# R-Curve Behavior of Polyhedral Oligomeric Silsesquioxane (POSS)-Epoxy Nanocomposites
## 3 Results  
Figure 3 shows the load-displacement curve of POSS-epoxy nanocomposites. The graph indicates that with the inclusion of POSS, the peak load increases before failure. The other interesting observation from the load-displacement curve suggests that at higher loading of POSS in epoxy resin the failure mode changes from brittle to ductile. Hence, measuring fracture toughness by using linear elastic fracture mechanics (LEFM) is no longer valid for more than 1 wt.% of POSS reinforcement. Figure 4 shows the excessive ductile behavior in the POSS-epoxy nanocomposites at higher POSS loading. Various studies have been done to investigate the nonlinear fracture behavior by using either the load separation method [14, 15, 16, 17] or multiple specimen method [18, 19] to develop the \(J\)-\(R\) curve. Both of these techniques show good agreement in the results [20, 21]. In order to keep the specimen preparation constant in this study, we have used multiple specimen methods to quantify the resistance against the stable crack growth. This multiple specimen method approaches uses phenomena of the J-integral method for the assessment of the nonlinear material. The crack initiation resistance (\(J_{IC}\)) have been measured [13] by using ASTM D 6068. Figure 5 shows the variation in the value of \(J\) (fracture resistance) with increase in the crack length (\(\Delta a_{p}\)). Figure 4: Ductile failure of 8 wt.% POSS–epoxy nanocomposite. Figure 3: Load displacement curve of glycolidyl POSS–epoxy nanocomposite at different POSS percentage. The \(J\)-\(R\) curve confirmed (Figure 5) that POSS-epoxy nanocomposite follows the \(J\)-integral fundamental. The formation of the \(J\)-\(R\) curve indicates that the inclusion of glycidylI POSS makes the polymer chain more flexible, which leads to ductile behavior in POSS-epoxy nanocomposite at higher POSS loading. Initially, in the \(J\)-\(R\) curve, \(J\) increases linearly with crack length because more energy is needed to break the flexible chain. After that \(J\) shows no or very less variation with the further crack extension. This may be because the energy required to break the same amount of POSS-epoxy chains becomes constant and leads to steady-state crack growth. The change in the failure behavior with the increase in POSS reinforcement can be explained concerning the formation of the compliant domain at higher loading of POSS molecule as discussed in our previous literature [10,11]. From the Figure 5, we also observed that the resistance trend against crack extension fits the \(J\) curve data in accordance to a power law as per the equation below. \[J=C_{1}\Delta{a_{P}}^{C_{2}}. \tag{4}\]  
Table 1 shows the value of \(C_{2}\) obtained after power law curve fit that confirms the validity of \(J\)-\(R\) curve for 3, 5 and 8 wt.% as obtained values are less than 0.99. At lower POSS loading, POSS-epoxy nanocomposites exhibit brittle behavior. Hence, the LEFM phenomena can be used to calculate the fracture resistance against the crack propagation in terms of the critical stress intensity factor. Figure 6a illustrates that with the inclusion of the POSS molecule increases the fracture toughness of the nanocomposite increase by an average of 50% compared to neat resin. In order to understand the initiation toughness, first, we have converted the critical stress intensity factor (\(K_{IC}\)) into \(J_{IC}\) (initiation fracture toughness). The \(J_{IC}\) of the brittle nanocomposite was calculated from \(K_{IC}\) and elastic modulus (\(E\)) by using the equation given below [22]:  
\[J_{IC}=\frac{K_{IC}^{2}}{E}. \tag{5}\]  
The elastic modulus of the epoxy resin is taken as 3 GPa ( based on literature value [10]). For ductile POSS-epoxy nanocomposites the fracture resistance at initial crack growth has been taken as initiation fracture toughness as shown in Figure 6b. The initiation fracture  
Figure 5: Variation of J value with the increase in crack extension, for different percentage of glycidylI POSS.