bluuebunny/crossref_metadata_2025 huggingface dataset:
Coordinate Free Tensorial Representation of the OrientationDistribution Function With Harmonic Polynomials
Authors: Sam David D. , Onat E. Turan , Etingof Pavel I. , Adams Brent L.
Published: April 2008

The crystallite orientation distribution function (CODF) is reviewed in terms of classical spherical function representation and more recent coordinate free tensorial representation (CFTR). A CFTR is a Fourier expansion wherein the coefficients are tensors in the three‐dimensional space. The equivalence between homogeneous harmonic polynomials of degree k and symmetric and traceless tensors of rank k allows a realization of these tensors by the method of harmonic polynomials. Such a method provides for the rapid assembly of a tensorial representation from microstructural orientation measurement data. The coefficients are determined to twenty‐first order and expanded in the form of a crystallite orientation distribution function, and compared with previous calculations.
Texture Analysis of a Zinc Layer on a Steel Substrate Using Neutron Diffraction
Authors: Brokmeier H.-G.
Published: April 2008

This paper describes the application of neutron diffraction to investigate the texture of a zinc layer
8 μm in thickness. In a nondestructive way both the texture of the zinc layer as well as the texture of
the steel substrate were studied. Therefore, pole figures of iron ((110), (200) and (211)) and of zinc
((0002), , ; and /) were measured; additionally the orientation distribution
function of iron and zinc were calculated.
Development of a {111} Recrystallization Texture Associated WithDynamic Strain Aging During Hot Rolling in the Ferrite Region
Authors: Matsuoka Saiji , Sakata Kei , Satoh Susumu , Kato Toshiyoki
Published: April 2008

Hot rolling in the ferrite region is applied in an extra‐low C sheet steel without cold rolling by employing
dynamic strain aging. When the amount of solute C is about 10 ppm before rolling, the r‐value and
{222} intensity ratio of sheet steel annealed after rolling are maxima at the rolling temperature of 773K,
during which dynamic strain aging occurs. The {222} residual strain in the specimen rolled at 773K
is higher than that in specimens rolled at other temperatures. It is proposed that dynamic strain aging
would provide high stored energy in the {111} component of an as‐rolled specimen, with the result
that the region of high stored energy would recover and nucleate rapidly so that a strong {111}
recrystallization texture develops.
Review of Deterministic Methods of Calculation of PolycrystalElastic Constants
Authors: Morawiec A.
Published: April 2008

The paper is a critical review of non‐stochastic (referred here as deterministic) methods of calculation
of effective elastic constants of single phase statistically homogeneous polycrystals. The methods are
briefly described. They are compared and grouped according to their basic assumptions. Their degree
of generality is discussed. The analysis of their compliance with formal requirements is provided.
Moreover, the possible but unknown completions and generalizations of some methods are considered.
For most methods, example calculations are carried out for a special case of quasi‐isotropic aggregate
with cubic crystal symmetry. To make the paper self‐contained, well‐known essentials of the problem
of effective constants are included.
On the Numerical Determination of Optimal Textures of Aluminium
Authors: Burgholzer P. , Scherzer O.
Published: April 2008

In this paper a mathematical algorithm is studied to improve the deep‐drawing quality of an aluminium
sheet. The deep‐drawing quality is usually expressed in terms of the normal anisotropie. In our
mathematical model we use Taylor theory and ideal orientations to reformulate this problem as a
nonlinear optimization problem for the normal anisotropie. Some numerical examples are presented.
Grain Axes Coincidence Model: Relaxed Constraints and FiniteStrains Revisited
Authors: Bolmaro R. E.
Published: April 2008

The problem of the kinematics of grain reorientation in polycrystalline plasticity has been addressed
many times in the past. A particular grain and the matrix in which that grain is embedded must deform
guaranteeing compatibility if no debonding or failure are allowed. This requirement is satisfied by the
condition of keeping the main axes of the grain and the hole lodging that grain collinear and of the
same size during the whole deformation process. It is not clear yet which one of the many definitions
of spin should be considered and how the Taylor model is reproduced for nearly round crystals. The
problem is directly connected with spin definitions in continuum mechanics and finite strains. The present
paper will be concerned with a rigorous treatment of the many spins and rotations that affect a grain
in a polycrystal. It will also be shown that this new treatment suggests a new kind of constraint relaxation
that, unfortunately, can not be calculated “a priori” with complete ignorance of the kinetics. However
some textures can be simulated. The Los Alamos Polycrystal Plasticity code was modified in order
to allow relaxation of some strain components while keeping the reorientations less than a prescribed
limit. The resultant textures show the same pattern but different strength than the ones obtained under
Taylor assumptions. This Grain Axes Coincidence Model (GACM) has both the Taylor and the Relaxed
Constraints and Self Consistent models as natural limits for round and very flat grains respectively.
It is shown that the constraint relaxation concept that comes out from the GACM is qualitatively different
from the usual in RC and SC models. Strain path changes under the new assumptions are also discussed.
Prediction of Forming Limit Diagrams of Al‐Mg Rolled Sheets TakingTexture Into Account
Authors: Ratchev P. , van Houtte P. , Verlinden B. , de Smet P. , Neutjens P. , Baartman R. , Drent P.
Published: April 2008

