TY - JOUR

T1 - Material models for the thermoplastic material behaviour of a dual-phase steel on a microscopic and a macroscopic length scale

AU - Zeller, Sebastian

AU - Baldrich, Martina

AU - Gerstein, Gregory

AU - Nürnberger, Florian

AU - Löhnert, Stefan

AU - Maier, Hans Jürgen

AU - Wriggers, Peter

N1 - Funding information: The results presented in this paper were obtained within the Collaborative Research Centre 1153 ’Process chain to produce hybrid high performance components by Tailored Forming’ in the subproject C4 and within the Collaborative Research Centre TR73 ’Sheet-Bulk Metal Forming’ in the subprojects C2 and C4. The authors thank the German Research Foundation (DFG) for the financial and organisational support of these projects.

PY - 2019/8

Y1 - 2019/8

N2 - Material models for the thermoplastic material behaviour of a dual-phase steel on a microscopic and a macroscopic length scale are developed in a continuum mechanics framework. Since the microstructure of the material is composed of the two phases martensite and ferrite, appropriate model assumptions on the behaviour of the phases have to be made. In the present model, it is assumed that the martensitic phase behaves purely elastic and the temperature dependent yielding behaviour of the dual-phase steel is determined by the ferritic phase. In this phase, plastic deformation is the result of the movement of dislocations in the atomic lattice on preferred planes in preferred directions. As experiments have shown, the resistance to this movement is determined by an evolving dislocation arrangement as well as by the atomic lattice itself. Based on this experimental observation, dislocation densities are introduced as state variables to formulate a constitutive equation for the resistance to plastic deformation and to capture the dependence of the material behaviour on deformation and temperature history on a microscopic length scale. By analysing the elementary processes of multiplication and annihilation of dislocations and the dependence of these processes on temperature and deformation rate, evolution equations for the dislocation densities are formulated. Thermal activation is used to describe these dependences. Supplying constitutive equations for the Helmholtz free energy and the heat flux, the initial boundary value problem for the thermomechanically coupled problem on a microscopic length scale is formulated. To validate the developed material model, processes applied in experiments with single crystal specimens of pure iron are simulated and a comparison is made between experimental and numerical results. The material model on a macroscopic length scale is motivated by the model on a microscopic length scale. A state variable representing the total dislocation density is introduced to describe the influence of the deformation and temperature history on the material behaviour. For the validation of the material model, a comparison is made between experimental results obtained from forming of sheet metal specimens and the numerical model prediction.

AB - Material models for the thermoplastic material behaviour of a dual-phase steel on a microscopic and a macroscopic length scale are developed in a continuum mechanics framework. Since the microstructure of the material is composed of the two phases martensite and ferrite, appropriate model assumptions on the behaviour of the phases have to be made. In the present model, it is assumed that the martensitic phase behaves purely elastic and the temperature dependent yielding behaviour of the dual-phase steel is determined by the ferritic phase. In this phase, plastic deformation is the result of the movement of dislocations in the atomic lattice on preferred planes in preferred directions. As experiments have shown, the resistance to this movement is determined by an evolving dislocation arrangement as well as by the atomic lattice itself. Based on this experimental observation, dislocation densities are introduced as state variables to formulate a constitutive equation for the resistance to plastic deformation and to capture the dependence of the material behaviour on deformation and temperature history on a microscopic length scale. By analysing the elementary processes of multiplication and annihilation of dislocations and the dependence of these processes on temperature and deformation rate, evolution equations for the dislocation densities are formulated. Thermal activation is used to describe these dependences. Supplying constitutive equations for the Helmholtz free energy and the heat flux, the initial boundary value problem for the thermomechanically coupled problem on a microscopic length scale is formulated. To validate the developed material model, processes applied in experiments with single crystal specimens of pure iron are simulated and a comparison is made between experimental and numerical results. The material model on a macroscopic length scale is motivated by the model on a microscopic length scale. A state variable representing the total dislocation density is introduced to describe the influence of the deformation and temperature history on the material behaviour. For the validation of the material model, a comparison is made between experimental results obtained from forming of sheet metal specimens and the numerical model prediction.

KW - Crystal plasticity

KW - Dislocations

KW - Finite strain

KW - Multiscale method

KW - Thermomechanical constitutive behaviour

UR - http://www.scopus.com/inward/record.url?scp=85065712560&partnerID=8YFLogxK

U2 - 10.1016/j.jmps.2019.04.012

DO - 10.1016/j.jmps.2019.04.012

M3 - Article

AN - SCOPUS:85065712560

VL - 129

SP - 205

EP - 228

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

ER -