Issue 39

M. Romano et alii, Frattura ed Integrità Strutturale, 39 (2016) 226-247; DOI: 10.3221/IGF-ESIS.39.22 241 | M y,a | = 0,1085· Õ -1,806 | M y,a | = 0,0481· Õ -2,014 | M y,a | = Õ -1,5 1 10 100 1000 0,001 0,010 0,100 | M| im u rel - w rel -Diagramm Grad der Ondulation Õ = A / L analytically for 4 4 rel 101 ... 101     u 3 3 rel 101 ... 101     u analytically for upper bound for exponent = -1,5 | M y,a | = 0,1085· Õ -1,806 | M y,a | = 0,0481· Õ -2,014 | M y,a | = Õ -1,5 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0,00 0,01 0,02 0,03 0,04 0,05 | M| im u rel - w rel -Diagramm Grad der Ondulation Õ = A / L ~ . . . . . . . . . . . . . . . . . Degree of ondulation Õ = A / L Degree of ondulation = / L | M y, a | in the u rel - w rel -di gram ~ | M y, a in the u rel - w rel -diagram ~ ~ ~ ~ ~ ~ ~ analytically for 4 4 rel 101 ... 101     u 3 3 rel 101 ... 101     u analytically for upper bound for exponent = -1,5 . . . Figure 5 : Absolute values of the slopes, i. e. a, ~ y M , over the selected degrees of ondulation O ~ plotted against the selected degrees of ondulation O ~ in a linear equidistant scale (left) and in a double logarithmic scale (right). Results of the FE-calculations In case of the two-sided elastic support the opposed positions of evaluation in the transversal direction ( y -direction) behave symmetrically and contrary identical, because of the symmetry of the model and the boundary conditions. In contrast in case of the one-sided elastic support the free position behaves distinctly more sensitive as the supported position. The consideration of the longitudinal direction ( x -direction) in both cases of the elastic support the evaluated results behave identically. Thereby the evaluation of Eq. (20) and Eq. (23) yields causally determined comprehensible and significant correlations. The evaluated results over the degree of ondulation O  for the applied deformations x  of the numerical model are listed in Tab. 4 for the kinematic parts y ,kin  (20) in terms of the slopes y M  , and in Tab. 5 for the difference of the applied and evaluated longitudinal deformation x ,kin  (23) in terms of the slopes x M  . The results are graphically illustrated in Fig. 6 and Fig. 7, respectively. With an increasing degree of ondulation O  the results show an increasing sensitivity in terms of the absolute values of the slopes M  . In case of the kinematic parts y ,kin  (20) it is possible to imply a sigmoidal correlation. The case of the one-sided elastic support shows a 1.8 times higher sensitivity to the mesomechanic kinematic as the case of the two-sided one. In case of the difference of the applied and evaluated longitudinal deformation x ,kin  it is possible to imply a quadratic correlation, where the one-sided elastic support shows again a higher sensitivity as the two- sided one. Discussion Due to its geometric similarity the results of the analytical model and of the numerical investigations of the plain weave fabric are comparable to each other, although they are partially identified by strongly simplifying presumptions. However both provide a description of the kinematic behavior by trend. The elastic parts of the ondulated roving due to the applied deformation are not negligible. Additionally, it has a certain bending stiffness due to its extent in the direction of the thickness. Both effects are considered by the numerical investigations with the FE-calculations. Furthermore the difference of the structural mechanic behavior of fiber reinforced plastics under tensile and compression load, the quality of the inter- and intralaminar adhesion between the single components (interphase) or the single layers (interlaminar shear stiffness) or other damages as imperfections, influence the real material behavior. Aspects considered in previously published contributions regarding mesomechanic kinematic correlations in fabric reinforced plastics are generally non-linear, especially when the kinematic correlations for dry fabrics without matrix system under uniaxial and biaxial loading as well as under shear loading are considered [11, 14, 15, 18]. Thereby at high rates of positive deformations the smoothing or flattening of the loaded yarns causes an upsetting of the transversally