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- Title
A Variational Approach to Dynamic Recrystallization Using Probability Distributions.
- Authors
Nguyen, Hai Van; Hackl, Klaus; Renner, Jörg
- Abstract
We investigate a model of dynamic recrystallization in polycrystalline materials. A probability distribution function is introduced to characterize the state of individual grains by grain size and dislocation density. Specifying free energy and dissipation within the polycrystalline aggregate we are able to derive an evolution equation for the probability density function via a thermodynamic extremum principle. Once the distribution function is known macroscopic quantities like average strain and stress can be calculated. For distribution functions which are constant in time, describing a state of dynamic equilibrium, we obtain a partial differential equation in parameter space which we solve using a marching algorithm. Numerical results are presented and their physical interpretation is given. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
- Subjects
POLYCRYSTALS; DISLOCATION density; PROBABILITY density function; DISTRIBUTION (Probability theory); FREE energy (Thermodynamics); MATHEMATICAL models
- Publication
PAMM: Proceedings in Applied Mathematics & Mechanics, 2013, Vol 13, Issue 1, p275
- ISSN
1617-7061
- Publication type
Article
- DOI
10.1002/pamm.201310133