Dynamics of Necking and Fracture in Ductile Porous Materials

The onset of necking in dynamically expanding ductile rings is delayed due to the stabilizing effect of inertia, and with increasing expansion velocity, both the number of necks incepted and the number of fragments increase. In general, neck retardation is expected to delay fragmentation as necking is often the precursor to fracture. However, in porous ductile materials, it is possible that fracture can occur without significant necking. Thus, the objective of this work is to unravel the complex interaction of initial porosity and inertia on the onset of necking and fracture. To this end, we have carried out a series of finite element calculations of unit cells with sinusoidal geometric perturbations and varying levels of initial porosity under a wide range of dynamic loading conditions. In the calculations, the material is modeled using a constitutive framework that includes many of the hardening and softening mechanisms that are characteristics of ductile metallic materials, such as strain hardening, strain rate hardening, thermal softening, and damage-induced softening. The contribution of the inertia effect on the loading process is evaluated through a dimensionless parameter that combines the effects of loading rate, material properties, and unit cell size. Our results show that low initial porosity levels favor necking before fracture, and high initial porosity levels favor fracture before necking, especially at high loading rates where inertia effects delay the onset of necking. The finite element results are also compared with the predictions of linear stability analysis of necking instabilities in porous ductile materials.