Forming limi diagrams of an AA5754 Al‐Mg alloy have been calculated, taking the sheet texture into account. An approach based on the Marciniak‐Kuszynski defect model for calculating forming limit diagrams (FLD’s) has been used. The influence of different initial parameters on the formability curve has been studied. The influence of different ideal texture components on simulated curves has been investigated as well. A comparison between the simulated and the measured FLD is given and critically discussed.
Texture Evolution During the Drawing of Low Carbon Steel
Authors: Schuman C. , Esling C. , Philippe M. J. , Hergesheimer M. , Jallon M. , Lefort A.
Published: April 2008

This study deals with the texture evolution during drawing of interstitial‐free low carbon steels under
different conditions to study the possible influence of the drawing direction, deformation rate and metal/die friction coefficient. The drawing has been carried out without intermediary annealing, with constant die angle and deformation rate per pass. In all cases, a 〈110〉 fibre texture has been observed at the early stage of deformation (a few percents). The drawing direction, whether alternate or unidirectional, has little effect on texture. Slight differences only in the intensity of peaks on pole figures (PFs) are noted. Alternate drawing leads to higher drawing limits. The grain size affects both the texture and the mechanical properties, which are improved by fine grains. For industrial drawing, i.e. at a high deformation rate, no texture gradient has been clearly observed. Nevertheless, slight differences have been noted in the PF intensities, with generally a slightly sharper texture in the core, compared to the surface. The microhardness tests show no hardness gradient. In slow drawing (low deformation rate), there is a weak texture gradient which disappears at larger deformation. In order to visualize the influence of the metal/die friction, we used a material covered with copper. Results show that at a given reduction rate, the material covered with copper shows peak intensities on the (110) PF which are half these of a material drawn under conventional conditions. The drawing textures of BCC materials always present
a 〈110〉 fibre texture. A modeling of the texture evolution during drawing has also been carried out
using the Taylor model.
Model Calculations of Plastic Deformation of Two‐Phase MaterialsWith Fibre Structure
Authors: Bunge H. J. , Böcker W.
Published: April 2008

Plastic flow in two‐phase fibre composites during axially symetric deformation is modelled assuming
homogeneous deformation of the fibres of the harder phase and inhomogeneous flow in the softer matrix.
The distribution of flow between fibres and matrix is described by the deformation ratio α which follows
from the assumption of minimum deformation work. The main features of the model agree quite well
with experimental results obtained in several powder metallurgically prepared two‐phase composites.
Transformation Texture Analysis of BCC and BCT Ferrous Martensite
Authors: Miyaji Hirofumi , Furubayashi Ei-Ichi
Published: April 2008

The theoretical prediction of transformation textures, that developed in thin sheet without external stress,
was carried out based on the Bain‐Strain and Twinning‐Shear model, respectively. To examine the
validity of the prediction, the experiments were conducted with X‐ray pole figure method on Fe‐30Ni
and Fe‐30Ni‐0.8C alloy sheets. The results obtained are as follows:

(1) Variant selection phenomenon depends on the crystal orientation of the parent phase and on the Bain strain in the martensitic transformation.

(2) The effect of the anisotropic constraint stress on the shear deformation involved in the lattice
change and on the Bain distortion appears most remarkably in the BCT martensite transformed
from the cube textured parent phase.

(3) It became clear that such a variant that has the largest Bain strain component to the sheet normal,
that is, the variant, of which the Bain distortion is prevented least of all by the anisotropic constraint
stress, forms predominantly.
A New Approach to Describing Three‐Dimensional OrientationDistribution Functions in Textured Materials–Part I: Formation of Pole Density Distribution on Model Pole Figures
Authors: Dnieprenko V. N. , Divinskii S. V.
Published: April 2008

New method for simulation of orientation distribution functions of textured materials has been proposed. The approach is based on the concept to describe any texture class by a superposition of anisotropic partial fibre components. The texture maximum spread is described in a “local” coordinate system connected with the texture component axis. A set of Eulerian angles γ1,γ2,γ3 are introduced with this aim. To specify crystallite orientations with respect to the sample coordinate system two additional sets of Eulerian angles are introduced besides γ1,γ2,γ3. One of them, (Ψ0,θ0,ϕ0), defines the direction of the texture axis of a component with respect to the directions of the cub. The other set, (Ψ1,θ1,ϕ1), is determined by the orientation of the texture component and its texture axis in the sample coordinate system. Analytical expressions approximating real spreads of crystallites in three‐dimensional orientation space have been found and their corresponding model pole figures have been derived. The proposed approach to the texture spread description permits to simulate a broad spectrum of real textures from single crystals to isotropic polycrystals with a high enough degree of correspondence.
Texture Evolution During the Biaxial Stretching of FCC SheetMetals
Authors: Zhou Y. , Neale K. W.
Published: April 2008

