Place: Arbeitskreise Mikrostrukturmechanik im FA Materials Modelling, Simulation and Data Siegen, Germany
Ralf Hielscher, TU Chemnitz, Chemnitz, Germany
The microstructure of polycrystalline metals strongly affects its mechanical properties. Some of the most prominent features of microstructural which capture both the mechanical properties and manufacturing history are grain size and texture. Such materials are usually characterized by diffraction experiments using either X-rays, electron or neutron. With the advancement in the experimental setup and the ease of availability, the characterization of polycrystalline metals with the electron backscatter diffraction (EBSD) has gained popularity. Such experimental data typically contain a large number of data points, which must be significantly reduced to use such orientation distribution sets for numerical modeling. For example in micromechanical modeling, representative volume elements (RVE) of the real microstructure are generated and the mechanical properties of these RVEs are studied by the crystal plasticity finite element method (CPFEM). The challenge in such data reduction is, however, to preserve the main characteristics of the experimental data, while reducing the data volume and thus the degrees of freedom to be dealt with in CPFEM. In the present work, we develop a new method for extracting a reduced set of orientation from experimental data. This approach is based on the established integer approximation, but it minimizes the shortcomings of this method. Furthermore, a well defined error function is introduced, by which the degree of the approximation can be quantitatively assessed, and the convergence behavior can be controlled. This method is implemented in MATLAB using Mtex. The method is tested on 4 experimental data sets and applied to some simple examples to demonstrate its possibilities. With the help of this new method, the purposeful reduction of a set of orientations into equally weighted orientations suitable for numerical simulation, and also shows improvement in results in comparison to the current solutions. Furthermore, to asses, the ability of this method in preserving material properties after reduction, a synthetically generated test case of rolled copper is used. A micromechanical model working in the CPFEM framework is created using the full set of orientations. This model is utilized to calibrate the CP parameters, which are kept constant for all further simulations. The mechanical behavior is represented in the form of a virtual uniaxial tensile test and it is presented in the form of stress-strain flow behavior. This method is utilized to reduce the aforementioned set of orientations, which is then used to generate a micromechanical model. The results are compared with reference flow behavior to check its ability to preserve its ability to predict mechanical behavior after reduction.