bluuebunny/crossref_metadata_2025 huggingface dataset:
Evolution of r-Value During the Tensile Deformation of Aluminium
Authors: Savoie J. , Jonas J. J. , Macewen S. R. , Perrin R.
Published: April 2008

The elastic strain ratios associated with specific ideal orientations as well as with particular experimental
textures were derived from the second order Hill approximation. The single crystal elastic constants
for pure aluminum and copper were used. Plastic strain ratios were then calculated for the experimental
textures using the FC (full constraint), RC (relaxed constraint) and LW (least work) crystal plasticity codes. Tests were also carried out to determine the r-values along various directions in the sheet during Lüders band propagation, as well as the dependence on strain of the plastic r-value. It is shown that the observed strain dependence of the r-value is related to Lüders band propagation and to the evolution of the texture and not to the elastic‐plastic transition.
Procedures for Residual Stress Analysis in Textured and in Coarse Grained Materials
Authors: Reimers W. , Dupke R.
Published: April 2008

For the investigation of residual stresses by means of X‐ray diffraction, special procedures for the
registration and evaluation of the experimental strain data are necessary for textured and coarse
grained materials. In both cases inhomogeneous diffraction intensity patterns are present which lead
to the formation of intensity poles or even to Bragg reflections. Such experimental findings
indicate also that the material properties within the investigated gauge volume are anisotropic so
that the evaluation of the experimental strain up to stress values requires the introduction of
anisotropic elastic constants. For the residual stress investigation of textured and fine grained
materials averaging procedures using short wavelength radiation are discussed. A more detailed
insight also in the microstress states may be obtained from the measurement of several different
reflections whereby the effects of the elastic anisotropy may be corrected for by including the orientation
distribution function as calculated from different poles figures. For coarse grained materials it is
experimentally possible to determine the strain state of the individual crystallites so that their anisotropy
is directly included in the evaluation of the stress data by using the single crystal elastic constants.
The macroscopic residual stress values may then be obtained from the averaging over stress values
of several crystallites.
Calculation of Domains of Dependence for Pole Figures With an Ultrahyperbolic Differential Equation
Authors: Savyolova T. I.
Published: April 2008

X‐ray and neutron methods of texture investigation are used to get experimental pole figures (PF) of
polcrystalline samples and geological materials (Bunge, 1982). Usually several PF are used, 1–4 for
polycrystalline samples with cubic, hexagonal lattice symmetry (copper, iron, beryllium…), 6–19 for
low‐symmetry materials of geological samples (quartz, biotite…). Pole figures are the sum of solutions
of two ultrahyperbolic equations (Savyolova, 1982). If the solutions of ultrahyperbolic equations are
known in some domains we can determine them uniquely in other domains using the Asgeirsson′s
theorem (Courant, 1962) and their generalizations by ultra‐Lorentz transformations. We get the domains
of dependence of pole figures and the methods of continuations of solutions of ultrahyperbolic equations.
Orientation Determination by Continuous Etching Patterns in Copper and Copper Alloys
Authors: Wang W. H. , Sun X. , Köhlhoff G. D. , Lücke K.
Published: April 2008

A new method for determination of grain orientations using etch patterns was developed for copper
and copper alloys. This method is based on the fact, that one gets etch patterns characteristic for the
crystallographic orientation of the etched surface, if a specimen of copper or copper alloys is etched
in conc. HNO3. In contrast to etch pits, the etch patterns are developed continuously over the whole
grain. This allows a direct and continuous observation of the orientation changes within and between
the grains, which is not possible for many other orientation determination methods. The determination
accuracy of the new method depends on the crystallographic orientation of the etched surface and varies
between 2° and 10°. For some special surface orientations the etch patterns allow even the determination
of very small orientation changes (≤ 2°), occurring e.g. in a deformed grain.
Texture Formed by Platelet Alignment in Ceramic Platelet Ceramic Matrix Composites
Authors: Li W-Y. , Sørensen O. T.
Published: April 2008

3 mol% yttria stabilized zirconia matrix has been incorporated with 10 wt% single crystal α‐alumina
platelets to enhance the mechanical reliability. The composites have been produced by different forming
techniques, namely, slip casting, tape casting, and injection moulding followed by pressureless
sintering. Relative density ∼99% has been obtained. Alignment of the platelets in the material was
analyzed by processing the images taken from scanning electron microscopy. Strong texture was
formed by the alignment of platelet. Mechanical properties of the composites were evaluated, and
co‐related to the alignment of the platelets.
Deformation and Texture Evolution of a 3004 Aluminium Alloy During Ironing
Authors: Heymès F. , Embury J. D. , Sowerby R. , Kocks U. F.
Published: April 2008

The production of drawn and ironed (D&I) beverage cans represents an important example of process
optimisation. The aluminium alloy 3004 H19 is widely used for the can body, since it has a good
combination of formability and strength and results in very little earing after deep drawing. These
desirable properties are achieved by exercising careful control of the rolling schedule of the can stock
sheet. During the ironing stage the wall thickness is reduced by a factor of about three, and these large
strains determine the resulting texture in the can wall. Large shear strains are also present and these
can vary through the wall thickness. The present work deals with the deformation and texture evolution
when ironing strips of 3004 aluminium. The strip material was in either a cold rolled or an annealed
condition. The texture on each surface of the ironed strips, as well as at the mid‐plane, was determined
experimentally. The experimental results were then compared with the results from a computer program
which was capable of predicting the texture evolution.
Determination of Domains of Dependence Through the Solution of an Ultrahyperbolic Differential Equation
Authors: Savyolova T. I.
Published: April 2008

