A model for diffusive and displacive phase transitions in steels

Maraldi, Mirko (2010) A model for diffusive and displacive phase transitions in steels, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Ingegneria delle macchine e dei sistemi energetici, 22 Ciclo. DOI 10.6092/unibo/amsdottorato/2929.
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Heat treatment of steels is a process of fundamental importance in tailoring the properties of a material to the desired application; developing a model able to describe such process would allow to predict the microstructure obtained from the treatment and the consequent mechanical properties of the material. A steel, during a heat treatment, can undergo two different kinds of phase transitions [p.t.]: diffusive (second order p.t.) and displacive (first order p.t.); in this thesis, an attempt to describe both in a thermodynamically consistent framework is made; a phase field, diffuse interface model accounting for the coupling between thermal, chemical and mechanical effects is developed, and a way to overcome the difficulties arising from the treatment of the non-local effects (gradient terms) is proposed. The governing equations are the balance of linear momentum equation, the Cahn-Hilliard equation and the balance of internal energy equation. The model is completed with a suitable description of the free energy, from which constitutive relations are drawn. The equations are then cast in a variational form and different numerical techniques are used to deal with the principal features of the model: time-dependency, non-linearity and presence of high order spatial derivatives. Simulations are performed using DOLFIN, a C++ library for the automated solution of partial differential equations by means of the finite element method; results are shown for different test-cases. The analysis is reduced to a two dimensional setting, which is simpler than a three dimensional one, but still meaningful.

Tipologia del documento
Tesi di dottorato
Maraldi, Mirko
Dottorato di ricerca
Scuola di dottorato
Ingegneria industriale
Settore disciplinare
Settore concorsuale
Parole chiave
Phase transitions, thermodynamics, phase-field model, DOLFIN
Data di discussione
30 Aprile 2010

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