Analytical modelling of grain growth in metals and alloys in the presence of growing and dissolving precipitates—I. Normal grain growth

Abstract

The present investigation is concerned with analytical modelling of grain growth in metals and alloys in the presence of growing and dissolving precipitates. In Part I, the different components of the normal grain growth model are outlined and differential equations presented which allow the mean grain size to be calculated as a function of time and temperature. These equations have then been solved for fixed starting conditions by means of analytical and numerical methods to evaluate the matrix grain coarsening behaviour during isothermal heat treatment. The results are presented in the form of novel “mechanism” maps (by utilizing the concept of group variables) which show the conmpetition between the various processes that lead to normal grain growth in metals and alloys in the presence of unstable second phase particles. An analytical approach to the modelling of abnormal grain growth is described in an accompanying paper (Part II).