Pole figures are represented as the sum of solutions of two ultrahyperbolic differential equations. We
derive the domains of dependence for pole figures and apply the method of continuation to solve the
ultrahyperbolic equations.
Plastic Anisotropy Prediction by Ultrasonic Texture Data
Authors: Serebryany V. N.
Published: April 2008

The plastic anisotropy parameters (R coefficient and height of ears of the drawn cup) have been
calculated from ultrasonic orientation distribution function (ODF) coefficients on the basis of Taylor
theory for low carbon steel and aluminium alloy sheets. The ODF coefficients were defined by Sayers
method and using the iterative procedure on the basis of measurement of bulk longitudinal and shear
wave time delays.
Joints Orientation Distributions in Sedimentary Rocks
Authors: Belousov T. P. , Mukhamediev Sh. A. , Kurtasov S. F.
Published: April 2008

The results of several years (1980–1994) field observations of rock joints at the former USSR territory
are integrated. New methods of data processing and interpretation are proposed and developed. With
the local data set for an exposure we connect the symmetric positively defined second order tensor
J characterizing the density and relative position of joint systems as well as their orientation in space.
The complete set of tensors J for any region depicted in appropriate manner gives the integral “portrait”
of tectonic fracturing of the region. The regular changes of such integral characteristics for Great
Caucasus as an example are determined.
Modelling of Texture Development and Deformation Mechanisms in a Ti20V Alloy Using a Self Consistent Polycrystal Approach
Authors: Mercier S. , Tóth L. S. , Molinari A.
Published: April 2008

Modellisations of the deformation texture development in a Ti20V alloy (20 volumic % Vanadium) during rolling have been carried out using the viscoplastic self consistent model of Molinari and Tóth (1994). The model parameters and the slip and twinning systems were identified from experimental data. The experimental texture evolution is well reproduced with only a small contribution of the twinning activity.
Development of Texture in an ELC‐BH Sheet With Very High R¯‐Value During Annealing
Authors: Guan Xiaojun , Hu Xiaojun , Wu Qiulin , Yu Ke
Published: April 2008

The texture change in an ELC‐BH sheet steel with very high value produced through a new technology
invented in our laboratory during annealing has been successfully investigated by means of the methods
of ODF analysis and metallographic structure observation in this paper. Thus, the developmental law
of the texture which consists of even stronger {111} texture with main {111} < 110 > components as compared with that of texture in conventional technology during annealing has been discovered. The experimental results are described as follows: 1) It is different from conventional technology that the velocity of both nucleation and growth to the recrystallization grains of {111} < 110 > orientations is always larger than that of {111} < 112 > orientations. 2) The cause why this law is engendered may be related to that the advantage, that cold deforming stored energy of {111} < 110 > orientation grains is higher than that of {111} < 112 > orientation grains, is brought into fully play in the cold rolled sheet with stronger {111} texture during annealing.
The Modified Maximum Entropy Method (MMEM) in QTA for Lower Symmetry Polycrystalline Aggregates
Authors: Wang Y. D. , Xu J. Z. , Liang Z. D.
Published: April 2008

A new algorithm of quantitative texture analysis (QTA), which is called the modified maximum entropy method (MMEM), has been proposed and applied to determination of textures in polycrystalline samples of lower crystal symmetry with overlapping diffraction peaks (Wang and Xu, 1995a). By introducing directly the maximum entropy principle into the least square procedure of pole figure inversion (Bunge, 1969), then both minimizing the differences between experimental and postulated pole figure data, and maximizing entropy may be satisfied simultaneously. Thus, the maximum entropy principle is applied to the entire process of QTA in frame of the harmonic method (HM). The detailed comparisons among the three pole figure inversion methods, i.e. the traditional HM, the primary maximum entropy method (MEM) and the MMEM, are given through a model example of simulated fiber texture. It is shown that the precise and stable solution of inverse pole figure for the polycrystalline samples with smooth or sharp textures will be obtained by the MMEM even using a less number of pole figures. The minimum range of polar angle and the least number of pole figures, which are needed in the QTA for pretended tetragonal materials by the MMEM, are discussed in detail.
Microtexture, Grain Boundary and Grain Junction Evolution in Al‐Li Sheet During Superplastic Forming
Authors: Randle Valerie , Lewis Simon G.
Published: April 2008

The microtexture of superplastically deformed 8090 Al‐Li sheet has been measured using electron backscatter
diffraction, for true strains of 0, 0.25, 0.75, 1.5 and 2.4. The data has been interpreted in terms of individual texture variants, grain boundary types (low angle or high angle) and grain junction types (I‐lines or U‐lines, as defined by an extension to the O‐lattice theory). A key feature of the results is that local textures tend to be dominated by only one or perhaps two orientation variants, which leads directly to the presence of a high proportion of low or medium angle boundaries and hence a high proportion of I‐line grain junction types. These effects decrease with increasing superplastic strain. Since it has been previously suggested that the presence of I‐lines indicates dislocation‐related phenomena,
and the presence of U‐line grain junction types denotes diffusion‐related phenomena, the proportion of each of these provides as indication of the predominant accommodation mechanism.
Single Grain Orientation MeasurementsApplied to the Formation and Growth ofRecrystallization Nuclei
Authors: Engler O. , Escher C. , Gottstein G.
Published: April 2008

