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On a microscopic length scale dual-phase steels exhibit a polycrystalline microstructure consisting of ferrite and martensite. In this work a material model for the temperature dependent hardening behaviour of the ferritic phase is presented. As the dislocation structure determines the resistance to dislocation glide, dislocation densities are introduced as state variables to capture the dependence of the material behaviour on the loading history. Motivated by the elementary processes of multiplication by the Frank-Read-mechanism and annihilation by cross-slip, evolution equations for the dislocation densities are introduced. Based on the interaction of dislocations on different slip systems and the Peierls-stress, the resistance to dislocation motion with its temperature dependence is formulated to describe the hardening behaviour.

Since Tailored Forming is a complex process and the joining zone of the hybrid solid component is a possible weakness, our goal is to simulate the thermomechanical material behaviour of the joining zone during the Tailored Forming process. Investigations on the steel component of the joining zone show a polycrystalline microstructure with the two constituents pearlite and ferrite. In this work, the pearlitic phase is considered to be purely thermoelastic whereas the material model for the ferritic phase represents thermoplastic material behaviour. Besides reasons for the choice of the mentioned material models, we present the thermoplastic material model developed by Zeller et al. [1]. Based on the experimental observation that the persistent deformation is a result of slip of dislocations, state variables are defined to formulate a necessary shear stress to move dislocations as well as temperature and deformation dependent evolution equations for the introduced state variables.

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On a microscopic length scale dual-phase steels exhibit a polycrystalline microstructure consisting of ferrite and martensite. In this work it is assumed that the martensitic phase behaves purely thermoelastic while for the ferritic phase a thermoplastic material model was developed based on the assumption that the driving mechanism for persistent deformation is the movement of dislocations on preferred planes in preferred directions. The necessary shear stress to move dislocations at a certain temperature and deformation rate is assumed to possess contributions from the atomic lattice, alloying atoms and the dislocation structure. To consider the influence of the dislocation structure, dislocation densities are introduced as state variables for which temperature and deformation rate dependent evolution equations are formulated. Since for general loading histories the model equations cannot be integrated analytically, a time discretized form of the model equations with an appropriate solution algorithm is presented.