Issue 39

M. Romano et alii, Frattura ed Integrità Strutturale, 39 (2016) 226-247; DOI: 10.3221/IGF-ESIS.39.22 238 Assignment of the structural mechanic material properties to the different region The assignment of the structural mechanic material properties to the different region follows according to the respective input mask of the FE-preprocessor of ANSYS [34]. For the HT-carbon fiber reinforced regions the input mask of an orthotropic material behavior is used. For a complete and consistent FE-simulation the input of 3D-properties are required, although 2D-properties are applied due to the carried out 2D-analyses. Nine independent structural mechanic material properties are required. Yet, the five independent values of the 0°-unidirectionally reinforced regions suffice, as pairwise equal inputs are made in the plane of isotropy for simulation of transversal isotropic material behavior. Tab. 2 contains the input values of the structural mechanic material properties of the fiber reinforced regions. To the regions of pure matrix without fiber reinforcement are assigned the isotropic material properties E m 3, 3 GPa  and m 0.35   as indicated in Tab. 1. According to the case-by-case analysis, considering the two basically different boundary conditions, the elastic support k el,HT carbon EP 9.5 GPa    acting in transversal y -direction of the FE-model is assigned to. The detailed calculation of the value of the elastic support, by the weighted average of the perpendicular stiffnesses E 2 and E m in the plane of the representative sequence, based on the relative part of the areas of the different regions, is carried out according to Barbero 2006 [10], 2011 [35] and 1995 [36] as well as to Byun 2000 [4]. R ESULTS AND DISCUSSION he obtained results of both the analytical model and the numerical investigations by the FE-analyses are evaluated and compared to each other. The acting mechanisms of the mesomechanic kinematic in fabrics due to the degree of ondulation and its sensitivity to geometric parameters and boundary conditions are described and discussed. Aspects of the evaluation The variation of the two characteristic geometric dimensions of the ondulation in five substeps each provides 25 combinations of different degrees of ondulation O  in total. For each of the models, the same selected deformations are applied in two decades of ten equidistant steps each. The relevant results are evaluated for every degree of ondulation O  at every substep n 0, , 39   and plotted against the selected deformations. These are u rel (7) in the analytical model and ε x in the numerical investigations (17). Positions of evaluation and separation of elastic and kinematic parts The relevant positions of evaluation of the analytical model correspond to the ones of the FE-model. In case of the plain representative sequence of a plain weave fabric they are the two extrema, namely maximum and minimum of the sine. In case of the numerical investigations these are located on the theoretical center-line of the longitudinally cut ondulated warp yarn. The evaluation of the results is carried out by the linearly presumed correlation between the applied displacements and the considered relevant values, analog to Ottawa et al. 2012 [23]. In the FE-calculations the resulting elastic deformation basically consists of two parts. These consist of the purely kinematic parts due to geometric constraints and of the resulting elastic behavior of the linear-elastically modeled material. In order to identify the kinematic part only, the elastic part has to be separated from the total deformation. Sensitivity to the mesomechanic kinematic In each case almost linear correlations can be identified, especially in the smaller interval. A direct and linear coupling between deformation and shape of the ondulation in fabric reinforced single layers can be stated, and the absolute value of the negative slope       y y x y x x x w M O u M O M O rel ,a rel , kin , kin d d d in case of the analytical model and  and in case of the numerical model d d d              (18) as a function of the degree of ondulation O  represents the sensitivity to the mesomechanic kinematic. With the definition of the slopes M  (18) another relative value is introduced. Thereby, a higher slope M  or a higher absolute value of it T