Measurements of the crystallographic orientation of individual grains provide information on the spatial
arrangement and distribution of orientations in a crystalline solid, i.e. on the orientation topography,
which can be utilized to establish a basis for a deeper understanding of the microstructural mechanisms
during deformation and recrystallization of metallic materials.

Techniques for the convenient measurement of single grain orientations with high accuracy by
evaluation of Kikuchi diagrams in a TEM and SEM (EBSD) are introduced. The principles of Kikuchi
pattern formation as well as the measuring and evaluation procedures are outlined. Particular attention
is focused on the automation of pattern indexing in order to provide fully automated evaluation routines.
The unique potential of these techniques is demonstrated by two examples pertaining to the
microstructural evolution during the formation of recrystallization nuclei and their subsequent growth.
Recrystallization of KCL CrystalsAfter Pressure Induced PolymorphicTransformation. Twin Growth, GrainBoundary Migration
Authors: Borisenko B. E. , Gnesin A. B.
Published: April 2008

Crystals KCl as undergone pressure induced polymorphic transformation were investigated. Microstmcture
and crystallographic orientations of the crystals were studied at once after the pressure removal
and as stayed at room temperature for some time. The occurrence of at least six systems of plane defects
connected with high pressure treatment at 20 kMPa is found. Their crystallographic indices are
determined. It is found that in KCl crystals after pressure induced polymorphic transformation
recrystallization takes place at room temperature. Two stages of recrystallization at room temperature
were observed: growth of twins of cubic texture and grain boundary migration.
Effect of Annealing on Hot BandTexture of Ferritic Stainless Steel
Authors: Singh C. D.
Published: April 2008

The textural and microstructural banding through the thickness of 17%Cr ferritic stainless steel hot
band has been investigated. The surface texture is nearly random and consists of shear texture
components formed by simultaneous action of shear deformation and dynamic recrystallisation. The
texture in the central layer is a strong recrystallisation‐type. The through‐thickness textural and
microstructural banding, to a large extent, has been weakened by annealing the hot band in two‐phase
(α + γ) region, as opposed to single‐phase (α) annealing.
Towards Three‐Dimensional Modelling of Subgrain Coalescence
Authors: Saetre T. O.
Published: April 2008

Hu (1962, 1963) suggested that the nucleation process during recrystallisation can arise from subgrain
coalescence. In the present paper, a new modelling approach has been presented for subgrain rotations.
It is suggested that the required mass transfer due to compatibility criteria, can be modelled as geometric friction forces. By employing this new concept, it has been shown that three‐dimensional models can
be derived, based on classical mechanics. The derived model has shown‐that the small and regular
subgrains are the most likely candidates for rotation. Subgrain coalescence is strongly temperature
dependent since diffusion of vacancies are required for the rotation.
On the Crystallographic Basis of Yield Criteria
Authors: Hosford William F.
Published: April 2008

Consideration of crystallographic texture has lead to a much better understanding of anisotopic yielding
behavior than yield criteria postulated without regard to deformation mechanisms. Continuum anisotropic
yield criteria have been developed to simulate the results of calculations based on the crystallographic
nature of slip. These criteria, which involve high stress exponents, describe actual forming behavior
much better than the quadratic yield criterion postulated by Hill. Today it is possible to calculate
anisotropic yielding behavior directly from texture data, although for metal forming analyses, some other
means must be used to characterize the strain‐hardening behavior.
A Sixth Order Inverse PotentialFunction for Incorporation ofCrystallographic Texture IntoPredictions of Properties ofAluminium Sheet
Authors: Savoie Jean , MacEwen Stuart R.
Published: April 2008

In order to simulate adequately the formability of sheet, it is necessary to generate a yield criterion
that takes into account the anisotropy of the crystallographic texture. This yield function must be in
a form that can be used easily in finite element analysis. In addition, the formulation should allow the
possibility to update the yield surface during simulation to take into account the texture evolution. This
work investigates the use of a sixth‐order strain rate potential that, when differentiated with respect
to the strain rate, gives the components of stress. A method is given to solve the non‐convexity problems
that can arise when the proposed analytical sixth‐order function is used. Examples are given for one
cold rolled and one annealed aluminium sheet.
The Variation of Strain Ratio at the Tensile Test Described by a Hyperbolic Function
Authors: Truszkowski W. , Kloch J.
Published: April 2008

The function describing the variation of plastic anisotropy r at the uniaxial deformation ε is a
compendium of knowledge on polycrystalline metals subdued to plastic working. In real single crystals
r(ε) function characterizes the degree of imperfection of the crystallographic orientation (“texture of
a single crystal”). It has been shown that the best fitting function of the r‐ε relationship for single crystals
as well as for polycrystalline metals is that based on a hyperbolic function.
Estimation of the Range of Elastic Interaction Due to Grain Misorientation
Authors: Kiewel H. , Bunge H. J. , Fritsche L.
Published: April 2008

