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• 1.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics.
Phase change with stress effects and flow2013Doctoral thesis, comprehensive summary (Other academic)

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.

• 2.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Effect of external loading on the martensitic transformation - A phase field study2013In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 61, no 20, p. 7868-7880Article in journal (Refereed)

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.

• 3.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Phase field modeling of martensitic transformation- Effect of grain and twin boundariesManuscript (preprint) (Other academic)

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.

• 4.
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Phase-field modelling of martensitic transformation: the effects of grain and twin boundaries2013In: Modelling and Simulation in Materials Science and Engineering, ISSN 0965-0393, E-ISSN 1361-651X, Vol. 21, no 8, p. 085003-Article in journal (Refereed)

In this work, we present the non-linear elasto-plastic phase-field model and simulation of the martensitic transformation in a polycrystalline material including the effects of grain and twin boundaries. The phase-field microelasticity theory proposed by Khachaturyan is used to perform 2D and 3D simulations of fcc -> bct martensitic transformation in a 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 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 the martensitic microstructure in a polycrystal, as opposed to previous models where the effects of grain and twin boundaries are neglected.

• 5.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. Micro systems technology programme, Uppsala University.
Modeling and analysis of a phase change material thermohydraulic membrane microactuator2013In: Journal of microelectromechanical systems, ISSN 1057-7157, E-ISSN 1941-0158, Vol. 22, no 1, p. 186-194Article in journal (Refereed)

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.

• 6.
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Effects of external stresses on the martensitic transformation in a 3D polycrystalline material using the phase field method2013In: Materials Research Society Symposium Proceedings: Proceedings of the Multiscale Materials Modeling 2012 Conference, Materials Research Society, 2013, p. 62-68Conference paper (Refereed)

In the current study an elasto-plastic phase field (PF) model, based on the PF microelasticity theory proposed by A.G. Khachaturyan, is used to investigate the effects of external stresses on the evolution of martensitic microstructure in a Fe-0.3%C polycrystalline alloy. The current model is improved to include the effects of grain boundaries in a polycrystalline material. The evolution of plastic deformation is governed by using a time dependent Ginzburg-Landau equation, solving for the minimization of the shear strain energy. PF simulations are performed in 2D and 3D to study the effects of tension, compression and shear on the martensitic transformation. It has been found that external stresses cause an increase in the volume fraction of the martensitic phase if they add to the net effect of the transformation strains, and cause a decrease otherwise. It has been concluded that the stress distribution and the evolution of martensitic microstructure can be predicted with the current model in a polycrystalline material under applied stresses.

• 7.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. Outokumpu Stainless Research Foundation. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
Phase-Field Modeling of Sigma-Phase Precipitation in 25Cr7Ni4Mo Duplex Stainless Steel2017In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 48A, no 10, p. 4914-4928Article in journal (Refereed)

Phase-field modeling is used to simulate the formation of sigma phase in a model alloy mimicking a commercial super duplex stainless steel (SDSS) alloy, in order to study precipitation and growth of sigma phase under linear continuous cooling. The so-called Warren-Boettinger-McFadden (WBM) model is used to build the basis of the multiphase and multicomponent phase-field model. The thermodynamic inconsistency at the multiple junctions associated with the multiphase formulation of the WBM model is resolved by means of a numerical Cut-off algorithm. To make realistic simulations, all the kinetic and the thermodynamic quantities are derived from the CALPHAD databases at each numerical time step, using Thermo-Calc and TQ-Interface. The credibility of the phase-field model is verified by comparing the results from the phase-field simulations with the corresponding DICTRA simulations and also with the empirical data. 2D phase-field simulations are performed for three different cooling rates in two different initial microstructures. A simple model for the nucleation of sigma phase is also implemented in the first case. Simulation results show that the precipitation of sigma phase is characterized by the accumulation of Cr and Mo at the austenite-ferrite and the ferrite-ferrite boundaries. Moreover, it is observed that a slow cooling rate promotes the growth of sigma phase, while a higher cooling rate restricts it, eventually preserving the duplex structure in the SDSS alloy. Results from the phase-field simulations are also compared quantitatively with the experiments, performed on a commercial 2507 SDSS alloy. It is found that overall, the predicted morphological features of the transformation and the composition profiles show good conformity with the empirical data.

• 8.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Three dimensional elasto-plastic phase field simulation of martensitic transformation in polycrystal2012In: Materials Science & Engineering: A, ISSN 0921-5093, E-ISSN 1873-4936, Vol. 556, p. 221-232Article in journal (Refereed)

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.

• 9.
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). KTH, School of Engineering Sciences (SCI), Mechanics.
Modeling of the primary rearrangement stage of liquid phase sintering2016In: Modelling and Simulation in Materials Science and Engineering, ISSN 0965-0393, E-ISSN 1361-651X, Vol. 24, no 7, article id 075009Article in journal (Refereed)

The dimensional variations during the rearrangement stage of liquid phase sintering could have a detrimental effect on the dimensional tolerances of the sintered product. A numerical approach to model the liquid phase penetration into interparticle boundaries and the accompanied dimensional variations during the primary rearrangement stage of liquid phase sintering is presented. The coupled system of the Cahn-Hilliard and the Navier-Stokes equations is used to model the penetration of the liquid phase, whereas the rearrangement of the solid particles due to capillary forces is modeled using the equilibrium equation for a linear elastic material. The simulations are performed using realistic physical properties of the phases involved and the effect of green density, wettability and amount of liquid phase is also incorporated in the model. In the first step, the kinetics of the liquid phase penetration and the rearrangement of solid particles connected by a liquid bridge is modeled. The predicted and the calculated (analytical) results are compared in order to validate the numerical model. The numerical model is then extended to simulate the dimensional changes during primary rearrangement stage and a qualitative match with the published experimental data is achieved.

• 10.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Three-dimensional phase-field modeling of martensitic microstructure evolution in steels2012In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 60, no 4, p. 1538-1547Article in journal (Refereed)

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.

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