# Experimental and Numerical Investigation of the Mesoscale Size Effect in Notched Woven Composites
## 3 Results
### Failure Properties
The circular hole thus leads to two different effects in the stress field:  
1. Stress concentration. The affected volume scales up with the hole diameter. This leads to an increased probability of encountering a weak point within the structure that causes premature failure, and, consequently, a decrease in load-bearing capability. Indeed, as observed in Table 3, the nominal strength of the notched specimen, which is the ratio between the maximum force and the nominal notched cross-section, decreases with the hole diameter. This effect can also be quantified by the ratio of the remote longitudinal stress \(\sigma_{1}^{\infty}\) --defined earlier--to the maximum longitudinal stress in the entire specimen \(\sigma_{1}^{MAX}\). 2. Stress localization. Close to the hole, stress sharply rises in a very limited volume. This leads to an observed local increase in material strength. This effect can be described by the ratio between the longitudinal tensile strength of the material in the notched specimens \(S_{1}\) --determined as per Section 2.3.2--to the same property in the unnotched specimen, indicated as \(S_{1}^{0}\). The specimen-level tensile behavior results from a superposition of these two effects, one beneficial and the other detrimental. This is highlighted in Figure 10a, where the two effects are plotted as non-dimensional stress ratios for different hole diameters. The yellow curve, \(\sigma_{1\ ratio}\), describes the stress concentration and localization. Increasing hole sizes lead to an intensification of the stress, a larger affected area, and a consequent decrease in the ratio between the remote stress and maximum stress. On the other hand, looking at the ratio between the notched and unnotched tensile strength of the material \(S_{1\ ratio}\) (blue curve), a roughly 2.5-fold increase in strength is locally noted in the tow material. In this case, the local strength increases with increasing hole size. The two effects can be combined by dividing the strength increase by the stress intensification, as represented by the green curve. This curve follows the trend of the reduction in nominal ultimate tensile strength \(UTS_{nom}\) compared to the unnotched value \(UTS_{nom}^{0}\) (black dashed line) commonly used in traditional specimen-level assessment of open hole stress concentration. This can be better observed in Figure 10b, where only  
Figure 9: Plots of the stress state values at the most heavily loaded elements at failure on (**a**) the \(\sigma_{yy}\)-\(\tau_{xy}\) plane (fiber direction in the material); (**b**) the \(\sigma_{xx}\)-\(\tau_{xy}\) plane (matrix direction in the material). The grey cloud contains all stress states of the elements in the plain specimen at failure. these two latter curves are plotted. The overlap of these curves can be interpreted as an equivalence between a mesoscale-level and a macroscale-level stress concentration curve. A decrease in slope in the nominal stress curve is observable with increasing hole diameters, in agreement with traditional semi-empiric models like the point stress and average stress criteria. This change in slope can be now interpreted as a change in the balance between the two effects described above, occurring with size scaling. For increasing hole diameters, the increase in local material strength due to stress localization outweighs the decrease that occurs in parallel due to the larger affected area.