PSI - Issue 77

Sergio Cicero et al. / Procedia Structural Integrity 77 (2026) 56–63 Sergio Cicero et al./ Structural Integrity Procedia 00 (2026) 000 – 000

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complexity and accuracy of the predictions. The PM is the simplest approach and assumes that fracture occurs when the stress reaches the inherent strength at a distance of L/2 from the defect tip (Peterson (1938)). The failure criterion is therefore: ( 2 )= 0 (2) The LM, on the other hand, considers that fracture occurs when the average stress over a distance of 2L (measured from the defect tip) reaches the inherent strength ( σ 0 ). Therefore, the fracture condition is established by equation (3): 2 1 ∫ ( ) 0 2 = 0 (3) Additionally, K N mat can be estimated for U-shaped notches by combining the Creager-Paris stress field at the notch tip (Creager and Paris (1967)) with the TDC fracture criteria. In the case of LM, the resulting estimate is given by equation (4): = √1+ 4 (4) When experimental results of K N mat are available for different notch radii, fitting equation (4) with L as the fitting parameter allows this material property to be calibrated. This process is the one that will be followed in the following section for the five materials of interest, also taking into account that L quantifies the sensitivity of the material to the notch effect, such that low L values imply a high sensitivity to the notch effect, and (on the contrary) high L values mean that the material experiences a reduced notch effect. 3. Results and analysis The tensile properties of the different materials, for each raster orientation, are shown in Table 1. Figure 2 shows the apparent toughness results in absolute terms for the five materials and three orientations. Both the individual experimental results and their best fit according to equation (4) and the least squares criterion are shown. Finally, Figure 3 shows the same fitting results in relative terms, normalizing the apparent toughness fittings by the corresponding fracture toughness (obtained in cracked conditions), while Table 2 shows the different L values. Regarding tensile properties on polymers, ABS presents the highest strength, PLA the highest stiffness (E), and ASA the lowest strength values (and the highest average ductility). PLA properties are more sensitive than ABS and ASA properties to the raster orientation. Concerning the two composites being analyzed, graphene (1 wt.%) moderately increases E in PLA-Gr (when compared to the pristine PLA), with negligible effect on the strength. However, CF (10 wt.%) generates significant increases of both E and tensile strength in ASA-CF (when compared to the pristine ASA), and reduces the ductility. Regarding the fracture behavior, the initial evidence is that, among the polymers, PLA generates the highest apparent fracture toughness values across the entire range of notch radii being analyzed. ASA, on the other hand, is in the opposite situation. Furthermore, both ABS and ASA have a fairly similar notch effect in the three raster orientations, with substantially parallel fitting curves. However, in the case of PLA, the 45/-45 orientation has a much greater notch effect than the 0/90 and 30/-60 orientations. While fracture toughness is clearly lower in the 45/-45 orientation under cracked conditions, this same orientation presents the highest apparent fracture toughness values for larger notch radii. Looking at the two composites (Figure 2b), both the graphene and the carbon fiber increase the fracture resistance of the corresponding original polymers, with CF generating a far more evident effect. As it was the case in PLA, the 45/-45 orientation in ASA-CF has a much greater notch effect than the corresponding 0/90 and 30/-60 orientations, but this time the notch effect in PLA-Gr is rather similar in the three raster orientations.