# Experimental and Numerical Investigation of the Mesoscale Size Effect in Notched Woven Composites
## 3 Results
### Failure Properties  
Table 4 shows the failure strengths determined for the constituent material according to the methodology described in Section 2.3.2. Consistent with the hypotheses made in Section 2.3.2, the maximum longitudinal stress was always reached in elements belonging to longitudinal rows, and maximum transverse and shear stresses in horizontal tows. The volume of material affected by the notch was calculated to estimate the entity of stress intensification. This volume was defined as the sum of the volumes of the portions of \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Specimen** & **S\({}_{1}\) [MPa]** & **S\({}_{2}\) [MPa]** & **S\({}_{12}\) [MPa]** \\ \hline C20 & 2131 & 370 & 117 \\ C21 & 3623 & 616 & 125 \\ C22 & 3676 & 586 & 170 \\ C23 & 3922 & 631 & 190 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Failure properties. Figure 7: **(a)** Comparison between experimentally and numerically determined stress and strain curves; **(b)** Example of a comparison between experimentally (left) and numerically determined longitudinal strain maps for Specim C22. material around the integration points, the stress of which at failure load was higher than the remote stress in the specimen. In turn, remote stresses (\(\sigma_{1}^{\infty}\) and \(\sigma_{2}^{\infty}\)--subscript referring to the local material direction) were defined as the maximum reached in a region far from the fixture and the stress concentration areas, as wide as the specimen and multiples in height of the characteristic size of the tows. Volumes were separately identified and calculated for vertical and horizontal tows. The values calculated for each specimen are laid out in Table 5, where \"Volume 1\" and \"Volume 2\" refer to the volume subjected to the intensification of the stress along the material directions 1 and 2, respectively. The volumes subjected to intensification are also mapped out in Figure 8.  
The affected volume scales up with the hole diameter. Interestingly, the interaction of the stress concentration with the non-homogeneous material structure can be also observed. For specimens C21 and C22, with respective hole diameters of 2 and 4 mm, both smaller than the 5-mm tow size, the stress concentration remains localized. On the other hand, in specimen C23, with its 8-mm diameter hole, the notch is not contained within a tow and more than one diagonal row of tows is interrupted. Entire bundles of vertical fibers passing through the hole are not bearing any load above and under it, which must be transferred by shear stresses to the tows on the left and right of the hole. This more inefficient use of the material leads to a wider distribution of affected volume. Figure 9 shows the highest stress integration points for all specimens on the \(\sigma_{yy}\)-\(\tau_{xy}\) and \(\sigma_{xx}\)-\(\tau_{xy}\) plane for the three specimens. There is a distinct separation in stress states between the vertical and horizontal tows--with the former bearing the highest fiber-direction tensile stresses, and the latter the highest matrix tensile and shear stresses. It can be noted how,  
Figure 8: Maps showing the percentage of the volume of material per element in the two orientations, the longitudinal stress of which surpasses the remote one, in the proximity of the hole. Remote stress was calculated as the maximum stress in a portion of the specimen away from the stress concentration. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Specimen** & **Volume 1 [mm\({}^{3}\)]** & **Volume 2 [mm\({}^{3}\)]** & **Total Volume [mm\({}^{3}\)]** \\ \hline C21 & 5.65 & 4.33 & 9.99 \\ C22 & 15.51 & 8.99 & 24.50 \\ C23 & 82.61 & 60.96 & 143.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Volumes affected by the stress concentration in vertical tows (Volume 1), in horizontal tows (Volume 2), and in the whole specimen. despite an apparent higher ultimate tensile strength, every single element in the unnotched specimen (grey point cloud) is in a much lower stress state.