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F. V. Antunes et alii, Frattura ed Integrità Strutturale, 25 (2013) 54-60; DOI: 10.3221/IGF-ESIS.25.09 57 This phenomenon explains the peak values observed in Fig. 3 and 4 at the beginning of crack propagation. The difference between elements E2 and E8 is relatively small, which explains the stabilization observed in Fig. 3 and 4. 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 4.9 5.1 5.3 5.5 5.7 5.9 6.1 x [mm]  p,eq Kinematic Mixed Isotropic 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 4.9 5.1 5.3 5.5 5.7 5.9 6.1 x [mm]  p,eq Plane strain, M8 Plane stress, M8 Plane stress, M16 Figure 3 : Equivalent plastic strain along crack flank (  max =47.5 MPa;  min =0.8 MPa, Mesh M16). Figure 4 : Equivalent plastic strain along crack flank (Mixed hardening,  max =47.5 MPa;  min =0.8 MPa). As already observed in Fig. 2a and 2b, the size of finite elements at the crack tip has a major influence on plastic deformation level. Fig. 6 shows the effect of element reduction down to nanometer sizes on maximum plastic deformation. There is a progressive increase of plastic deformation with mesh refinement without convergence, typical of a singular behavior. The finite element mesh used to model crack propagation, composed of a regular pattern of square elements ahead of initial crack tip, as can be seen in Fig. 1 and 5a, assumes a sharp crack, which has a singular behavior. Assuming a finite value for the crack tip radius, convergence is obtained with mesh refinement. However, depending on radius, the mesh required may be quite refined and the modeling of crack propagation to form the residual plastic wake is not easy with a finite crack tip radius. -5 -4 -3 -2 -1 0 1 2 3 4 5 0.00 0.02 0.04 0.06 0.08 0.10  yy  yy /  ys E1 E2 E8 Figure 5 : a) Near crack tip elements. b) Stress- strain curves (Mixed hardening,  max =47.5 MPa;  min =0.8 MPa). E1 E2 E8 C0