Issue 33

F.V. Antunes et alii, Frattura ed Integrità Strutturale, 33 (2015) 199-208; DOI: 10.3221/IGF-ESIS.33.25 202 being c a constant. In numerical studies the CTOD is usually defined as the distance between two points found by intersecting the finite element model with two (+45º and -45º) lines originated from the crack tip. The size of reversed plastic zone has also been considered a main parameter of crack growth  40, 41  . Ould Chick et al.  42  showed that da/dN has a linear variation with the square of the cyclic plastic zone size (r pc 2 ): 2 ( ) pc da A r dN  (3) where A depends on the yield stress. Other authors suggested that the total plastic dissipation per cycle occurring in the reversed plastic zone is a driving force for fatigue crack growth in ductile solids, and can be closely correlated with fatigue crack growth rates  43, 44  . Dissipated energy approaches to fatigue crack growth prediction have since been the subject of numerous analytical  45, 46  and experimental  47, 48  investigations. N UMERICAL MODEL Middle-Tension specimen was considered to predict the crack opening level, having W=60 mm and a straight crack with an initial size a 0 of 5 mm ( a 0 /W=0.083). A small thickness was considered (t=0.1 mm) to simulate the plane stress state. Two materials were considered in this research: the 6016-T4 aluminium alloy and a High Strength Steel (DP600). Since PICC is a plastic deformation based phenomenon, the hardening behaviour of the material was carefully modelled. The hardening behaviour of this alloy was represented using an isotropic hardening model described by a Voce type equation, combined with a non-linear kinematic hardening model described by a saturation law. Table 1 indicates the load parameters defined in the different sets of constant amplitude tests considered for 6016-T4 aluminium alloy and DP600 steel, respectively. Sets with constant K min , K max ,  K and R were studied, as can be seen. Set 1 (K min =0) Set 2 (K max =6.4) Set 3 (K max =2.2) Set 4 (K max =4.6)  K R  K R  K R  K R 2.9 0 3.8 0.43 2.2 0 2.3 0.5 3.8 0 5.7 0.14 4.4 -1 4.6 0.0 4.8 0 7.7 -0.14 6.6 -2 6.8 -0.5 6.7 0 9.6 -0.43 8.9 -3 9.1 -1 8.6 0 11.5 -0.71 11.0 -4 12.5 -1.75 9.6 0 13.4 -1.00 13.6 -5 13.3 -2 10.5 0 15.3 -1.29 15.9 -6 14.8 -2.25 Set 5 (R=0.2) Set 6 (  K=4.8) Set 7 (  K=6.7) Set 8 (K max =9.1)  K R  K R  K R  K R 3.1 0.2 4.8 -2 6.7 -2 1.4 0.88 3.8 0.2 4.8 -1 6.7 -1 2.5 0.75 4.6 0.2 4.8 -0.5 6.7 -0.5 4.6 0.5 5.4 0.2 4.8 0 6.7 0 6.9 0.25 6.1 0.2 4.8 0.25 6.7 0.25 9.1 0 6.9 0.2 4.8 0.5 6.7 0.5 11.3 -0.25 Table 1 : Loading parameters for 6016-T4 aluminium alloy (  K, K max , K min  =MPa.m 1/2 ) A