Modeling of Dynamic Necking in Bars

Abstract

Necking of thin bodies (bars, plates) loaded in tension is one form of strain localization in ductile materials that may lead to failure. The phenomenon of necking has been studied extensively, initially for quasistatic loading and then for dynamic loading. Nevertheless, many issues concerning necking are still unclear. Among these are: 1) is necking a random or deterministic process; 2) how does the specimen choose the final neck location; 3) to what extent do perturbations (material or geometrical) influence the neck forming process; and 4) how do various parameters (material, geometrical, loading) influence the final neck location. Here we address these issues using computer simulations with a hydrocode. Among other things we find that: 1) neck formation is a semi deterministic process. Changing one of the parameters monotonously usually moves the final neck location monotonously as well, but there are exceptions; 2) final neck location is sensitive to the radial velocity of the end boundaries, and as this boundary condition is not fully controlled in tests, this may be the reason why neck formation is sometimes regarded as random; and 3) neck formation is insensitive to very small perturbations, but may be influenced by larger perturbations.