Theoretical and numerical investigation of the impact of out-of-plane compressive stress on sheet metal formability. (September 2017) - Bettaieb, M. Ben; Abed-Meraim, F.
Highlights: Numerical tools are developed to study the impact of out-of-plane stresses on sheet metal formability. The impact of out-of-plane compressive stresses on the enhancement of sheet formability is highlighted. The predictions given by the bifurcation theory are compared to those yielded by the M–K approach. The numerical predictions in terms of limit strains are favorably compared with some analytical results. Abstract: In modern sheet metal forming processes, such as hydroforming and single point incremental forming, sheet metals are often subjected to out-of-plane compressive stresses in addition to traditional in-plane stresses. However, the effect of these out-of-plane stresses on the onset of plastic strain localization is not considered when classic necking criteria are used, as the latter are generally formulated based on the plane stress assumption. The main objective of the present investigation is to overcome this limitation by developing numerical tools and analytical relations that allow considering the influence of these compressive stresses on the prediction of localized necking. In the different tools developed, and for comparison purposes, finite strain versions of both the deformation theory of plasticity and the rigid-plastic flow theory are used to describe the mechanical behavior of the metal sheet. Furthermore, both the bifurcation theory and the initial imperfection approach are employed to predict the onset of strain localization. Various numerical predictions are reported to illustrate the effect of normal stress on the occurrence of localized necking in sheet metals. From these different results, it is clearly demonstrated that out-of-plane stresses may notably enhance sheet metal formability and, therefore, this property can be effectively used to avoid the initiation of early strain localization. Graphical abstract: