Issue 49

C. Bellini et alii, Frattura ed Integrità Strutturale, 49 (2019) 791-799; DOI: 10.3221/IGF-ESIS.49.70 792 represented, in terms of main strain measured in the sheet plane (maximum strain and minimum deform strain), by a graph of the necking and/or fracture conditions. In order to ascertain the success of a sheet metal forming process, the adopted finite element code is equipped with an FLC dependent on the mechanical properties of the material. FEM verification involves a comparison between the calculated strain during the stamping process and the FLC for that material. The FLC can be derived from Hill’s localized necking theory and Swift’s diffuse necking one [12, 13]. It depends on the hardening index obtainable from the results of a tensile test on the studied material. Figure 1 : Typical formability limit curve of metal sheets. β represents the ratio between the principal strains, that are ε max and ε min , evaluated in the sheet plane: min max     (1) while the formability limit parameter can be calculated through the following relation: max min ( ) FLP FLC    (2) in which FLC (ε min ) constitutes an analytical description of the FLC as a function of the principal strain ε min . Therefore, on the assumption that β≤0, it can be stated that: min ( ) 1 n FLC     (3) while, for β>0, it is: 2 min 2 1 ( ) 2 (1 )(2 2 ) FLC n             (4) The use of the FLP allows monitoring, by means of FEM analysis, the moment and the position in which the instability condition arises (FLP = 1) during a plastic deformation process. The FLC can be determined using experimental methods [14], theoretical (that is based on necking or fracture criteria of the material) [12, 13, 15] and hybrids [16] (that is combining experimental results with analytical or numerical methods).