The discontinuities of the elastic constants across grain boundaries in polycrystalline aggregates can
be considered as sources of “compatibility” strains in the adjacent crystals under the action of an external
stress. This effect was studied theoretically using the cluster model of Kiewel and Fritsche. In order
to distinguish the contributions of individual grains, the orientation of only one grain was changed
whereas all others in the cluster were kept constant. The orientation dependent part of the strain field
thus allows to estimate the range over which the influence of an individual grain reaches. The results
shows that this part decreases faster than 1/r3 with the distance from the centre of the considered grain.
It has virtually vanished at two or three times the grain diameter.

The magnitude of the compatibility strains depends on grain shape. It was found higher in a cluster
of cubic grains than in clusters consisting of dodecahedral or cubo‐octahedral grains.

The compatibility strains vary systematically when the orientation of the considered grain is changed
continuously. The influence of even small misorientations <5° is distinctly visible.

The results show that grain shape and orientation correlation must be taken into consideration
additional to the texture in order to obtain narrower bounds for the effective elastic constants than those
by Voigt and Reuss. They show, however, also that orientation correlations of higher than next‐nearest
neighbours have virtually no influence.
Experimental Investigation and Numerical Simulation of theCorrelation of Recovery and Texture in Bcc Metals and Alloys
Authors: Raabe D. , Roters F. , Marx V.
Published: April 2008

Depending on the strain and temperature regime examined recovery of bcc metals during hot rolling
or annealing subsequent to cold deformation often leads to the preservation of certain deformation texture
components. A broad variety of mesoscopic and macroscopic texture data from both hot rolled and
cold rolled and annealed bcc metals (Fe, Ta, Mo, Nb) and alloys (low‐carbon steels, ferritic stainless
steels, transformer steels) is re‐examined with respect to such phenomena. The data suggest that two
conditions promote strong recovery of certain bcc deformation texture components (e.g. {001}
<110>), namely, the absence of kinetic instabilities, and the absence of thermodynamic and mechanic
instabilities. The first case applies if the grains do not tend to generate large local misorientations in
their interiors during plastic deformation. The second case applies if the stored dislocation density is
low. Both features depend on the grain orientation. The experimental observations are complemented
by three types of numerical simulations. The influence of the number of Burgers vectors equally involved
during preceding deformation on the kinetics of static recovery is numerically studied using 2
dimensional dislocation dynamics. The orientation dependent inclination to generate local misorientations
in the grain interiors is simulated using a Taylor type approach with different constraints on either side
of the grain. The influence of the orientation dependence of recovery on the final annealing texture
is simulated using a 3 dimensional cellular automation. Experiment and simulation show that both the
recovery kinetics and the tendency to form kinetic instabilities considerably depend on the orientation.
The latter effect seems to be essential for the prevalence of either RX or RC.
Simulation of the Recrystallization Textures of Al‐Alloys on the Basis of Nucleation and Growth Probability of the Various Textures Components
Authors: Engler O.
Published: April 2008

The recrystallization textures of cold rolled Al‐alloys are simulated under the assumption of a growth
selection of the typical recrystallization texture components out of a limited spectrum of preferentially
formed nucleus orientations. The probability of nucleation is derived from the distribution of the potential
nucleus orientations which was determined by EBSD local texture analysis for the most important
nucleation sites in cold rolled commercial Al‐alloys, i.e. Cube‐bands, grain boundaries and second phase
particles. If several nucleation sites are active simultaneously, the total nucleation probability is
composed of the respective contributions of each nucleation site. The growth probability is derived from
a 40°<111> transformation of the rolling texture. The resulting recrystallization textures are simulated
by multiplying these two probability functions, i.e. the ODF of the nucleus orientations with the ODF
of the 40°<111>‐transformed rolling texture.
A Nearly Equal Distant Grid of Orientations for QuantitativeTexture Analysis
Authors: Helming K.
Published: April 2008

The construction of a nearly equal distant grid of orientations is presented. Based on that grid texture components can be determined automatically. The obtained set of components can be interpreted as an ensemble of single orientations representing the texture. The grid may be used for the simulation of texture modifying processes. As examples textures of experimental deformed rock salt and aluminium are compared with results of numerical simulations of deformation (Taylor model).
Modelling Primary Recrystallization in fcc and bcc Metals by Oriented Nucleation and Growth With the Statistical Compromise Model
Authors: Bunge H. J. , Köhler U.
Published: April 2008

Statistical models of primary recrystallization are described. Particularly the superposition model and the
compromise model must be distinguished. Both models are able to consider oriented nucleation, orientation
dependence of driving force, and misorientation dependence of boundary mobility. The superposition
model requires abundant nucleation, whereas the compromise model corresponds to sparse nucleation. In
order to model the two‐step recrystallization observed in low carbon steel the compromise model was
generalized for the case of inhomogeneous (two‐step) recrystallization. The compromise model was applied
to the recrystallization textures of fcc‐copper type and brass‐type metals as well as to bcc‐metals, i.e. low
carbon steel. All these textures are well represented by the model on the basis of experimentally established
input parameters, i.e. the growth laws 40°〈111〉, 27° + 84°〈110〉 and α〈111〉 respectively for fcc‐ and bcc‐ metals.
Development of Hot Band Annealing Texture in Austenitic Stainless Steel
Authors: Singh C. D.
Published: April 2008

