Papers by Author: Ph. Gerber

Abstract: A newly developed model based on vertex concept is presented in this paper. Contrary to its standard version, which is strictly deterministic, some concepts of Monte-Carlo type method were introduced. It makes the model more flexible and allows to introduce some parameters appearing in vertex movement equations, which are not easy to express in analytical form. Initial microstructure in the model is characterized by topology, crystallographic orientations and stored energy values of the grains. The boundary energies and mobilities are anisotropic in general. Nucleation mechanism of a given type is selected at the beginning of calculations. Deformation texture, stored energy distribution and initial microstructure are input parameters of the model. The aim of the calculations is to predict the texture and microstructure modifications during recrystallization. The model was also applied to the study of the kinetics of grain growth and recrystallization. The preliminary tests of the model are presented.

Abstract: In this work, EBSD (Electron Back Scattered Diffraction) measurements have been performed on deformed, partially and fully recrystallized cold rolled copper to 70 and 90 % reduction. The twin fraction as well as its existing relation with the parent crystallographic orientation has been followed in relation with respect to the recrystallized fraction. It has been shown thanks to this quantitative analysis that annealing twinning is more active when recrystallization nuclei slowly develop. The experimental observations are briefly discussed according with the twins selection principles [1].

Abstract: The stored energy of two cold rolled IF-Ti steels is calculated using finite element method from an EBSD microstructure. Because the thermo-mechanical treatments are different for the two materials, the parameters of the behaviour law used in the simulation and identified using a polycrystalline model and an inverse method from experimental results are also different. Their variation is due to the number of experimental tests taken into account for their identification and obviously to the thermo-mechanical path. The stored energy is mainly influenced by Lu which represents the mean free path of the mobile dislocations gliding on the system u and which is expressed as a function of a K material parameter. Using one tension test, the experimental stored energy values estimated from neutron diffraction measurements can be reproduced only for a material parameter K fixed.

Abstract: The crystallographic texture of electrolytic tough pitch copper has been investigated by neutron diffraction after deformation by cold wire-drawing (reduction of area between 51 and 94 %) and after static recrystallization. The deformation texture characterized by a strong <111> fiber is reinforced with increasing strain, while the volume fraction of <100> fiber is reduced. In turn, we show that the <100> fiber is strongly reinforced after recrystallization when intensity of the <100> maxima increases with the level of deformation. Since the <111> fiber disappears first during annealing, the static recrystallization has been followed “in situ” by measurements of the diffracted intensity evolution in the center of the {111} pole figure. From these experimental data and taking into account the Arrhenius equation, the activation energy of the recrystallization process has been determined for each deformation rate.

Abstract: The recrystallization process of two low-carbon ferritic steels with low fraction of alloying elements are modelled. The difference in chemical composition and initial thermomechanical treatment between these two steels can be the cause of the difference in the stored energy distribution after 40% deformation by cold rolling or plane compression simulated by Finite Element Modelling (FEM). In both cases the deformation texture is characterized by the presence of a g- fibre with a reinforcement for the {111}<112> component. The microstructure simulated by FEM is used as initial structure for Monte-Carlo simulations of recrystallization. In these simulations, the variation in chemical composition and initial thermo-mechanical treatment is introduced by the difference in stored energy distribution while recovery, nucleation and grain growth are simulated assuming that grain boundary properties mainly depend on misorientation. Modelling results are in agreement with experimental observations: that is the presence of a g- recrystallization fibre which corresponds to the initial deformed state and the development of {111}<110> component which is not sharp in the deformation microstructure.

Abstract: A three-dimensional Monte Carlo computer simulation technique has been applied to the problem of normal grain growth. A continuum system is modelled employing a discrete lattice. In this paper we investigate the connectivity of the points that represent the discretized microstructure. The lattice can have a strong influence on the result of the simulation. Only the BCC lattice with 14 neighbours gives similar results than the traditional simple cubic model with 26 neighbours. If we consider the computing time and the required computer memory, the BCC-14 model is a good alternative to the SC-26 model for simulating normal grain growth.

Abstract: Recently, some authors have used the Monte Carlo modelling using complete set of experimental data to get a better correlation between experimental observations and calculations concerning recrystallization process [1, 2]. Simulations using Monte Carlo technique have been performed these last years for IF-Ti steels in order to predict the microstructure and the texture evolution after high reduction amounts by cold rolling [3, 4]. On the contrary, in the present work, this evolution is simulated in an IF-Ti steel cold rolled after low deformation amount (reduction amount R = 40 %). Microstructure is characterized by Electron Back-Scattered Diffraction and introduced in the model. The quality index of the Kikuchi patterns (EBSD data) is used to qualitatively evaluate the stored energy for each grain. Different hypothesis of nucleation mechanisms have been introduced into the model. It has been shown that the better recrystallization texture correlation between experiment and simulation is obtained by taking into account the nucleation in the low stored energy sites and highly misorientation regions. Finally a simulation issue was compared with EBSD and TEM experimental results: microstructure, recrystallization kinetics and Avrami coefficients values.

Abstract: In order to simulate the recrystallization process, Monte Carlo modelling has been applied to the case of wire-drawn copper deformed to a moderate strain. The complete experimental set of data was taken mainly from Electron Back Scattered Diffraction measurements in a Scanning Electron Microscope. Several nucleation hypothesis have been introduced and tested into the model. It has been shown that nucleation taking into account the sites associated with the highest stored energy and highest local misorientation leads to the best results in terms of recrystallization microstructure and texture. An important number of new orientations - that come only from annealing twinning - are not reproduced with the model, indicating the major role of this particular mechanism during the recrystallization process.

Abstract: Cold-drawn Electrolytic Tough Pitch copper wires have been investigated with Neutron Diffraction and Electron Back Scattered Diffraction. The drawn copper wires (38% reduction in area) develop major <111> and minor <001> fiber textures. It appears that the texture intensity of the reinforcements within the <111> and <001> fibers is more pronounced in the center and intermediate part of the wires. During the first annealing time, it is found that the recrystallization kinetics is enhanced when oxygen content is increased. The recrystallized fraction within the intermediate zone of the wire is two times larger in the cathode with higher oxygen content. The mechanisms at the origin of this acceleration of recrystallization kinetics will be discussed taking into account the presence of Cu2O type oxides.

Abstract: Wire-drawn Electrolytic Tough Pitch copper deformed at moderate strain has been investigated with Electron Back Scattered Diffraction in a Scanning Electronic Microscope in order to evaluate the recrystallization mechanisms at the meso-scale. Experimentally, it has been shown that the static recrystallization takes place first in the highly deformed and misoriented areas, in the intermediate regions of the wire. The grains related to the <100> fiber nucleate and grow first in these regions, but some other orientations (including the <111> oriented grains) - that have a combined nucleation/growth potential - develop in second time. The annealing twinning is active from the beginning of the recrystallization and tends to randomize the final recrystallization texture.