## 3 Results and Discussion  
The fracture toughness (\(\mathrm{K_{IC}}\)) of GPPS and PMMA materials are easily derived by substituting the fracture loads and sample dimensions listed in Tables 1 and 2 into Equations (1) and (3), using \(\mathrm{P_{f}}\) (average values of fracture loads) as \(\mathrm{P_{max}}\). Table 4 gathers the resulting values of \(\mathrm{K_{IC}}\), where it can be observed that the results are dependent on the size of the specimen, with larger values in the larger samples. Table 5 gathers the values of the notch fracture toughness obtained for PMMA and GPPS in RVNBD and RVSCB specimens. As in the K\({}_{\text{Ic}}\) values, Table 5 reveals that K\({}_{\text{Ic}}\)\({}^{V,\rho}\) depends on the size of the specimen and becomes larger as the size of the specimen grows. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Specimen** & **Material** & **Specimens** & **Crack Length** & **P\({}_{\text{f,average}}\)** & **K\({}_{\text{Ic}}\)** & **Standard** \\  & & **Radius, R** & **(a or d)** & **P\({}_{\text{f,average}}\)** & **K\({}_{\text{Ic}}\)** & **Deviation (\%)** \\ \hline \multirow{6}{*}{CBD} & \multirow{6}{*}{PMMA} & 5 & 5 & 753.5 & 0.983 & 5.5 \\  & & 10 & 10 & 1125.5 & 1.038 & 5.3 \\  & & 20 & 20 & 1654.8 & 1.079 & 4.4 \\  & & 35 & 35 & 2244.0 & 1.106 & 5.4 \\ \cline{2-6}  & & 5 & 5 & 558.2 & 0.729 & 5.6 \\  & & 10 & 10 & 952.8 & 0.879 & 5.3 \\  & & 20 & 20 & 1550.3 & 1.011 & 4.4 \\  & & 35 & 35 & 2136.0 & 1.053 & 5.4 \\ \hline \multirow{6}{*}{SCB (S/R = 0.8)} & \multirow{6}{*}{PMMA} & 5 & 2.5 & 205.2 & 1.976 & 3.7 \\  & & 10 & 5 & 362.4 & 2.468 & 5.6 \\ \cline{1-1}  & & 20 & 10 & 546.3 & 2.630 & 2.8 \\ \cline{1-1}  & & 35 & 17.5 & 749.4 & 2.727 & 4.6 \\ \cline{1-1} \cline{2-6}  & & 5 & 2.5 & 127.1 & 1.224 & 3.7 \\ \cline{1-1}  & & 10 & 5 & 226.8 & 1.545 & 5.5 \\ \cline{1-1}  & & 20 & 10 & 415.1 & 1.998 & 2.8 \\ \cline{1-1}  & & 35 & 17.5 & 578.0 & 2.104 & 4.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: K\({}_{\text{Ic}}\) values for PMMA and GPPS obtained from CBD and SCB specimens with different sizes (dimensions in mm, load values in N, K\({}_{\text{Ic}}\) in MPam\({}^{1/2}\)). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Specimen** & **Material** & **2\(\alpha\)** & **Specimen** & **K\({}_{\text{Ic}}\)\({}^{V,\rho}\)** \\  & & **(deg)** & **Radius, R** & **K\({}_{\text{Ic}}\)\({}^{V,\rho}\)** \\ \hline \multirow{6}{*}{PMMA} & \multirow{6}{*}{60} & 5 & 1.86 MPa.m\({}^{0.4986}\) \\  & & & 10 & 2.36 MPa.m\({}^{0.4986}\) \\  & & & 20 & 3.94 MPa.m\({}^{0.4986}\) \\  & & & 35 & 3.94 MPa.m\({}^{0.4986}\) \\ \cline{2-6}  & & & 5 & 1.88 MPa.m\({}^{0.4878}\) \\  & & & 10 & 2.48 MPa.m\({}^{0.4878}\) \\  & & & 20 & 3.14 MPa.m\({}^{0.4878}\) \\  & & & 35 & 4.07 MPa.m\({}^{0.4878}\) \\ \cline{2-6}  & & & 5 & 2.46 MPa.m\({}^{0.4552}\) \\  & & & 10 & 3.14 MPa.m\({}^{0.4552}\) \\  & & & 20 & 4.04 MPa.m\({}^{0.4552}\) \\  & & & 35 & 5.11 MPa.m\({}^{0.4552}\) \\ \cline{2-6}  & & & 5 & 1.15 MPa.m\({}^{0.4986}\) \\  & & & 10 & 1.51 MPa.m\({}^{0.4986}\) \\  & & & 20 & 2.01 MPa.m\({}^{0.4986}\) \\  & & & 35 & 2.52 MPa.m\({}^{0.4986}\) \\ \cline{2-6}  & & & 5 & 1.22 MPa.m\({}^{0.4878}\) \\  & & & 10 & 1.61 MPa.m\({}^{0.4878}\) \\  & & & 20 & 2.01 MPa.m\({}^{0.4878}\) \\  & & & 35 & 2.63 MPa.m\({}^{0.4878}\) \\ \cline{2-6}  & & & 5 & 1.57 MPa.m\({}^{0.4552}\) \\  & & & 10 & 2.09 MPa.m\({}^{0.4552}\) \\  & & & 20 & 2.63 MPa.m\({}^{0.4552}\) \\  & & & 35 & 3.28 MPa.m\({}^{0.4552}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: K\({}_{\text{Ic}}\) values for PMMA and GPPS obtained from RVNBD and RVSCB specimens with different sizes (dimensions in mm, load values in N). The determination of \(\mathrm{d_{c}}\) for each combination of sample size, sample type (CBD and SCB specimens) and material (PMMA and GPPS) is the first step in the [PERSON]'s and MMS criteria. To do this, the values of \(\mathrm{K_{lc}}\) values listed in Table 4 are replaced into Equations (9) and (12).