Strain localization and dynamic recrystallization in polycrystalline metals: Thermodynamic theory and simulation framework

Abstract

We describe a theoretical and computational framework for adiabatic shear banding (ASB) and dynamic recrystallization (DRX) in polycrystalline materials. The Langer-Bouchbinder-Lookman (LBL) thermodynamic theory of polycrystalline plasticity, which we recently reformulated to describe DRX via the inclusion of the grain boundary density or the grain size as an internal state variable, provides a convenient and self-consistent way to represent the viscoplastic and thermal behavior of the material, with minimal ad-hoc assumptions regarding the initiation of yielding or onset of shear banding. We implement the LBL-DRX theory in conjunction with a finite-element computational framework. Favorable comparison to experimental measurements on a top-hat AISI 316L stainless steel sample compressed with a split-Hopkinson pressure bar suggests the accuracy and usefulness of the LBL-DRX framework, and demonstrates the crucial role of DRX in strain localization.

Thermodynamic theory of crystal plasticity: Formulation and application to polycrystal fcc copper

“…The second of these inequalities constrains the Taylor-Quinney factor which determines the amount of plastic power that goes into heating up the material, as has been discussed in Lieou et al (2019). The implications of the first inequality can be seen by writing…”

“…What distinguishes the present approach from conventional theories is that the evolution of the dislocation density are derived from energetic and entropic considerations alone, subject to the constraints of the first and second laws of thermodynamics. Our derivation here is largely parallel to that described in simpler and isotropic set-ups (e.g., Langer et al, 2010;Langer, 2015;Lieou and Bronkhorst, 2018;Lieou et al, 2019), but is now adapted to incorporate finite deformation and different slip systems with some initial accounting for dislocation interactions.…”

“…This general theory based upon atomic scale principles then provides a disciplined thermodynamic framework to describe structural features such as dislocations, dislocation subcells, grain boundaries, and so on. In our prior work (Lieou and Bronkhorst, 2018;Lieou et al, 2019) and other recent applications of this theory (Langer, 2016(Langer, , 2017aLe et al, 2018;Le, 2018Le, , 2019 the atomic disorder component or dislocation, subcell, grain boundary representation was done only through isotropic and scalar representations of these states. There was but one dislocation density and grain boundary density measure used in the theory and subsequent simulations of experimental results.…”

“…There was but one dislocation density and grain boundary density measure used in the theory and subsequent simulations of experimental results. Here we advance upon the work in (Lieou and Bronkhorst, 2018;Lieou et al, 2019) by applying this general thermodynamic approach to an advanced continuum theory of single crystal behavior for FCC systems. In this way, we significantly advance the description of the disorder (structure) partition component applied to specific crystallographic structure and begin to address the challenging questions raised above (Berdichevsky, 2006(Berdichevsky, , 2017(Berdichevsky, , 2018b(Berdichevsky, ,a, 2019aAnand et al, 2015;Le, 2018Le, , 2019Hochrainer, 2016;Levitas and Javanbakht, 2015a;Arora and Acharya, 2019;Po et al, 2019;Chowdhury and Roy, 2019;Jiang et al, 2019;Nieto-Fuentes et al, 2018;Jafari et al, 2017;Shizawa et al, 2001;del Castillo and Huang, 2012;Langer et al, 2010;Langer, 2015;Acharya, 2005, 2006;Acharya, 2010).…”

Some Facts We Can Learn from Analytical Modeling of DDRX in Pure Metals and Solid Solutions

“…Such numerical computations provide the most detailed description of microstructural evolutions, but their ability to reach DDRX steady states, i.e., large to very large strains, is still questionable considering the current computing speeds. Finally, a new microscopic (and more ambitious) approach based on a thermodynamic theory of dislocation plasticity has been proposed [11,12] and applied to the interaction between DRX and adiabatic shear banding under high strain rate loading conditions. A review of DRX including modeling has been published recently by Huang and Logé [13].…”