Recent Developments in Material Microstructure: a Theory of Coarsening

2015 ◽  
Vol 1753 ◽  
Author(s):  
K. Barmak ◽  
E. Eggeling ◽  
M. Emelianenko ◽  
Y. Epshteyn ◽  
D. Kinderlehrer ◽  
...  
Keyword(s):  
Steady State ◽  
Energy Density ◽  
Grain Boundary ◽  
Cellular Networks ◽  
Empirical Distribution ◽  
Relative Length ◽  
Planck Equation ◽  
Boltzmann Distribution ◽  
Grain Boundary Character Distribution ◽  
Lattice Misorientation

ABSTRACTCellular networks are ubiquitous in nature. Most engineered materials are polycrystalline microstructures composed of a myriad of small grains separated by grain boundaries, thus comprising cellular networks. The recently discovered grain boundary character distribution (GBCD) is an empirical distribution of the relative length (in 2D) or area (in 3D) of interface with a given lattice misorientation and normal. During the coarsening, or growth, process, an initially random grain boundary arrangement reaches a steady state that is strongly correlated to the interfacial energy density. In simulation, if the given energy density depends only on lattice misorientation, then the steady state GBCD and the energy are related by a Boltzmann distribution. This is among the simplest non-random distributions, corresponding to independent trials with respect to the energy. Why does such simplicity emerge from such complexity? Here we describe an entropy based theory which suggests that the evolution of the GBCD satisfies a Fokker-Planck Equation, an equation whose stationary state is a Boltzmann distribution.

Predictive Theory for the Grain Boundary Character Distribution

2012 ◽  
Vol 715-716 ◽  
pp. 279-285 ◽  
Author(s):  
Katayun Barmak ◽  
Eva Eggeling ◽  
M. Emelianenko ◽  
Y. Epshteyn ◽  
David Kinderlehrer ◽  
...  
Keyword(s):  
Steady State ◽  
Grain Boundary ◽  
Relative Length ◽  
Boltzmann Distribution ◽  
Grain Boundary Character Distribution ◽  
Boundary Character ◽  
Grain Boundary Character ◽  
Character Distribution ◽  
Boundary Character Distribution ◽  
Lattice Misorientation

Mesoscale experiment and simulation permit harvesting information about both geometric featuresand texture in material microstructures. The grain boundary character distribution (GBCD) is an em-pirical distribution of the relative length (in 2D) or area (in 3D) of interface with a given lattice misori-entation and grain boundary normal. During the growth process, an initially random texture distribu-tion reaches a steady state that is strongly correlated to the interfacial energy density [9]. In simulation,it is found that if the given energy depends only on lattice misorientation, then the steady state GBCDand the energy are related by a Boltzmann distribution. This is among the simplest non-random dis-tributions, corresponding to independent trials with respect to the energy. Why does such a simpledistribution arise from such a complex system?.

Mesoscale Simulation of the Evolution of the Grain Boundary Character Distribution

2004 ◽  
Vol 467-470 ◽  
pp. 1063-1068 ◽  
Author(s):  
D. Kinderlehrer ◽  
Irene Livshits ◽  
Gregory S. Rohrer ◽  
Shlomo Ta'asan ◽  
Peng Yu
Keyword(s):  
Steady State ◽  
Grain Boundary ◽  
Boundary Energy ◽  
Grain Boundary Character Distribution ◽  
Grain Boundary Energy ◽  
Boundary Character ◽  
Grain Boundary Character ◽  
Character Distribution ◽  
Boundary Character Distribution ◽  
Lattice Misorientation

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.

Five-Parameter Grain Boundary Character Distribution in Fe-1%Si

2004 ◽  
Vol 467-470 ◽  
pp. 727-732 ◽  
Author(s):  
Tricia A. Bennett ◽  
Chang Soo Kim ◽  
Gregory S. Rohrer ◽  
Anthony D. Rollett
Keyword(s):  
Grain Boundary ◽  
Grain Boundary Character Distribution ◽  
Crystalline Materials ◽  
Boundary Character ◽  
Grain Boundary Character ◽  
Symmetric Tilt ◽  
Character Distribution ◽  
Tilt Boundaries ◽  
Boundary Character Distribution ◽  
Lattice Misorientation

The grain boundary character distribution in an Fe-1%Si steel has been measured as a function of lattice misorientation and boundary plane orientation. There is a weak texture in the space of grain boundary planes that favors the {110} orientation. At specific misorientations, the anisotropy is larger. For example, when the lattice misorientation is 60° around [111], symmetric tilt boundaries comprised of two {110} planes on either side of the interface dominate the population. The results are consistent with observations suggesting that in a range of crystalline materials, the low energy, low index surface planes are found to dominate the distribution of internal interfaces.

