Microstructure and normal grain growth in metals and ceramics. Part I. Theory

Abstract

By extending the theory of Feltham and combining it with the work of Rhines and Craig, a detailed statistical theory of normal grain growth has been constructed. The theory exhibits all four attributes of normal grain growth: uniformity, scaling, stability, and lognormality. A prime new feature of the theory is the division of the grains into topological classes (14 planar, 34 spatial), each with a lognormal distribution of grain sizes. Growth is found to be controlled by the rate of loss of grains from the lowest topological class. Complete solutions are found for the grain growth kinetics of each class, as well as the transfer rates between classes. The latter result is used to explain how the median diameter of those classes in which grains are shrinking still manages to increase in the manner required to keep their number a constant fraction of the total population. A parabolic growth law is found for the median grain size of the whole population as well as the median grain size in each topological class. The growth constant for each class is found to increase approximately as the cube of the planar topological parameter or the square of the spatial topological parameter. The Rhines‐Craig structural gradient is shown to be independent of time and hence a basic constant of normal grain growth. Stability is due to a maximum in the grain boundary velocity with increasing grain size. The ratio of the maximum to median grain diameter is found to be e(=2.718). A comparison of the present theory is made with that of Hillert. Possible origins of the lognormality are discussed.