numero25

F. V. Antunes et alii, Frattura ed Integrità Strutturale, 25 (2013) 54-60 ; DOI: 10.3221/IGF-ESIS.25.09 59 and consequently, crack closure. Subsequent unloading and loading cycles takes material from behind the crack tip reducing closure. A similar phenomenon was observed for elastic-perfectly plastic behaviour. For plane strain state was observed independently of material model, however this affects the extent of the phenomenon. The same phenomenon has been reported also by Antunes et al. [12] and Jiang et al . [13] for pure kinematic hardening models in 2D plane stress analysis. Toribio et al. [14] developed a high-resolution finite-element simulation of a plane-strain tensile crack with finite radius. Elastic-perfectly plastic behaviour was assumed and deformed shapes revealed the mechanism of material transfer from the crack front onto lateral faces of the crack. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0.01 0.03 0.05 0.07 0.09 K max /  ys [m 0.5 ]  p,eq Plane stress Plane strain [11] [10] 0 0.0005 0.001 0.0015 0.002 0.0025 5.75 5.8 5.85 5.9 5.95 6 6.05 6.1 x [mm] dy [mm] Figure 7 : Size of plastic zone perpendicularly to crack flank. Figure 8 : Effect of load cycles without propagation on crack profile (pure kinematic hardening, plane stress, L 1 =16  m). C ONCLUSIONS lasticity induced crack closure is intimately linked to crack tip plastic deformation. Along crack flank, the plastic deformation presents an initial peak of plastic deformation. This peak was explained by the initial plastic deformation occurring at the first loading. The elements suffering progressive increase of load level showed lower plastic deformation levels as a consequence of hardening. The crack propagation stabilizes the plastic deformation and the plasticity induced crack closure (PICC). The decrease of mesh size was found to increase progressively the maximum plastic deformation without convergence, which is typical of a singular behavior. Convergence is achieved considering a finite value for the crack tip radius, but conciliate crack propagation modeling with a finite crack tip radius is not easy. The size perpendicularly to crack flank was measured and compared with literature models. Significant differences were found relatively to literature models. However these models were defined for  =0º, i.e., ahead of crack tip, and for static loads, while the present results were obtained for a residual plastic wake formed by crack propagation. A KNOWLDGMENTS he authors are indebted to the Portuguese Foundation for the Science and Technology (FCT) and to FEDER (European Regional Development Fund) for the financial support (Project PTDC/EME-PME/114892/2009; COMPETE: FCOMP-01-0124-FEDER-015171) R EFERENCES [1] Elber, W., Fatigue crack closure under cyclic tension, Engng Fracture Mechanics, 2 (1970) 37-45. P T