# Phase change with stress effects and flow

Sammanfattning: In this thesis two kinds of phase change i.e., solid state phase transformation in steels and solid-to-liquid phase transformation in paraffin, have been modeled and numerically simulated. The solid state phase transformation is modeled using the phase field theory while the solid-to-liquid phase transformation is modeled using the Stokes equation and exploiting the viscous nature of the paraffin, by treating it as a liquid in both states.The theoretical base of the solid state, diffusionless phase transformation or the martensitic transformation comes from the Khachaturyan's phase field microelasticity theory. The time evolution of the variable describing the phase transformation is computed using the time dependent Ginzburg-Landau equation. Plasticity is also incorporated into the model by solving another time dependent equation. Simulations are performed both in 2D and 3D, for a single crystal and a polycrystal. Although the model is valid for most iron-carbon alloys, in this research an Fe-0.3\%C alloy is chosen.In order to simulate martensitic transformation in a polycrystal, it is necessary to include the effect of the grain boundary to correctly capture the morphology of the microstructure. One of the important achievements of this research is the incorporation of the grain boundary effect in the Khachaturyan's phase field model. The developed model is also employed to analyze the effect of external stresses on the martensitic transformation, both in 2D and 3D. Results obtained from the numerical simulations show good qualitative agreement with the empirical observations found in the literature.The microactuators are generally used as a micropump or microvalve in various miniaturized industrial and engineering applications. The phase transformation in a paraffin based thermohydraulic membrane microactuator is modeled by treating paraffin as a highly viscous liquid, instead of a solid, below its melting point. The fluid-solid interaction between paraffin and the enclosing membrane is governed by the ALE technique. The thing which sets apart the presented model from the previous models, is the use of geometry independent and realistic thermal and mechanical properties. Numerical results obtained by treating paraffin as a liquid in both states show better conformity with the experiments, performed on a similar microactuator. The developed model is further employed to analyze the time response of the system, for different input powers and geometries of the microactuator.

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