The microstructural and textural analysis of the hot band reveals that the surface grains are fully
recrystallised and possess the orientation elements of the shear texture, distributed along <110>// RD and <110> 30°ND fibres, while the grains, in the central layer, are partially recrystallised and their texture is composed of orientation elements of recrystallisation texture (<100>// RD) and of copper type texture (<110> 60°ND), with {001} <100> and {011} <112> as the major components, respectively. The other interesting feature of the hot band microstructure is the formation of recovery twins in the grains of {011} <112>. The short time annealing of the hot band leads to the formation of annealing twins in addition to the growth of the surface grains and to the complete recrystallisation of the grains in the central layers. Many physical processes such as the growth of the recovery twins and of the grain boundary nucleated grains contribute to the development of final annealing textures of the annealed
hot band, which are like the textures present in the surface and the central layers of the hot band.
Texture Analysis of Quartz in a Granite Mylonite byEBSP‐Orientation Imaging Microscopy
Authors: Pearson A. , Heidelbach F. , Wenk H. R.
Published: April 2008

The crystallographic preferred orientation (texture) of the quartz phase in a mylonitic
leucogranite from the Santa Rosa mylonite zone was investigated using automated
analysis of electron backscattering patterns (EBSP) in the scanning electron microscope
(SEM). The separation of the quartz diffraction patterns from patterns of other constituents
(feldspar, mica, etc.) in this polymineralic rock was achieved using an image
quality parameter. The quartz phase displays a texture typical for high temperature
mylonites (c‐axis maximum in the intermediate strain direction). The misorientation
distribution between next neighbors is dominated by Dauphiné twins.
Normal Distribution on the Rotation Group So(3)
Authors: Nikolayev Dmitry I. , Savyolov Tatjana I.
Published: April 2008

We study the normal distribution on the rotation group SO(3). If we take as the normal
distribution on the rotation group the distribution defined by the central limit theorem in
Parthasarathy (1964) rather than the distribution with density analogous to the normal
distribution in Eucledian space, then its density will be different from the usual ()
exp⁡(−(x − m) 2/2σ2) one. Nevertheless, many properties of this distribution will be
analogous to the normal distribution in the Eucledian space. It is possible to obtain
explicit expressions for density of normal distribution only for special cases. One of these
cases is the circular normal distribution.

The connection of the circular normal distribution SO(3) group with the fundamental
solution of the corresponding diffusion equation is shown. It is proved that convolution
of two circular normal distributions is again a distribution of the same type. Some projections
of the normal distribution are obtained. These projections coincide with a
wrapped normal distribution on the unit circle and with the Perrin distribution on the
two‐dimensional sphere. In the general case, the normal distribution on SO(3) can
be found numerically. Some algorithms for numerical computations are given. These
investigations were motivated by the orientation distribution function reproduction
problem described in the Appendix.
Generalized Spherical Harmonics for Cubic‐Triclinic Symmetry
Authors: Morris Peter R.
Published: April 2008

An explicit representation is suggested for orthogonal generalized spherical harmonics
with cubic‐crystal and triclinic‐sample symmetries. The representation employs sums and
differences of orthogonal generalized spherical harmonics with cubic‐crystal symmetry,
previously described by Bunge for orthorhombic (or higher) sample symmetry, and is
illustrated, for , i = 4, 9, μ = 1, υ = 1 to 5. This representation facilitates crystallite
orientation distribution (COD) analysis (aka ODF analysis) for these symmetries, using
the Bunge formalism.
Calculation of the Effective Absorption Coefficient in Multi‐Phase Powders
Authors: Reefman D.
Published: April 2008

A calculation of the effective absorption coefficient μeff in multi‐phase powders is presented. Characteristic in
the calculation is, that the distribution function of the grains
is similar to the correlation function for fluids. It is shown,
that for average grain diameters comparable to the inverse of the
absorption coefficients, the commonly used formulae for μeff (either a linear combination of the contituting μ′s or simply μ for a single component) do not hold.

The analytical expressions derived for μeff are compared with numerical simulations, which show that, within certain limits, the former give reasonable estimates of μeff. The simulations also show, however, that shape effects can have influence on μeff which are not included (yet) in the formulae.

