During high strain rate deformations of metals and metallic alloys, narrow regions of intense plastic deformations have been observed experimentally. The phenomenon is termed strain localization and is usually a precursor to catastrophic failure of a structure. Similar phenomenon has been observed in glassy polymers deformed both at slow and high strain rates. Whereas strain localization is attributed to material softening due to thermal heating in metallic alloys, it is believed to be due to the reorganization of the molecular structure in polymers. Here we numerically study the strain localization in Tungsten Heavy Alloys (WHAs), and glassy polymers.

WHAs are heterogeneous materials and thus inhomogeneities in deformations occur simultaneously at several places. Thus strains may localize into narrow bands at one or more places depending upon the microstructure of the alloy. We analyze the strain localization phenomenon during explosion and implosion of WHA hollow cylinders. We have developed a procedure to generate three-dimensional microstructures from planar images so that the two have the same 2-point correlation function. The WHA considered here is comprised of W particulates in a Nickel-Iron (NiFe) matrix, and each constituent is modeled as a heat conducting, strain hardening, strain-rate hardening and thermally softening elastic-plastic material. Furthermore, the porosity is taken to evolve in each constituent and the degradation of material properties due to porosity is incorporated into the problem formulation. It is found that the strain localization initiation in WHA hollow cylinders does not significantly depend on microstructural details during either explosive or implosive loading. However, the number of disconnected regions of localized deformations is influenced by the microstructure.

We have generalized constitutive equations for high strain rate deformations of two glassy polymers, namely, Polycarbonate (PC) and poly (methyl methacrylate) (PMMA). These have been validated by comparing computed results with test findings in uniaxial compression at different axial strain rates, and subsequently used to study strain localization in a plate with a through-the-thickness elliptic hole at the centroid and pulled axially at a nominal strain rate of 5,000 /s. For the problems studied, the intensely deformed narrow regions have very high shear strains in WHAs, but large axial strains in glassy polymers.