No abstract

The model describing evolution of dislocation population based on fundamental works of Kocks, Estrin and Mecking (KEM) is a useful tool in modelling of metallic materials processing. In combination with the Sandstrom and Lagneborg approach it can predict changes of the dislocation density accounting for hardening, recovery and recrystallization. Numerical solutions of a one-parameter model (average dislocation density), as well as for two types of dislocations and three types of dislocation are described in the literature. All these solutions were performed for deterministic variables. On the other hand, an advanced modelling of materials requires often an information about distribution of parameters. This is the case when uncertainty of the model has to be evaluated or when an information about distribution of product properties is needed. The latter is crucial when deterioration of local formability is caused by sharp gradients of properties. Thus, the investigation of possibilities of numerical solution for the KEM model with stochastic variables was the main objective of the present work. Evolution equation was written for the distribution function and solution was performed using Monte Carlo method. Analysis of the results with respect to the reliability and computing costs was performed. The conclusions towards selection of the best approach were formulated.

The aim of this work was to improve the previously developed model of austenite-ferrite phase transformation by its identification for selected steels and by performing sensitivity analysis. Created model allows prediction of phase transformation kinetics for non-isothermal conditions. Model is characterized by very short computing time and relatively good predictive capabilities. There are five input coefficients in the model, which should be identified for each steel on the basis of dilatometric tests. In the previous works model was used to predict phase transformation kinetics in various DP steels for different thermal cycles. In the first part of this work sensitivity analysis of the model was performed using three methods: quality method, factorial design method and Morris analysis method. Obtained sensitivity coefficients described how changes of the model input parameters influence the response of the model and which of these parameters are the most significant. The second part of the work was devoted to model identification for the selected steels. Identification problem was turned into optimization task which was solved using Hooke-Jeeves method. Obtained model’s parameters allowed describing austenite-ferrite phase transformation in the conditions of varying temperatures. Validation of the model was performed by comparison with the results obtained from the advances numerical model based on the solution of the diffusion equation in the austenite. Results obtain from both models for typical thermal cycled used to obtain multiphase microstructure were compared.