Necking modes in multilayers and their influence on tearing toughness

Periodic bifurcation modes that occur in ductile multilayered plates or sheets stretched in plane strain tension are analyzed to reveal whether necks are likely to localize at the scale of the thickness of individual layers or at the scale of the full thickness of the multilayer. The energy dissipated in tearing a ductile multilayer scales with the extent of the localized thinning region in the tensile direction. If plates or sheets with high tearing toughness are desired, the combination of layers should be chosen to suppress necking localization at the scale of individual layers. Insight into the properties and thicknesses of the layers required to suppress short-wavelength necking is revealed by a bifurcation analysis of multilayers comprised of metal layers having different strength and hardening behaviors and multilayers combining metal and elastomer layers. Several examples suggest that when localization takes place at the scale of the individual layers it may occur in the form of a band inclined through the thickness.