Effect of kinematic hardening on localized necking in substrate-supported metal layers

Abstract

Prediction of necking limits in thin substrate-supported metal layers, which are typically used as functional components in electronic devices, represents nowadays an ambitious challenge. The specific purpose of the current work is, first, to numerically investigate the effect of kinematic hardening on localized necking in a freestanding metal layer. Second, the impact of adding a substrate layer on the ductility evolution of the resulting elastomer/metal bilayer will be analyzed. The materials in the metal and substrate layers are assumed to be isotropic, incompressible and strain-rate independent. The behavior of the metal layer is described by a rigid-plastic model with mixed (isotropic and kinematic) hardening. The isotropic hardening contribution is modeled by the Hollomon law, while kinematic hardening is modeled by the Armstrong-Frederick law. The substrate layer is made of elastomer material whose mechanical behavior is assumed to be hyperelastic and modeled by a neo-Hookean constitutive law. The Marciniak-Kuczynski imperfection analysis is used to predict plastic flow localization. Through various numerical simulations, the influence of kinematic hardening on localized necking as well as the impact of the addition of an elastomer layer are specifically emphasized. Comparisons with experimental results are also carried out to assess the relevance of incorporating kinematic hardening in the constitutive modeling of freestanding metal sheets.

A general and efficient multistart algorithm for the detection of loss of ellipticity in elastoplastic structures

“…According to the latter analysis, in a homogeneously strained domain, a strain localization band can develop when two parallel surfaces fulfill the loss of ellipticity criterion, 9 although other local or global instability modes can occur prior to loss of ellipticity in the form of buckling or necking modes. For instance, it is commonly used for the analysis of thin metal sheets forming limits 10 in a plane stress framework. The loss of ellipticity analysis is strictly a local analysis, however, nothing is said about the structural aspect with this criterion.…”

Investigation of the Geometry of Metal Tube Walls after Necking in Uniaxial Tension

“…Numerous studies were conducted to characterize the material's behavior after necking [20][21][22][23][24][25][26][27][28][29][30]. We could get some inspiration and reference from those of metal sheets and round bars.…”