Hans Joachim Bunge

Elastic properties of polycrystals—influence of texture and stereology

Abstract The macroscopic elastic properties of polycrystalline materials depend on the elastic properties of the crystallites and the way how these are ‘arranged’ in the polycrystalline aggregate. This comprises the volume fraction of crystal orientations (texture) as well as their arrangement in space (stereology). It is estimated that the stereological aggregate parameters may contribute up to 25% of the maximum texture influence. Model calculations of the effective macroscopic elastic properties were carried out using a grain cluster model which is a finite discretization of the aggregate function g(x) describing the complete ‘orientation-stereology’ of the polycrystalline material. The most important stereological parameters influencing the effective elastic constants are grain shape expressed by two axis ratios, grain packing expressed by the space filling factor of the lattice of grain centres and orientation pair correlation of neighbouring grains expressed by the misorientation distribution function. By rotating the orientation of only one grain it can be shown that grain interaction strains decrease rapidly and may be neglected beyond the second order neighbours.

Texture analysis with high-energy synchrotron radiation

Texture measurement with short-wave X-ray synchrotron radiation in the range of λ ≃ 0.1 A is described. The measurements were carried out with the multipurpose diffraction instrument at the high-field wiggler, high-energy beamline BW5 at HASYLAB. The instrument was equipped with an on-line image-plate area detector for diffraction-image registration and a Eulerian cradle for sample orientation. The particular features of texture measurement with the BW5 instrument are: good resolution in the Bragg angle, extremely high angular resolution in crystal orientation (pole-figure angles) and particularly high penetration depth of several millimetres to centimetres, comparable with that of neutrons but at high spatial resolution. Several examples illustrate the particular advantages of this method for texture studies using large or encased samples (in situ studies in complicated environments, such as cryostats, furnaces, vacuum or pressure chambers, with no serious window problems). This allows, among others, non-destructive texture analysis in technological parts and whole components. Because of the extremely high beam intensity (short exposure times) compared with all other methods of texture measurement, the new technique is particularly suited for the study of large sample series (as is often necessary in industrial applications).

Texture and microstructure analysis with high-energy synchrotron radiation

High-energy synchrotron radiation with wavelengths in the range of 0.1 A is an excellent tool to measure the orientational and spatial distribution of crystallites in polycrystalline materials of any kind. A particular sweeping method for continuous imaging of texture and microstructure with high resolving power is described. In grain-resolved structures, the orientation stereology of the grains can thus be obtained. High-energy synchrotron radiation has penetration depths in most materials comparable with that of neutrons. It is thus very well suited for the study of big samples and for non-destructive testing of complex technological components.

Determination of preferred orientation textures in Al2O3 ceramics

Abstract Strongly preferred orientation textures are observed in some Al 2 O 3 ceramics. In these textures the basal plane is parallel to the sheet plane. Textures of this type can be best represented by the basal plane pole figure, i.e. the c-axis distribution. This pole figure is difficult to measure by X-ray diffraction because of a very low structure factor. It can, however, be calculated mathematically from other measured pole figures. The reliability of this procedure was proved with the help of neutron diffraction. In this latter method the structure factor is high enough to measure the basal plane pole figure directly.

Development of Cross-rolling Textures in AlMn1

True cross-rolling and pseudo cross-rolling (with only one change of the rolling direction after half of the total deformation degree) was investigated in an alloy AlMn1 up to 93% deformation. The texture formation was studied in terms of ODF. After true cross-rolling (multi-stage rolling) a strong two-component ideal orientation near (011)[322] was found with maximum densities up to 60 times random. Pseudo cross-rolling (two-stage rolling) resulted in weaker, but still strong deformation textures with maximum densities up to twenty times random which were intermediate between unidirectional and true cross-rolling textures. In both cases, the originally present cube texture decreased continuously with increasing deformation degree.

Effect of the Grain Shape on the Elastic Constants of Polycrystalline Materials

We examine the influence of the grain shape on the effective elastic moduli of polycrystalline materials. For that purpose the real material is simulated by a cluster of Wigner-Seitz cells. For clarity each aggregate consists of grains with only one type of shape. Therefore we can classify each cluster by the coordination number of its grains. To determine the elastic moduli a homogeneous deformation is subjected to the surface of the cluster. The solution of this boundary value problem yields the average stress and strain governing inside the material whose interconnection by Hookes law leads to the sought-for effective constants.

Development of Cross-rolling Textures in Armco-Iron

ARMCO-iron was cross-rolled in two different modes, i.e. with a rotation of the rolling direction through 90° after each individual pass or after half of the reduction in thickness only. In the first case, which corresponds to a truly tetragonal straight deformation path, the orientation {001}〈110〉 assumes an extremely high orientation density of 50 × random after 93% reduction. Besides this, the texture contains a nearly ideal 〈111〉‖ND-orientation tube, the intensity of which increases to about 10 × random. The texture of the second mode is similar to that of the first one up to about 50% reduction. After that the density in the orientation {001}〈110〉 decreases and increases again at the highest deformation degrees. Two minor orientation components {001}〈100〉 and {011}〈100〉 were found with intensities in the range of 3 to 5 × random at low deformation degrees of about 10%.

MODEL CALCULATIONS OF RECRYSTALLIZATION TEXTURE FORMATION BY GROWTH SELECTION

Model calculations of recrystallization texture formation are carried out on the basis of growth selection according to the 40∘〈111〉 orientation relationship. It is shown that the fastest growing “compromise” orientation depends very sensitively on the nature of the deformation texture components, their relative amount and their spread, as well as on the value of the rotation angle and the spread range of the growth rate law. On this basis the cube recrystallization texture as well as the brass recrystallization texture can be modelled without further assumptions. Also modifications of the recrystallization texture due to modifications of the starting deformation texture are sufficiently described by the model.

Texture - The Key to Physics in Polycrystalline Matter

Physical properties of condensed matter depend on its structure. In polycrystalline matter this comprises crystal structure and aggregate structure. An essential part of aggregate structure is crystal orientation g in each location x of the material i.e. the ideal aggregate function g(x). This function can be measured with modern experimental techniques i.e. location resolved electron diffraction methods. The aggregate function g(x) describes the crystallite orientation comprehensively compared with the statistical orientation distribution function f(g). On the basis of g(x) comprehensive mathematical models of physical properties of polycrystalline matter can be developed. The polycrystalline state of condensed matter can thus be treated on comparable principles as the single-crystalline state. In this sense the texture of material expressed by the comprehensive aggregate function g(x) is the key to physics in polycrystalline matter. A discretization of g(x) is a cluster g i (x i ). This model allows to take grain interactions across grain boundaries into account. As an example the elastic properties are considered here. The function g(x) describes the structure of a sample comprehensively, it is, however, valid only for this one sample. Hence, several generalized textural quantities have been deduced from it which represent statistically relevant parameters for all samples of the same material.

Recrystallization Texture and Microstructure in Ni and AlMg1Mn1 Determined with High-Energy Synchrotron Radiation

The newly developed “sweeping detector” technique with high energy synchrotron radiation allows to measure textures and microstructures of materials with high location and orientation resolution. This method was applied to hot rolled aluminium manganese alloys and to rolled nickel samples in different recrystallization stages. The grain-resolved measurements show, impressively, many details of the recrystallization process which can otherwise not be seen. That can be the base for comprehensive recrystallization theories.