A Comparative Study of Different Necking Criteria for Numerical and Experimental Prediction of FLCs

Abstract

For sheet metal forming, the determination of the onset of localized necking directly influences the formability evaluation and construction of forming limit curves (FLCs). Several necking criteria in the literature have been proposed and widely used, however, there are some restrictions, e.g., some criteria are suitable for numerical methods but not for the experimental phase. In this study, numerical and experimental procedures are carried out to seek an appropriate necking criterion for the prediction of FLCs. This article begins with the FE modeling of the Marciniak test with ABAQUS. Based on the FE simulation, different necking criteria (global and local ones) are reviewed and analyzed in detail, and the FLCs for a 5086 aluminum sheet are constructed with these criteria. On the other hand, a quasi-static experimental Marciniak test is carried out to study the formability for this given sheet. With a chosen necking criterion, the limit strains are experimentally determined. The comparison between experimental and numerical results shows that the chosen necking criterion could be effective to numerically and experimentally evaluate the global formability of this aluminum alloy on the wide range of strain states.

Determination of Forming Limit Diagrams Based on Ductile Damage Models and Necking Criteria

“…This strategy allows delimiting the limit strains for stretched sheet metals that should not be exceeded in order to ensure a good quality of the final product. The FLDs are determined using necking or fracture criteria, which may be based on sound theoretical developments (see, e.g., Hill, 1952;Stören and Rice, 1975;Yamamoto, 1978;Abed-Meraim et al, 2014) or on finite element (FE) simulations (see, e.g., Zhang et al, 2011;Lumelskyy et al, 2012, Martínez-Donaire et al, 2014Kami et al, 2015). These criteria are generally combined with constitutive models for the prediction of limit strains in sheet metal forming.…”

“…More specifically, the onset of strain localization is associated with the maximum of the thickness strain acceleration, which is obtained by computing the second time derivative of thickness strain in the localized zone (see, e.g., Situ et al, 2006Situ et al, , 2007Situ et al, , 2011Zhang et al, 2011;Lumelskyy et al, 2012;Martínez-Donaire et al, 2014). After the maximum in the second time derivative of thickness strain (i.e., thickness strain acceleration) is reached, the localized thinning in the sheet proceeds gradually until the onset of fracture.…”

Numerical Predictions of the Occurrence of Necking in Deep Drawing Processes

“…More specifically, the strain paths are almost linear for the specimens having widths ranging from 12 mm to 60 mm (i.e., corresponding to a negative minor strain), while they are clearly nonlinear for the specimens having widths ranging from 72 mm to 120 mm (i.e., corresponding to a positive minor strain). In the latter case, the strain paths remain linear until a sudden transition to some plane-strain state, which indicates the onset of localized necking (see, e.g., [40,43]). The strain paths generated by the simulations of the simple sheet stretching test and the Erichsen test for all specimen widths are reported in Figure 17.…”

“…The first criterion is based on the analysis of the evolution of the thickness strain for each specimen. The occurrence of necking is detected when a sudden change in the evolution of the thickness strain in the central area is observed (see, e.g., [40]). The minor and major in-plane principal strains, corresponding to the occurrence of necking, are then reported into the FLD.…”

“…The second numerical criterion is based on the analysis of the thickness strain acceleration, which is obtained by computing the second time derivative of thickness strain in the central region of the specimen (see, e.g., [11,40,42]). According to this criterion, the critical minor and major in-plane principal strains at the occurrence of necking are obtained when the second time derivative of the thickness strain, i.e., thickness strain acceleration, reaches a maximum.…”