Thierry Baudin

Simulation of normal grain growth by cellular automata

Grain growth is one of the most important parameters in the control of microstructure. Energy of grain boundaries at equilibrium and topological requirements are considered as two important factors in modelling of grain growth. From a more general point of view, grain growth is one of the natural structure evolving processes. The grain boundary network is similar to the pattern of biological cells, geographical and ecological territories. They have some similar characters. A method named cellular automata has been widely used in simulation of the development of biological systems and seems to be hopeful in simulation of grain growth. Hesselbarth and Goebel firstly applied cellular automata in primary recrystallization simulations and successfully described the theory of Johnson-Mehl-Avrami-Kolmogorov. The authors have been encouraged by this work and combined the way of the Monte Carlo method for microstructure representation with Hesselbarth`s idea of using cellular automata to make the present model as an amended one to simulate grain growth. Microstructure evolution, grain size and side distributions are investigated together and the results show that the present model well represents normal grain growth in every detail.

Effect of temperature on the processing of a magnesium alloy by high-pressure torsion

It is now well known that processing by SPD can significantly increase the strength of metallic materials by refining the grain structure and increasing the density of defects. The rapid increase in strength observed in the early stages of deformation is expected to slow down and saturate at large strains because of an increasing recovery of the material. Therefore, a saturation strength is anticipated that will depend on the processing temperature. This investigation analyses this parameter by determining the evolution of hardness of a magnesium alloy processed by high-pressure torsion at different temperatures.

IN-SITU NEUTRON DIFFRACTION STUDY OF THE CUBE CRYSTALLOGRAPHIC TEXTURE DEVELOPMENT IN Fe53%-Ni ALLOY DURING RECRYSTALLIZATION

Laboratoire de physico-chimie de l’e´tat solide, U.M.R. 8648, Baˆt. 410, 91405 Orsay, France(Received February 24, 2000)(Accepted in revised form April 3, 2000)Keywords: Texture; Recrystallization and recovery; Iron-nickel alloyIntroductionMany investigations have been carried out on the recrystallization crystallographic texture of rolledmetallic materials. However, the formation mechanism of the recrystallized grains with a preferredorientation has not been clarified yet. In particular, in the case of fcc metals and alloys from mediumto high stacking fault energy such as FeNi alloys, the cube texture {100},001. development duringrecrystallization is not clearly understood in spite of intensive studies. Several mechanisms have beenproposed to explain this phenomenon and two main alternative theories are generally proposed: orientednucleation (1) and oriented growth (2). Nevertheless, these theories are not satisfactory to explain fullythe cube texture development during recrystallization and in particular, they can not give any infor-mation on the time scale of the phenomenon. In this purpose, “in situ” texture measurements duringrecrystallization have been performed.The Fe53%-Ni alloy is widely used as soft magnetic sheet materials. After high reduction, cold rolledtexture is characterized by three main components considered as a typical copper-type texture (3): the“brass” {110} ,112. (B), the “aluminium” {123} ,634. (S) and the “copper” {112} ,111. (C)components. After annealing, a typical strong cube texture {100},001. development is observed.The aim of this paper is to study the crystallographic texture evolution of the Fe-53%Ni alloy duringannealing and the influence of the annealing temperature on the recrystallization kinetics. Then, the useof neutron diffraction is particularly requisite on the one hand to achieve good statistic measurement,even for small texture volume fraction and, on the other hand to use complex sample surroundings, asa furnace, necessary for the “in-situ” recrystallization study.Experimental ProcedureAfter hot rolling, the Fe-53%Ni alloy was cold rolled with a 95% reduction, until a final thickness sheetof about 0.2 mm. So in order to perform “in-situ” texture measurements by neutron diffraction, a pileup of 50 pieces (1cm 3 1cm) is realized in a vanadium (almost “transparent” for neutron diffraction)cubic container (1cm

Determination of the total texture

The orientation distribution function (ODF) calculation is usually performed using pole figures measured by X-ray or neutron diffraction. However, this kind of experimental technique does not allow total ODF to be determined, since the odd terms of the series expansion are not directly accessible from pole figures. The individual orientation measurement technique can be used, but it is necessary to evaluate the right orientation number necessary for a statistically reliable ODF. For samples at the surface, at the fifth of thickness from the surface and at the center of a Fe 3 pct Si sheet, this study shows that only 100 orientations are sufficient to find the principal components of the texture, but this number must be increased by a factor of 10 to evaluate with rather good accuracy the heights of the peaks. Indeed, to obtain a good correlation with an ODF calculated from pole figures measured by X-ray diffraction, the number of orientations needed is about 1000.

Microstructure and texture evolution in a magnesium alloy during processing by high-pressure torsion

Magnesium alloys often exhibit cracking and segmentation after equal-channel angular pressing (ECAP) at room temperature. With torsion shear deformation and a hydrostatic stress, high-pressure torsion (HPT) has an advantage over ECAP in the processing of hard-to-deform materials like magnesium alloys at room temperature. In this report, HPT was used on extruded AZ31 Mg alloy at temperatures of 296, 373 and 473 K for 1 and 5 turns. After HPT processing, the hcp crystal c-axis rotated from the disc (r,θ) plane towards the torsion axis. The angle between the c-axis and the torsion axis (Φ) has a relationship with the HPT processing temperature. It was found that the c-axis was 10o from the torsion axis at 296 and 373 K but 5o from the torsion axis at 473 K. The activity of the basal slip and the twinning exert significant contributions to the deformation. Microstructural features such as the grain size and grain size distributions were examined and correlated with the mechanical properties through the microhardness values.