Using a rate‐sensitive crystal plasticity model together with the full constraint Taylor theory, the
formation of textures during biaxial stretching of FCC sheet metals is investigated in detail. Three‐dimensional
lattice rotation fields, orientation evolution and polycrystalline texture development are
simulated for the entire range of biaxial strain ratio. The investigation discloses the paths of orientation
development and respective stable end orientations, as well as the relation between the evolution paths
and the biaxial strain ratio. Our results show that the formation of textures depends mainly on the
behaviour of the α‐ and βρ fibres in biaxial stretching. The strain ratio affects the composition of the βρ‐fibre, as well as the flow direction and velocity of orientations towards and along α and βρ, and thus results in different biaxial‐stretching textures. The predictions of FCC biaxial‐stretching textures are compared with experimental observations reported in literature. Finally, we discuss the influence of complex strain paths on texture formation.
Examination of the Iterative Series‐Expansion Method for Quantitative Texture Analysis
Authors: Raabe D.
Published: April 2008

Three‐dimensional orientation distributions of grains in polycrystalline aggregates are referred to as
crystallographic textures. Commonly, they are computed from two‐dimensional centro‐symmetric pole
figures by employment of series expansion techniques or so called direct inversion methods. Both
approaches lead to inaccuracies which are due to the absence of the odd coefficients and by truncation
errors in the first case and to the under‐determination of the set of linear equations combining cells
in the pole figures and in the three‐dimensional orientation space in the second case. For both types
of calculation methods various correction procedures were suggested. In case of the series expansion
methods the introduction of the non‐negativity condition was reported to considerably improve the
obtained solution. However, before large series of experimental data can be processed by such a method,
its reliability has to be checked by use of analytical tools. Hence, in the present study a recently
introduced iterative series‐expansion method which accounts for the non‐negativity condition is
examined by use of standard functions.
Group‐Theoretical Approach to Reduced Orientation Spaces for Crystallographic Textures
Authors: Yashnikov V. P. , Bunge H. J.
Published: April 2008

A unified group‐theoretical approach to the reduction problem for the orientation space of a
crystallographic texture is developed. After preliminary considerations of the three‐dimensional rotation
group SO(3) the concept of the invariant inner distance function in the group space has been introduced.
Left and right group translations, inner auto‐morphisms, motions of general form, and inversion
transforms in the space SO(3) are analysed. The concept of Dirichlet‐Voronoi partition dual to an
arbitrary finite set of rotations has been considered. It is shown that the Dirichlet‐Voronoi partition,
dual to the proper point group for the grain lattice of original orientation, is regular with respect to
the group of motions generated by elements of proper point group.

It is demonstrated that the true orientation space of a texture (at the absence of specimen symmetry)
may be obtained by passing to the topological closure of any Dirichlet‐Voronoi domain with the next,
identifying crystallographically equivalent rotations belonging to its topological boundary. Thus an
invariant derivation for the reduced (true) orientation space is given that does not require using any
particular parametrization for the group space SO(3).

Symmetry properties of Dirichlet‐Voronoi domains are studied in conclusion. It is shown that any
domain of such kind admits a finite group of symmetries generated by elements of a proper point group
and by an appropriate inversion of the group space SO(3). It is proved that only part of them may
be extended onto the true orientation space.
Investigation on the Texture of an ELC‐BH Sheet With Very High R−‐Value Processed by New Technology
Authors: Xiaojun Guan , Xianjin Wang , Qiulin Wu , Xiaojun Hu
Published: April 2008

The texture of an extra low‐carbon and high strength bake‐hardening sheet steel (i.e. ELC‐BH sheet)
processed in our laboratory through a new invented technology has been investigated by means of
ODF method, so that the cause of the very high ‐value of this sheet has been discovered. Experimental results are shown as follows: ① The ‐value of the experimental sheet treated by the new process is as high as 2.67 and this is the highest ‐value published so far for phosphorus – added high strength and deep drawing sheet steels. At the same time, the contradiction between deep‐drawability and
strengthening is successfully solved too. ② A nucleus of the new technology is supplying a good cold rolled parent state which benefits to the development of {111} annealing textures through controlling texture, while strong development of {111} annealing textures can cause very high ‐value. ③ The cold rolling and annealing texture obtained by the new technology are quite different as compared with that of conventional process. New cold rolling texture has stronger {111} components and weaker {100} components than conventiopnal cold rolling texture. The concentrations of {111} components of new annealing texture are not only distinctly general increase but also the crystal orientations corresponding to the peak values of orientation concentrations of the texture have been also changed from conventional orientations to orientations.
Effect of Crystal Rotation on Limit Strains of Textured Materials Under Equi‐Biaxial Tension
Authors: Chan K. C.
Published: April 2008

In this paper, a numerical procedure has been proposed to predict limit strains of textured sheets under
equi‐biaxial tension by means of the MK model and taking into account of crystal rotation. Limit
strains have been predicted for three common crystallographic orientations and an annealed aluminium
sheet. The effect of crystal rotation on limit strains was shown to be significant. However, no general
trend of the effect has been observed. It is argued that the effect is quite complicated and dependent
on various factors such as the initial orientation or texture, groove orientation and the initial
inhomogeneous factor. The incorporation of texture change in the analysis of sheet metal forming was
found essential.
Characterization of Microstructure and Texture of a Titanium Alloy Corona 5
Authors: Benhaddad S. , Quesne C. , Penelle R.
Published: April 2008

Both parameters, microstructure and texture, are studied on several samples for different processes.
The same route, thermomechanical treatment (forging or rolling) followed by solutioning and ageing
is carried out with various temperature and deformation amount on an identical titanium alloy CORONA 5.

