Issue 49

M. Hadj Miloud et alii, Frattura ed Integrità Strutturale, 49 (2019) 630-642; DOI: 10.3221/IGF-ESIS.49.57 636 Results and Discussions Fig. 4 shows the Load-Diametric reduction curve for the notched specimens (AN2) and that obtained from numerical simulation. At the point ‘P’, there is a sharp change in the slope and drastic fall in load showing the final step of failure process(fracture). The results (Fig. 4 and Tab. 1) present the identification by inverse analysis of the f N and f C parameters of GTN model. The plastic behavior part of the material 12NiCr6 is modeled with introducing the experimental hardening curve into the software Abaqus by tabulated form. This hardening curve was obtained from a smooth tensile bar test [30]. The GTN parameters identified do not allow the best description of the fracture point because there is a gap between the experimental and numerical hardening zone of the Load-Diametric Reduction curves. In addition, the fracture point is not clearly observed in the numerical curve. Figure 4 : Numerical/experimental comparison of the Load vs. Diametric Reduction curve in the case of GTN model identification with a pre-defined hardening σ(ε) . Initial parameters Interval of variation Identified parameters Fixed f F 0.1 0.1 0.1 f C 0.0100 0.0100 to 0.0800 0.0100 f N 0.0040 0.0005 to 0.0070 0.0011 Cost function 19.75% ----------------------- 5.51% Table 1 : GTN parameters identified with pre-defined σ(ε) . The comparison between identification and experiment of Load/diametric contraction is shown in the Fig. 5 and the Tab. 2. In this identification process, the GTN model is coupled with Voce hardening law. Starting by the hardening parameters, we note that L  = 0.0214 parameter which characterizes the Lüder bands allows a good representation of the yielding zone. The yielding stress is about 0  = 339.8 MPa. The plastic parameters of Voce (  = 9.380 and S  = 659MPa) let to a good agreement in hardening zone between experimental and numerical curves. The GTN damage parameters ( f C =0.048 and f N =0.0065) give the best description of the fracture point ‘P’ (Fig. 5). For the following results, the comparison (Fig. 6 and Tab. 3) is done for GTN model coupled with Ludwick hardening law. The strain at the Lüder band limit L  =0.026 is close to that identified for Voce law. The yielding stress is about 0  =339.8MPa. and it’s exactly the same obtained for the Voce law. The plastic parameters of Ludwick ( K =428.6MPa and n =0.3) give also a good agreement in hardening zone between numerical and experimental curves. The GTN damage parameters ( f C =0.052 and f N =0.0088) are also close for the Voce law to describe the fracture point ‘P’ (Fig. 6). The results of the used inverse identification are summarized in the Tab. 4. The global comparison between experimental and computed load versus diametric contraction curve is also presented in Fig. 7. We note that the GTN parameters identified ( f C and f N ) with Voce and Ludwick hardening laws are similar to those of the reference [9] and give approximately the same experimental fracture point. 0 5 10 15 20 25 0 0,5 1 1,5 2 Load (kN) Diametric Reduction (mm) Experimental data[9] GTN Identification with Predifined σ(ε) P