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Phase change with stress effects and flow
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics.
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

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.

##### Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. , p. x, 58
##### Series
Trita-MEK, ISSN 0348-467X ; 2013:04
##### Keywords [en]
Martensitic transformation, phase-field method, polycrystal, stress-effects, microactuator, finite-element simulations.
##### National Category
Materials Engineering Mechanical Engineering
##### Identifiers
ISBN: 978-91-7501-655-9 (print)OAI: oai:DiVA.org:kth-118451DiVA, id: diva2:606230
##### Public defence
2013-03-13, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:15 (English)
##### Note

QC 20130219

Available from: 2013-02-19 Created: 2013-02-18 Last updated: 2013-02-19Bibliographically approved
##### List of papers
1. Three-dimensional phase-field modeling of martensitic microstructure evolution in steels
Open this publication in new window or tab >>Three-dimensional phase-field modeling of martensitic microstructure evolution in steels
2012 (English)In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 60, no 4, p. 1538-1547Article in journal (Refereed) Published
##### Abstract [en]

In the present work a 3-D elastoplastic phase-field (PF) model is developed, based on the PF microelasticity theory proposed by A.G.Khachaturyan and by including plastic deformation as well as anisotropic elastic properties, for modeling the martensitic transformation (MT) by using the finite-element method. PF simulations in 3D are performed by considering different cases of MT occurring in an elastic material, with and without dilatation, and in an elastic perfectly plastic material with dilatation having isotropic as well as anisotropic elastic properties. As input data for the simulations the thermodynamic parameters corresponding to anFe–0.3%C alloy as well as the physical parameters corresponding to steels acquired from experimental results are considered. The simulation results clearly show auto-catalysis and morphological mirror image formation, which are some of the typical characteristics of a martensitic microstructure. The results indicate that elastic strain energy, anisotropic elastic properties, plasticity and the external clamping conditions affect MT as well as the microstructure.

Elsevier, 2012
##### Keywords
Phase-field models, Martensitic phase transformation, Microstructure, Steels
##### National Category
Metallurgy and Metallic Materials
##### Identifiers
urn:nbn:se:kth:diva-62804 (URN)10.1016/j.actamat.2011.11.039 (DOI)000301989500010 ()2-s2.0-84856194252 (Scopus ID)
##### Funder
Swedish e‐Science Research Center
##### Note

QC 20120424

Available from: 2012-01-20 Created: 2012-01-20 Last updated: 2017-12-08Bibliographically approved
2. Three dimensional elasto-plastic phase field simulation of martensitic transformation in polycrystal
Open this publication in new window or tab >>Three dimensional elasto-plastic phase field simulation of martensitic transformation in polycrystal
2012 (English)In: Materials Science & Engineering: A, ISSN 0921-5093, E-ISSN 1873-4936, Vol. 556, p. 221-232Article in journal (Refereed) Published
##### Abstract [en]

The Phase Field Microelasticity model proposed by Khachaturyan is used to perform 3D simulation of Martensitic Transformation in polycrystalline materials using finite element method. The effect of plastic accommodation is investigated by using a time dependent equation for evolution of plastic deformation. In this study, elasto-plastic phase field simulations are performed in 2D and 3D for different boundary conditions to simulate FCC -> BCT martensitic transformation in polycrystalline Fe-0.3%C alloy. The simulation results depict that the introduction of plastic accommodation reduces the stress intensity in the parent phase and hence causes an increase in volume fraction of the martensite. Simulation results also show that autocatalistic transformation initiates at the grain boundaries and grow into the parent phase. It has been concluded that stress distribution and the evolution of microstructure can be predicted with the current model in a polycrystal.

Elsevier, 2012
##### Keywords
Martensitic transformation, Phase field modeling, Microstructure evolution, Polycrystal, Finite element method
##### National Category
Metallurgy and Metallic Materials
##### Identifiers
urn:nbn:se:kth:diva-95304 (URN)10.1016/j.msea.2012.06.080 (DOI)000309497300026 ()2-s2.0-84865441956 (Scopus ID)
hero-m
##### Funder
VinnovaSwedish e‐Science Research Center
##### Note

QC 20121130

Available from: 2012-05-21 Created: 2012-05-21 Last updated: 2017-12-07Bibliographically approved
3. Phase field modeling of martensitic transformation- Effect of grain and twin boundaries
Open this publication in new window or tab >>Phase field modeling of martensitic transformation- Effect of grain and twin boundaries
##### Abstract [en]

In this work we are presenting, for the first time, the elasto-plastic phase field modeling and simulation of the martensitic transformation in a polycrystalline material including the effect of grain and twin boundaries. The phase field microelasticity theory proposed by Khachaturyan is used to perform 2D and 3D simulations of FCC$\rightarrow$BCT martensitic transformation in an Fe-0.3\%C polycrystalline alloy, incorporating the effect of both coherent and incoherent boundaries. The effect of plastic accommodation is also introduced into the model, by solving a time dependent equation, during the solid-to-solid phase transformation. It is found that the given phase field model, with the effect of grain boundaries, not only respects the morphological features of martensite but it also conforms well with the physics of the problem. Different sets of simulations are performed to validate the model and it is concluded that the given model can correctly predict the evolution of martensitic microstructure in a polycrystal as opposed to the previous models where the effects of grain and twin boundaries are neglected.