According to three temperature fields: low (α + β), β and high (α + β) three important microstructures are obtained: equiaxed, acicular and bimodal.

All measured textures present two components which vary with deformation mode and temperature of both forging and solutioning.
Influence of the Initial Grain Size on the Rolling and Recrystallization Textures in the Alloy Al‐1.8% Cu
Authors: Engler O.
Published: April 2008

The influence of the initial grain size prior to deformation on the rolling and recrystallization textures is investigated in the alloy Al‐l.8wt%Cu by X‐ray macrotexture analysis. Two different particle stages are examined: (i) Small shearable precipitates give rise to shear band formation and, during annealing, to nucleation of recrystallization at shear bands. (ii) Large particles cause particle stimulated nucleation of recrystallization (PSN). The microstructural evolution, particularly during recrystallization nucleation, is elucidated by metallographical investigations supported by EBSD local texture analysis.

Both the initial grain size and the precipitation state strongly influence the evolution of the rolling textures. The results are interpreted with the help of Taylor‐type deformation models. The recrystallization textures of Al‐alloys emerge from a superposition of the orientations stemming from the various nucleation sites, i.e. Cube‐bands, shear bands and particles. An increase of the initial grain size prior to deformation substantially shifts the recrystallization texture from the Cube‐orientation towards the orientations being attributed to the other nucleation sites (shear bands, particles) which is interpreted by the spatial density of the various nucleation sites.
Textures in Ceramics
Authors: Bunge H. J.
Published: April 2008

The texture is defined as the orientation distribution of the crystallites in a polycrystalline material.
This definition is the same for all kinds of materials. Also the motivation for texture studies is the
same in all materials i.e. the formation of textures by anisotropic solid state process and the influence
of textures on anisotropic physical or technological properties. Nevertheless, there are some differences
in detail between texture analysis in metals and ceramics. These are mainly due to the more complex
nature of diffraction diagrams of ceramics as compared to those of the basic metals. The aggravations
of texture analysis in ceramics can, however, be overcome by modern experimental techniques e.g. by
using a position sensitive detector. Texture analysis in ceramics has also been carried out by
microscopical methods. The so obtained “shape texture” is related to the crystallographic texture by
a “habitus” function. The particular conditions for texture analysis in cermics are very similar to those
encountered in geological materials.
Textures in Pure Shear Deformed Rock Salt
Authors: Skrotzki W. , Helming K. , Brokmeier H.-G. , Dornbusch H.-J. , Welch P.
Published: April 2008

Texture formation in pure shear deformed rock salt has been studied by neutron diffraction. The
textures developed are comparable to those of rolled face‐centered cubic metals with high stacking
fault energy. At room temperature the texture consists of a strong S and copper and a weaker brass
component. It is replaced by static and/or dynamic recrystallization by a strong cube and a subordinate
Goss component. Comparison of the experimental textures with simulations based on different models
shows that the low temperature high strain deformation texture can be qualitatively well explained
by the Taylor model using slip on {110}〈110〉, {100}〈110〉 and {111}〈110〉 systems with equal
critical resolved shear stresses. Relaxation with increasing temperature introduces the cube and Goss
component, which may represent the nuclei for recrystallization. The study shows that texture
simulations on salt without considering recrystallization lead to misleading conclusions.
Texture in Aluminum Titanate Ceramic Materials
Authors: Schmalzried C. , Kim J.-W. , Hennicke H. W.
Published: April 2008

Dry pressing and filtration of a mixture of platelike corundum and rutile powders shows a slight to
sharp texture of the corundum particles. The reaction sintering forming aluminum titanate destroys the
texture of the green compact. When starting with a rutile texture in the green compact there exists a
texture of tielite in the reaction product. Furthermore we developed a process for production of platelike
tielite monocrystalline particles which should be very suited for texturing of the ceramic material.
Texture Formation in a Glass Ceramic of Li2O · 2SiO2 Composition
Authors: Engel Katja , Frischat Günther Heinz
Published: April 2008

