To determination a distribution law of subgrain sizes formed in the cold plastic deformation process

Abstract

The method for determination and identifying the distribution law from experimental data on the subgrain sizes distribution obtained in the cold plastic deformation process by rolling is proposed. For this purpose, normalized histograms are constructed from experimental data on the random variable distribution. These data are compared with the densities of continuous distribution laws known from literature’s sources. The selected laws have the closest form of the distribution density function to normalized experimental histograms. For these distribution laws, their parameters are determined by solving the problem of minimizing the square deviation of experimental and theoretical data for the distribution density function of subgrain sizes. For all considered statistical laws, the mean value of residual for different rolling reduction is found, the best law with the smallest deviation is chosen. For this law parameters dependence approximation on strain intensity is constructed that allows estimating distribution of the random variable (subgrain sizes) in an arbitrary moment of deformation, different from available in experiments.