Richard Penelle

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.

Microstructure and creep deformation of a near beta titanium alloy 'β-CEZ'

Abstract The relationship between titanium alloy processing, structure and properties received great attention in recent years. The aim of this paper is to determine the influence of the microstructure of a titanium alloy on its creep properties at intermediate temperature. A pronounced influence of the microstructure, quantified by image analysis, on the steady-state creep rate was found. Structures exhibiting large values of length, width, surface and/or perimeter of the primary intragranular alpha phase ( α p ) and thus low values for the total interfacial area between the α p and β matrix, show low creep strength at 400°C. In addition, the influence of various parameters such as the texture of the alpha phase, the size and the morphology of the α phase (at prior beta grain boundaries and secondary alpha phase) and the prior beta grain size were investigated. The effects of temperature and stress level on the creep response of the alloy were investigated in the temperature range of 400 to 470°C. The stress dependence of the steady-state creep rate indicates that an increase in temperature introduces a gradual decrease in the stress exponent n and a change of creep mechanism at 400 to 450°C, depending on the stress level. The apparent activation energy of creep was determined for different stress levels. Transmission electron microscopy observations of deformed dislocation structures developed during creep are used to interpret creep properties, and deformation mechanisms are proposed for the primary and secondary intragranular alpha phases.

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.

Texture and grain size dependence of grain boundary character distribution in recrystallized Fe-50%Ni

The grain boundary character distribution (GBCD) has been demonstrated to exert a noticeable influence on those boundary-related physical properties and metallurgical process that take place in polycrystalline materials. In the present study the Electron Back Scattered Diffraction (EBSD) technique was used in order to investigate the influence of microtexture and grain size on GBCD as well as the effect of such influence on the evolution of bulk texture in primary recrystallized Fe-50%Ni samples.

Texture and Evolution of Recrystallization in Low Carbon Steel Wire

The effect of cold wire drawing on texture of industrial low carbon steel wire was investigated. On the other hand, the mechanism of recrystallization of drawn-wire was studied during different isothermal annealing below 723 °C. The structural evolution of wire was studied by optical microscopy, SEM, EBSD and X-Ray diffraction. From this study, a fiber texture was observed in deformed wire. However, a recrystallization reaction occurs after critical temperature during annealing.

Monte Carlo Modeling of Low Carbon Steel Recrystallization: Role of Thermo-Mechanical Treatment and Chemical Composition

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.

Deformation textures and plastic anisotropy of steels using the Taylor and nonhomogeneous models

The deformation textures of B.C.C. polycrystals (uniaxial tension, rolling) and the Lankford coefficient are predicted using the Taylor model and a nonhomogeneous model. The mixed glide conditions {110}〈111〉 + {112}〈111〉 are imposed using the yield polyhedron proposed by Orlans-Jolietet al. [1988]. The nonhomogeneous model is based on the Arminjon model [1987]; however, Arminjon used the pencil glide condition. An original calculation is proposed to simulate with a high precision deformation textures (orientation distribution functions O.D.F. F′(g)), without using the harmonic method, which leads to truncation errors. No restrictions are imposed on the eventual symmetry of the initial O.D.F. F(g). Using experimental and calculated textures of low carbon steels, it is shown that the homogeneous Taylor model gives good results for low deformations (uniaxial tension), whereas the nonhomogeneous model improves the Taylor model for high deformations (rolling).

Monte Carlo Method for Simulating Grain Growth in 3D Influence of Lattice Site Arrangements

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.

Influence of Thermo-Mechanical Treatments on the Stored Energy Simulated by FEM for Two Low Carbon Steels

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.

Evolution of Microstructure and Texture during Annealing of a Copper Processed by ECAE

A submicron-grained (SMG) microstructure, with an average grain size of ~0.4 µm was produced by equal channel angular extrusion (ECAE). The SMG microstructure was composed of large dynamic recrystallized grains within a matrix of deformed elongated cells. Samples were annealed for various times at 473 K and then examined using transmission electron microscopy (TEM) and electron back scattered diffraction (EBSD). The results specify that a large recovery takes place during the first annealing times. Moreover, MET investigations show nucleation of grains which orientations are found in the recrystallized texture. The EBSD measurements established that, after 7min30s at 473 K, the microstructure is equiaxed and stable with an average grain size of about 2 µm.