Issue 28

P.Valentino et alii, Frattura ed Integrità Strutturale, 28 (2014) 1-11 ; DOI: 10.3221/IGF-ESIS.28.01 7 As the basalt fibre and the polymeric matrix can be considered as homogeneous isotropic materials, the respective shear moduli can be calculated by G=E/2(1+ ν) , where the corresponding values are listed in Tab. 1. Mixture law, according to Chamis [19, 22], canbe applied inorder to calculate threemore independent linear-elastic properties of the yarns, namely: 1 2 1 1 , m m f y f E E E E E                     (5) 12 13 1 1 , m m f y f G G G G G                     (6)   12 13 1 , , f y f f y m           (7) The remaining parameters, needed to fully define thematerial properties of the RVE, have been calculated exploiting the Maxwell-Betti's law, E i ν ji =E j ν ij , as below: 2 21 31 12 1 E E      (8) Finally, the last independent parameters, i.e. G 23 , G 32 ,  23 and  32 have been calculated 23 32 23 1 1 , , m m f y f G G G G G                     (9) 2 23 32 23 1 2 E G            (10) Finally, appropriate boundary conditions have been applied to theRVE inorder to: 1. ensure a purely longitudinal deformation; 2. allow contractionof the cross-sections due toPoisson’s effects; 3. avoid twisting andbending effects. R ESULTSAND D ISCUSSION Experimentally and numerically determined stiffness esults, in terms of stress-strain response, for both of the fabric reinforcements, i.e. twill 2/2 and twill 1/3, are reported inFig. 8(a) andFig. 8(b), respectively. Figures clearly exhibit an high repeatability of the response in all the cases. This can be attributed to a constant material quality over the whole test panel. However, whereas the 2/2 fabric type shows a clear difference, in terms of stiffness and strength, along the warp and fill direction, the 1/3 fabric type does not show substantial variations. Furthermore, the textile exhibits higher stiffness and strength along the warp direction than the fill one for both of the fabric types. Using the weighted averagemethod, as a first approximation [21, 22], the stiffness of the specimens have been calculated as secant modulus E s.0.5% at a strain value of ε =0.5% and tangent modulus E t.0.1% (as a Secant Modulus at a strain of ε =0.1%) according toGerman standardDINEN 2747 [7]. For each textile specimen and layup the average values and standard deviations have been calculated, respectively [23-25]. Fig. 9 and Fig. 10 show the stiffness related to each textile semi-finished product as secant modulus E s.0.5% and tangent modulus E t.0.1% with the respective standard deviations. In particular, whereas Fig. 9 shows the secantmoduli and tangent R