Synthesizing Annealing Twins in Three-Dimensional Voxel-Based Microstructures

2012 ◽  
Vol 715-716 ◽  
pp. 549-549
Author(s):  
Lisa H. Chan ◽  
Gregory S. Rohrer ◽  
Anthony D. Rollett
Keyword(s):  
Grain Boundary ◽  
Three Dimensional ◽  
Fatigue Cracking ◽  
Coincident Site Lattice ◽  
Orientation Distribution ◽  
Grain Boundary Character Distribution ◽  
High Symmetry ◽  
Face Centered Cubic ◽  
Annealing Twins ◽  
Lattice Misorientation

The five-parameter grain boundary character distribution (GBCD) of a material contains both the grain boundary plane orientation and the lattice misorientation information. This work focuses on generating three-dimensional microstructures that match the full five-parameter GBCD obtained from experimentally observed microstructures. In face-centered cubic metals, the density of high symmetry boundaries is often maximized in order to improve grain boundary dependent properties, such as the resistance to intergranular corrosion and fatigue cracking. Twinning events have been found to be very effective in introducing these high symmetry boundaries that are denoted by low sigma values for Coincident Site Lattice relationships. Therefore, in this investigation, microstructures that contain annealing twins are of particular interest. The statistics that are used to quantify the differences between the synthetic and experimentally observed structures are texture or orientation distribution (OD), GBCD, number and area fractions of S3 and coherent S3 boundaries, S3 cluster distribution, and twin density.

The Grain Boundary Diffusion Kinetics in Nanocrystalline Zirconia

1996 ◽  
Vol 458 ◽  
Author(s):  
A. P. Zhilyaev ◽  
V. Y. Gertsman ◽  
J. A. Szpunar
Keyword(s):  
Grain Boundary ◽  
Oxidation Rate ◽  
Boundary Diffusion ◽  
Grain Boundary Diffusion ◽  
Grain Boundary Character Distribution ◽  
Grain Boundary Character ◽  
Character Distribution ◽  
Different Types ◽  
Nanocrystalline Zirconia ◽  
Boundary Character Distribution

ABSTRACTIt is expected that the grain boundary diffusion is the principal contributor to the transport properties of nanocrystalline zirconia, and that it controls the oxidation kinetics and hydrogen permeation. This process depends on the grain boundary character distribution (i.e. the fractions of different grain boundary types) and on the topological characteristics of the grain boundary network. Modeling of the random walk problem on a planar honeycomb network for different types of the grain boundary misorientation distributions (GBMD) in nanocrystalline zirconia film is presented in the current paper. The GBMD was calculated using the model texture. Changes of the oxidation rate for different types of the grain boundary character distribution and different ratios of the bulk and grain boundary diffusion coefficients are analyzed. In this study it was found that an increase of the frequency of low energy boundaries lowers the oxidation rate.

scholarly journals Influence of Processing Method on the Grain Boundary Character Distribution and Network Connectivity

1999 ◽  
Vol 586 ◽  
Author(s):  
Adam J. Schwartz ◽  
Mukul Kumar ◽  
Wayne E. King
Keyword(s):  
Grain Boundary ◽  
Annealing Temperature ◽  
Thermomechanical Processing ◽  
Processing Method ◽  
Grain Boundary Character Distribution ◽  
Deformation Path ◽  
Inconel 600 ◽  
Grain Boundary Character ◽  
Character Distribution ◽  
Boundary Character Distribution

ABSTRACTThere exists a growing body of literature that correlates the fraction of “special” boundaries in a microstructure, as described by the Coincident Site Lattice Model, to properties such as corrosion resistance, intergranular stress corrosion cracking, creep, etc. Several studies suggest that the grain boundary character distribution (GBCD), which is defined in terms of the relative fractions of “special” and “random” grain boundaries, can be manipulated through thermomechanical processing. This investigation evaluates the influence of specific thermomechanical processing methods on the resulting GBCD in FCC materials such as oxygenfree electronic (ofe) copper and Inconel 600. We also demonstrate that the primary effect of thermomechanical processing is to reduce or break the connectivity of the random grain boundary network. Samples of ofe Cu were subjected to a minimum of three different deformation paths to evaluate the influence of deformation path on the resulting GBCD. These include: rolling to 82% reduction in thickness, compression to 82% strain, repeated compression to 20% strain followed by annealing. In addition, the influence of annealing temperature was probed by applying, for each of the processes, three different annealing temperatures of 400, 560, and 800°C. The observations obtained from automated electron backscatter diffraction (EBSD) characterization of the microstructure are discussed in terms of deformation path, annealing temperature, and processing method. Results are compared to previous reports on strainannealed ofe Cu and sequential processed Inconel 600. These results demonstrate that among the processes considered, sequential processing is the most effective method to disrupt the random grain boundary network and improve the GBCD.

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