## 3 Results and Discussion
### Estimation of Load Carrying Capacity  
The LCC of the different keyhole notched specimens with tip radii of 1 mm and 2 mm was performed by using the corresponding FE stress analyses, and applying the MTS and the MS criteria with the values of \(r_{c}\) and \(\sigma_{c}\) shown above. When considering the MTS criterion, the critical load is reached when the compressive stress at the critical distance \(r_{c}\) in front of the notch tip reaches the critical stress \(\sigma_{c}\). When using the MS criterion, the critical load is obtained when the mean value of the compressive stresses over the critical distance \(\mathrm{d_{c}}\) attains \(\sigma_{c}\). Here it should be noted that, because of the contact between the two parallel edges of the keyhole notches during the loading process, and due to the resulting dependence of the contact area on the load being applied, a trial-and-error procedure is essentially needed to extract the critical loads according to MTS and MS criteria. Normally, when determining the critical load in non-contacting notches analyzed using linear elastic fracture mechanics (LEFM), an arbitrary load is first applied to the notched member and the corresponding stress distribution is obtained around the notch. Then, the arbitrary load is multiplied by a known factor, which is actually the ratio between the critical stress and the normal stress obtained for the arbitrary load at the critical distance (or the average normal stress over the critical distance), to achieve the critical load. In other words, the stress field is simply scaled to obtain the critical condition. This strategy cannot be used in the analyzed keyhole notches, as the resulting contacts impede the scaling procedure. Thus, a trial-and-error process is required: an arbitrary load is first applied to the keyhole notched sample, and the compressive stress at the critical distance \(r_{c}\) is computed. Depending on its value, the load is increased or decreased until the stress attains the compressive critical stress of the material. This procedure may continue several times to reach the critical load according to the MTS criterion. An analogous approach is followed for the MS criterion but, this time, determining the mean stress over the critical distance \(\mathrm{d_{c}}\). The theoretical and experimental LCCs, together with their discrepancies for the keyhole notched PMMA and GPPS samples, are gathered in Table 4. The results show that both the MTS and the MS criteria are fully capable of providing accurate predictions of the fracture loads of the keyhole notched polymeric specimens under compressive loading conditions. Note that since the critical stress and the critical distances are derived from the experimental calibration, in which the test data of the keyhole notches with the tip radii 0.5 and 4 mm are included, the discrepancies for the keyhole notch tip radii 0.5 and 4 mm are zero. The discrepancies found for notch radii of 1 mm and 2 mm are lower than 10%, with the estimations being conservative in all cases (i.e., estimated fracture loads below the experimental fracture loads). On this occasion, for both PMMA and GPPS, the MTS criterion is more accurate than the MS criterion. Figure 11: Variations of mean compressive stress versus the distance from the notch tip: (**a**) PMMA; (**b**) GPPS. As shown above, and since the behaviors of the PMMA and GPPS polymers in the standard compression tests are nonlinear, the compressive critical loads of the keyhole notched samples can be computed by the application of the Equivalent Material Concept (EMC). Therefore, the EMC will be employed here to calculate the critical stresses of the two polymers. Subsequently, the EMC (through the resulting critical stresses) will be coupled with the MTS and the MS criteria to predict the critical loads of the keyhole notched polymeric samples. With this aim, it is only necessary to assume that the critical stress \(\sigma_{c}\) is equal to the compressive strength of the equivalent linear-elastic material.