Issue 41

F.V. Antunes et alii, Frattura ed Integrità Strutturale, 41 (2017) 149-156; DOI: 10.3221/IGF-ESIS.41.21 152 Figure 1 : (a) CTOD versus load. (b) Plastic CTOD versus load (6082-T6 AA; plane stress). An additional measurement was made at the center of the M(T) specimen, which replicates the experimental measurement made with a pin extensometer. The measurement point has coordinates: x=0, y= 1.75 mm. Therefore, it is at a distance of 6.5 mm from the crack tip (x=6.272 mm, y=0). The corresponding values of  CTOD p are significantly lower than those obtained at a distance less than 1 mm from crack tip. This seems to indicate that sensitivity relatively to the measurement point always decrease with distance d. Anyway, the measurement at a quite remote position is able to capture some plastic deformation, which is remarkable. Similar trends were obtained for all the other loads and materials studied. The same trend was also obtained for plane strain state. Note that the values of  CTOD p presented are relatively small, lower than 1  m. This is certainly a challenge for the experimental determination of plastic CTOD. Effect of crack propagation In the numerical simulation of FCG, there is a transient behaviour at the beginning of crack propagation. In fact, some crack propagation is required to stabilize the plastic deformation at the crack tip. Fig. 3a presents the variation of  CTOD p with crack increment,  a. The first values are relatively high, which can be explained by the low hardening of the material and by the relatively low values of crack closure. Initially the material is virgin in terms of plastic deformation, and, as could be expected, predictions tend to stabilize, as the crack propagates. As can be seen in Fig. 3a, a propagation  a=552  m, which corresponds to 70 crack increments of 8  m, is enough to stabilize the predictions of  CTOD p . After stabilization there is a progressive increase of plastic CTOD with crack propagation, because since the tests are made at constant load, there is a progressive increase of  K at the crack tip. For all load cases studied, 100 crack increments were found enough to stabilize the values, however 160 propagations were considered. The distance for stabilization increases with load range. Fig. 3b shows, in the 7050-T6 aluminum alloy, the effect of stress state on  CTOD p versus  a plots. The general behavior is similar for plane stress and plane strain states. In both cases there is an initial decrease, which is more relevant for the plane stress state. The stabilization is relatively fast, compared with that observed in Fig. 3a for the AA6082-T6. After stabilization, there is a relatively fast increase of  CTOD p with  a, particularly for plane strain state. The comparison between Figs. 3a and 3b shows the importance of material behavior on the crack tip plastic deformation, here quantified by the plastic CTOD. The analysis of the CTOD versus load plots showed that the 7050-T6 aluminum alloy has no crack closure. Effect of finite element mesh The finite element mesh is a main parameter in finite element analyses. Fig. 4 shows the effect of the size of crack tip elements on the predictions of plastic CTOD. There is a relatively low influence of finite element mesh on plastic CTOD. This difference vanishes when the measurement point is relatively far from crack tip. This seems to indicate that the 0.0 0.5 1.0 1.5 2.0 2.5 0 20 40 60 80 100 CTOD [  m]  [MPa] Node 5 Node 1 A E G H F B C D 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0 20 40 60 80 100 CTOD p [  m]  [MPa] Node 1 Node 3 Node 5 Node 10 (a) (b)