Papers by Author: Brigitte Bacroix

Abstract: Formation of residual stresses and crystallographic textures during rolling have been studied using elasto-plastic deformation for polycrystalline material (Leffers-Wierzbanowski model). The rotation of grain crystal lattices is the basic mechanism of texture formation and anisotropic behavior of metals during plastic deformation. The classical definition of crystal lattice rotation leads in some cases to different texture predictions than the definition based on the orientation preservation of selected sample planes and/or directions (preservation condition). Also predicted residual stresses can be influenced by a choice of rotation definition. In the used deformation model of polycrystalline material, the intensity of grain-matrix interaction is described by the parameter L= aG, where G is shear modulus and a is elasto-plastic accommodation parameter. Model calculations have been done for different values of this parameter and for two definitions of lattice rotation. The predicted second order residual stresses and crystallographic textures for cold rolled ferrite steel are compared with experimental ones.

Abstract: The crystallographic texture formation in low carbon steel during asymmetric rolling was studied experimentally and analysed numerically. Modelling of plastic deformation was done in two scales: in the macro-scale using the finite element method ( FEM) and in crystallographic scale using the polycrystalline deformation model (LW model). The stress distribution in the rolling gap was calculated using FEM and next these stresses were applied in LW model of polycrystalline plastic deformation. In general, the predicted textures agree very well with experimental ones.

Abstract: The stored energy distribution versus crystal orientation in polycrystalline copper was determined using synchrotron radiation. This distribution is an important input data for recrystallization models. The stochastic vertex model of recrystallization was used in the present work. It is a mixture of the classical vertex model and the Monte Carlo algorithm. Both grain boundary energy and stored energy are taken into account in the calculations. In each elementary step, a reasonably small, random modification of a given vertex position is generated and a corresponding total energy change of a system is calculated. A new vertex position is retained with a probability proportional to the Boltzmann factor. In such a way one avoids solving a complex system of equations. This approach is also closer to the stochastic nature of recrystallization process. The inclusion of the stored energy distribution in the above model enables a good explanation of the recrystallization process. The recrystallization textures for polycrystalline copper rolled to low and high reductions were predicted in agreement with experimental results.

Abstract: The development of deformation texture and microstructure was examined for four different initial textures. IF steel sheets with a majority of α-, ε-, and γ-fiber and near random texture were prepared and cold rolled. The specimens exhibited characteristic behaviors in rolling texture evolution and deformation-induced misorientation development, according to their initial textures, especially at small strain levels. Due to the orientation dependence of intra-granular misorientation accumulation, the different texture evolutions affected the induced misorientation distribution. A larger fraction of γ-fiber orientations was related to more prominent misorientation development, while the initial texture stability simultaneously affected the misorientation development. The unstable, initial ε-fiber texture showed a stronger tendency of misorientation accumulation than the stable α-fiber during the subsequent cold rolling.

Abstract: Plastic deformation induces the dislocation and residual stress fields, which rest in a material after releasing of applied external forces. One can distinguish the stored energy connected with dislocation density and that with residual stresses. The stored energy distributions can be determined experimentally by diffraction experiments and also can be predicted by deformation models. The so obtained distributions of the stored energy versus crystal orientation were correlated with deformation and recrystallization textures of low carbon steel.

Abstract: Classical vertex model till now described only the grain growth stage and not the primary recrystallization. In the present work the vertex model is first extended in order to take into account the both stages of recrystallization process. The influence of the stored energy is taken into account and some phenomenological laws describing the evolution of grain boundary energy and mobility with misorientation angle are used. Nucleation is considered to be site-saturated. The experimentally determined stored energy values, crystallographic orientations and boundary misorientation distributions are used in order to characterize the initial microstructure. The model is tested to study the recrystallization of 70% and 90% cold rolled polycrystalline copper during an annealing treatment. In order to explain the texture evolution in both cases, it is necessary to introduce an energy threshold for grain boundary movement, i.e. a minimal value of the stored energy difference between a nucleus and the deformed material necessary to provoke grain boundary motion. The developed model is shown to predict texture evolutions in good agreement with experimental data.

Abstract: The generalized deterministic vertex model was successfully used to study the recrystallization process and the corresponding results were published elsewhere [1]. In its classical form the vertex model has analytical formulation, basing on the total energy (i.e. boundary energy and stored energy) minimization. A change of grain boundary configuration in classical vertex model is found by the calculation of vertex velocities. Consequently, a global and complex system of equations has to be solved in each step. In order to simplify calculations and to handle the problem in a more flexible way, the statistical model was proposed. Typical elements of Monte Carlo algorithm were incorporated into the vertex model: a random (and small) modification of microstructure is accepted with the probability proportional to Boltzmann factor. This approach is closer to the stochastic nature of recrystallization process. The model was used to study the recrystallization of 70% and 90% cold rolled polycrystalline copper. It predicts correctly recrystallization textures for high and low strains.

Abstract: In order to elucidate the predominance of Goss grains after SIBM in electrical steel sheets, Goss, D-Cube and {111}<112> grains after temper rolling of 5 and 9% reduction were observed by TEM. In 5% strain the amount of dislocations in Goss grains was the smallest of the three orientations. In 9% strain dislocations in Goss grains were distributed more heterogeneously than the other two types of grains. It is considered that {111}<112> grains have large amounts of dislocations owing to high Taylor factors and the differences of microstructures between Goss and D-Cube grains are due to orientation stabilities. Goss grains are speculated to be easy to recover and therefore they are predominant after SIBM.

Abstract: Nucleation and normal or abnormal grain growth of new grains have been observed in several metals and alloys during annealing after various levels of strain (from few percents for abnormal grain growth in steel and aluminium to 90 % strain for static recrystallization of highly deformed copper, zirconium and steel). For each of these cases, the links between the initial deformation state of the polycristalline samples and their final textures after annealing are analyzed in some details, by taking into acount the distribution of orientations and misorientations within the samples, as well as the repartition of stored energy . With the help of polycristalline models for the simulation of deformation and recrystallization processes, some general conclusions regarding the nucleation and growth processes are finally drawn.

Abstract: The evolution of crystallographic texture in a Zr-2Hf alloy has been investigated during deformation, primary recrystallisation and normal grain growth. The as-deformed states (50-90% deformation) are characterized by a major tilted {0001}<1010> texture component and this component is reinforced with increasing deformation. A decrease in the intensity of the tilted {0001}<10 10> component and a continuous increase in the intensity of the tilted {0001}<1120 > component take place during primary recrystallisation. Normal grain growth is associated with the coarsening of grains with the {0001}<1120 > orientation. This texture evolution is interpreted on the basis of the evaluation of the stored energy and the consideration of specific grain boundaries with low energy and/or high mobility.