# Fracture Behavior of Two Biopolymers Containing Notches: Effects of Notch Tip Plasticity
## 3 Results and Discussion  
Figure 7a shows the variations of the load-carrying capacity (LCC) of the BC UNBD specimens versus the notch tip radius for MTS and MS criteria as well as for the experiments. Analogously, Figure 7b also represents the results of MTS, MS, EMC-MTS and EMC-MS criteria for the DM UNBD specimens together with those of the fracture tests. Moreover, Table 3 presents the discrepancies (%) between the theoretical and experimental results. Negative values mean that the predictions underestimate the experimental critical loads, whereas positive values imply overestimations of the load-carrying capacity. According to Figure 7a and Table 3, when predicting fracture loads in the BC material, the MS criterion provides more accurate results than those obtained with the MTS criterion. Concerning the DM, Figure 7b and Table 3 show that both the EMC-MTS and the EMC-MS coupled criteria provide more accurate predictions than those provided by the MTS and MS criteria. This is because both coupled criteria consider the nonlinear behavior of the DM. The accuracy of both coupled criteria is similar, and since it is easier to apply the EMC-MTS criterion and it seems more conservative, this latter option is recommended here to analyze biomaterials with similar levels of nonlinear behavior. Figure 8 illustrates the variations of linear elastic tangential stress versus the notch tip radius at different distances (0 mm to 1 mm) from the notch tip, for an arbitrary load of 100 N. As mentioned before, for the DM UNBD specimens, the critical distance \(r_{\text{c}}\) of EMC-MTS criterion is found equal to 0.04 mm. In Figure 8a it is observed that, at a distance of 0.04 mm, the stress significantly decreases when comparing specimens of notch radii 1 mm and 2 mm, and develops a much smaller decrease when comparing 2 mm and 4 mm radii. This implies that the fracture load increases considerably from UNBD specimens with 1 mm notch radius to UNBD specimens with 2 mm notch radius, and has a subsequent slight increase for UNBD specimens with 4 mm notch radius. Figure 7: Comparison between experimental results and predictions. (**a**) BC material, including maximum tangential stress (MTS) and mean stress (MS) predictions; (**b**) DM, including MTS, MS, Equivalent Material Concept (EMC)-MTS and Equivalent Material Concept (EMC)-MS predictions. However, in the BC material, r\({}_{\rm c}\) is equal to 0.17 mm. Figure 8b shows the stress at similar distances from the notch tip for different notch radii in UNBD specimens (again, for an arbitrary load of 100 N). In this particular case of r\({}_{\rm c}\) values and specimen geometry, it can be observed that the higher the notch radius the higher the resulting stress, which implies that critical loads decrease with the notch radius. This result justifies not only the evolution of the critical load estimations, but also the evolution of the experimental results (which are in agreement). However, when applying the MTS (or the MS) criterion to the DM, it can be observed that the predictions generally reveal a decrease in the load-carrying capacity when the notch radius increases, something which is quite different from the experimental observations (see Figure 7b). This is because of the effects of the plastic zone that forms around the notch tip during loading. Figure 9 shows an example of elastic-plastic finite element (FE) analysis, that demonstrates that the size of the plastic zone at the onset of fracture increases by increasing the notch tip radius, and also that this size is not negligible if compared to other relevant dimensions (e.g., r\({}_{\rm c}\)). These plastic zones lead to the development of larger amounts of energy before fracture, and then to increases in the load-carrying capacity. As a consequence, the MTS criterion, which does not take into account the influence of the plastic deformations on fracture, is not an appropriate criterion for fracture load predictions of DM UNBD specimens.