Determination of volume fractions of texture components with standard distributions in euler space
- PDF / 514,990 Bytes
- 12 Pages / 606.24 x 786 pts Page_size
- 116 Downloads / 159 Views
2/20/04
11:02 AM
Page 1075
Determination of Volume Fractions of Texture Components with Standard Distributions in Euler Space JAE-HYUNG CHO, A.D. ROLLETT, and K.H. OH 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 g0, 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.
I. INTRODUCTION
A polycrystalline material consists of many crystals with different phases, shapes, sizes, and orientations. For this article, a single-phase, fully dense solid is assumed with uniform chemical composition. The orientations of the crystals or grains in a polycrystal are typically not randomly distributed after thermomechanical processing and the dominance of certain orientations may affect materials properties. The orientation distribution function (ODF, f(g)) in Euler space is the probability density of orientation in a polycrystalline material. The ODF has normalized positive values and there are two limiting cases, i.e., the random distribution and singlecrystal case. The former corresponds to f (g) 1 and the latter is represented by a delta function, f(g) 82(g g0), where the orientations of all crystallites have the same orientation g g0. The summation over the ODF is unity by normalization. Quantitative texture analysis based on pole figures is a kernel problem, and several methods such as the series expansion, the WIMV, and the Vector methods, are used for t
Data Loading...
