Issue 28

P. Valentino et alii, Frattura ed Integrità Strutturale, 28 (2014) 1-11; DOI: 10.3221/IGF-ESIS.28.01 6 the one to assign the mechanical properties of the warp yarns and the other one to assign the fill yarns properties, respectively. Isotropic linear elastic properties have been assumed for the matrix and data listed in Tab. 1 have been assigned to it. This assumption requires no further specificationof themeshorientation. (a) (b) Figure 7 : FEmodels of theRVEs (a) Twill weave 2/2; (b) Twill weave 1/3. In order to correctly assign the mechanical properties to the yarns, it has to consider that each tow is characterized by a big percentage of fibres immersed in epoxy matrix. Furthermore, the calculation of the material properties should be based on the experimentally determined values of the fibre volume content φ f , previously described. However, the latters have been calculated based on a bigger volume of material than the RVE, therefore, in order to match the data and to correctly assign the material properties to the yarns, the fibre volume content of the yarns in the RVE, φ f,y , has been determined bymodifying the one experimentally calculated, φ f , as below: 1 , RVE f y y f y y V V X      (3) where V RVE is the RVE volume, V y is the tow volume of the RVE, x is the relative volume of yarns in the RVE. Details of the new data are listed inTab. 3. Fabric type and test direction φ f experimentally determined Region in theRVE Relative volume x in theRVE φ f,y basedon exp. values φ f,y standardized to 50% in theRVE Twill weave 2/2 51.85% Warp and fill yarns 76.00% 68.22% 65.79% Warp Polymericmatrix 24.00% Twill weave 2/2 47.88% Warp and fill yarns 76.00% 63.00% 65.79% Fill Polymericmatrix 24.00% Twill weave 1/3 49.17% Warp and fill yarns 79.00% 62.24% 63.29% Warp Polymericmatrix 21.00% Twill weave 1/3 54.75% Warp and fill yarns 79.00% 69.30% 63.29% Fill Polymericmatrix 21.00% Table 3 : Calculated fibre volume content, φ f,y , to used inFE-analyses. The new calculated values of the fibre volume content φ f,y are based on the relative volumes ratio of the different phase of the RVEs and on the fibre volume content experimentally calculated, φ f . Therefore, the geometric dimensions of the yarns, the thickness of the RVEs [15, 16, 18] as well as the accuracy of the experimental determination of φ f , affect this calculation. The yarn is considered as a unidirectional reinforced phase with a transversally isotropic behaviour, therefore, nine elastic constants (five are independent) are required to assign the transversally isotropic properties to the reinforced regions of theRVE. The evaluation is described in the following. Inparticular, in the predominant direction the stiffness canbe calculated bymeans of themixture law, as below:   1 1 , , f y f f y m E E E      (4)