Issue 48

F. V. Antunes et alii, Frattura ed Integrità Strutturale, 48 (2019) 666-675; DOI: 10.3221/IGF-ESIS.48.63 671 Fig. 5 presents the variation of plastic CTOD range,  p , with crack growth for different notch radius. The increase of crack length tends to increase  p and therefore fatigue crack growth rate. However, for notch radius of 1 and 2 mm, there is a rapid decrease of  p at the beginning of crack growth, followed by a progressive increase. The progressive increase of  p with notch radius, R n , is steeper for plane strain state. For plane stress state, a convergence to the same value is evident, as the crack departs from the notch. This asymptote is expected to be the value of  p not affected by the notch. For plane strain state, this convergence is not so evident, which seems to indicate that the effect of the notch is more extensive. The decrease of notch radius increases  p , due to the increase of stresses. Figure 5 : Variation of plastic CTOD range with crack growth. (a) Plane stress state. (b) Plane strain state. Fig. 6 presents the effect of stress state for different notch radius. At the beginning of crack growth plane stress state gives higher values of  p . However, rapidly the values for plane strain state raise above those for plane stress state, and become significantly higher. The higher crack growth rate observed for plane strain state explains the curvature of crack fronts in through-cracked specimens. Fig. 6 shows the variation of crack closure level, quantified by: F F open min U 100 clos F F max min     (1) being F min , F max and F open the minimum, maximum and opening loads, respectively. This parameter quantifies the portion of load cycle during which the crack is closed. The plane stress predictions are clearly higher than plane strain results. For plane strain state and notch radius of 1 and 2 mm, there is an initial peak of U clos followed by a progressive stabilization. This peak is linked to an odd deformation produced by the first load cycle. All the curves converge rapidly to about U clos =10%.For plane stress state there is a progressive increase of crack closure with crack length, as the plastic wake is being formed. The decrease of notch radius increases U clos , which has a faster stabilization. The results in Fig. 5 are explained by the relatively low level of crack closure observed for plane strain state. The trends of Fig. 4 are also explained by crack closure. For plane stress state there is a faster stabilization of  p for shorter notch radius because the crack closure level increases more rapidly. The crack closure is responsible for the convergence of all the curves. For plane strain state, the crack closure level is relatively low, therefore the increase of crack length if felt more intensively on  p . 0 0.1 0.2 0.3 0.4 0 0.5 1 1.5 2  p [  m] x n [mm] Rn=1 mm Rn=2 mm Rn=4 mm Rn=8 mm 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5 1 1.5 2  p [  m] x n [mm] Rn=1 mm Rn=2 mm Rn=4 mm Rn=8 mm R n x n (a) (b)