Glass ceramics of the composition Li2O · 2SiO2.were prepared with an oriented microstructure. The
oriented crystalline phase is orthorhombic lithium disilicate. This orientation was achieved by
crystallization of glass fibers and bulk glasses in a temperature gradient and under isothermal conditions.
Both bulk and surface crystallization were achieved. Further, oriented crystalline films were prepared
on glassy and crystalline substrates by a sol‐gel method. Scanning electron microscopy and atomic force
microscopy were used to characterize the microstructure. The degree of orientation was investigated
by X‐ray pole figure measurements from which orientation distribution functions and inverse pole figures
were calculated. The (002) plane of the surface crystallized material shows a strong fiber texture parallel
to the surface of the sample.
On the Influence of Cross‐Rolling on Shear Band Formation and Texture Evolution in Low Carbon Steel Sheets
Authors: Huh M. Y. , Engler O. , Raabe D.
Published: April 2008

In order to understand the influence of the crystallographic texture and the dislocation structure on the deformation mechanism in low carbon steels, the development of the texture and the microstructure in cross‐rolled specimens was investigated by employing X‐ray texture measurements and TEM observations. The cross‐rolled specimens were obtained by rotating the rolling direction by various angles up to 90° after 30% initial straight‐rolling of the hot rolled band. Whereas only few shear bands were found in the straight‐rolled specimen even after heavy deformation, in the cross‐rolled specimen shear bands were often found at reductions in excess of 60%. This observation is discussed in terms of the rotation of the arrangement of dislocations and microbands during cross‐rolling. The rolling textures observed in the various samples were interpreted by means of Taylor type deformation models.
Texture Development in Gypsum During Crystallisation
Authors: Vogel D. , Jacobi H. , Follner H. , Klein H.
Published: April 2008

Gypsum was set on polyethylene foil of different origin and on cellophane foil. Experiments were
also carried out in an electric field (5‐25 kV direct‐current). In all cases (especially in the electric
field) (010) textures developed on the contact surfaces and were overlapped by a (121) texture. Brinell
hardness tests show a greater hardness of the contact areas than those of the upper sides of the samples.
Those samples set in an electric field yielded, partly, greater differences. The values, however, diverge
greatly.
Textures of Silver‐Halide Infrared Fibres
Authors: Böcker W. , Brokmeier H. G. , Bunge H. J.
Published: April 2008

Fibres consisting of a silver chloride core, a silver bromide cladding and a metallic silver coating were produced by co‐extrusion followed by wire drawing and annealing. In most cases the core material was initially single crystalline. Together with the different flow stresses of core and cladding this may lead to inhomogeneous, non‐axially symmetric flow. Particularly it may lead to a non‐circular shape of the boundary between core and cladding which must be avoided when the fibres are to be used as infrared light conductors.

The deviation from axially symmetric flow was studied with the help of texture investigations using neutron diffraction. The high penetration depth of neutrons allows the simultaneous measurement of the textures of all three phases of the composite fibres. Using neutron diffraction texture analysis as a sensitive flow indicator, coated “core‐cladding” as well as “graded” fibres with sufficient axial symmetry could thus be obtained. The fibres are well suited as infrared light conductors.
The Incorporation of Texture‐Based Yield Loci Into Elasto‐Plastic Finite Element Programs
Authors: Van Houtte P. , Van Bael A. , Winters J.
Published: April 2008

Elasto‐plastic finite elements (FE) methods are nowadays widely used to simulate complex metal forming processes. It is then useful to generate an anisotropic yield criterion from the crystallographic texture and incorporate it into such model. The theory of dual plastic potentials (one in strain rate space and one in stress space) helps to achieve this. There is however a certain danger of losing the convexity of the yield locus during this procedure. Examples of this phenomenon are given and discussed. It is furthermore explained how the yield locus can be used to generate an elasto‐plastic modulus for implementation in the FE code. Finally several examples of successful applications of the anisotropic FE code to metal forming problems are given.
Texture and Microstructure Development in Al2O3‐Platelet Reinforced Ce‐ZrO2/Al2O3 Laminates Produced by Centrifugal Consolidation
Authors: Roeder Ryan K. , Bowman Keith J. , Trumble Kevin P.
Published: April 2008

A dispersed, low‐solids‐fraction suspension containing Ce‐ZrO2, fine Al2O3 and 5 vol% Al2O3‐platelets
was segregated using centrifugal consolidation to produce functionally gradient laminates (FGLs).
Platelet alignment facilitated efficient packing of highly anisometric platelets to high densities. The
complexity and anisotropy of the microstructure warrants a quantitative analysis of the microstructural
evolution prior to any property evaluation. Quantitative image analysis was used to examine changes
in the volume fraction, dimensional anisotropy, and gradient of pores and platelets with sintering time.
In all cases, special attention was given to the effects of texture during microstructural evolution. Platelet
alignment enhanced densification via anisotropic shrinkage, overcoming constraint that otherwise inhibits
densification in platelet‐containing materials. Also, platelet alignment and microstructural design were
used to initiate and control anisotropic grain growth. Platelet growth (at the expense of smaller particles
of the same phase) during annealing promoted further phase segregation and produced higher platelet
content composites consisting of larger platelets, without having to consolidate high contents of large
platelets.
Axisymmetric Textures in Alumina
Authors: Medendorp, Nicholas W. , Kruger Keith L. , Bowman Keith J. , Jensen Dorte Juul , Sørensen O. Toft
Published: April 2008

