On the Reproduction of the Orientation Distribution Function of Texturized Samples from Reduced Pole Figures Using the Conception of a Conditional Ghost Correction

Practical problems of the reproduction of the orientation distribution function (ODF) from pole figures (PFs) using discrete methods (with special attention paid to Imhof's method,) are analysed A new variant of the iteration method for the determination of the ODF in arbitrarily defined size of cells in the orientation space, is suggested The special case, in which the centro-symmetrical equivalency of the PFs is induced by the elements of proper rotations in crystal symmetry, is considered



Es werden praktische Probleme der Reproduktion der Orientierungsverteilungsfunktion (OVF) aus Polfiguren (PFn) bei Anwendung diskreter Methoden (bei besonderer Beachtung der Imhof Methode) analysiert Eine neue Variante des Iterationsverfahrens fur die Bestimmung des OVF mit einer Wahlfreiheit der Zellengrose im Orientierungsraum wird vorgeschlagen Es wird ein Spezialfall betrachtet, in dem Elemente der eigentlichen Drehungen in der Kristallsymmetrie eine zentrosymmetrische Gleichwertigkeit in den PFn induzieren

Determination of the orientation distribution function from pole figures in arbitrarily defined cells

Using texture components in crystal plasticity finite element simulations

The intensities of texture components are modeled by Gaussian distribution functions in Euler space. The multiplicities depend on the relation between the texture component and the crystal and sample symmetry elements. Higher multiplicities are associated with higher maximum values in the orientation distribution function (ODF). The ODF generated by Gaussian function shows that the S component has a multiplicity of 1, the brass and copper components, 2, and the Goss and cube components, 4 in the cubic crystal and orthorhombic sample symmetry. Typical texture components were modeled using standard distributions in Euler space to calculate a discrete ODF, and their volume fractions were collected and verified against the volume used to generate the ODF. The volume fraction of a texture component that has a standard spherical distribution can be collected using the misorientation approach. The misorientation approach means integrating the volume-weighted intensity that is located within a specified cut-off misorientation angle from the ideal orientation. The volume fraction of a sharply peaked texture component can be collected exactly with a small cut-off value, but textures with broad distributions (large full-width at half-maximum (FWHM) need a larger cut-off value. Larger cut-off values require Euler space to be partitioned between texture components in order to avoid overlapping regions. The misorientation approach can be used for texture’s volume in Euler space in a general manner. Fiber texture is also modeled with Gaussian distribution, and it is produced by rotation of a crystal located at g
 0, around a sample axis. The volume of fiber texture in wire drawing or extrusion also can be calculated easily in the unit triangle with the angle distance approach.

Determination of volume fractions of texture components with standard distributions in Euler space

The evolution of texture in a cold rolled Ti–5Ta–1.8Nb alloy sheet, during the α → β → α transformation has been studied using EBSD and XRD techniques, for different cooling rates. The sheet exhibited a basal plane type texture upon cold rolling, and a sharp ‘{1 1 −2 0}||rolling plane’ transformation texture was inherited after the heat treatment. The microtexture analysis of the lamellar α/β structure, suggested that this transformation texture arises from the {1 1 1}〈1 1 0〉 type of high temperature β texture, obeying the Burgers orientation relationship. The strength of the transformation texture was found to sharply increase with decrease in cooling rates, denoting variant selection. Two types of parent β orientations with [1 1 0] parallel to either rolling directions are possible, and among their α product variants, 3 of them are common, and can be preferentially formed at the prior-β grain boundaries. The role of grain boundary-α in influencing variant selection and the transformation texture for different cooling rates is described in this paper.

Effect of cooling rate on transformation texture and variant selection during β → α transformation in Ti–5Ta–1.8Nb alloy

Describing the ODF of texturized materials by model components quantitative statements about the intensities of the several components can be made. However, depending of the form of the model components and of the chosen χ2-function drastic deviations from the true intensities can appear, which are connected with the metric of the G-space. Lorentz-like standard functions are described and existing fit-strategies are analysed.



Wird die OVF texturierter Materialien durch Modellkomponenten dargestellt, konnen quantitative Aussagen uber die Intensitaten der verschiedenen Komponenten getroffen werden. In Abhangigkeit von der Form der Modellkomponenten und der gewahlten χ2-Funktion konnen jedoch drastische Abweichungen von den echten Intensitaten auftreten, die mit der Metrik des G-Raums in Verbindung stehen. Lorentz-formige Standardfunktionen werden beschrieben sowie die existierenden Fitstrategien analysiert.

S. Matthies

Papers

Form Effects in the Description of the Orientation Distribution Function (ODF) of Texturized Materials by Model Components