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 <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>&#x2329;</mml:mo><mml:mrow><mml:mn>110</mml:mn></mml:mrow><mml:mo>&#x0232A;</mml:mo></mml:mrow></mml:mrow></mml:math> 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 <mml:math id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>&#x2329;</mml:mo><mml:mrow><mml:mn>110</mml:mn></mml:mrow><mml:mo>&#x0232A;</mml:mo></mml:mrow></mml:mrow></mml:math> fibre texture. A modeling of the texture evolution during drawing has also been carried out
using the Taylor model.

C. Schuman

C. Esling

M. J. Philippe

M. Hergesheimer

M. Jallon

A. Lefort

Texture Evolution During the Drawing of Low Carbon Steel

Discrete methods of orientation distribution (ODF) analysis are applied to quartz and calcite rocks with
trigonol crystal and triclinic sample symmetry. ODF&#x2019;s are calculated from pole figures measured by
neutron diffraction. A particular complication for quartz is the presence of overlapping peaks which
can be separated with the WIMV or ADC algorithms based on diffraction intensity differences. Both
methods provide similar solutions. Characteristic differences are discussed. By comparing ODF&#x2019;s
obtained from different data subsets (changing number and extent of pole figures) it is concluded that
quantity and quality of data, as well as the texture type, have a crucial influence on resolution. It is
demonstrated that discrete methods provide the possibility to obtain quantitative texture information
from minimal experimental data.

H. R. Wenk

K. Pawlik

J. Pospiech

J. S. Kallend

Deconvolution of Superposed Pole Figures by Discrete ODF Methods:
Comparison of ADC and WIMV for Quartz and Calcite With Trigonal
Crystal and Triclinic Specimen Symmetry

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&#x2019;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.

P. Ratchev

P. van Houtte

B. Verlinden

P. de Smet

P. Neutjens

R. Baartman

P. Drent

Prediction of Forming Limit Diagrams of Al-Mg Rolled Sheets Taking
Texture Into Account

A method for measuring strain by analyzing sharpness of Electron Channeling Pattern (ECP) with Image
analysis has been newly developed. The relative value of sharpness of first-order pseudo-Kikuchi line
in ECP is used as a parameter of strain. Strain change of Fe-3.25&#x25;Si alloy single crystal and polycrystal
during deformation and recrystallization was analyzed by this method. This method was compared with
the conventional methods; hardness and line broadening of X-ray. This method can be used for
measuring strain in material with any crystal orientation.

Y. Yoshitomi

K. Ohta

J. Harase

Y. Suga

A Method for Measuring Strain by Analyzing Sharpness of ECP With
Image Analysis

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 &#x201C;a priori&#x201D; 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.

R. E. Bolmaro

Grain Axes Coincidence Model: Relaxed Constraints and Finite
Strains Revisited

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.

P. Burgholzer

O. Scherzer

On the Numerical Determination of Optimal Textures of Aluminium

Sections of a three-dimensional Orientation Distribution Function (ODF) for the &#x3B1;-Fe rolling texture
typical for most b.c.c. metals have been constructed on the basis of the proposed new method for ODF
simulation through the representation of a crystallite orientation by nine rotations, only three of which
are varied for a given component. The description of texture by superposition of partial fibre components
in used. A comparison of such a model ODF with an ODF reconstructed from experimental pole figures
by series expansion is presented. As a result all really encountered textures can be simulated by variation
of the crystallite spread parameters, texture axis positions, and predominant preferred orientations in
terms of a common approach.

V. N. Dnieprenko

S. V. Divinskii

A New Approach to Describing Three-Dimensional Orientation
Distribution Functions in Textured Materials&#x2014;Part II: Model ODF for Rolling Textures

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.

A. Morawiec

Review of Deterministic Methods of Calculation of Polycrystal
Elastic Constants

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Texture, Stress, and Microstructure

Table of Contents

Table of Contents: 1994

Texture Evolution During the Drawing of Low Carbon Steel

Deconvolution of Superposed Pole Figures by Discrete ODF Methods: Comparison of ADC and WIMV for Quartz and Calcite With Trigonal Crystal and Triclinic Specimen Symmetry

Prediction of Forming Limit Diagrams of Al-Mg Rolled Sheets Taking Texture Into Account

A Method for Measuring Strain by Analyzing Sharpness of ECP With Image Analysis

Grain Axes Coincidence Model: Relaxed Constraints and Finite Strains Revisited

On the Numerical Determination of Optimal Textures of Aluminium

A New Approach to Describing Three-Dimensional Orientation Distribution Functions in Textured Materials—Part II: Model ODF for Rolling Textures

Review of Deterministic Methods of Calculation of Polycrystal Elastic Constants