The occurrence of axisymmetric textures prevails over a wide range of processing approaches for
alumina‐based materials. Mechanisms ranging from dislocation slip, recrystallization, anisometric grain
rotation and grain growth all can contribute to the development of textures with similar characteristics.
This paper documents neutron texture measurements of axisymmetric textures in hot‐pressed, hot‐forged
and tape‐cast alumina. Strong basal textures were introduced in the tape‐cast samples during long term
annealing in finer, non‐tabular aluminas if glass and dopant additions are introduced. The implications
of these results versus prior reports of textures in alumina and alumina matrix composites are discussed.
Some Physical Errors of X‐Ray Texture Measurements
Authors: Perlovich Yu.
Published: April 2008

Typical experimental situations of texture measurements are demonstrated involving failure to take into
account some physical factors responsible for an inadequate texture description or imaginary texture
changes. Among these factors there are inevitable texture inhomogeneities, inhomogeneous distribution
of defects in deformed metal materials and resulting inhomogeneous lattice perfection by their heat
treatment. It is shown that a formal approach to texture analysis does not allow to reveal a number
of important regularities of structure formation.
A Brief Survey of Spherical Interpolation and Approximation Methods for Texture Analysis
Authors: Schaeben H.
Published: April 2008

In texture analysis there are several instances when mathematical methods of spherical interpolation
or approximation are required. Ad hoc adaptions of univariate or bivariate methods to the topology
of spherical manifolds usually fail in one way or another. Therefore, this contribution will provide
a brief survey of genuinely spherical methods.
Elastic Properties of Statistically Equivalent Materials With Varying Individual Grain Orientations
Authors: Kiewel H. , Bunge H. J. , Fritsche L.
Published: April 2008

The elastic properties of copper metal with different individual grain orientations exhibiting the same
texture are determined. We simulate the real material by two different types of clusters. The first one
consists of 365 cubic grains, the second cluster is an arrangement of 181 Wigner‐Seitz cells of a body
centred cubic (bcc)‐lattice. For each type of cluster we let the local grain orientations vary. The
displacement field inside these aggregates as a result of a homogeneous deformation acting on the
surface of the clusters is calculated. Although the resulting local deformation field for different individual
grain orientations varies strongly, the macroscopic elastic moduli are in the frame of this simulation
identical for any cluster of the same type, as it has to be for statistically equivalent materials.
Preferred Orientations of Mica Bearing Rocks Described by Texture Components
Authors: Helming K. , Schmidt D. , Ullemeyer K.
Published: April 2008

Up to now Texture investigations of phyllosilicates were restricted to pole density measurements of
the (001) basal plane. Because of the tabular grain shape parallel to the basal plane an axial symmetry
of the texture is assumed usually. This assumption was proved for four mica bearing samples by
calculating the ODF from neutron diffraction data. Beside the mica‐texture the textures of the other
major fractions like quartz and feldspar were determined to detect correlation between them. The
textures are explained by components. Each component is characterised by a preferred orientation or
fibre axis, a corresponding spreading and an intensity Iʿ describing the volume fraction of all crystallites
belonging to the component. The presented component method can be applied to any crystal symmetry
and to polyphase materials with overlapped pole figures.
Moment Pole Figures in Residual Stress Analysis
Authors: Matthies S.
Published: April 2008

The basic formulas (Reuss′s approximation) for residual stress analysis are given in a revised form.
All ODF‐burdened information reduces to five “moment pole figures” simply to, calculate using modern
direct algorithms. The corresponding harmonic expressions are also more compact than other formulas
known from literature. For texture components described by Standard Gaussian Functions the
corresponding expressions can be given in an analytically closed form. The use of the concept of
the geometrical mean approximation for calculating elastic constants (avoiding Reuss′s limitations)
will be explained in connection with the determination of residual stresses.
Textures of Phases in Al2O3 ‐ ZrO2 (Y2O3) Eutectic Composites
Authors: Gnesin B. A. , Starostin M. Yu.
Published: April 2008

Crystallograhic textures of phases in eutectics Al2O3 + ZrO2 (Y2O3) were investigated by means of X‐ray diffraction. In all studied eutectic polycrystalls (grown from the melt by EFG technique) a
preferred orientation [0001] of Al2O3 along the growth direction in all the samples was revealed for
both initial orientations of Al2O3 seeding crystal:
<0001> and <1011>. For a cubic ZrO2 there were
two types of a preferred orientations: sharp ones, close to <123> with a 6‐fold symmetry and more
spread <110>. Such a 6‐fold symmetry for a cubic phase appears in eutectic due to a joint crystallization.
Statistical Methods for Property Calculation of Textured Materials
Authors: Shermergor T. D.
Published: April 2008

