically definitely defined model provides the determination of stress and strength aspects. Finally, the possible adaption of the presented idealized geometry to other types of fabric constructions is mentioned. Hivet and Duong 2010 [18] carry out similar numerical investigations for dry fabric reinforcements under shear load conditions. Thereby the load is applied by a picture-frame mechanism. Nonlinearities are detected regarding the angle of deformation and the resulting orientation of the yarns in the fabric. Ansar, Xinwei and Chouwei 2011 [19] give a review about modeling strategies. Even if 3D woven composites are focused, a parametric consideration of the geometric dimensions is supposed. Correlations between geometric and technical parameters are indicated. Different approximations for modeling the cross-section, amongst others a lens-shaped cross- section, of the single tows are listed. Kreikmeier et al. 2011 [20] introduce sine-shaped fiber-orientation in the in-plane direction as an imperfection due to a selected manufacturing process. The sine as an analytical function is processed analytically for a basic description of the phenomenon, yet without parametric variation of the geometric dimensions. Valentino et al. 2013 [21] and Valentino et al. 2014 [22] mechanically characterize basalt fiber reinforced plastics with different fabric reinforcements by experimental tensile tests and FE-calculations. In ranges of small deformations and at a comparable fiber volume content the fabric reinforced specimens exhibit slightly lower stiffnesses as the comparable 0°- unidirectionally reinforced ones. Pursued mechanical principle The aim of the carried out investigations is the identification and verification of a mesomechanic kinematic caused by ondulations in fabric reinforced composites. Based on a sine as a purely analytic trigonometric function according to Eq. (2) a so called plain representative sequence of a balanced plain weave fabric reinforced layer can be derived. The amplitude A and the length L are the characteristic geometric parameters. They define an entire cross-section of one complete ondulation. Two reasonable basic geometries for further analytical processing and for the carried out FE- analyses are shown in Fig. 1 left. The simplified geometry of the ondulation for the carried out FE-analyses represents an idealized cross-section of the warp yarn of a fabric reinforced single layer cut along its theoretic center line perpendicular to the crossing fill yarns. Three structural mechanically different regions can be identified. Regarding their stiffnesses as the characteristic structural mechanical properties there are  the warp yarn with predominant direction following the longitudinal sine and so E 1 following the sine and E 2 perpendicular to it,