Also shown is that surface roughness can give effects comparable to those of microabsorption, but can be much more sensitive to particle statistics.
X‐Ray Stress Analysis by Use of an Area Detector
Authors: Schubert A. , Kämpfe B. , Goldenbogen S.
Published: April 2008

The most commonly known techniques of X‐ray residual stress analysis use diffractometers with conventional counters or position sensitive detectors. The sin⁡2Ψ‐method is often applied to X‐ray stress determination, but requires various measurements at different sample positions. This technique was combined with an imaging plate, which is an X‐ray digital area detector. The use of a two‐dimensional detector like an imaging plate offers the possibility to get diffraction in one measurement from lattice planes lying on the whole diffraction cone. Thus the number of measurements for the calculation of the stress components can be significantly reduced. In addition, the use of an imaging plate has several advantages for the stress calculation even for materials having relatively large grains or a strong texture. Measurements on an electron beam hardened steel sample are described as an application example.
X‐Ray Scanning Apparatus for Mapping Texture and Element Distributions
Authors: Schwarzer R. A. , Wehrhahn M.
Published: April 2008

The past decade has seen some remarkable progress in spatially resolved texture analysis due to new computer‐aided techniques of electron diffraction with the SEM and TEM. To avoid, however, some limitations specific for electron microscopy, an x‐ray scanning apparatus has been developed for the mapping of texture and element distributions on bulk samples. The set‐up consists of a “white” x‐ray source, a collimator system to produce a fine primary beam spot, an x‐y sample stage operated by stepper motors, and an EDX detecting system for peak separation.

Energy dispersive x‐ray diffraction and x‐ray fluorescence analysis are used for data acquisition. The density distributions of selected crystallographic directions or of element concentrations in the sample surface are acquired spot by spot, and represented by pseudocolour or grey shade maps. Several texture distribution as well as element composition maps can be obtained simultaneously. Spatial resolution is presently limited to 50 μm by the low level of primary beam intensity.
Silicon in Fe‐Si Alloys: Correction of X‐Ray Intensities for Preferred Orientation
Authors: Figueiredo M. O. , Margarido F.
Published: April 2008

A texture effect in the silicon phase of industrial Fe‐Si alloys was noticed in the X‐ray diffraction patterns through the reinforcement of the 111 reflection. A similar effect was also apparent in a commercial silicon standard pellet used as reference material and supposed to be texture‐free.

A quick correction procedure to account for preferred orientation effects was developed, based on a previous algorithm currently applied for the automatic profile fitting of powder diffractometer data. “Modified Wilson plots” are established for visualizing the efficiency of texture correction according to the proposed method.
The Determination of Orientation Distribution Function From Incomplete Pole Figures ‐ an Exampleof a Computer Program
Authors: Jura Jerzy , Pospiech Jan
Published: April 2008

The use of incomplete pole figure data for
defining the orientation distribution function (ODF) in
a polycrystalline material is of great practical importance,
because it enables the use of experimental data
from a simplified measurement. The present paper provides
the source text of a computer program for calculating
the coefficients of ODF series expansion, . The data for computations are in the incomplete pole figures of rhombic symmetry as determined by the
back reflection or transmission technique for crystalline
solids of the cubic system. Also described is the
numerical method of determining the coefficients ,
and the results so obtained are discussed.
The Prediction of Plastic Properties of Polycrystalline Aggregates of BCC Metals Deforming by <111> Pencil Glide
Authors: Morris Peter R. , Semiatin S. L.
Published: April 2008

The Bishop and Hill‐type isostrain analysis for the deformation of BCC crystals by pencil glide has been re‐examined. Expressions have been derived for slip‐plane orientations and shears for simultaneous slip along four <111> directions. The expressions for shears, in conjunction with expressions for the stress states previously calculated by Piehler and Backofen, permit comparison of external and internal work, which must be equal for the active stress state. Additional relations are introduced which must be satisfied for simultaneous operation of three <111> slip systems. These relations permit a straightforward computational procedure for determining possible stress states, and insure that external and internal work are equal. If for a possible stress state involving activation of three slip directions, the shear stress on the supposedly inactive system is less than the yield stress, that stress state is active.
Microplasticity Predictions of r‐Values and Yield Loci of Low Carbon Sheet Steels Deforming by <111> Pencil Glide
Authors: Semiatin S. L. , Morris P. R. , Piehler H. R.
Published: April 2008

The plastic deformation of low carbon sheet steels has been analyzed using microplasticity models and Hill′s theory of anisotropic continuum plasticity. The analytical methods used to determine the crystallite stress states which must be generated for the isostress (lower‐bound) and isostrain (upper‐bound) cases are briefly discussed and then applied to predict yield loci for three cold‐rolled, annealed low‐carbon steels (enameling iron, aluminum‐killed steel, and interstitial‐free steel) whose textures were characterized by crystallite orientation distribution functions. While measured r‐values correlate best with upper‐bound yield loci predictions for enameling iron, those for the aluminum‐killed steels show better agreement with lower‐bound yield loci predictions. In the case of the interstitial‐free steel, measured r‐values could not be accounted for by either upper‐ or lower‐bound predictions. The yield loci measurements and predictions are reviewed in the context of Hill′s continuum theory.
Textural Studies of Thermomechanically Treated Eutectoid Steel
Authors: Querales A. , Byrne J. G.
Published: April 2008

The important class of metallurgical treatments known as thermomechanical treatment (TMT) is especially appropriate for textural studies because the crystallographic disposition of the matrix largely determines the final properties of the material. The current work utilized regular and inverse pole figure measurements of the ferrite matrix in TMT eutectoid steel to monitor the effects of various processing steps such as degree of cold rolling and the temperature and time of rapid annealing. Textural results provided the key to understanding fatigue life differences between longitudinally and transversely oriented sheet samples. The most favored ferrite slip system was not well oriented to act in the transverse samples. This in turn retarded the slip which nucleates fatigue cracking and hence extended the total fatigue life of transverse samples.
An Analytical Method for the Quantitative Determination of the Volume Fractions in Fiber Textures
Authors: Tomov Ivan , Bunge H. J.
Published: April 2008

In order to evaluate pole‐figure measurements quantitatively, one
needs the normalization factor which reduces measured intensity
values to multiples of the random density. This factor may be
determined experimentally by measuring the intensities of a random
sample or it may be calculated by integrating over the whole
pole‐figure or its asymmetric unit. If pole‐figure values are not
available in the whole angular range 0 ≤ φ ≤ 90° (incomplete pole‐figures), then the calculation is in
general much more difficult and it usually presumes the knowledge
of several pole‐figures.

