numero25

F. V. Antunes et alii, Frattura ed Integrità Strutturale, 25 (2013) 54-60; DOI: 10.3221/IGF-ESIS.25.09 55 N UMERICAL MODEL Middle-Tension (M(T)) specimen, in agreement with ASTM E647 standard, is studied here. An initial crack length of a 0 =5 mm was assumed. Due to symmetry conditions, only 1/8 of the MT specimen was simulated, considering adequate symmetry conditions. The material used for this research was the 6016-T4 aluminium alloy (HV0.5=92). In order to model the hardening behaviour of this aluminium alloy, three types of mechanical tests were performed: uniaxial tensile tests and monotonic and Bauschinger shear tests. From the experimental data and curve fitting results, for different constitutive models, it was determined that the mechanical behaviour of this alloy is better represented using an isotropic hardening model described by a Voce type equation: 0 (1 ) p v n sat Y Y R e      (1) combined with a non-linear kinematic hardening model described by a saturation law:   p x sat X X C X X                (2) In previous equations Y is the equivalent flow stress, p  is the equivalent plastic strain, Y 0 is the initial yield stress, R sat is the saturation stress, n  , C x and X sat are material constants,  σ is the deviatoric stress tensor, X is the back stress tensor, p   the equivalent plastic strain rate and p   the equivalent stress. The materials constants determined for the batch of material in study, that were used in the numerical simulations, are: Y 0 =124 MPa, R sat =291 MPa, n  = 9.5, C x = 146.5 and X sat = 34.90 MPa [2]. Fig. 1 presents the finite element mesh, which was refined at the crack front to model the severe plastic deformation gradients and enlarged at remote positions to reduce the numerical effort. The size considered for the linear isoparametric square elements around the crack front was L 1 =8  m, 16  m or 16  m. To overcome convergence difficulties, crack propagation was simulated by successive debonding of nodes at minimum load. Each crack increment (  a i ) corresponded to one finite element and two load cycles were applied between increments. In each cycle, the crack propagates uniformly over the thickness by releasing both current crack front nodes. Figure 1 : Finite element mesh. a) Frontal view. b) Detail of frontal view. The numerical simulations were performed with the Three-Dimensional Elasto-Plastic Finite Element program (DD3IMP) that follows a fully implicit time integration scheme [3, 4]. The mechanical model and the numerical methods used in the finite element code DD3IMP, specially developed for the numerical simulation of metal forming processes, takes into account the large elastic-plastic strains and rotations that are associated with large deformation processes. To avoid the locking effect a selective reduced integration method is used in DD3IMP18. The optimum values of the numerical parameters of the DD3IMP implicit algorithm have been already established in previous works, concerning the numerical simulation of sheet metal forming processes [5] and plasticity induced crack closure [6]. N UMERICAL RESULTS ig. 2a and 2b show stress-strain curves registered for a Gauss point when the crack propagates approaching it, as illustrated in Fig. 2c. The Gauss point suffers plastic deformation at the first load cycle, which indicates that it is within the first forward plastic zone, but it doesn’t experience reversed plasticity. As the crack tip approaches the A F a) b)