Abnormal Grain Growth and Texture Development

A theory for abnormal grain growth (AGG) in polycrystalline materials is revisited and extended in order to predict AGG in textured polycrystals. The motivation for the work is to improve our understanding of the origins of the Goss texture component, {110}<001>, during annealing of Fe-Si sheet. Since the AGG phenomenon in grain-oriented electrical steels is known to be dependent on the presence of a dispersion of fine second phase particles, the grain boundary properties are treated as representative of the homogenized behavior of the material, and not necessarily the properties that would be measured directly. The predictions of AGG are presented in the form of maps in Euler space, showing which texture components are most likely to grow abnormally. For different models of grain boundary properties applied to a theoretically derived texture, different sets of texture components are predicted to grow; neither model, however, predicts growth of the Goss component. Introduction The motivation for this paper is to re-visit the question of grain boundary properties and the extent to which they may account for abnormal grain growth. This paper adds to previous work by combining a theory of abnormal grain growth with realistic textures described by full threeparameter orientations. The abnormal grain growth [AGG] theory is based on work by Rollett and Mullins [1] in which the classical “n-6 rule” was adapted to account for variable grain boundary energy and mobility; the main outcome of the theory is a prediction of the maximum relative size of abnormal grains. This result is combined with an analysis of an orientation distribution to obtain both an average energy and mobility for the polycrystal, and the average energy and mobility of a boundary between each texture component and the polycrystal. From these quantities, maps are derived that indicate the likelihood of any given texture component growing abnormally. The motivation for this approach is to examine once again the long-standing puzzle of growth of the {110}<001> (Goss) texture component during secondary recrystallization of Fe-Si sheet steel. Although all the evidence, starting with May & Turnbull [2] affirms the critical role of second phase particles, the correlation of the occurrence of the AGG with annealing temperatures near the dissolution point of the “inhibitor” particles does not reveal the controlling mechanism(s). Morawiec has reviewed the various theories for abnormal growth of the Goss component based on grain boundary properties [3]. His conclusion was that none of the theories based on misorientation could provide the selectivity observed because the spread in orientation of the final Goss component is characteristically narrow (less than 10°) whereas the initial textures tend to be weak. For example, the “high energy boundaries” hypothesis suggests that boundaries with misorientations in the range 15-25° exhibit the highest energies in bcc metals and therefore should be most mobile: such an approach based on misorientation magnitude alone cannot, however, be sufficiently selective. Much effort has been put into investigating the frequency of special boundary types based on the coincident lattice site (CSL) theory, especially the Σ9 type. Ushigami, Hutchinson and others have published extensively on the interaction between grain boundaries and the inhibitor particles and have hypothesized that the Σ9 boundaries are more easily unpinned than others, which could lead to selective growth of the Goss oriented grains [4,5]. Again, however, detailed calculations to verify the mechanism are lacking. Baudin et al. have performed simulations of grain growth that represent the growth process but these have always used strongly simplified models of grain boundary properties [6]. It should also be noted that the possibility of a size advantage associated with Goss grains has been negated by experimental evidence to the contrary [7]. Abnormal Grain Growth Theory Upper Limit for Abnormal Growth. Rollett and Mullins [1] developed a theory for abnormal grain growth as a function of the properties (energy and mobility) of the perimeter of a single abnormal grain embedded in a matrix of grains with uniform boundary properties. The energy of the boundaries in the matrix is γmatrix and the mobility is Mmatrix; the average grain size in the matrix is . The ratio of the energy of the perimeter of the abnormal grain to the matrix grain boundary energy is defined as Γ, and the corresponding mobility ratio as μ. The theory was based on an adaptation of the development of the topological theory of grain growth leading to the wellknown “n-6” rule (Mullins 1957). The main result was to define a growth rate, dρ/dt, for the (potentially) abnormal grain relative to the coarsening rate of the matrix.