Micromechanical-Based Viscoplastic Constitutive and Computational Models
In this research work, the modeling of the adiabatic and isothermal plastic flow stresses of stainless steel is achieved at low and high strain rates and over a wide range of temperatures. Since the microstructure composition of stainless steel contains bcc and fcc crystal components, the combination of both bcc and fcc models are utilized using the additive decomposition of the thermal and athermal stresses. Both thermal and athermal flow stresses of steel are plastic strain dependent, however, the majority of the thermal part of the flow stress belongs to the yield stress, whereas, the plastic hardening dominates the athermal flow stress.
A general consistent thermodynamic framework for elasto-viscoplastic deformations is presented in this study to introduce the constitutive model of stainless steel. An explicit viscosity-temperature relationship is derived to impose the effect of the accumulated heat on the adiabatic deformation. A proper definition for the magnitude of the viscoplastic flow is also achieved in order to characterize the dynamic behavior of the material.
Computational aspects of the proposed model are addressed through the finite element implementation in the finite element code (ABAQUS) using the material subroutine VUMAT and an implicit stress integration algorithm. The radial return algorithm which is a special case of the backward-Euler method is used to introduce a nonlinear scalar equation in terms of the viscoplastic multiplier for the case of the Consistency viscoplastic model. Numerical examples are presented in this work in order to validate and test the proposed computational framework and numerical algorithm for AL-6XN stainless steel. Introducing realistic definitions for the material parameters of the proposed constitutive relations helps in achieving a proper understanding of the localization behavior of steel under different loading conditions.
It is clear that material rate dependence, no matter how small, leads to well-posed boundary value problems with unique solutions. This objectivity is achieved by mesh independency results of localization problems. This is due to the incorporation of a length scale parameter in the governing equations through the viscosity definition used in the rate dependent formulations of the constitutive relations. In addition to its regularizing effect on the description of the localization problem, this viscosity helps to improve the convergence rate by constraining the deformation process at the initial stage of the material plasticity viscoplasticity.
