In the present paper we have put together some results of a cluster method that allows the calculation
of linear and also non-linear effective elastic constants of polycrystalline materials within an iterative
self-consistent scheme. The conceptual idea consists in simulating the real material by a suitably chosen
cluster of single grains. One can then determine the elastic properties of the material under study by
examining the elastic behavior of the cluster. The method is capable of resolving the effect of the grain
shape, that is determined by the coordination number of the grains on the effective constants.

H. Kiewel

H. J. Bunge

L. Fritsche

Calculation of Linear and Non-Linear Elastic Properties of Polycrystalline Materials by Use of a Cluster Model

Mathematical modelling and computer simulation of physical phenomena is a rapidly growing field of work in all areas of pure and applied sciences. In principle, mathematical modelling of physical phenomena has been the field of theoretical physics from the very beginning of physics although the computer has increased the potentials of this method by many orders of magnitude. Modelling and simulation are often used as synonyms. It may, however, be meaningfull to distinguish the development of a mathematical model from its use in computer simulation. Also, a mathematical model in this sense must be distinguished from mathematical expressions interpolating experimental data. In the field of textures, models of texture formation, models of materials properties, as well as the combination of the two are being used. In this connection it is important whether a texture formation model is linear or non-linear. In the first case the texture formation operator can be reduced to the orientation space whereas a non-linear operator operates in the full texture space.

Some Remarks on Modelling and Simulation of Physical Phenomena

In this study both primary static recrystallization and static recovery of cold rolled bcc and fcc metals and alloys are numerically simulated using a three-dimensional model that is based on a modified cellular automaton approach. The model considers the influence of the initial deformation texture and microstructure on both static recovery and primary static recrystallization with a high spatial resolution. The cellular automat technique provides both local and statistical information about the kinetics, the morphology and the texture change during annealing. The influence of nucleation and growth can be studied in detail. The simulations are compared to experimental results obtained on fcc and bcc polycrystals.

V. Marx

D. Raabe

O. Engler

G. Gottstein

Simulation of the Texture Evolution During Annealing of Cold Rolled Bcc and Fcc Metals Using a Cellular Automation Approach

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&#xB0;&#x3C;111&#x3E; 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&#xB0;&#x3C;111&#x3E;-transformed rolling texture.

Simulation of the Recrystallization Textures of Al-Alloys on the Basis of Nucleation and Growth Probability of the Various Textures Components

A new technique for the simulation of microtexture evolution during cold deformation which is based
on 2 dimensional &#x28;2D&#x29; dislocation dynamics is presented. In the simulation all involved dislocations
are regarded as infinite straight line detects which are embedded in an otherwise isotropic linear elastic
medium. As the model is 2D only edge dislocations are considered.In the first simulation step the net local stresses are derived and used to calculate the resulting
dislocation motion. Dislocation multiplication, annihilation and reactions are taken into account. Thermal
activation is included. In the second step the local misorientations arising from the dislocation
distribution are calculated.This method shows in microscopic detail how misorientations are generated and distributed within
grains during plastic deformation.

F. Roters

2 Dimensional Dislocation Dynamics &#x2013; A New Technique for the Simulation of Deformation Microtextures

The description of textures in terms of texture components is an established conception in quantitative
texture analysis. Recent developments lead to the representation of orientation distribution functions
as a weighted sum of model functions, each corresponding to one anisotropic texture component. As
was shown previously, an adequate texture description is possible with only a very small number of
anisotropic texture components. As a result, textures and texture changes can be described by a small
number of vivid parameters and their variations, namely by volume parts, half widths and ideal
orientations.The texture of a tensile tested commercial aluminum alloy was investigated by decomposition into
anisotropic components. The texture evolution during tensile testing is represented by the corresponding
changes of the component parameters and compared with results from an iterative series expansion
analysis.

Th. Eschner

J.-J. Fundenberger

Application of Anisotropic Texture Components

Dierk Raabe

Forword

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 &#x28;Taylor model&#x29;.

K. Helming

A Nearly Equal Distant Grid of Orientations for QuantitativeTexture Analysis

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 &#x28;two-step&#x29; 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&#xB0;<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>111</mml:mn></mml:mrow><mml:mo>&#x0232A;</mml:mo></mml:mrow></mml:mrow></mml:math>, 27&#xB0; + 84&#xB0;<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> and &#x3B1;<mml:math id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>&#x2329;</mml:mo><mml:mrow><mml:mn>111</mml:mn></mml:mrow><mml:mo>&#x0232A;</mml:mo></mml:mrow></mml:mrow></mml:math> respectively for fcc- and bcc- metals.

U. K&#xF6;hler

Modelling Primary Recrystallization in fcc and bcc Metals by Oriented Nucleation and Growth With the Statistical Compromise Model

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Texture, Stress, and Microstructure

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