Estimation of the Minimum Grain Number for the Orientation Distribution Function Calculation from Individual Orientation Measurements on Fe–3%Si and Ti–4Al–6V Alloys

The calculation of characteristics describing texture as well as relations between orientations and morphological features of microstructure are based on single orientation measurements. For such experimental data, it is essential to estimate the number of necessary measurements of single orientations for a statistically significant representation of the investigated quantity, which, in the present paper, is the orientation distribution function (ODF). In a previous article [Pospiech, Jura & Gottstein (1993) Mater Sci. Forum, 157–162, 407–412], this number has been estimated by a criterion that is used here for a cubic and a hexagonal material. This approach is very useful since it allows one to estimate the minimum orientation number with or without referring to an ODF calculated from pole figures measured by X-ray or neutron diffraction.

In situ electron backscatter diffraction investigation of recrystallization in a copper wire.

The microstructural evolution of a cold drawn copper wire (reduction area of 38%) during primary recrystallization and grain growth was observed in situ by electron backscatter diffraction. Two thermal treatments were performed, and successive scans were acquired on samples undergoing heating from ambient temperature to a steady state of 200°C or 215°C. During a third in situ annealing, the temperature was continuously increased up to 600°C. Nuclei were observed to grow at the expense of the deformed microstructure. This growth was enhanced by the high stored energy difference between the nuclei and their neighbors (driving energy in recrystallization) and by the presence of high-angle grain boundaries of high mobility. In the early stages of growth, the nuclei twin and the newly created orientations continue to grow to the detriment of the strained copper. At high temperatures, the disappearance of some twins was evidenced by the migration of the incoherent twin boundaries. Thermal grooving of grain boundaries is observed at these high temperatures and affects the high mobile boundaries but tends to preserve the twin boundaries of lower energy. Thus, grooving may contribute to the twin vanishing.

Impurities Effects on the Stored Elastic Energy in Cold-drawn Copper Wires

After wire-drawing, the orientation dependent stored elastic energy was measured by neutron diffraction in electrolytic tough pitch copper (ETP 99.99% Cu) wires to improve the knowledge on the chemical composition effect on the static recrystallization behavior. The line broadening measurements on relatively low deformed samples have shown that the stored energy related to the main fibers--the texture develops major {111}⟨uvw⟩ and minor {001}⟨uvw⟩ fibers--is about 2-4 J/mol and that the stored energy ratio {111}⟨uvw⟩/{001}⟨uvw⟩ decreases when the total impurity content increases. Some hypotheses about the relationship between recrystallization process, recovery and stored energy are finally proposed, and some assumptions about the recrystallization mechanisms are set.

Dynamic Recrystallization Modeling during Hot Forging of a Nickel Based Superalloy

A crystalline modeling of deformation implemented in the Finite Element code Abaqus® coupled to a recrystallization Cellular Automaton code is proposed and applied to the hot forging process. A sequential modeling is used in order to obtain a better understanding of the experimental observations and to improve our knowledge of the dynamic recrystallization process. Modeling is performed on aggregates built up from Electron Back Scattered Diffraction measurements. At the deformation temperature, the material presents two phases with a γ matrix of FCC structure and a γ’ hardening phase under a precipitate shape (Ni3(Ti,Al)) of SC structure. The crystalline approach can describe the interactions between the two phases and can compute the evolution of the local strain and stress fields as well as the dislocation density and the lattice rotation in the different grains. A Cellular Automaton algorithm is used for simulating the microstructure evolution during dynamic recrystallization. Nucleation and grain boundary mobility depend on the misorientation and on the local variation in stored energy. This presentation mainly details the different assumptions introduced in the recrystallization code and their influences on the microstructure evolution.

Texture Evolution in Invar® Deformed by Asymmetrical Rolling

Asymmetrical rolling, in which the circumferential velocities of the working rolls are different, is a method to impose shear deformation and in turn shear deformation texture to sheet through the thickness. The Invar® alloy has been deformed by asymmetrical rolling with a 84% thickness reduction. The texture of the deformed and annealed alloy was measured by X-ray diffraction at different levels through the thickness: upper side- middle- down side, with unidirectional rolling. The deformed texture is a copper type texture but the components were rotated about 5-7° around the Transverse Direction (TD) axis as compared to the ideal position of these components in the pole figure representation. During recrystallization, the rolling components (brass {011}<112>,copper {112}<111>, aluminum {123}<634>) decrease quickly whereas the cube component {001}<100> is preferentially developed after a short annealing time. However, the rolling components do not disappear completely after complete recrystallization (120 minutes annealing). As a consequence the final texture contains a high cube component and rolling components.