This chapter is aimed at describing the Monte Carlo method for the simulation of grain growth and recrystallization. It has also been extended to phase transformations and hybrid versions (Monte Carlo coupled with Cellular Automaton) of the model can also accommodate diffusion. If reading this chapter inspires you to program your own version of the algorithm and try to solve some problems, then we will have succeeded! The method is simple to implement and it is fairly straightforward to apply variable material properties such as anisotropic grain boundary energy and mobility. There are, however, some important limitations of the method that must be kept in mind. These limitations include an inherent lattice anisotropy that manifests itself in various ways. For many purposes, however, if you pay attention to what has been found to previous work, the model is robust and highly efficient from a computational perspective. In many circumstances, it is best to use the model to gain insight into a physical system and then obtain a new theoretical understanding, in preference to interpreting the results as being directly representative of a particular material. Please also keep in mind that the “Monte Carlo Method” described herein is a small subset of the broader use of Monte Carlo methods for which an excellent overview can be found in the book by Landau and Binder (2000).

The Monte Carlo Method

Since the automation of the electron backscatter diffraction (EBSD) technique, EBSD systems have become commonplace in microscopy facilities within materials science and geology research laboratories around the world. The acceptance of the technique is primarily due to the capability of EBSD to aid the research scientist in understanding the crystallographic aspects of microstructure. There has been considerable interest in using EBSD to quantify strain at the submicron scale. To apply EBSD to the characterization of strain, it is important to understand what is practically possible and the underlying assumptions and limitations. This work reviews the current state of technology in terms of strain analysis using EBSD. First, the effects of both elastic and plastic strain on individual EBSD patterns will be considered. Second, the use of EBSD maps for characterizing plastic strain will be explored. Both the potential of the technique and its limitations will be discussed along with the sensitivity of various calculation and mapping parameters.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S1431927611000055

A review of strain analysis using electron backscatter diffraction.

Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction

Lengthscale-dependent, elastically anisotropic, physically-based hcp crystal plasticity: Application to cold-dwell fatigue in Ti alloys

The accelerating rate at which new materials are appearing, and transforming the engineering world, only serves to emphasize the vast potential for novel material structure, and related performance. Microstructure-sensitive design (MSD) aims at providing inverse design methodologies that facilitate design of material internal structure for performance optimization. Spectral methods are applied across the structure, property and processing design spaces in order to compress the computational requirements for linkages between the spaces and enable inverse design. Research has focused mainly on anisotropic, polycrystalline materials, where control of local crystal orientation can result in a broad range of property combinations. This review presents the MSD framework in the context of both the engineering advances that have led to its creation, and those that complement or provide alternative methods for design of materials (meaning ‘optimization of material structure’ in this context). A variety of definitions for the structure of materials are presented, with an emphasis on correlation functions; and spectral methods are introduced for compact descriptions and efficient computations. The microstructure hull is defined as the design space for structure in the spectral framework. Reconstruction methods provide invertible links between statistical descriptions of structure, and deterministic instantiations. Subsequently, structure–property relations are reviewed, and again subjected to representation via spectral methods. The concept of a property closure is introduced as the design space for performance optimization, and methods for moving between the closures and hulls are presented as the basis for the subsequent discussion on microstructure design. Finally, the spectral framework is applied to deformation processes, and methodologies that facilitate process design are reviewed.

Microstructure Sensitive Design for Performance Optimization

https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1534&context=facpub

Viewpoint: experimental recovery of geometrically necessary dislocation density in polycrystals

Techniques are described that have been used to create a statistically representative three-dimensional model microstructure for input into computer simulations using the geometric and crystallographic observations from two orthogonal sections through an aluminum polycrystal. Orientation maps collected on the observation planes are used to characterize the sizes, shapes, and orientations of grains. Using a voxel-based tessellation technique, a microstructure is generated with grains whose size and shape are constructed to conform to those measured experimentally. Orientations are then overlaid on the grain structure such that distribution of grain orientations and the nearest-neighbor relationships, specified by the distribution of relative misorientations across grain boundaries, match the experimentally measured distributions. The techniques are applicable to polycrystalline materials with sufficiently compact grain shapes and can also be used to controllably generate a wide variety of hypothetical microstructures for initial states in computer simulations.

Statistically representative three-dimensional microstructures based on orthogonal observation sections

Automated orientation measurement on a local basis is now widely accepted for characterization of materials The technique relies upon indexing of electron backscatter diffraction patterns in a scanning electron microscope In order to exploit the available information, it is important to understand the limitations with respect to accuracy Experiments were carried out to measure orientation fields from a silicon single crystal The orientation dispersion was 1° Disorientation correlation maps revealed anisotropy in the spatial variation in measured orientation

Studies on the Accuracy of Electron Backscatter Diffraction Measurements

Microstructure controls the properties of most useful materials. Thus an ability to control microstructure through the processing of materials is a key to optimization of materials performance. Most materials are polycrystalline and their grain structure is a very important aspect of their microstructure. Thanks to their complexity there is a great variety of grain boundary types even in relatively isotropic materials such as the cubic metals. Simply describing the crystallography requires five (macroscopic) parameters (e.g. disorientation and inclination). Evidently, acquiring a knowledge of the variation of properties such as energy and mobility as a function of grain boundary type would be of great value in predicting properties and optimizing processing. This paper outlines the methods being employed to extract such properties from the geometry and crystallography of triple junctions between grain boundaries.

http://mimp.materials.cmu.edu/rohrer/papers/2001_12.pdf

Grain Boundary Property Determination through Measurement of Triple Junction Geometry and Crystallography

Advances in experimental methods for determination of the geometricallynecessary dislocation (GND) tensor, based on electron backscattering diffraction, are described. Data are presented for directionally-solidified 99.999% Aluminum possessing a strong columnar texture, with the primary focus being the interactions of the plastic deformation field with grain boundaries. Alternate methods of solving for the GND content are illustrated and compared. Implications of the observations for strain-gradient plasticity theory are discussed.

/pdf/advances-in-experimental-method-and-analysis-for-estimation-1kojhy5ykc.pdf

Bassem S. El-Dasher

Papers

Viewpoint: experimental recovery of geometrically necessary dislocation density in polycrystals

Statistically representative three-dimensional microstructures based on orthogonal observation sections

Studies on the Accuracy of Electron Backscatter Diffraction Measurements

Grain Boundary Property Determination through Measurement of Triple Junction Geometry and Crystallography

Advances in Experimental Method and Analysis for Estimation of Geometrically-Necessary Dislocations