Stochastic model of visco-brittle transition in steels

Abstract

A stochastic model of ductile-brittle (DB) transition based on a bimodal representation of random processes the critical temperature range of brittleness is proposed. Modeling was carried out in two stages. The results of impact tests of more than 1200 Charpy samples were used at the first stage to construct a stochastic model of the DB transition which revealed a bimodal distribution of the impact strength in the region of the DB transition. The model was based on the use of a fractional-power distribution to describe the probability of occurring the impact strength values. An analytical dependence of the probability of obtaining a given value of the impact strength at a given test temperature is proposed. At the second stage, the inverse problem was solved. The impact strength values were calculated from the given probability and test temperature. For this purpose, a generator of random numbers distributed according to the proposed bimodal law using the Monte Carlo method was constructed. The impact strength values were obtained using numerical methods. It is shown that the developed model does not contradict the existing experimental data and, probably, can be used to describe the DB transition both for well-known and new promising structural materials.