A Constitutive Model for the Simulation of the Deformation Behavior of TWIP Steels

Abstract

Due to their high strength (tensile strength > 1GPa) in combination with an extreme ductility (failure strain 30-50%) TWinning Induced Plasticity–steels (TWIP-steels) can be considered as promising materials for the production of lightweight automotive components. The industrial application of TWIP-steels requires a fundamental experimental validation of the mechanical behavior as basis for an user-friendly but at the same time accurate constitutive framework and its implementation into commercial Finite Element codes. Related investigations and implementations in order to allow for the simulation of TWIP-steel forming processes are currently conducted within the research project “TWIP4EU”, executed as a cooperation of Fraunhofer - Institut für Werkstoffmechanik IWM in Freiburg (Germany), Salzgitter Mannesmann Forschung GmbH (Germany), Swerea KIMAB (Sweden), Faurecia Autositze GmbH (Germany / France), DYNAmore GmbH (Germany) and ESI GmbH Engineering System (Germany / France).The monotonic one-dimensional hardening behavior of TWIP-steels as a function of the twin volume fraction and dislocation density has been described by Bouaziz et al. (2008), Bouaziz et al. (2011). This model has been proven to be adequate for the description of the flow behavior of TWIP-steels and serves as basis for the constitutive model, presented here. This Bouaziz-model has been extended to a three-dimensional elasto-plastic formulation, including the influence of different loading conditions, anisotropy and kinematic hardening. The present paper deals with the implementation for solids and shells in the commercial Finite Element Code LS-DYNA®and appropriate validation simulations will be presented.

Implementation of a Constitutive Model for the Mechanical Behavior of TWIP Steels and Validation Simulations

“…Within a time step and for a given strain increment ∆ , the constitutive equations given in Haufe et al [2] are solved iteratively by a classical "elastic-predictor" (trial step) -"plastic-corrector" scheme, see Fig. 1 and 3.…”

“…for 0 an iterative stress return map is performed. For this, the increments or residual changes respectively of the internal variables, following from the continuous equations given in [2], [4], [5], are given in the following. Herein, denotes the burgers vector, k the forest hardening parameter, the threshold number of stopped dislocation, whereas the variable n describes the flux of dislocations which have arrived at a twin or a grain boundary.…”

“…In order to include anisotropy, kinematic hardening (Bauschinger effect) and cyclic loading situations, the original Bouaziz-Allain model has been extended (see Haufe et al [2], Butz et al [4], Zapara et al [5]) and implemented as a three-dimensional elasto-plastic formulation in LS-DYNA. The results of the mechanical and microstructural experimental analysis of a new TWIP steel grade HSD ® -Steel produced by Salzgitter Mannesmann Forschung GmbH (Germany) have been used to validate the material formulation.…”

“…This paper deals with the implementation of a constitutive model for the macroscopic deformation behavior of TWIP steels under mechanical loading with the aim of simulating metal forming processes and representing the behavior of TWIP-steel components -for example under crash loading -with the Finite Element code LS-DYNA ® and refers to our recently published papers: [2],[4], [5]. Within the present paper we focus on the implementation of the model formulated in [2] and its extension to stress dependent twinning effects.…”