There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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.

Processes of severe plastic deformation (SPD) are defined as metal forming processes in which a very large plastic strain is imposed on a bulk process in order to make an ultra-fine grained metal The objective of the SPD processes for creating ultra-fine grained metal is to produce lightweight parts by using high strength metal for the safety and reliability of micro-parts and for environmental harmony In this keynote paper, the fabrication process of equal channel angular pressing (ECAP), accumulative roll-bonding (ARB), high pressure torsion (HPT), and others are introduced, and the properties of metals processed by the SPD processes are shown Moreover, the combined processes developed recently are also explained Finally, the applications of the ultra-fine grained (UFG) metals are discussed

Severe Plastic Deformation (SPD) Processes for Metals

Microstructure and strength of nickel at large strains

Microstructure and strengthening mechanisms in cold-drawn pearlitic steel wire

Microstructural evolution of IF-steel during cold rolling

Twinning behavior of a strongly basal textured AZ31 Mg alloy during warm rolling

Identification and analysis of twinning variants during compression of a Mg–Al–Zn alloy

The stored energy of plastic deformation has been estimated from transmission electron microscope measurements of dislocation boundary spacings and misorientation angles using Al (99.99 pct) cold rolled to reductions of 5 to 90 pct as an example system. In order to obtain the most accurate estimate of stored energy, it is necessary to take into account the presence of two classes of dislocation boundary, considering the boundary misorientation angle distribution and the stereology of each class independently. Stereological relationships are developed to predict the stored energy estimates that would result from electron backscatter pattern (EBSP) investigations on these microstructures. The calculations show that EBSP investigations can be used to estimate the stored energy, but that at low strains, the limited angular resolution will lead to a significant underestimation. A relationship between the flow stress (0.2 pct offset) and the stored energy is found, though the relationship differs significantly for the low and high strain regimes. At low strains, the flow stress is linearly related to the square root of the stored energy (E
 s
 ) according to σ − σ
 0 = Mα[(G/K)E
 s
 ]0.5, where G is the bulk modulus, M is the Taylor factor, and K and α are constants.

Andrew Godfrey

Papers

Microstructure and strengthening mechanisms in cold-drawn pearlitic steel wire

Microstructural evolution of IF-steel during cold rolling

Twinning behavior of a strongly basal textured AZ31 Mg alloy during warm rolling

Identification and analysis of twinning variants during compression of a Mg–Al–Zn alloy

Stored energy, microstructure, and flow stress of deformed metals