Necking and drawing of rubber–plastic laminate composites: Finite element simulations and analytical model

Many plastics show necking and drawing behavior in tension, sometimes called “cold drawing”. In contrast, elastomers stretch homogeneously in tension. We examine the tensile behavior of rubber–plastic laminate composites using 3D finite element simulations and an analytical model. A rate-independent constitutive behavior was adopted in which the modulus at small-strain, strain hardening at large strain, and yield stress (only for the plastic) can all be varied independently. For sufficiently small rubber/plastic thickness ratio, layered composites show necking and drawing wherein a tensile bar coexists in two strain states, one with a large stretch (necked region) and the other with a modest stretch (unnecked region). With increasing rubber/plastic thickness ratio, the two strain states approach each other in a manner resembling a second order phase transition culminating in a critical point. Above this critical rubber/plastic thickness ratio, the layered composites stretch homogeneously. An analytical model based on adding the First Piola–Kirchoff stresses of the rubber and plastic layers, along with a modification for inelastic deformation, is shown to capture most of the results of 3D simulations accurately. We comment on the practical relevance of these results to toughening relatively brittle plastics, and more specifically, the critical importance of strain hardening of the rubber.