Investigation of localized necking in substrate-supported metal layers: Comparison of bifurcation and imperfection analyses

Abstract

a b s t r a c tLocalized necking is often considered as precursor to failure in metal components. In modern technologies, functional components (e.g., in flexible electronic devices) may be affected by this necking phenomenon, and to avoid the occurrence of strain localization, elastomer substrates are bonded to the metal layers. This paper proposes an investigation of the development of localized necking in both freestanding metal layers and elastomer/ metal bilayers. Finite strain versions of both rigid-plastic flow theory and deformation theory of plasticity are employed to model the mechanical response of the metal layer. For the elastomer, a neo-Hookean constitutive law is considered. Localized necking is predicted using both bifurcation (whenever possible) and Marciniak-Kuczynski analyses. A variety of numerical results are presented, which pertain to the prediction of localized necking in freestanding metal layers and metal/substrate bilayers. The effects of the constitutive framework and the presence of an elastomer substrate on strain localization predictions have been specifically highlighted. It is demonstrated that the addition of an elastomer layer can retard significantly the occurrence of localized necking. It is also demonstrated that the results of the Marciniak-Kuczynski analysis tend towards the bifurcation predictions in the limit of a vanishing size for the geometric imperfection.

Influence of the Yield Surface Curvature on the Forming Limit Diagrams Predicted by Crystal Plasticity Theory

“…However, for positive strain paths ( 0 r > ), the trend is completely different for the RSL framework, in which the determinant decreases very slightly for 0.1 r = and keeps practically a constant value for 1 r = or 0.5 r = . As discussed in the literature, most often within phenomenological constitutive frameworks (see, e.g., Rice, 1976;Hutchinson and Neale, 1978;Ben Bettaieb and Abed-Meraim, 2015), it is found that when the shearing components of the tangent modulus keep their high elastic values, the use of bifurcation theory as localization criterion yields unrealistically high localization strains in the positive biaxial stretching range. Here, the localization predictions suggest values for the critical strains far beyond 2.…”

“…As discussed above, the application of the bifurcation approach leads to unrealistically high limit strains in the right-hand side of the FLD, when the flow theory with associative plasticity and smooth yield surface is used (Rice, 1976;Ben Bettaieb and Abed-Meraim, 2015). In the framework of micromechanical modeling, based on crystal plasticity, one can wonder how realistic the predicted FLDs would be if a rounded yield surface is used instead of the sharper yield surface associated with the classical Schmid law.…”

Ductility prediction of substrate-supported metal layers based on rate-independent crystal plasticity theory

“…For each loading (determined by a strain path and a band orientation), the computations are stopped when the norm of the jump vector PS PS C increases rapidly, thus marking the localization of the deformation in the band zone. Further numerical and algorithmic details regarding the M-K approach can be found in [7].…”

“…The current paper may be viewed as an extension of the investigations carried out in [7], which were restricted to a phenomenological description for the mechanical behavior of the metal layer.…”

Theoretical and numerical investigation of the impact of out-of-plane compressive stress on sheet metal formability

“…These numerical tools have been originally developed in [14] and recently revisited and improved in [15] . In these tools, two main strain localization criteria have been used to predict the occurrence of localized necking: the bifurcation theory and the Marciniak and Kuczynski approach (also referred to as the initial imperfection approach).…”