Chapter 15 - Control of Recrystallization
Abstract Various applied aspects of recrystallization are discussed, many of which involve control of grain size and texture. Examples include the need to control the texture of aluminum sheet stock used for beverage cans, grain-oriented electrical steels, deep drawing quality steel sheet and metallic superplastic sheet materials. For aluminum can stock, texture control is important for quality control because texture affects the reliability of the can making equipment. Texture and grain size control in electrical steels, especially those used in large transformers, is crucial for optimizing performance. A fine grain size is considered essential for obtaining high strain rate sensitivity and thus superplastic behavior in many alloy systems. Fine grain size is useful for optimizing mechanical properties in general and severe plastic deformation has become an important processing route for achieving this.
Chapter 4 - The Structure and Energy of Grain Boundaries
Abstract The structure and energy of grain boundaries is briefly reviewed. Crystallographic character is explained in terms of mis- or dis-orientation angle and axis with the full five degrees of freedom also requiring definition of the boundary inclination. Grain boundary energy depends on all five parameters although simplified descriptions based on only the angle is sometimes sufficient. Low angle boundaries, for example, have well defined dislocation structures unlike high angle boundaries that are considered to be disordered. The coincidence site lattice concept has led to the technology of grain boundary engineering although most of the property enhancement is based on increased fractions of twin boundaries. Local equilibrium along triple lines explains much of the topology of grain boundary networks and how they evolve. Second phase particles exert a drag on moving grain boundaries because boundary area is removed wherever a particle intersects a boundary. Despite several simplifying assumptions, the Smith-Zener theory of grain boundary pinning results in good predictions of limiting grain size. Modifications of the approach are discussed that improve the agreement.
Chapter 16 - Computer Modeling and Simulation of Annealing
Abstract Computer simulation of annealing provides a way to model annealing processes at the grain scale. The various methods available to simulate grain growth and recrystallization are reviewed. Although they all are designed to simulate the evolution of grain structures, some of the algorithms, such as vertex or finite element models, can be classified as front tracking because their data structure represents the grain boundary structure explicitly. Other algorithms, such as the Potts model and cellular automata, contain implicit descriptions of the boundary structure because their data structure is akin to a pixelated image. All models can accommodate texture and grain boundary properties that depend on the lattice misorientation. The algorithms with explicit representations of the boundary, e.g., finite element, or those with continuous functions, e.g., phase field and level set, are better suited to including boundary properties that depend on the inclination, i.e., boundary normal.
Chapter 11 - Grain Growth Following Recrystallization
Abstract The process of grain growth is analyzed. The driving force is the reduction in surface area per unit volume and therefore depends on grain boundary energy. This in turn means that local equilibrium along triple lines often determines the local curvature of boundaries and thus their motion. In two dimensions, the von Neumann-Mullins theory predicts the growth or shrinkage of individual grains, leading to the famous N-6 Rule . In three dimensions, integrating curvature over the surface of a grain was more recently solved by Macpherson and Srolovitz. The presence of second phase particles, or voids limits the maximum grain size and the Smith-Zener analysis has proven to be a reliable guide. In many metallic materials grain growth is the process of microstructural evolution that follows recrystallization although in a consolidated powder, grain growth is the main process. Abnormal grain growth, in which a minority of grains grow at the expense of the majority, is often observed. Despite its easily recognized morphology, the causes are manifold and include, anisotropic grain boundary properties (especially mobility and energy), particle pinning (or its cessation), variable stored energy and, possibly, solute drag. Many challenges in the theory of grain growth remain, especially with respect to texture and the anisotropic properties of grain boundaries.
Chapter 2 - The Deformed State
Abstract This chapter addresses the features of the plastically deformed state which dominate the process of recrystallization from the perspective of both nucleation and growth. Strain hardening is reviewed as defining the accumulation of dislocation density, which provides the driving force for recrystallization. The heterogeneities that appear during deformation such as orientation gradients, slip bands, transitions bands, and twinning provide a source of new grains (nuclei). At the scale of the dislocation substructure, fluctuations in dislocation density strengthen with strain into a cell structure and, at high temperature, subgrain boundaries. The characteristic accumulation of dislocations of one sign results in misorientation increase across cell walls, which results in a distinction between statistically stored versus geometrically necessary dislocations. The effect of particles on deformation heterogeneity is described. Coarse particles above about one micron promote local heterogeneity, which leads to accelerated nucleation, known as particle stimulated nucleation. Fine particles tend to stabilize dislocation networks and minimize shear banding, for example. Mechanical twinning is important in lower symmetry materials, most notably unalloyed hexagonal metals, and typically provides significant interfacial strengthening.