Statistical methods for calculating the effective static and dynamic characteristics of textured
microheterogeneous materials such as polycrystals, composites and rocks are considered. Effective static
characteristics based on the example of the elastic modules tensor are analyzed. Effective dynamic
characteristics based on the example of the dielectric permeability tensor in calculating the scattering
factor, phase and group velocities of the propagation of plane electromagnetic waves are presented.
On the Possible Mechanisms of the Formation of Piezoelectric Active Rocks With Crystallographic Textures
Authors: Nikitin A. N. , Ivankina T. I.
Published: April 2008

The volume piezoelectric effect in polycrystalline rocks occurs if, in addition to preferred orientations
of electric axes of crystals, these axes have orientational polarity. The present paper allows conclusions
about some peculiarities of the processes and mechanisms leading to the formation of texturized rocks
with piezoelectric properties. Information on the textures of rocks with peizoelectric activity was
obtained by means of neutron diffraction, which gives the most complete information on the textures
of large polycrystalline samples. These data, in combination with sample electrometric measurements,
make possible the explanation of, for example, how the electric axes of quartz grains aligned in
polycrystals. Three practicable mechanisms are suggested.
Physical Versus Mathematical Aspects in Texture Analysis
Authors: Bunge H. J.
Published: April 2008

Texture deals with the orientational aspects of the crystal lattice in polycrystalline aggregates. This
comprises the classical orientation distribution function ODF as well as higher‐order textural quantities.
The quantitative treatment of these quantities requires a good deal of mathematical methods. This
concerns particularly the representation of orientation data including all kinds of symmetries, the
transformation of experimentally measured raw data into the required distribution functions, as well
as mathematical models of texture formation by physical processes and of the texture‐property
relationship.

When physical facts are idealized in terms of a mathematical description or by mathematical models
then the physical limits, within which these are valid, must be known. Such physical limits are, for
instance, definition of crystal orientation by the crystal lattice which leads to an unsharpness relationship
between location and orientation resolution as well as a relationship between statistical relevance and
angular resolving power. Other physical limits are given by the “fuzzyness” of sample symmetry. A
central problem is pole figure inversion i.e. the inversion of the projection equation. This problem may
have a “physical” solution even if it does not have a mathematical one. Finally, in the problem of
rationalizing orientation distribution functions in terms of a low number of “components”, mathematical
aspects may be quite different from physical ones.

In all these problems it is thus necessary to keep the mathematical aspects apart from physical aspects.
Multiple Pole Figure Extraction from Pulsed White Beam Angle‐Dispersive Neutron Diffraction Data
Authors: Jansen E. , Schäfer W. , Kockelmann W. , Will G.
Published: April 2008

The continuous wavelength spectrum available at pulsed neutron sources and the use of a position sensitive detector can drastically reduce the number of sample orientations during pole figure scanning compared to the conventional method using monochromatic neutrons. This advantage has to be paid for by a more complex way in extracting pole figures from the measured data. The paper describes the experimental setup, the scanning procedure and the data evaluation of neutron diffraction texture measurements at a spallation source. A multitude of individual pole figures can be measured simultaneously within a reasonable time. The paper focuses on strategy and practical management to obtain pole figures from two‐dimensional time‐of‐flight diffraction patterns.
Analysis of Crystallographic Texture in Small Sample Areas
Authors: Helming K. , Rauschenbach B. , Schwarzer R. A.
Published: April 2008

The description of texture by means of a small number of components (preferred orientations) is an exceptionally concise method. It may reveal relevant information about the texture modifying process
even in those cases where the texture information, contained in the experimental pole figures, is rather limited. Some examples for texture estimates and interpretation of local textures in thin layers (SiC films synthesized by carbonization of silicon with fullerenes) and bulk materials (shear bands in brass and titanium) are presented.
On Sub‐Structure and Texture Development in Warm Rolled Copper
Authors: Lim E. C. H. , Duggan B. J.
Published: April 2008

Preliminary results on the effects of rolling strain rate and deformation temperature on warm rolled
copper are presented. It is shown that in single pass rolling the textures are less intense than those
produced by homogeneous rolling over the temperature range 30℃–500℃. Deformation banding is
present in homogeneous rolling at room temperature and in single pass rolling at 500℃ and is drastically
reduced in single pass rolling at 30℃–350℃. The results are discussed in terms of slab widening, rate
and temperature effects on slip processes.
Neutron Texture Investigations on Natural Mt. Isa Chalcopyrite Ore–Part I: Preferred Orientation of one and the Same Chalcopyrite Sample Before and After Experimental Deformation
Authors: Jansen E. M. , Brokmeier H.-G. , Siemes H.
Published: April 2008

Natural chalcopyrite samples from Mt. Isa, Australia were axially shortened with a constant strain rate
of 3 · 10−5sec−1, at a constant confining pressure of 300 (400) MPa and at different temperatures. Neutron
diffraction texture analyses were carried out before and after experimental deformation on one and the
same sample. The preferred orientation of the experimentally undeformed samples consists of three main
orientation components, which become weaker with deformation at temperatures up to 200℃. One or
two new components develop with the c‐axes perpendicular to the principal strain direction. At a
deformation temperature of 300℃ two very different new components develop, the original components
are completely dissolved.
Variational Micro‐Macro Model and Deformation Textures Predicted for Steels
Authors: Arminjon Mayeul , Imbault Didier
Published: April 2008

