Issue 49

M. Hadj Miloud et alii, Frattura ed Integrità Strutturale, 49 (2019) 630-642; DOI: 10.3221/IGF-ESIS.49.57 633 The critical void volume fraction f C signifies the onset of coalescence. In most investigations, only the critical void volume fraction f c is considered as a material parameter. It is obtained by fitting the numerical curves, determined by Finite Element (FE) modeling, with experimental data of notched tensile bar tests [16-21]. A method is proposed for the determination of f N and f C , using the experimental fracture strain ε f [9]. The experimental parameter ε f is extracted from the load–diametric reduction curve of an axisymmetric notched tensile bar test AN2. The inverse method is also widely used to identify the GTN-model. In the work of Springmann and Kuna [8, 22], the damage mechanical constitutive laws parameters are identified by locally measured displacement fields and measured force– displacement curves. For the material parameter identification a non-linear optimization algorithm is applied, to render the objective function to a minimum by means of a gradient based method. The force-displacement curves are obtained from tensile tests on notched flat specimens of StE690 steel, which allows the material parameters to be identified [8]. In the work of Jouabi et al. [23], a coupled elastic–plastic/damage is adopted in order to describe tensile behavior with validation on the deep-drawing test of a DP980 Dual Phase steel sheet. The GTN damage model is used. The used hardening laws are those of Swift (non-saturating law), Voce (saturating law) and Hockett-Sherby (saturating law). An identification method for elastic–plastic parameters and GTN damage model parameters has been presented using the software modeFRONTIER [23]. In the literature, there are consistent methods to determine GTN model parameters, but with a pre-defined hardening laws i.e. without identification of hardening laws in the same processes of GTN parameters determination. Recently, many works [24-26] are devoted to identify simultaneously GTN model and hardening laws parameters. Other interesting works of [27 and 28] consist to link the micro-scale to the macro-scale by studying the crack propagation using the GTN model and then determining the R-curves for cracked specimens. In the first part of this work, we propose a numerical inverse procedure to determine the GTN damage model with and without hardening laws. This procedure is carried out on the software package Abaqus [29]. Within this software, a VUHARD subroutine is implemented to carry out the hardening laws. The experimental data, used in the inverse analysis, are extracted from the load-diametric contraction curve of an axisymmetric notched tensile bar test (AN2) made with 12NiCr6 steel [20]. In the second part, and in order to validate the identified parameters of the GTN model, a numerical simulation of the ductile tear test of a CT25 specimen was performed. The numerical results of the force-displacement curve are compared to those determined experimentally by Wilsius [30]. GTN AND HARDENING PARAMETERS IDENTIFICATION he aim of the first step of this work is to identify simultaneously the GTN model and the hardening laws of the 12NiCr6 steel. Hence, a numerical procedure of the inverse analysis, based on the FE method, is used to model the tensile test of an axisymmetric notched bar (Fig. 2). This numerical model is coupled with an optimization tool. Figure 2 : Specimen geometry and FE model of axisymetric notched bar with 2 mm radius (AN2). T