Melting and solidification of pure metals by a phase-field model

In this paper, we study melting and solidification for metallurgical processes related with phase transitions of pure metals, which during the solid phase show an evident ductility. So, the transition is between a viscous fluid and a viscoplastic state. In this work these particular phenomena can be well described by a phase field fractional model, whose evolution has to satisfy a Ginzburg- Landau equation. Then, we prove the compatibility with the Thermodynamic Laws. Hence, for metallurgical phase transitions, we have considered a similar model by a new fractional derivative and compared the behavior of the first with this second model. Finally, a generalization to finite deformation for the same models is presented in the last section.