PD Dr. rer. nat. Franz Roters (Max-Planck-Institut für Eisenforschung, Düsseldorf)
A7 Multi-field microstructure mechanics
In the first period, a constitutive model of twinning was developed and implemented both in analytical form [1, 2] and into a Crystal Plasticity-FEM (CPFEM) code. The twinning model was improved in the second period and the overall model was extended to account for the TRIP effect. The CPFEM implementation is part of the software package DAMASK Düsseldorf Advanced MAterial Simulation Kit ), developed in the group of the part project leader and freely distributed as open source software . DAMASK also includes a spectral solver as alternative to the FEM .
The spectral solver has significant advantages over the FEM when simulating representative Volume Elements (RVEs), being orders of magnitude faster using less computer memory. This allows the treatment of much larger/better resolved meshes. The spectral solver will, therefore, be used I the third period to calculate effective material properties. Due to the complex mechanical behavior of the materials studied, the exact treatment of boundary conditions will be essential. Future simulations will, therefore, no longer be purely mechanical but incorporate additional fields. For this purpose, the spectral solver will be complemented with phase field like solvers. First results on damage were very promising.
As additional fields, first temperature and damage will be studied. The importance of temperature arises from the high strength of the material, which leads to significant (local) heating during deformation. This temperature rise might in turn change the activated deformation mechanisms. Damage significantly changes the mechanical boundary conditions leading to strong changes in stress and strain distribution. For the simulation of damage, the models developed in part project C6 will be implemented in DAMASK.
Finally, the influence of hydrogen on mechanical properties (HELP) and damage (hydrogen stabilized vacancies, HEDE) will be studied, again using results from other part projects. Extending the spectral solver into a general multi field solver even hydrogen diffusion could be looked at.
The close cooperation with part project B2 will be further tightened studying at the unusual spring back behavior of high Manganese steels.
 D. R. Steinmetz; T. Jäpel; B. Wietbrock; P. Eisenlohr; I. Gutierrez-Urrutia; A. Saeed-Akbari; T. Hickel; F. Roters; D. Raabe: Revealing the strain-hardening behavior of twinning-induced plasticity steels: Theory; simulations; experiments. Acta Materialia 61 (2013) 494 – 510
 D. R. Steinmetz A constitutive model of twin nucleation and deformation twinning in high-Mn austenitic TWIP steels - A temperature-sensitive model of fcc metals that twin PhD Thesis RWTH Aachen 2013
 F. Roters: Advanced material models for the crystal plasticity finite element method - development of a general CPFEM framework. Habilitationsschrift; Fakultät für Georessourcen und Materialtechnik; RWTH Aachen; URL: http://darwin.bth.rwth-aachen.de/opus3/volltexte/2011/3874/
 F. Roters; P. Eisenlohr; C. Kords; D.D. Tjahjanto; M. Diehl; D. Raabe: DAMASK: the Düsseldorf Advanced MAterial Simulation Kit for studying crystal plasticity using an FE based or a spectral numerical solver. IUTAM Symposium on Linking Scales in Computations: From Microstructure to Macro-scale Properties; Procedia IUTAM 3 (2012) 3 – 10
 P. Eisenlohr; M. Diehl; R.A. Lebensohn; F. Roters: A spectral method solution to crystal elasto-viscoplasticity at finite strains. Int. J. Plasticity 46 (2013); 37 – 53
The occurrence and interaction of multiple deformation mechanisms is the reason for the high formability, ductility and at the same time high strength of the new iron based material system Fe-Mn-C. The goal of this subproject, therefore, is to incorporate the two main deformation mechanisms besides ordinary dislocation glide into an existing crystal plasticity (CP) framework. These mechanisms are the TWIP effect (Twinning Induced Plasticity), i.e. plasticity and hardening by massive formation of twins, and planar slip, which leads to localisation (slip band formation).
In this process the following topics will be treated in view of constitutive modelling and algorithmic implementation into CP-FEM: First, the tensorial formulation of nucleation and growth of mechanical twins in addition to the already implemented slip system geometry; second, the addiction to planar slip; third, the effect of back stresses due to compatibility requirements when forming the twins by means of geometrically necessary dislocations; fourth, the formation of new boundaries by the twins; fifth, the interaction of dislocations with these boundaries. The first two aspects will be formulated in dependence on the stacking fault energy. This will allow the direct incorporation of ab initio calculated values for the stacking fault energy when available.
The elastic modulus and the enthalpy of vacancy migration are additional physical parameters entering the model. The implementation as user subroutine into commercial FE software allows the prediction of mechanical behaviour under complex loads. Besides the homogenised elastic modulus stress strain curves along predefined loading paths as well as parameters for complex analytical yield surface models (e.g. Hill, Barlat) and their development during forming can be obtained as simulation results. In addition the distributions of crystal orientation (i.e. texture), dislocation density and fraction twinned can be specified within a formed part. These values are at the same time used for model validation by comparing them with experimental findings of other subprojects.