Representative reduction of crystallographic orientation data

Abstract

Experimental techniques [e.g. electron backscatter diffraction (EBSD)] yield detailed crystallographic information on the grain scale. In both two-and threedimensional applications of EBSD, large data sets in the range of 10 5 -10 9 singlecrystal orientations are obtained. With regard to the precise but efficient micromechanical computation of the polycrystalline material response, small representative sets of crystallographic orientation data are required. This paper describes two methods to systematically reduce experimentally measured orientation data. Inspired by the work of Gao, Przybyla & Adams [Metall. Mater. Trans. A (2006), 37, 2379-2387], who used a tessellation of the orientation space in order to compute correlation functions, one method in this work uses a similar procedure to partition the orientation space into boxes, but with the aim of extracting the mean orientation of the data points of each box. The second method to reduce crystallographic texture data is based on a clustering technique. It is shown that, in terms of representativity of the reduced data, both methods deliver equally good results. While the clustering technique is computationally more costly, it works particularly well when the measured data set shows pronounced clusters in the orientation space. The quality of the results and the performance of the tessellation method are independent of the examined data set.

Grain scale simulation of local deformation behavior

“…The detailed explanation of the fundamental zone could be found in [10,26]. In Figure 10, the initial crystal orientations of the grains transformed in the fundamental zone are shown.…”

“…Crystallographic texture data allow for the characterization and prediction of the anisotropic plasticity in heterogeneous materials by using statistical models. Some representative studies of different polycrystalline materials with focus on the texture evolution are given, e.g., by [2][3][4][5][6][7][8][9][10]. In the intensive increase of computer powerful tool, modelling and simulation have contributed to predict the mechanical behavior and to facilitate the material design with particular properties.…”

Quantifying the Contribution of Crystallographic Texture and Grain Morphology on the Elastic and Plastic Anisotropy of bcc Steel

“…The orientation information, that is, texture, for the fourth and fifth set of microstructure representation is created in the following way: First, a discrete ODF with a bin size of 5.0°is created from the BUNGE-EULER angle representation of the crystallographic orientations without taking the sample symmetry into account. Second, using the HYBRIDIA method developed by Eisenlohr and Roters [28], the 1000 orientations that best represent the whole ODF are selected (see Reference [29] for a different approach to reduce the orientation data.). A comparison of texture index and entropy using MTEX 4.5.0 by Bachmann et al [30] between the full texture and the selected orientation reveals a good approximation, especially there is no significant sharpening or weakening of the texture when using the approximation by 1000 orientations.…”

Predicting deformation-induced polymer–steel interface roughening and failure

“…The dominant Euler angles and their respective fractions are extracted from the EBSD measurement shown in Fig. 2(b) using the methodology proposed by Jöchen & Böhlke [21]. The representative Euler space (the rotation angles φ 1 , Φ, φ 2 ) is divided into 432 (24 φ 1 , 3 Φ and 6 φ 2 divisions) boxes within which the average Euler angle and fraction is calculated.…”