Modeling and simulation framework for dynamic strain localization in elasto-viscoplastic metallic materials subject to large deformations

Abstract

This paper describes a theoretical and computational framework for the treatment of adiabatic shear band formation in rate-sensitive polycrystalline metallic materials. From a computational perspective, accurate representation of strain localization behavior has been a long-standing challenge. In addition, the underlying physical mechanisms leading to the localization of plastic deformation are still not fully understood. The proposed framework is built around an enhanced-strain finite element formulation, designed to alleviate numerical pathologies known to arise in localization problems, by allowing a localization band of given finite width (weak discontinuity) to be embedded within individual elements. The mechanical threshold strength (MTS) model is used to represent the temperature and strain rate-dependent viscoplastic response of the material. This classical flow stress model employs an internal state variable to quantify the effect of dislocation structure evolution (work hardening and recovery). In light of growing evidence suggesting that the softening effect of dynamic recrystallization may play a significant role, alongside thermal softening, in the process of shear band formation and growth, a simple dynamic recrystallization model is proposed and cast within the context of the MTS model with the aid of the aforementioned internal state variable. An initiation criterion for shear localization in rate and temperature-sensitive materials is introduced and used in the present context of high-rate loading, where material rate-dependence is pronounced and substantial temperature increases are achieved due to the dissipative nature of viscoplastic processes. In addition, explicit time integration is adopted to facilitate treatment of the dynamic problems under consideration, where strain rates in excess of 104 s−1 are typically attained. Two series of experiments are conducted on AISI 316L stainless steel, employing the commonly used top-hat sample geometry and the Split-Hopkinson Pressure Bar dynamic test system. Axi-symmetric finite element simulation results are compared to cross-sectional micrographs of recovered samples and experimental load–displacement results, in order to examine the performance of the proposed framework and demonstrate its effectiveness in treating the initiation and growth of adiabatic shear banding in dynamically loaded metallic materials. These comparisons demonstrate that thermal softening alone is insufficient to induce shear localization behaviors observed in some materials, such as stainless steel, and support the hypothesis that dynamic recrystallization and/or other softening mechanisms play an essential role in this process.