In the case of fiber textures (axial symmetry), consisting of only
a few strongly preferred orientations with the crystal directions
〈uvw〉i parallel to the axis of symmetry, the normalization factor and hence the volume fractions of the components i may be calculated in a rather simple way requiring only one, possibly incomplete, pole figure.
Recrystallization Textures of Silver, Copper and α‐Brasses With Different Zinc‐Contents as a Function of the Rolling Temperature
Authors: Schmidt Ursula , Lücke Kurt
Published: April 2008

The recrystallization textures of copper and different Cu‐Zn alloys as well as the rolling and recrystallization textures of silver of varying purity were investigated as a function of the rolling temperature. In all cases in which the pure copper type rolling texture was present the cube texture was found as recrystallization texture, whereas in the case of the pure brass type rolling texture the brass type recrystallization texture (326) developed. In the transition range a large number of well defined and reproducible recrystallization orientations occurred. The high accuracy of the present pole figure measurements allowed a detailed discussion of the results with regard to the mechanisms of formation of the recrystallization textures.
Pole Figures From Time‐of‐Flight Measurements Using Neutrons of a Pulsed Spallation Source
Authors: Jansen E. , Schäfer W. , Will G.
Published: April 2008

A new method of pole figure scanning is described, where the number of different sample orientations can be reduced by about one order of magnitude compared to the conventional scanning procedure using monochromatic neutrons at a steady state reactor source. The method is based: (1) on time‐of‐flight techniques using white neutrons at a pulsed spallation neutron source; and (2) on data collection using a large time and position resolving detector device. The detector allows the simultaneous measurement of many pole figures and reduces the number of sample orientations needed to get complete pole figures. The method has been tested at the spallation source ISIS; examples of pole figure results on natural quartzites are presented.
An Investigation on Grain Growth in a Commercial Al–Mg Alloy
Authors: Samajdar I. , Rabet L. , Verlinden B. , Van Houtte P.
Published: April 2008

Alloy AA5182 contains coarse constituent particles and submicron dispersoids. While the
former may cause particle stimulated nucleation (PSN) during primary recrystallization,
the fine dispersoids may ‘arrest’ grain growth during subsequent annealing. Abnormal
grain growth was observed after dissolution/coarsening of the dispersoids. Mainly S [{123}〈634〉] grains, but also some Brass [{011}〈112〉] and Cu [{112}〈111〉] grains, were observed to grow abnormally. Both the grain size and the grain boundary character distribution (GBCD) possibly played a role in the selection of the grains for abnormal grain growth. A dramatic increase in the number fraction of extremely low angle (1−5°) boundaries was observed with annealing, the increase being more at 470°C (when dispersoids were stable and grain growth was arrested more effectively) than at 500°C/530°C (when inhibition to grain growth was less). The nature of the CSL boundaries did not change significantly with annealing time/temperature.
Influence of Grain Refinement of Hot Band and Cold Rolling Reduction on the Formation of Textures and R‐Value of Cold RolledPlain Extralow‐Carbon Steel Sheets
Authors: Senuma Takehide , Hashimoto Natsuko
Published: April 2008

A textural analysis was carried out to explain the cause of the planar anisotropy of r‐value
of cold rolled plain extralow‐carbon steel sheets. For a detailed analysis, a model for
calculating r‐values from ODF‐data of texture was applied and the influence of each or a
group of crystal orientations of the recrystallization texture on the planar anisotropy of
r‐values was studied. The following results were obtained:

A development of {111}〈110〉 − {443}〈110〉 − {332}〈110〉 − {221}〈110〉 enhanced the V‐type
planar anisotropy of r‐values. A decrease in the intensity of these orientations by
increasing the cold rolling reduction or the refinement of the hot band microstructure
reduced the r‐values in L and C directions and hardly affected the r‐value in D direction,
and as a result, the V‐type planar anisotropy of r‐values was improved. On the other
hand, an increase in the intensity of {111}, {334} orientation by increasing the cold rolling
reduction or the refinement of the hot band microstructure raised r‐values in sequence of
L < D < C
directions and contributed to the reduction of V‐type planar anisotropy of r‐values as a whole.
New Parameter Model for TextureDescription in Steel Sheets
Authors: Delannay L. , Van Houtte P. , Van Bael A.
Published: April 2008

A new model is proposed for the characterisation of steel sheet textures. This model relies
on the identification of 25 relevant parameters in the Orientation Distribution Function
(ODF). Textures consisting of alpha‐ and gamma‐fibres and/or cube and Goss components
can be generated. The model is mathematically formulated and an automatic parameter
identification technique is presented.

