# Possibilities of the numerical solution of the dislocation evolution equation for stochastic variables

## Possibilities of the numerical solution of the dislocation evolution equation for stochastic variables

Ivan Milenin, Łukasz Rauch, Danuta Szeliga, Maciej Pietrzyk

AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland.

DOI:

https://doi.org/10.7494/cmms.2019.4.0647

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.

Cite as:

Milenin, I., Rauch, Ł., Szeliga, D. & Pietrzyk, M. (2019). Possibilities of the numerical solution of the dislocation evolution equation for stochastic variables. Computer Methods in Materials Science, 19(4), 169 – 173. https://doi.org/10.7494/cmms.2019.4.0647

Article (PDF):

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