This variational micro‐macro model is presented in the context of the “pure” and “relaxed” Taylor
models, from which it evolved, but also in relation to the Sachs‐type models and, more generally, in
the context of volume‐fraction or “one‐point” models. It will indeed be shown that any one‐point model
must set statistical assumptions and that, to this general frame, the present model adds only one essential
assumption‐ namely a plausible principle of minimal inhomogeneity. The numerical implementation is
summarized. Predictions for the strain distribution are discussed. Predicted deformation textures are
compared with measurements on steel sheets.
A Technique to Determine the Relative Strengths of Deformation Mechanisms in Hexagonal Materials
Authors: Tóth L. S. , Serghat M.
Published: April 2008

A new technique is presented which permits to obtain the relative critical strengths of the slip and
twinning systems in polycrystalline materials. It consists in an experimental and a simulation part. In
the experience, slip line analysis and grain orientation measurements are carried out and the operating
slip and twinning systems are identified in each selected grain. In the subsequent simulations, a crystal
plasticity code is used to modelise the plastic behaviour, especially, the slip activity of the grains. The
relative crss values of the slip systems are then varied and the simulations are repeated iteratively until
the experimental slip activity is reproduced with the very same combination of crss for all the grains.
An application is presented for a Titanium alloy (Ti40).
Orientation Selection During Static Recrystallization of Cross Rolled Non‐Oriented Electrical Steels
Authors: Kestens L. , Jonas J. J. , van Houtte P. , Aernoudt E.
Published: April 2008

Very sharp deformation textures, with single maxima of more than 50x random centred on the rotated
cube component ({001}<110>), were produced by submitting a non‐oriented electrical steel sheet to various sequences of cross‐rolling. The cold rolled sheets were subsequently annealed at 730ºC for 3 min. The resulting recrystallization textures were much weaker than the cold rolling textures, displaying
maxima of about 5x random at locations some distance away from the {001}<110> cross rolling
component.

Due to the very sharp character of the rolling texture, the conventional low and high stored energy
nucleation mechanisms were effectively prevented from operating. Thus orientation selection could only
take place by the selective growth of nuclei external to the dominant rolling component. Quantitative
analysis of the experimental ODFs revealed that the rolling and recrystallization components are related
by Σ27 (31.6º<110>) and Σ7c (38.2º<111>) coincidence site lattice (CSL) orientation relations.
Simulations of the annealing texture on the basis of random nucleation and combined Σ27‐Σ7c selective
growth produced reasonable agreement between the predictions and the experimental results.
Recrystallization Texture of Plane Strain Compressed Aluminum Single Crystal
Authors: Lee Dong Nyung
Published: April 2008

Butler, Blicharski and Hu found a rotated cube recrystallization texture after annealing an aluminum
crystal with the (112) and (112) deformation texture, which was obtained by plane strain
compressing the aluminum single crystal with an initial orientation of (001)[110]. The unexplained
formation of the rotated recrystallization has been discussed based on a recrystallization model
recently suggested by the present author.
The Effect of Particles on Recrystallisation Textures and Microstructures
Authors: Vatne Hans Erik , Benum Steinar , Daaland Ole , Nes Erik
Published: April 2008

The way in which large and small particles influence on recrystallised grain size and texture is considered
with special emphasis on the processing of aluminium. It is well known that large particles might induce
nucleation of recrystallised grains, while finely dispersed small particles will exert a pinning force on
boundary movement. It the present paper, these two effects of particles will be discussed in detail. The
discussion will to some extent be in an overview form, but also new ideas and recent experimental
results will be presented. These include cases where strong effects are caused by small precipitated
particles.
Ultrasonic Characterization of Rolling and Recrystallization Textures in Aluminum
Authors: Anderson A. J. , Thompson R. B. , Bolingbroke R. , Root J. H.
Published: April 2008

Crystallographic texture, which plays an important role in many forming operations, is developed during sheet metal processing. Improved product quality could be achieved if the texture could be measured, quickly and inexpensively, during different stages of the processing. One potential scheme, involving
measurement of the angular dependence of the speed of ultrasonic waves propagating in the plane of the sheet is described, as applied to aluminum. While this technique has been successfully used in steel sheets, application to aluminum is more difficult because of the smaller elastic anisotropy of the crystallites. This paper presents the results of a detailed study of the strengths and weaknesses of the approach. Included are discussions of signal processing factors, the accuracy of the ultrasonically determined
, and a comparison between
measured by ultrasonics and by diffraction techniques (both X‐ray and neutron). It is found that relative velocity measurements are very good for determining and
. These measurements can easily distinguish between rolling and recrystallization textures, and can also detect more subtle variations in recrystallization textures. A systematic offset in the prediction of is also reported, which is believed to be a consequence of unknown alloy dependence of the single crystal elastic constants and texture free velocities, quantities which play a key role in inferring this quantity from absolute measurements.