The earing behaviour during a cup drawing test was studied for a wide range of low carbon steel sheets,
in order to check the validity of an existing model for the earing of anisotropic metal sheets. The
modelling of the anisotropic behaviour of the metal sheet was made using the Taylor theory of
polycrystal plasticity, which was implemented in a simplified cinematic model for the material flow
during a cup-drawing test.Both the relaxed constraints and full constraints model were tested and mutually compared. This
evaluation was one of the main goals of the research.It will be shown that by using the full constraints Taylor theory, a very good correlation can be
found between measured and predicted ear heights after cup drawing. Deviations of the predicted
behaviour can be explained on the basis of literature data about the texture evolution during a cup
drawing test. The model could however not predict the average cup height accurately. This is probably
due to the fact, that the model does not take the ironing effect that takes place during the cup drawing
test into account.

Rafael Schouwenaars

Paul van Houtte

Albert van Bael

Jan Winters

Koen Mols

Analysis and Prediction of the Earing Behaviour of Low Carbon Steel Sheet

Three different methods are used for the quantitative local texture analysis of fibre textures. Two methods are based upon the evaluation of BRAC-BRENTANO diffraction diagrams. In the first method relative intensity parameters are calculated, whereas in the second Rietveld preferred orientation factors are determined. The third method uses measured pole figures and the series expansion (Bunge).The method is applied to hot backward extruded NdFeB ring magnets. A local texture determination dependent on a sample surface distance is possible. The results are compared with magnetic measurements.

D. Schl&#xE4;fer

T. Walker

N. Mattern

W. Gr&#xFC;nberger

D. Hinz

Analysis of Texture Distribution in NdFeB Hard Magnets by Means of X-Ray Diffraction in BRAGG-BRENTANO Geometry

A new X-ray diffraction method for a more accurate determination of film pole densities is developed by introducing a secondary extinction correction. To this end an equation based on the kinematic theory of X-ray diffraction and the mosaic crystal model is derived. Pole densities were computed either by using the two order reflections techniques or by the least-square method. The discussion of results shows that the correct study of film structure by X-ray diffraction requires in general the secondary extinction to be taken into account.

I. Tomov

K. Ivanova

Secondary Extinction Correction Used in Pole Density Measurements by X-Ray Diffraction

It is shown that the deformation banding tendency in copper increases as deformation temperature
increases. After 70&#x25; compression, the average number of deformation bands per grain increases from
16 to 36 as the deformation temperature increases from 25 to 300&#x2103;. An orientation dependence of
banding tendency is also observed. Grains with near &#x7B;110&#x7D; orientation are found to have the lowest
banding tendency. The textures of samples compressed below 300&#x2103; are similar and consist mainly
of a &#x7B;110&#x7D; fibre and a weak &#x7B;100&#x7D; fibre. While the &#x7B;110&#x7D; component remains when deformation
temperature is increased to 300&#x2103;; the &#x7B;100&#x7D; component becomes weaker. 300&#x2103; is in fact the temperature at which large scale dynamic recrystallisation occurs. It is suspected that the decay of the
&#x7B;100&#x7D; component is due to dynamic recrystallisation which takes place preferentially at thin deformation
bands where most of the &#x7B;100&#x7D; oriented material is found.

C. S. Lee

C. F. Lee

R. E. Smallman

Texture and Microstructure of Compressed Copper

The values of the orientation density distribution function (ODF) depend as a rule on the applied
calculation method. In the series expansion method the calculation result is influenced by truncation
of the series. With decreasing of the expansion order <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math> the width of smoothing around the ODF maximum increases and its height decreases.It is shown that the smoothing of the orientation density caused by series truncation can be described analytically by a Gaussian type function. Disturbing undulations of negative and positive values around ODF maxima characteristic for harmonic expansion can be suppressed by using additional smoothing functions.

