## 3 Results and Discussion
### Calibration of Critical Stresses and Critical Distances  
The completion of the FE analyses mentioned above, allowed the distribution of compressive stresses around the different U-notches (and materials) to be numerically obtained. Moreover, as stated above, because the fracture toughness, \(K_{lc}\), defined in Equation (3) is not a meaningful fracture mechanics parameter under negative mode I loading, an alternative experimental calibration was required to obtain the critical stresses and the critical distances of GPPS and PMMA polymers, which were necessary parameters for theoretical predictions following the MTS and the MS criteria. The calibration is elaborated as follows: in the first step, FE models are created for the specimens with a notch tip radii of 0.5 and 4 mm, having the maximum and the minimum stress concentration, respectively, and the mean values of their corresponding experimental fracture loads (see Table 2) are applied to them. Then, a straight path is defined on the bisector line of the U-noth from the notch tip. To employ the MTS model, the variation of compressive stress versus the distance from the notch tip is extracted for the PMMA and GPPS specimens, as shown in Figure 8. In both graphs, the tangential stress is shown (i.e., the stress along the loading direction, perpendicular to the notch middle plane; i.e., the Y-component). By drawing the stress-distance curves at failure conditions for 0.5 and 4 mm radii in a single graph, the point at which these two curves intersect each other is obtained. Finally, following the MTS criterion, the coordinates of this point are defined as the critical stress, \(\sigma_{C}\), and the critical distance, \(\text{r}_{C}\), for each material, with the results being shown in Table 3. This kind of calibration can be considered as an extension of the well-established theory of critical distances (TCD) [50], from the positive mode I loading to negative mode I loading. A similar method can also be followed when using the MS criterion by taking into account the mean compressive stress (again, the Y component). First, several distances from the notch tip are chosen on the notch bisector line, and over each distance, the mean stress is accurately computed by the integral method. Then, for each distance, one point is defined in a mean stress-distance (from the notch tip) plot. By connecting the points corresponding to the different distances together, a curve is obtained. Evidently, the accuracy of the curve increases as the number of distances chosen increases. By drawing the curves for 0.5 and 4 mm notch tip radii and illustrating them in a single plot, the intercept of the two curves gives the compressive critical stress, \(\sigma_{C}\), and the critical distance, \(d_{C}\). Figure 9 represents the mean stress-distance plots of MS criterion for PMMA and GPPS polymers, respectively, with the critical parameters being included in Table 3.  
Figure 7: Example of two tested specimens made of GPPS (\(\rho\) = 4.0 mm). Table 3 reveals that the critical stress values obtained from the experimental calibrations through the MTS and the MS criteria for PMMA deviated from each other by about 5%, which is quite acceptable. For GPPS, however, the values were much closer, with a deviation slightly higher than 1%. Regarding the values of the critical distances, it is evident that for both polymers studied, \(d_{C}\) was moderately less than \(4r_{C}\), and slightly higher than \(3r_{C}\). This issue requires future research in other materials to study the relation between the two critical distances under compressive loading conditions. Now, in order to obtain the theoretical values of the LCC for U-notch tip radii 1 and 2 mm, the critical load is determined from the MTS criterion by finding the load in the FE  
Figure 8: Compressive stress–distance curves at fracture for PMMA and GPPS materials. Figure 9: Compressive mean stress–distance curves at fracture for PMMA and GPPS materials.