##### Keywords
Martensitic transformation; Polycrystal; Grain boundaries; Phase field modeling; Simulations.
##### National Category
Materials Engineering
##### Identifiers
urn:nbn:se:kth:diva-118448 (URN)
##### Note

QS 2013

Available from: 2013-02-18 Created: 2013-02-18 Last updated: 2013-02-19Bibliographically approved
4. Effect of external loading on the martensitic transformation - A phase field study
Open this publication in new window or tab >>Effect of external loading on the martensitic transformation - A phase field study
2013 (English)In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 61, no 20, p. 7868-7880Article in journal (Refereed) Published
##### Abstract [en]

In this work, the effect of external loading on the martensitic transformation is analyzed using an elasto-plastic phase field model. The phase field microelasticity theory, incorporating a non-linear strain tensor and the effect of grain boundaries, is used to study the impact of applied stresses on an Fe-0.3%C polycrystalline alloy, both in two and three dimensions. The evolution of plasticity is computed using a time-dependent equation that solves for the minimization of the shear strain energy. Crystallographic orientation of the grains in the polycrystal is chosen randomly and it is verified that the said assumption does not have a significant effect on the final volume fraction of martensite. Two-dimensional (2-D) and three-dimensional (3-D) simulations are performed at a temperature significantly higher than the martensitic start temperature of the alloy with uniaxial tensile, compressive and shear loading, along with hydrostatic stresses. It is found that the 3-D simulations are necessary to investigate the effect of external loading on the martensitic transformation using the phase field method since the 2-D numerical simulations produce results that are physically incorrect, while the results obtained from the 3-D simulations are in good agreement with the empirical observations found in the literature. Finally, it is concluded that the given model can be used to predict the volume fraction of martensite in a material with any kind of external loading.

##### Keywords
External stress, Martensitic transformation, Phase field modeling, Polycrystal, Simulations
##### National Category
Materials Engineering
##### Identifiers
urn:nbn:se:kth:diva-118449 (URN)10.1016/j.actamat.2013.09.025 (DOI)000328179700033 ()2-s2.0-84886383574 (Scopus ID)
Vinnova
##### Note

QC 20140108. Updated from manuscript to article in journal.

Available from: 2013-02-18 Created: 2013-02-18 Last updated: 2017-12-06Bibliographically approved
5. Modeling and analysis of a phase change material thermohydraulic membrane microactuator
Open this publication in new window or tab >>Modeling and analysis of a phase change material thermohydraulic membrane microactuator
2013 (English)In: Journal of microelectromechanical systems, ISSN 1057-7157, E-ISSN 1941-0158, Vol. 22, no 1, p. 186-194Article in journal (Refereed) Published
##### Abstract [en]

Presented in this work, is a Finite Element Method (FEM)-based model for phase change material actuators, modeling the active material as a fluid as opposed to a solid. This enables the model to better conform to localized loads, as well as offering the opportunity to follow material movement in enclosed volumes. Modeling, simulation and analysis of an electrothermally activated paraffin microactuator has been conducted. The paraffin microactuator used for the analysis in the current study exploits the large volumetric expansion of paraffin upon melting, which combined with its low compressibility in the liquid state allows for high hydraulic pressures to be generated. The purpose of the study is to supply a geometry independent model of such a microactuator through the implementation of a fluid model rather than a solid model, which has been utilized in previous studies. Numerical simulations are conducted at different frequencies of the heating source and for different geometries of the microactuator. The results are compared with the empirical data obtained on a close to identical paraffin microactuator, which clearly show the advantages of a fluid model instead of a solid state approximation.

##### Keywords
Finite element methods, fluid dynamics, microactuators, microelectromechanical devices, steel
##### National Category
Other Mechanical Engineering
##### Identifiers
urn:nbn:se:kth:diva-118450 (URN)10.1109/JMEMS.2012.2222866 (DOI)000314726900026 ()2-s2.0-84873288511 (Scopus ID)
##### Funder
Swedish Research Council
##### Note

QC 20130219

Available from: 2013-02-18 Created: 2013-02-18 Last updated: 2017-12-06Bibliographically approved

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Cite
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