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.
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机译：本文涉及传统谷物生长动力学功能的可能概括。提出了一种新的概率模型，致力于合金中谷物生长预测。它基于贝克提出的传统电力法动力学方程的延伸。 Beck的等温动力学方程被定义为D（t）= a * exp（-e / Rt）* tm，其中d（t）是晶粒尺寸（直径），t是时间，e是激活能量，a是PREexponential因子M是时间指数，R是通用气体常数，T是绝对温度。提出的新型概率模型基于概率密度函数的混合物的概念。在该模型中，假设在晶粒生长期间，活化能量（E）不是恒定的，但其分布由合金的初始晶粒形态决定。更准确地说，假设激活能量是随机变量，其特征在于激活能量的概率密度函数G（e）。 By using appropriately selected probability density functions, different types of generalized grain growth kinetic equations can be established.基于计算机仿真，通过实施例证明了扩展晶粒生长动力学模型的应用。
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