It was found that the model can quantitatively reproduce almost any industrial steel
sheet texture. Based on this parameter model, a method is presented to systematically study
the sensitivity of material properties on texture.
Optimization of Texture Measurements. IV. The Influence ofthe Grain‐Size Distribution on the Quality of Texture Measurements
Authors: Luzin V.
Published: April 2008

It is the focus of attention that texture experiments deal with real samples which consist of a
finite number of crystallites of different size. Because of this the main sample‐induced
statistics (grain statistics and grain‐size statistics) have essential influence on the quality of
experimental data. This article quantitatively analyzes the dependence of the integral error
on the parameters of the mentioned statistics and the approximation goodness.
Investigation of Inhomogeneous Surface Textures With Constant Information Depth: Part 1: Fundamentals
Authors: Bonarski J. T. , Bunge H. J. , Wcislak L. , Pawlik K.
Published: April 2008

A method is described which allows to measure pole figures under
the condition of constant information depth. This is achieved by
using ω‐ and χ‐tilt simultaneously. In order to obtain satisfactory
integrated intensities the use of a position sensitive detector is
nearly indispensable. The functional relationship between
ω and χ for constant information depth and the transformation
of Euler angles {ϕ1, φ, ϕ2} to pole figure angles {α β} are given as well as the necessary intensity
correction. The use of ω‐tilt leads to blind areas in the centre of pole
figures which can, however, be compensated by increasing the
number of pole figures and using appropriate ODF programs.

The method was tested with composite samples obtained by stacking
aluminium foils with known textures but with exchanging rolling
and transverse direction of the uppermost foil. The results will
be shown in the second part of the paper.
The Influence of Molybdenum on the Texture and Magnetic Anisotropyof Fe–xMo–5Ni–0.05C Alloys
Authors: Abreu H. , Teodósio J. R. , Neto J. , Silva M. , Da Costa Viana C. S.
Published: April 2008

Diagrams of remanent induction, Br, versus saturation induction, Bs, for Fe–5Ni–xMo–0.05C alloys, where x is equal to 11%, 15% or 19%, were
determined for samples 60%, 80%, 90% and 97% cold
rolled and magnetically age‐annealed at 610°C for 1h. The
texture evolution in those alloys was analysed as a function of
rolling reduction, by means of the orientation distribution
function (ODF). The results show that a sharp {100} 〈110〉 texture component develops in the 11%‐Mo alloy for
rolling reductions in excess of 90%. This leads to the highest
values of the remanent induction, Br, and of the Br/Bs ratio for this alloy as a result of 〈100〉 directions, the easy magnetization directions, lying
at 45° to the rolling direction.
Mechanical Properties and Textures of ParticulatereinforcedAluminum Alloy Matrix Composite Under Hot‐ and Cold‐RollingConditions
Authors: Chen L. Q. , Lü Y. X. , Lee C. S. , Bi J. , Li R. K. Y.
Published: April 2008

A study has been made on the mechanical properties of an aluminum
alloy matrix (Al–3.0wt% Cu–1.5 wt% Mg–0.4wt%
Mn)composites reinforced with a volume fraction of
15% silicon carbide under hot‐ and cold‐rolling conditions. The preferred crystallite
orientation distribution functions (ODFs) of these rolled
sheets were measured. The tensile test results showed that the
ultimate tensile strength and plasticity of the hot‐rolled
composite sheet are better than those of the cold‐rolled one.
However, the cold‐rolled sheet specimen exhibits much higher
0.2% offset yield strength than that in the case of hot
rolling. The cold‐rolling texture of this sheet composite is
obtained from the development of hot‐rolled texture only by a
little rotation about the related axes. It consists of random
texture and three weak components, {001}〈110〉, {110}〈112〉
and {3314}〈773〉, while the hot rolling texture of the metal‐matrix
composite (MMC) sheet is almost random under the rolling reduction
employed. The preferred grain orientation has effect on the yield
strength and no much influence on the ultimate tensile strength of
the cold rolled sheet. The decrease in the ultimate tensile
strength of the cold‐rolled specimen is mainly attributed to the
micro‐damages in the microstructure produced during cold rolling.
Texture in Metallic and CeramicFilms and Coatings
Authors: Czerwinski F. , Szpunar J. A.
Published: April 2008

The properties of films and coatings can be optimized for a variety of applications by
modifying their texture. Understanding how the texture in thin films is formed and how it
can be controlled during film growth process is one of the most important areas of texture
research. Several examples were selected to illustrate how the texture in films and coatings
is developed and to explain how various properties of films are affected by texture. In
particular, texture development during electrodeposition of Zn‐based automobile coatings,
Ni and Ni‐based layers for magnetic recording as well as Fe and Fe‐based wearresistant
coatings, is presented. A new area of application of texture research to control the
high‐temperature oxidation resistance of engineering materials is described. Using
experimental data for Ni and Ti, the factors affecting texture formation during growth of
ceramic oxides are discussed, with special attention paid to the role of substrate texture.
The correlation between the oxide texture, grain boundary structure and diffusion of
metal and oxygen ions at high temperatures, is considered.