## 4 Discussion  
In this investigation, polycarbonate is assumed to fail at the onset of necking that is associated with an average true strain of 5.5%. This percentage only constitutes a small portion of the total deformation that polycarbonate can sustain knowing that the average true fracture strain obtained from this study is about 100%. An average true fracture strain of about 60% is reported for polycarbonate at different strain rates [6]. However, it is considered here that necking strain is a reasonable failure criterion for structural components. It is important to note that consideration of higher strain levels such as the true fracture strain may not possible within the current formulation of the strain energy density (SED) criterion. If the failure criterion is chosen to be the true fracture strain, then the strain energy density resulting from the total true stress-strain curve is going to be about 12.93 MJ/m\({}^{3}\). This is more than five times the energy obtained by considering the area under true stress-strain curve until the onset of necking that is \(W_{c,EMC}=2.357\) MJ/m\({}^{3}\). This strain energy density was obtained from the ratio of a total strain energy of 115.39 MJ and a control volume of 48.95 m\({}^{3}\). It is important to note that while performing finite element analysis on a notched specimen, the strain energy generated due to the application of the load is essentially the same regardless of the selected failure criterion. Thus, the control volume must be deceased in order to increase the strain energy density. The reduction of the control volume means that the critical radius, \(R_{c}\), must also be decreased. However, there is a geometrical and numerical limitations that bound the size of the critical radius. In fact, as illustrated in Figures 3 and 5, as the size of the critical radius gets smaller it becomes numerically challenging to model and mesh the control volume. It is clearly seen from the reported results in both Table 4 and Figure 13 that the EMC-SED method can estimate the fracture load of the notched specimens having a depth of 6.0 mm and different radii within absolute difference between 0.13% and 4.4% compared to the experimental observation. However, the accuracy of the estimation is reduced for the samples having equal radius of 3.5 mm and different depths. The sample with \(\rho=3.5\) mm and \(d_{p}=5.5\) mm is only 0.5 mm shorter in depth compared the one with \(\rho=3.5\) mm and \(d_{p}=6.0\) mm; however, the absolute difference between them is 1.5% for the former and 6.9% for the latter. On the contrary and while keeping the same radius of \(\rho=3.5\) mm, an increase of 1.0 mm to notch depth, i.e., \(d_{p}=7.0\) mm, increases the absolute difference to 14.1%. The highest absolute difference of 25.5% is obtained for the sample with \(\rho=3.5\) mm and \(d_{p}=4.0\) mm. In an attempt to explain these observations, the true strain fields analyzed using digital image correlation system for different notch radii and depths are shown in Figure 14. This figure shows the distribution of the true strain along the loading direction \(\varepsilon_{y}\). The nominal stress extension curves, shown in Figure 8, are superimposed with the images of the notched specimens to help explaining their fracture behaviors. In addition, contours corresponding to approximately the same true strain value of about 4.5% are drawn on each image. It can be seen from Figure 14a,b that the sizes of the strain counters are comparable which is also associated with similar stress-extension curves. Both