Mapping the Crystal Orientation Distribution Function to Discrete Orientations in Crystal Plasticity Finite Element Forming Simulations of Bulk Materials

The crystal plasticity finite element method (CPFEM) is probably the method with the best potential to directly incorporate crystal anisotropy and its evolution into forming simulations. However, when it comes to the simulation of bulk materials, the representation of the crystal orientation distribution function (ODF), i.e. of the statistical texture, within the CPFEM framework becomes a key issue for the efficiency of the approach. In this work two different approaches for sampling the ODF are compared. The first is the so called Texture-Component-CPFEM, where the discretisation is based on the representation of the ODF by texture components. The second approach is based on the representation of the ODF by series expansion and uses a direct mapping of the ODF represented in the form of C-coefficients to individual orientations as needed by the CPFEM. Both methods are compared using the textures of Aluminum hot band as well as cold rolled material.

Generalization of the Concept of Sample Symmetry- Fuzzy Symmetry, Symmetroids, Similarity

The crystal orientation distribution function of polycrystalline materials, i.e. the texture, may exhibit internal symmetries due to symmetries of the production steps, or more generally, to the whole materials history. The “sharpness” of such symmetries can be quantified in terms of various symmetry parameters. If the symmetries of subsequent production processes are different, e.g. of sheet rolling and deep drawing, then these symmetries may still be recognized in the final texture. In the same way also similarities of textures and properties of different materials can be quantified. Symmetry parameters have many practical applications. Examples of that are the determination of rolling direction corrections, determination of the “plastic spin”, estimation of coarse-grained materials, or finding the “correct” (symmetry adapted) axis system in a material.

Calculation of the crystal orientation distribution function from synchrotron radiation experimental data

Series-expansion coefficients for an orientation distribution function (ODF) of cold-rolled aluminium sheet were calculated from the intensity of Debye–Scherrer rings obtained in an experiment using synchrotron radiation. Calculated and observed pole figures demonstrate that a sufficiently good approximation to the ODF is obtained from coefficients calculated to l = 8.