Papers by Keyword: Vertex Model

Abstract: A local curvature multi-vertex model was developed. This model is the straightforward two-dimensional topological network model based on the physical principles which are the curvatures of grain boundaries and the grain boundary tensions at triple junctions. The model was applied to the artificial random microstructure under some conditions of grain boundary characters. The misorientation distribution was changed very little under constant grain boundary energy and mobility, but it was change much under grain boundary character dependent on misorientation. Therefore, in order to discuss actual textures, it is important to take grain boundary characters into account.

Abstract: We report the recent development of a 3D orientation data post-processing software, which we refer to as QUBE. Amongst other functionalities, it offers the possibility to specify the spatial and orientational distribution of boundary normals. We describe a method to reconstruct a voxel-accurate and smooth 3D boundary triangle mesh by algorithmic means. A proof of concept is given by a benchmark on a generic dataset and we demonstrate a first result with the description of selected grain boundaries in an Fe-28%Ni sample.

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: 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: 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: The recrystallization process in polycrystalline material was studied using the newly developed two–dimensional model based on the vertex concept. In the model presented below the microstructure of polycrystalline material is represented by two-dimensional network of grains. The initial microstructure is characterized by topology, crystal orientations and stored energy values of the grains. The boundary energies and mobilities are anisotropic in general. Additional driving forces in recrystallization, are exerted on vertices and are derived from the stored energy gradients between adjacent grains. The nucleation mechanism of a given type is selected at the start of the calculations. Two different nucleation types were tested. Deformation texture, stored energy distribution and initial microstructure are input parameters of the model. The goal of the calculations is the prediction of texture and microstructure modification during recrystallization. A comparison of predicted and experimental characteristics enables the verification of the model assumptions.