Phase field modeling of stressed grain growth: Effect of inclination and misorientation dependence of grain boundary energy
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Texture (cosmology)
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Based on the theoretical model of grain growth,combined with the curvature mechanism and probabilistic transition rules,a 2D cellular automata(CA) model was built under the conditions of anisotropic grain boundary mobility and grain boundary energy.This CA model was used to simulate the grain growth under isothermal condition,the microstructure evolution and kinetics characteristics as well as the grain size and edge number distributions were analyzed,and the effects of grain boundary mobility anisotropy and grain boundary energy anisotropy on grain growth were studied.The results show that the microstructure evolution was in accordance with the normal grain growth law,the relative distributions of grain size deviated from normal distribution and the grain edge number distribution was not time-dependent,the equilibrium angle of triple junctions grain boundary with small angle misorientations was 120°.Comparing with the isotropy,the anisotropic grain boundary mobility and grain boundary energy obviously decreased the grain growth rate,but the grain boundary mobility anisotropy alone did not significantly change the grain growth.The effect of grain boundary energy anisotropy on grain growth was greater than that of grain boundary mobility anisotropy.The simulation results corresponded with the theory of grain growth kinetics and the conclusion from relevant literature.
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Dislocation-accumulated grain boundaries were systematically investigated in terms of local atomic coordinates in the vicinity of grain boundary and energetics on grain boundary evolution by first-principles calculations. Detailed numerical analyses of energy and local atomic configuration at a grain boundary with fixed misorientation angle identified the most stable configurations both for the dislocation-distinctive model and the coincident-site-lattice model with kite-shaped structural units on grain boundary planes. The energy profiles of structural optimization using both initial models indicate that the distinctive dislocations at a grain boundary can be readily converted into kite-shaped structural units without noticeable energy barrier, though they look quite different, and reverse conversion may also be realized under external stress, enabling grain boundaries functioning as dislocation sources and sinks. Systematic calculations for grain boundary with misorientation angles ranging from 5.7° to 53.1° revealed that the interaction energy between dislocation is blunted within a dislocation core region. Furthermore, the energy needed to increase the misorientation angle during severe plastic deformation is quantitatively evaluated.
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Grain boundary strengthening
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To obtain a fundamental understanding of the effect of structure and geometry of grain boundary on the diffusion kinetics in nanocrystalline materials, the influence of grain boundary misorientation on the effective diffusion coefficient (apparent diffusivity) in nanocrystalline aluminum was investigated using molecular dynamics simulations. Nine series of [001] symmetric tilt grain boundaries, including high and low symmetric boundary planes, were studied. The apparent diffusivity in the samples was calculated in the temperature range from 423 K to 823 K by monitoring the mean square displacement of atoms as a function of simulation time. A temperature dependence of the effective diffusion coefficient according to the Arrhenius law was obtained for all samples. It is found that the apparent diffusivity is anisotropic and it is a strong function of grain boundary misorientation at low and high temperatures. At all temperatures, Σ29 [001]/(520) symmetric tilt grain boundary with misorientation angle of 43.68° exhibits the highest effective diffusion coefficient among the investigated grain boundaries. The simulation results show that the activation energy and pre-exponential factor are affected significantly by the grain boundary misorientation angle. Moreover, the results indicated that the misorientation dependence of activation energy for diffusion exhibits two local maxima, which correspond to two symmetric tilt grain boundaries. Additional calculation of misorientation dependence of the pre-exponential factor shows two local minima at the same symmetric tilt grain boundaries. The misorientation dependence of the effective diffusion coefficient was explained on the basis of grain boundary energy and the crystallographic structure of grain boundary.
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Abstract The role of grain boundary misorientation angles on the dislocation–grain boundary interactions was incorporated into a micro hardening scheme. The current formulation is applicable to both coarse‐ and ultrafine‐grained alloys, and evidences the experimentally observed dominant role of the misorientation angles on the deformation response of the latter.
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Abstract It has been suggested that the experimentally observed orientation dependence of the mobility of grain boundaries in f.c.c. metals may be related to the dependence of the rate of self diffusion in grain boundaries on the disorientation across the boundary. Later, this relative orientation effect on the rate of boundary diffusion and self diffusion was experimentally observed. It was shown by Hoffman and Turnbull that in bicrystals of silver misoricnted around (100) by 9° to 28°, self diffusion along the boundary (parallel to the common (100)) may be described in terms of a coefficient of self diffusion in individual grain boundary edge dislocation pipes, orders of magnitude larger than the coefficient of lattice self diffusion. It is significant that the coefficient of self diffusion in grain boundary dislocation pipes was found to be independent of the misorientation (i.e., of the density of edge dislocations in the boundary) at least up to 28°, suggesting that even a boundary of such a great misorientation may be considered as a network of dislocations, as far as self diffusion is concerned. In recent experiments the relative mobilities of boundaries in various orientations between a deformed (99.98% pure) aluminum single crystal and recrystallized grains growing in it in fairly well defined, lattice orientation relationships were compared. The matrix crystal was rolled to 80% R.A. on a (110) plane in a [112] direction, after which the strip still retained its initial orientation and the texture was very sharp. Recrystallized grains quite accurately oriented so as to have highest overall boundary mobility, i.e., corresponding to 40° rotations around the two 111 axes of the matrix grain lying in the rolling plane, were produced in large numbers by random nucleation on one side of the strip (rubbing one side with sandpaper and annealing). The re crystallized grains, that were at first growing in very large numbers and quite randomly but only in the thin surface layer highly deformed by abrasion (nucleation side), on annealing for 600 sec at 350°C grew across the whole thickness (0,010″) of the rolled single crystal. As a result of very selective growth, the recrystallized grains reaching the other side of the strip (growth side) showed a very sharp texture consisting of four components with the orientations described.
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Lattice diffusion coefficient
Grain boundary strengthening
Lattice (music)
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