Neck retardation under quasi-static and dynamic stretching
Professor J.W. Hutchinson
Harvard University
Neck retardation in stretching of ductile materials is promoted by strain hardening, strain-rate hardening and inertia. Neck retardation is usually beneficial because necking localization is often the precursor to ductile failure. As background and motivation, recent work will be discussed illustrating unexpectedly large neck retardation in elastomer-metal bilayer sheets stretched quasi-statically. The main emphasis in the seminar will be on the interaction of material behavior and inertia in necking retardation. The interaction is complicated, in part, because necking is highly nonlinear but also because the mathematical character of the response changes in a fundamental way from rate-independent behavior to rate-dependent behavior, whether due to material constitutive behavior or to inertia. For rate-dependent behavior, neck development requires the introduction of an imperfection, and the rate of neck growth in the early stages is closely tied to the imperfection amplitude. When inertia is important multiple necks can emerge. By contrast, in rate-independent materials deformed quasi-statically, a single neck is preferred and it can emerge in an imperfection-free specimen as a bifurcation. The interaction of material properties and inertia in determining neck retardation is unraveled using a variety of methods and models. The essential dimensionless parameters governing the phenomenon are identified, as are the regimes in which they play a significant role.
