numero25

F. V. Antunes et alii, Frattura ed Integrità Strutturale, 25 (2013) 54-60; DOI: 10.3221/IGF-ESIS.25.09 58 Another relevant aspect is the size of crack tip plastic zone. Fig. 7 shows the effect of load level and stress state on plastic zone size measured in the residual plastic wake perpendicularly to crack flank. The boundary was defined for a plastic deformation of 0.2%, which is usually considered to be the onset of plastic deformation in tension tests. The monotonic plastic zone increases with load level and, for the maximum load studied (K max =11.9 MPa.m 1/2 ;  max /  ys =70%), a size of 1.27 mm was observed. Lower values were obtained for plane strain state, but the effect of load is clearly dominant in Fig. 7. The size of crack tip plastic deformation zone has been widely studied for static loads, being usually represented in the form: 2 ( ) p ys K r    (3) where K is the stress intensity factor and  ys is material’s yield stress. Considering only the singularity stress field,  =1/6  for plane strain state and three times larger for plane stress state (  =1/2  ) [7]. However, Clavel et al. [8] proposed a factor of two. Considering the stress redistribution produced by plastic deformation, Rice [9] proposed  =1/3  and  =1/  for plane strain and plane stress states, respectively, assuming small scale yielding and a perfectly plastic behaviour. Dugdale [10] proposed  =  /8 for plane strain state. For steels and aluminium alloys and plane strain state, Dias et al. [11] proposed: 2 0.196 129 0.928 ced ced             (4) Fig. 7 shows the results obtained with the models of Dugdale and Dias, which are significantly different from the numerical predictions. However, notice that the literature models were obtained for  =0º, i.e., ahead of crack tip, and for static loads. In PICC studies the size perpendicularly to crack flank, i.e., for  =90º, is more relevant. The sizes proposed here for plane stress and plane strain states are, respectively: 2 0.11 ys K            (5) 3.1 1.64 ys K            (6) 0 0.5 1 1.5 2 2.5 0 5 10 15 20 25 30 35 L 1 [  m]  p,eq Série1 Figure 6 : Effect of mesh refinement on maximum equivalent plastic strain. The crack profile is also a main issue. A phenomenon of material removal was observed numerically under specific conditions, having a major influence of the closure level. Fig. 8 shows the variation of the near crack tip profile in a numerical simulation performed considering pure kinematic hardening behaviour and plane stress state. The crack was submitted to 15 propagations with 2 load cycles between each, and after that, 20 load cycles were applied without propagation. As can be concluded from the figure, the increasing number of load cycles affects the position of the node immediately behind the crack tip, moving it upward. Therefore, the first two loading cycles produce plastic deformation,