## 3 Results and Discussion
Additionally, the tensile strength \(\mathrm{\sigma_{u}}\) in these two equations is considered as 75.8 MPa for PMMA and 45.0 MPa for GPPS. The results are shown in Table 6, where it can be observed again that \(\mathrm{d_{c}}\) changes by altering the nominal dimension of the sample. To quantify the size-dependency of \(\mathrm{d_{c}}\), Equation (14) is utilized, while the fitting parameters A and B are determined from a linear regression between the variations of \(1/\mathrm{d_{c}}\) versus \(1/\mathrm{R}\), as shown in Figure 6. Once the parameters A and B are calculated for each material and sample, the evolution of \(\mathrm{d_{c}}\) with the sample size can be found. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Specimen** & **Material** &
\begin{tabular}{c} **Specimens** \\ **Radius, R** \\ \end{tabular} & \(\mathbf{K_{lc}}\) & \(\mathbf{d_{c}}\)-\&\(\mathbf{d_{c}}\)-\&\(\mathbf{d_{c}}\)-\&\(\mathbf{d_{c}}\)-\&\(\mathbf{d_{c}}\)-\&\(\mathbf{d_{c}}\)-\&MMS \\ \hline \multirow{6}{*}{CBD} & & 5 & 0.983 & 0.1070 & 0.1085 \\  & PMMA & 10 & 1.038 & 0.1194 & 0.1203 \\  & & 20 & 1.079 & 0.1290 & 0.1295 \\  & & 35 & 1.106 & 0.1356 & 0.1359 \\ \cline{2-6}  & & 5 & 0.729 & 0.1665 & 0.1702 \\  & GPPS & 10 & 0.879 & 0.2427 & 0.2466 \\  & GPPS & 20 & 1.011 & 0.3213 & 0.3247 \\  & & 35 & 1.053 & 0.3486 & 0.3509 \\ \hline \multirow{6}{*}{SCB} & & 5 & 1.976 & 0.4326 & 0.3628 \\  & PMMA & 10 & 2.468 & 0.6749 & 0.5861 \\  & & 20 & 2.630 & 0.7664 & 0.7049 \\ \cline{1-1}  & & 35 & 2.727 & 0.8240 & 0.7818 \\ \cline{1-1} \cline{2-6}  & & 5 & 1.224 & 0.4710 & 0.3896 \\ \cline{1-1}  & GPPS & 10 & 1.545 & 0.7504 & 0.6426 \\ \cline{1-1}  & & 20 & 1.998 & 1.2550 & 1.0998 \\ \cline{1-1}  & & 35 & 2.104 & 1.3917 & 1.2763 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The values of \(\mathrm{d_{c}}\) for PMMA and GPPS obtained from CBD and SCB samples. \(\mathrm{K_{lc}}\) in MPa.m\({}^{0.5}\), \(\mathrm{d_{c}}\) values in mm. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Specimen** & **Material** & \
\begin{tabular}{c} **2\(\alpha\)** \\ **(deg)** \\ \end{tabular} &
\begin{tabular}{c} **Specimen** \\ **Radius, R** \\ \end{tabular} & \(\mathbf{K_{lc}}^{\mathbf{V,\rho}}\) \\ \hline \multirow{6}{*}{RVSCB} & & & 5 & 2.33 MPa-m\({}^{0.4950}\) \\  & & 45 & 10 & 2.97 MPa-m\({}^{0.4950}\) \\  & & & 20 & 3.82 MPa-m\({}^{0.4950}\) \\  & PMMA & & 35 & 4.65 MPa-m\({}^{0.4950}\) \\ \cline{2-6}  & & & 5 & 3.34 MPa-m\({}^{0.4552}\) \\  & & 90 & 10 & 4.12 MPa-m\({}^{0.4552}\) \\  & & & 20 & 5.06 MPa-m\({}^{0.4552}\) \\  & & & 35 & 6.07 MPa-m\({}^{0.4552}\) \\ \cline{2-6}  & RVSCB & & & 5 & 1.35 MPa-m\({}^{0.4950}\) \\  & & 45 & 10 & 1.91 MPa-m\({}^{0.4950}\) \\  & GPPS & & 20 & 2.43 MPa-m\({}^{0.4950}\) \\ \cline{2-6}  & & & 35 & 2.99 MPa-m\({}^{0.4950}\) \\ \cline{2-6}  & & & 5 & 2.00 MPa-m\({}^{0.4552}\) \\  & & 90 & 10 & 2.71 MPa-m\({}^{0.4552}\) \\  & & & 20 & 3.22 MPa-m\({}^{0.4552}\) \\  & & & 35 & 3.79 MPa-m\({}^{0.4552}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._Now, the size-dependent values of \(\mathrm{d_{c}}\) from Equation (15) for each material are replaced into Equations (7) and (13) in order to determine the corresponding value of \(\mathrm{d_{c,V}}\) for each sample size. After that, the mode I notch fracture toughness value (\(\mathrm{K_{k}}^{\mathrm{V,\rho}}\)) for each tested specimen is predicted by substituting the parameter \(\mathrm{d_{c,V}}\) into Equation (5). The variations of \(\mathrm{K_{k}}^{\mathrm{V,\rho}}\) with the nominal radius (i.e., size) of the specimens are predicted by the MS-Schmidt's and the MMS criteria and compared with those obtained experimentally from the RVNBD and the RVSCB samples made of PMMA and GPPS, with the results being shown in Figures 7-10. According to these figures, it is observable that the MS-Schmidt's and the MMS criteria provide good estimations of \(\mathrm{K_{k}}^{\mathrm{V,\rho}}\) in BD and SCB samples made of PMMA and GPPS polymers containing RV notches.