A probabilistic model for predicting grain growth processes in alloys

Abstract

This paper deals with a possible generalization of the traditional grain growth kinetic functions. A novel probabilistic model devoted to the grain growth prediction in alloys is presented. It is based on the extension of the traditional power law kinetic equation proposed by Beck. The Beck’s isothermal kinetic equation is defined as D(t)=A*exp(-E/RT)*tm where D(t) is the grain size (diameter), t is the time, E is the activation energy, A is the preexponential factor, m is the time exponent, R is the universal gas constant and T is the absolute temperature. The novel probabilistic model proposed is based on the concept of the mixture of probability density functions. In this model it is assumed that during grain growth the activation energy (E) is not constant, but its distribution is determined by the initial grain morphology of alloys. More exactly speaking, it is supposed that the activation energy is a random variable which is characterized by the probability density function g(E) of the activation energy. By using appropriately selected probability density functions, different types of generalized grain growth kinetic equations can be established. Based on computer simulations, the application of the extended grain growth kinetic models is demonstrated by examples.