## 5 Adhesion Improvement Assessing  
### Theoretical Background  
Fragmentation tests were used to assess whether the polymerization technique increments the interfacial adhesion. Interfacial shear strength (ISS) is the result of static equilibrium between the tension force acting on the fiber and the shear force transferred through the interface of the matrix to the fiber [46,47]. According to the Kelly-Tyson approach [48], this value is defined as  
\[\textit{ISS}=\frac{\overline{\sigma}_{\textit{\tiny\beta(Lc)}}d}{2 Lc} \tag{1}\]  
where \(\overline{\sigma}_{\textit{\tiny\beta(Lc)}}\) is the mean fiber strength at the critical length, \(Lc\), and \(d\) is the diameter of the fiber. The value of the critical fragment length can be determined from the average length at saturation (Ls), assuming that the distribution of the fiber fragment lengths at the end of the rupture process is quasi-symmetrical:  
\[Lc=\frac{4}{3}Ls \tag{2}\]  
It is clear, from Equation (1) that the calculation of ISS implies that it is known how the fiber strength depends on the fiber length. In the present work, this relation was experimentally assessed by carrying out single filament tensile tests following ASTM 3379 standard [49]. These tests were conducted at a given gauge length and the data were fitted by a two-parameter Weibull distribution. According to the 'weakest link' approximation, it is assumed that a fiber of a length \(L\) is formed by \(N\) independent links of arbitrary unit lengths \(L_{0}\), each link failing or surviving at a given stress level, independent of its neighbors. The strength distribution of each link is also described by a simple Weibull distribution, characterized by identical shape parameters. Then, the Weibull cumulative distribution function F(\(\sigma\)), and the corresponding average strength, \(\overline{\sigma}_{\textit{\tiny\beta(Lc)}}\), respectively, are given by:  
\[F(\sigma)=1-\exp\Biggl{[}-L\Biggl{(}\frac{\sigma}{\sigma_{0}}\Biggr{)}^{m} \Biggr{]} \tag{3}\]  
\[\overline{\sigma}_{\textit{\tiny\beta(L)}}\ (L)=\sigma_{0}\Biggl{(}\frac{L}{L_{0}} \Biggr{)}^{\frac{1}{m}}\Gamma\Biggl{(}1+\frac{1}{m}\Biggr{)} \tag{4}\]  
where \(\Gamma\) is the Gamma function. The scale (\(\sigma_{0}\)) and shape (\(m\)) parameters of the Weibull distribution were estimated from strength data determined at one single gauge length by fitting the distribution of failure probability. The fiber tensile strength at any gauge length needed for the calculation of ISS was finally calculated on the basis of Equation 4.  
The mechanical strength of the fibers was measured on the starting sample; untreated and only MAO treated fibers. Notably, the latter study is to analyze whether the attack with MAO produces any change in the fibers' resistance. These changes may stem from a possible smoothing, including micro-cracks, surface hardening _etc._ Importantly, a preliminary observation with SEM/EDX of the fibers only attacked with MAO was done and the results are shown in Figure 11.  
In principle, it can be seen that a very smooth surface with a metallic brightness due to the aluminum oxide layer is formed. Its appearance in general does not differ from that of the starting GFs. Microcracks are not observed, however the final conclusion will only be possible by measuring the mechanical properties of the fibers. In turn, the EDX spectrum shows that treatment with MAO does not introduce major changes in the surface composition of fibers with respect to the starting GFs. No C peak can be seen and the Al/Si is maintained. Only an increase of peak O is observed, which is expectable due to the formation of the oxide. The fibers were characterized mechanically using tensile tests according to ASTM 1557. The fiber diameter was measured under an optical microscope. Average mechanical properties of fibers and their diameters are summarized in Table 2 where it can be seen that, in principle, the fibers remain unchanged, because the changes in mechanical properties are within the experimental error of measurements.