Papers by Keyword: Stored Energy

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: Stored energy is generally considered as a main driving force of recrystallization process. After plastic deformation a high dislocation density and residual stress field remain in a material. Both quantities are at the origin of the stored energy and we call them as the “plastic” and “elastic” parts of this energy. Their orientation distributions can be determined using diffraction and deformation models. Both components of the stored energy are studied in the present work. Their distributions and characteristics are studied for f.c.c. and b.c.c. materials.

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: Effect of deformation temperature on subsequent recrystallization characteristics of commercial purity titanium (CP-Ti) was investigated using EBSD and transmission electron microscopy. CP-Ti plates were rolled to at various temperatures between 25°C and 600°C to achieve 60% reduction, and were subsequently annealed at 600°C for various time periods. Increase in rolling temperature resulted in more refined microstructures, which could be attributed to coactivation of secondary slip systems such as basal slip or pyramidal slip in addition to prism slip. During subsequent annealing, a large number of recrystallization nuclei formed in the warm-worked (below 450°C) CP-Ti while nucleation of recrystallization was slower for coldrolled one. This led to the faster recrystallization kinetics and a finer microstructure in asrecrystallized state for warm-worked CP-Ti. Meanwhile, the rate of recrystallization in CP-Ti rolled at 600°C was significantly retarded because a good portion of strain energy stored in deformed matrix was released by dynamic recovery. In the present work, we show that the widely accepted explanation for the influence of the deformation temperature on the recrystallization characteristics, i.e., increase of the deformation temperature retards the recrystallization process, is not always true for the hcp metals since deformation at elevated temperature activates secondary slip systems, providing more sites for nucleation of recrystallization.

Abstract: Grain boundary mobility in preferential growth of cube grains ({100}<001>) was evaluated by in-situ electron back scattering diffraction pattern (EBSP) analysis in order to clarify the fundamental mechanism of primary recrystallization in pure aluminum foils of 99.9% purity thermo-mechanically processed in the industrial production route for aluminum foils for electrolytic capacitors. We have carried out the continuous EBSP measurements during recrystallization of the aluminum foils heated to various temperatures in the chamber of scanning electron microscopy (SEM). We have succeeded in dynamic observation of the preferential growth of cube grains by the in-situ EBSP analysis. The in-situ EBSP analysis could reveal the migration rate of grain boundaries surrounding the cube grains. It was clarified that the proportional relation between migration rate and annealing time was satisfied. The stored energy providing the driving force for the grain boundary migration during primary recrystallization could be estimated from the misorientation within the deformed grains. The mobility of the grain boundary could be evaluated using the measured grain boundary migration rate and stored energy. Then the activation energy could be estimated by the in-situ EBSP analysis at various temperatures ranging from 270°C to 310°C. The obtained activation energy was 124 kJ/mol, which approximately corresponded to that for the diffusion of impurity such as iron or silicon in aluminum. This suggested that the rate-determining process of the grain boundary migration of cube grains was impurity diffusion in the pure aluminum foils.

Abstract: The stored energy during cold working has been estimated by two approaches. In the first approach, line broadening measurements were determined by neutron diffraction. The second approach is based on the model developed by Dillamore et al. [1]. Therefore, great attention has been paid to the influence of the deformation cell morphology, cell size and the eventual presence of orientation gradient inside the grains according to their orientation. Experimental results show this hierarchy E{111} <112> >E{111} <110>>E{001} <110>.

Abstract: The evolution of texture and stored energy was studied for Ti bearing and Ti-Nb bearing IF high strength steel undergoing a double cold rolling and annealing treatment by using Orientation Imaging Microscopy. Ti bearing IF high strength steel showed a similar texture evolution of the α and γ fiber components to that of IF steel. On the contrary, Ti-Nb bearing IF high strength steel displayed a different texture evolution from the one observed in the former steels. The difference in texture and stored energy evolution between both high strength steels seemed to be affected by the segregation behavior of solute alloying elements such as P.

Abstract: A modified two dimensional (2-D) Monte Carlo (MC) technique was used to simulate primary recrystallization in automotive steels containing fine particles. In order to consider anisotropic properties of grain boundary energy and grain boundary mobility, functions of boundary misorientation were introduced. Orientation-dependent stored energy developed in 80% cold-rolled interstitial free (IF) sheet steel was evaluated by reconstructing of data measured using electron back-scattered diffraction (EBSD) analysis. A subgrain method based on subgrain structure is used for quantitative analysis of the stored energy. The simulation reveals that particles affect evolution of microstructure during recrystallization. The simulation provided a theoretical foundation for understanding effect of particles on the final microstructures and crystallographic textures.