Issue 49

M. Hadj Miloud et alii, Frattura ed Integrità Strutturale, 49 (2019) 630-642; DOI: 10.3221/IGF-ESIS.49.57 635 Figure 3 : Scheme of identification procedure by inverse analysis. The cost function to minimize is given by:     2 1 2 1 F F Q F Np i i exp num i Np i exp i       (10) with: F exp (or F num ) = { F i } with i=1, 2, … N p : Total number of experimental measures (or computed), η : Allowable error. The numerical/experimental comparison is conducted on the load versus diameter reduction of notched axisymmetric specimen. Parameters identification procedure Generally, the determination of GTN model parameters usually consists of a phenomenological procedure which requires a hybrid methodology of comparison between experimental data and numerical results. Hence, the GTN parameters, as it is also indicated in [8, 9, 23 and 31] are obtained by the best fit of the numerical curve with the experimental curve. The nucleation void volume fraction f N and the critical void volume fraction f C play a crucial role in the ductile failure process. Thus, the GTN model response is strongly influenced by these two parameters. Then, the identification by inverse analysis will be conducted on the f N and f C parameters. To show the effect of the hardening laws on the GTN parameters identification, in a first step, the GTN model parameters are identified separately of the hardening law σ(ε) . The hardening behavior is determined from standard uniaxial tensile test then it is introduced by tabulation in Abaqus (predefined hardening law). Secondly, the two hardening laws are included (Eqs. 8 and 9) in the inverse identification using a VUHARD subroutine coupled with GTN model. Q ≤ η Experimental data Yes Numerical model (VUHARD, Abaqus) Rheological test (AN2 tensile test) New parameters set Comparison: cost function ( Q ) No Initial parameters set Test conditions Material Observables: Numerical results Optimal parameters set (GTN and hardening Laws)