Materials Science Forum Vols. 467-470

Abstract: Space-filling in kinetically active 3-d network structures, such as polycrystalline solids at high temperatures, is treated using topological methods. The theory developed represents individual network elements—the polyhedral cells or grains—as a set of objects called average N-hedra, where N, the topological class, equals the number of contacting neighbors in the network. Average N-hedra satisfy network topological averages for the dihedral angles and quadrajunction vertex angles, and, most importantly, act as “proxies” for real irregular polyhedral grains with equivalent topology. The analysis provided in this paper describes the energetics and kinetics of grains represented as average N-hedra as a function of their topological class. The new approach provides a quantitative basis for constructing more accurate models of three-dimensional grain growth. As shown, the availability of rigorous mathematical relations for the curvatures, areas, volumes, free energies, and rates of volume change provides precise predictions to test simulations of the behavior 3-d networks, and to guide quantitative experiments on microstructure evolution in three-dimensional polycrystals.

Abstract: We compare the ability of three different types of microstructural model to simulate particle pinning. The microstructural models are the Phase Field model, the Front Tracking model and the Monte Carlo Potts model. The same 3D test geometry is simulated using each method. This is an hexagonal network with spherical particles located at the centre of each hexagonal grain. The hexagonal grain network provides a constant driving force for a moving boundary and includes triple line and quadruple point motion. This geometry allows detailed investigation of the boundary/particle interaction. The pinning force acting on the migrating curved grain boundary is calculated and compared with theoretical predictions for each model.

Abstract: With the development of new, fully three-dimensional metallographic techniques, there is considerable interest in characterizing three-dimensional microstructures in ways that go beyond twodimensional stereology. One characteristic of grain structures is the surface of lowest energy across the microstructure, termed the critical manifold (CM). When the grain boundaries are sufficiently weak, the CM lies entirely on grain boundaries, while when the grain boundaries are strong, cleavage occurs. A scaling theory for the cleavage to intergranular transition of CMs is developed. We find that a critical length scale exists, so that on short length scales cleavage is observed, while at long length scales the CM is rough. CMs for realistic polycrystalline grain structures, determined by a network optimization algorithm, are used to verify the analysis.

Abstract: In this paper we discuss the principles of a combined approach to solve the problem of solute drag as it occurs in microstructure evolution processes such as grain growth, recrystallization and phase transformation. A recently developed irregular grid cellular automaton is used to simulate normal grain growth, in which the energy of the grain boundaries is the driving force. A new, discrete diffusion model is used to simulate solute segregation to the grain boundaries. The local concentration of the solute is then taken into account in the calculation of the local grain boundary mobility and/or grain boundary energy, thereby constituting a drag force. The relation between solute concentration and grain boundary mobility/energy is derived from molecular dynamics simulations.

Abstract: Grain growth simulations using the microstructure simulation system Elle have been performed in materials with a pre-existing grain shape preferred orientation. As might be expected, the microstructure is completely modified by the end of the experiment, and grain areas have increased by a factor of seven. The area of material swept by the migrating grain boundaries was monitored, and it was found that at every stage, virtually all of the grains which survived the grain growth process contain one and only one core of unswept material. Remarkably these remnant unswept cores preserve a useable record of the grain size and orientation of the original grains. This work suggests that it may be possible to see past a grain growth episode to estimate the original grain shape and grain size of the polycrystal, and perhaps even reconstruct the grain boundary kinematics. The identification of unswept cores also has the potential to help unravel the evolution of grain boundary chemistry during grain boundary migration.

Abstract: Simulation is becoming an increasingly important tool, not only in materials science in a general way, but in the study of grain growth in particular. Here we exhibit a consistent variational approach to the mesoscale simulation of large systems of grain boundaries subject to Mullins Equation of curvature driven growth. Simulations must be accurate and at a scale large enough to have statistical significance. Moreover, they must be sufficiently flexible to use very general energies and mobilities. We introduce this theory and its discretization as a dissipative system in two and three dimensions. The approach has several interesting features. It consists in solving very large systems of nonlinear evolution equations with nonlinear boundary conditions at triple points or on triple lines. Critical events, the disappearance of grains and and the disappearance or exhange of edges, must be accomodated. The data structure is curves in two dimensions and surfaces in three dimensions. We discuss some consequences and challenges, including some ideas about coarse graining the simulation.

Abstract: A mesoscale, variational simulation of grain growth in two-dimensions has been used to explore the effects of grain boundary properties on the grain boundary character distribution. Anisotropy in the grain boundary energy has a stronger influence on the grain boundary character distribution than anisotropy in the grain boundary mobility. As grain growth proceeds from an initially random distribution, the grain boundary character distribution reaches a steady state that depends on the grain boundary energy. If the energy depends only on the lattice misorientation, then the population and energy are related by the Boltzmann distribution. When the energy depends on both lattice misorientation and boundary orientation, the steady state grain boundary character distribution is more complex and depends on both the energy and changes in the gradient of the energy with respect to orientation.

Abstract: This paper try to elucidate some aspects of the impact of using two different types of computational lattices on the solution of simple models like, for example, grain boundary migration and/or dynamic recrystallization.Not surprisingly, the final solution is obviously affected by anisotropy of used lattices but as we know, they are computational lattices.Ho wever, a material itself has its own anisotropy of its lattice probably different from those lattices used in model.Therefore, the main task in nowadays simulations is to get rid of the influence of computational lattice and to achieve the properties of the lattice of the simulated material.

Abstract: After primary recrystallization of highly rolled (>98% reduction) high purity Ni (99.999%) tapes the cube texture fraction can range from 45 - 65%. Annealing at temperatures >1000oC leads to cube texture volume fractions of >95% as a result of grain growth. A Monte Carlo Potts model was used to simulate this annealing process. The starting microstructures for the simulations were generated from experimental data taken using electron backscatter pattern analysis. The simulation results suggest that in addition to the grain boundary misorientation and energy functions used, the misorientation texture and grain sizes are also determining factors in the grain growth process. As the grain size after recrystallization is comparable to the tape thickness, the surface energy of the grains may also be an important factor. Simulations were therefore also carried using a surface energy term. If the cube grains have a lower surface energy then a stronger cube texture is predicted.

Abstract: Computer simulations of 2D normal grain growth have shown that size correlations between adjacent grains exist in 2D grain structures. These correlations prevail during the coarsening process and influence on the kinetics of the process and on the grain size distribution. Hillert’s analysis starts with the assumption that all grains in the structure have the same environment. Since computer simulations contradict this assumption, the mean-field theory for normal grain growth needs to be modified. A first attempt was made by Hunderi and Ryum, who modified Hillert’s growth law to include the effect of spatial grain size correlations. In the 1D case the distributions derived by means of the modified growth law agreed well with simulation data. However, the distribution derived for 2D grain growth retained unwanted properties of the Hillert distribution. We review some recent progress in developing a mean-field statistical theory. A paradox related to curvilinear polygons is shown to support the expectation that the grain size distribution has a finite cutoff.