Jan Pospiech

The Smoothing of the Orientation Distribution Density Introduced by Calculation Methods

Polycrystalline models are used for the calculation of the yield loci of hcp aggregates with different
crystallographic textures. Predictions are made using both a classical Taylor Full Constraints (FC)
approach and a viscoplastic selfconsistent (VPSC) formulation. Typical deformation modes for low and
high temperature are assumed to be active. The vertex configuration of the Single Crystal Yield Surface
(SCYS) and the relative activity of different deformation modes as a function of the applied stress are
also presented and discussed. For low temperature, when twinning is active, a non centro-symmetric
behavior is observed in textured polycrystals along the direction of the &#x3C;c&#x3E;-axis texture component.
Such effect, associated with the directionality of twinning, is well reproduced by the VPSC model. For
high temperature, the predicted yield loci are centro-symmetrical but also strongly dependent on the
texture of the aggregate.

R. A. Lebensohn

C. N. Tom&#xE9;

Yield Loci Calculation of Hexagonal Materials Using a Selfconsistent Polycrystalline Model

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&#x2103;&#x2013;500&#x2103;. Deformation banding is
present in homogeneous rolling at room temperature and in single pass rolling at 500&#x2103; and is drastically
reduced in single pass rolling at 30&#x2103;&#x2013;350&#x2103;. The results are discussed in terms of slab widening, rate
and temperature effects on slip processes.

E. C. H. Lim

B. J. Duggan

On Sub-Structure and Texture Development in Warm Rolled Copper

A three-component model of copper-based composite loaded by tensile forces is proposed. The effect of a nonhydrostatic stress state and the formation of microplastic zones cause the transition of the composite from an isotropic to an anisotropic state. We calculate the tensor of effective elastoplastic modulii of the model as a function of the applied load and of the microplastic zone concentration.

A. N. Nikitin

T. I. Ivankina

I. K. Arkhipov

On the Formation of Preferred Inclusion Shape Orientations in Copper-Based Composites

During primary recrystallization a population of new grains nucleates and grows within a cold-deformed
material until the latter is consumed. This process was studied from a combined microstructure, kinetics
and texture viewpoint in commercial aluminum. Experimentally, recrystallization microstructures were
quantified by stereological variables and Cahn-Hagel growth rates. The orientations of the grains being
measured stereologically were identified and experimentally determined using the back-scatteredelectron
pattern analysis. A geometrically-based, statistical mathematical model of recrystallization
kinetics, formulated analytically on nucleation and growth premises, was devised taking into account
both the behavior of individual recrystallization texture components and the complex geometrical
impingement patterns due to recrystallized grains occurring in clusters. By correlating and matching
the experimental stereological measurements with the analytical model, the nucleation behavior and
growth rates during recrystallization were estimated for each texture component. A 3-D computer
simulation verified the analytically-deduced microstructural and textural description of recrystallization
and allowed the as-recrystallized grain sizes and the grain size distributions to be modelled as well.
Using the combined approach, a complete nucleation and growth model for recrystallization of heavily
cold rolled AA1050 was established.

R. A. Vandermeer

D. Juul Jensen

Quantification of Microstructural
Evolution and Texture Development
During Recrystallization

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 <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mtext>C</mml:mtext><mml:mi>&#x03B9;</mml:mi><mml:mrow><mml:mi>&#x03BC;</mml:mi><mml:mi>&#x03BD;</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math>
, and a comparison between <mml:math id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mtext>C</mml:mtext><mml:mi>&#x03B9;</mml:mi><mml:mrow><mml:mi>&#x03BC;</mml:mi><mml:mi>&#x03BD;</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math>
 measured by ultrasonics and by diffraction techniques (both X-ray and neutron). It is found that relative velocity measurements are very good for determining <mml:math id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mtext>C</mml:mtext><mml:mtext>4</mml:mtext><mml:mrow><mml:mtext>12</mml:mtext></mml:mrow></mml:msubsup></mml:mrow></mml:math> and <mml:math id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mtext>C</mml:mtext><mml:mtext>4</mml:mtext><mml:mrow><mml:mtext>13</mml:mtext></mml:mrow></mml:msubsup></mml:mrow></mml:math>
. 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 <mml:math id="E5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mtext>C</mml:mtext><mml:mtext>4</mml:mtext><mml:mrow><mml:mtext>11</mml:mtext></mml:mrow></mml:msubsup></mml:mrow></mml:math> 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.

A. J. Anderson

R. B. Thompson

R. Bolingbroke

J. H. Root

Ultrasonic Characterization of Rolling and Recrystallization Textures in Aluminum

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Texture, Stress, and Microstructure

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