## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\rho\) (mm) & \(d_{p}\) (mm) & \
\begin{tabular}{c} **Estimated Fracture** \\ **Load, \(F_{Est}\) (N)** \\ \end{tabular} &
\begin{tabular}{c} **Avg. Experimental** \\ **Fracture Load, \(F_{arg}\) (N)** \\ \end{tabular} & \(\frac{F_{Est}-F_{arg}}{F_{erg}}\times\) **100 (\%)** \\ \hline
2.0 & 6.0 & 6804.1 & 6703.8 & 1.50 \\
2.5 & 6.0 & 6708.3 & 7018.3 & \(-4.42\) \\
3.0 & 6.0 & 6616.1 & 6798.4 & \(-2.68\) \\
3.5 & 6.0 & 6540.6 & 6637.3 & \(-1.46\) \\
4.0 & 6.0 & 6488.3 & 6448.8 & 0.61 \\
4.5 & 6.0 & 6455.7 & 6499.7 & \(-0.68\) \\
5.0 & 6.0 & 6435.6 & 6427.0 & 0.13 \\
3.5 & 4.0 & 8856.9 & 7054.3 & 25.55 \\
3.5 & 5.5 & 7039.0 & 6582.3 & 6.94 \\
3.5 & 7.0 & 5661.0 & 6591.0 & \(-14.11\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Estimation of fracture load using equivalent material concept-strain energy density (EMC-SED) method. of these specimens have the same notch depth of 6.0 mm, but their radii are \(\rho=1.5\) mm and \(\rho=3.0\) mm. Figure 14c shows the true strain field for another sample having a notch depth of 6.0 mm but with a radius of 5.0 mm. It can be seen from this figure that the strain contour is larger than that of the specimens shown in Figure 14a,b. The stress-extension curve for the specimen in Figure 14c indicates that the sample was undergoing plastic flow as observed in Figure 10. However, a common characteristic between the three samples in Figure 14a-c is the zone ahead of the notch that is relatively similar in size and is having an average strain magnitude of 8.65%. Similar analysis can be performed on the samples having the same notch radius \(\rho=3.5\) mm but notch depths of 7.0 mm and 4.0 mm as shown in Figure 14d,e, respectively. Clearly, the size of the strain contour is smaller for the sample with depth of 7.0 mm and it is significantly smaller for the sample with depth of 4.0 mm. In addition, the sample with depth of 7.0 mm exhibit smaller plastic flow compared to the one with the depth of 4.0 mm. However, a key difference between the samples in Figure 14d,e is the magnitude of the true strain that is 7.5% and 4.6%, respectively. The images shown in Figure 14 are captured and analyzed at the onset before crazing or significant plastic deformation are observed. Therefore, it is assumed that if the strain ahead of notch at this instance is not high enough to initiate crack, failure is dominated by plastic flow. This plastic flow is associated with severe localized damage and thinning of the cross-section ahead of the notch that results in a formation of small crack followed by a sudden failure. Conversely, if the strain level is high enough to initiate crack, failure is dominated by crack propagation that is also accompanied with localized severe plastic deformation. Within the limited results reported in this paper, it can be said that a strain magnitude above 7.5% would result in a crack propagation dominant failure. As for estimations by the EMC-SED method, the strain field in Figure 14 are not enough to explain why the accuracy of the method was reduced for the samples with different depth. Knowledge about the  
Figure 14: True strain fields along the loading direction obtained using digital image correlation for notched specimens: (**a–c**) specimens with different radii and depth \(d_{p}=6.0\) mm; (**d,e**) specimens with different depths and \(\rho=3.5\) mm. distribution of the strain energy density ahead of the notch may help understand this issue. However, this would require an independent elastic-plastic computational analysis that could be considered in future research. However, and without generalization, it can be said that the EMC-SED method provided reasonable estimation of the fracture load for the cases that developed localized strain zone with a magnitude of 7.5% or higher. These include the specimens shown in Figure 14a-d.