Issue 49

M. Hadj Miloud et alii, Frattura ed Integrità Strutturale, 49 (2019) 630-642; DOI: 10.3221/IGF-ESIS.49.57 634 Tensile tests on notched specimen AN2 The nickel chromium steel used in this investigation is the 12NiCr6 steel. The tensile test was carried out on the notched round tensile bar AN2 [9]. These specimens type have been originally developed for analyzing the hydrostatic stress effect on the failure by ductile tear. The onset necking of those specimens occur at the notch. On this latter a diametric extensometer was set up to measure the diametric reduction. The experimental data obtained from those tests allow to a successful FE identification of damage models [31]. The specimen geometry (Fig. 2-a) and FE model are represented in the Fig. 2-b and c. FE model of the uniaxial tensile test of AN2. From the data obtained by [9], the objective is to identify simultaneously the hardening laws and the GTN model of the studied material. The tensile test of AN2 is simulated using the FE software Abaqus/Explicit with taking into account the experimental conditions. In order to compare the numerical results with those experimental obtained in [9], the same specimen dimensions (Fig. 2-a) are considered in the numerical model. Given the symmetry of specimen geometry, only the specimen quarter is modelled in an axis-symmetry case. The quadrilateral elements, type four nodes CAX4R, are used in the meshing. A refined mesh is adapted at the notch zone of the specimen (Fig. 2-c). It should be noted that the element size could be important in FE damage analysis. The number of elements in FE mesh was 660. A velocity v(t) boundary condition was applied to the top of the FE model (Fig. 2-b). The test was performed in the quasi static case and the same velocity of 0.3mm/min is used in the numerical modelling. The resulting tensile load was determined from nodal forces versus displacement. The material of the specimen, 12NiCr6, is assumed have an isotropic elasto-plastic behavior. The density of the material is 7.8 × 10 -6 Kg /mm 3 . The elastic part is described by using Hooke’s model with Young’s modulus of E=194GPa and a Poisson’s ratio of ν = 0.3. For the plastic domain, the von Mises yield criteria is used. It’s added to the plastic part of the GTN damage parameters. This model already exists in the software Abaqus/Dynamic Explicit in porous metal plasticity option [29]. In the literature, several formulated laws exist to describe the hardening behaviors from numerous parameters. The adopted laws in this inverse identification procedure are those of Voce and Ludwick. The difference between those laws is that the Voce law is characterized by a saturated yielding stress σ s for high strains. However, the Ludwick law is characterized by a continuous evolution of the yielding stress. The Lüder bands are taken also into account in the hardening laws following the below equations: Voce Hardening law: 0 0 ( ) 0 if else ( ) ( ) L L L S S e                                  (8) Ludwick Hardening law: 0 0 n 0 if else ( ) K( ) L L L                            (9) Where: S  saturated yielding stress, 0  yielding stress, 0  yielding strain,  material dependent adimensioned parameter, K material consistency, n hardening exponent and L  strain limit of Lüder bands. The different behavior laws are implemented through a VUHARD type subroutine in the software Abaqus/dynamic explicit. Identification strategy The inverse procedure is used to determine the hardening law and the GTN parameters of studied 12NiCr6 steel, using the numerical model described above. This numerical procedure using the FE model is coupled to an optimization tool in order to minimize the gap between numerical results and experimental data. The optimization tool used « OPTPAR » was developed by Gavrus [32]. The optimal GTN parameters are obtained using the Gauss-Newton iterative algorithm by minimizing the cost function (Q). This tool was widely used in previously research works [32-35] mainly for characterizing the behavior of metallic alloys under static, dynamic, uniaxial and biaxial solicitation. The general scheme of the inverse procedure is shown in the Fig. 3.