Abstract
In this paper, both the bifurcation theory and the initial imperfection approach are used to predict localized necking in substrate-supported metal layers. The self-consistent scale-transition scheme is used to derive the mechanical behavior of a representative volume element of the metal layer from the behavior of its microscopic constituents (the single crystals). The mechanical behavior of the elastomer substrate follows the neo-Hookean hyperelastic model. The adherence between the two layers is assumed to be perfect. Through numerical results, it is shown that the limit strains predicted by the initial imperfection approach tend towards the bifurcation predictions when the size of the geometric imperfection in the metal layer vanishes. Also, it is shown that the addition of an elastomer layer to a metal layer enhances ductility.
Highlights
The ductility of a material is characterized by its ability to deform homogeneously under some imposed loading
The current paper proposes an efficient tool for the prediction of localized necking in substrate-supported metal layers
It is clear that the shape and the level of the predicted forming limit diagram (FLD) are significantly influenced by the amount of initial geometric imperfection
Summary
The ductility of a material is characterized by its ability to deform homogeneously under some imposed loading. Predicting the different limit strains that lead to localized necking is crucial for designing functional or structural components used in industrial devices. To this end, several numerical models have been developed to predict localized necking, which is represented in the form of forming limit diagram (FLD). The mechanical behavior at the single crystal scale is described by a finite strain rate-independent constitutive framework, where the Schmid law is used to model the plastic flow. To be consistent with the notations adopted for the metal layer, the different mechanical fields corresponding to the elastomer layer are denoted by capital letters. X in the elastomer layer of the band is denoted XE (B)
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