Experimental studies and phase field modeling of microstructure evolution during solidification with electromagnetic stirring

Thixocasting requires manufacturing of billets with non-dendritic microstructure. Aluminum alloy A356 billets were produced by rheocasting in a mould placed inside a linear electromagnetic stirrer. Subsequent heat treatment was used to produce a transition from rosette to globular microstructure. The current and the duration of stirring were explored as control parameters. Simultaneous induction heating of the billet during stirring was quantified using experimentally determined thermal profiles. The effect of processing parameters on the dendrite fragmentation was discussed. Corresponding computational modeling of the process was performed using phase-field modeling of alloy solidification in order to gain insight into the process of morphological changes of a solid during this process. A non-isothermal alloy solidification model was used for simulations. The morphological evolution under such imposed thermal cycles was simulated and compared with experimentally determined one. Suitable scaling using the thermosolutal diffusion distances was used to overcome computational difficulties in quantitative comparison at system scale. The results were interpreted in the light of existing theories of microstructure refinement and globularisation.

DIFFUSE-INTERFACE FIELD APPROACH TO MODELING SELF-ASSEMBLY OF HETEROGENEOUS COLLOIDAL SYSTEMS AND RELATED DIPOLE-DIPOLE INTERACTION PHENOMENA

Colloid self-assembly under external control is a new route to fabrication of advanced materials with novel microstructures and appealing functionalities. The kinetic processes of colloidal self-assembly have attracted great interests also because they are similar to many atomic level kinetic processes of materials. In the past decades, rapid technological progresses have been achieved on producing shape-anisotropic, patchy, core-shell structured particles and particles with electric/magnetic charges/dipoles, which greatly enriched the self-assembled structures. Multi-phase carrier liquids offer new route to controlling colloidal self-assembly. Therefore, heterogeneity is the essential characteristics of colloid system, while so far there still lacks a model that is able to efficiently incorporate these possible heterogeneities. This thesis is mainly devoted to development of a model and computational study on the complex colloid system through a diffuse-interface field approach (DIFA), recently developed by Wang et al. This meso-scale model is able to describe arbitrary particle shape and arbitrary charge/dipole distribution on the surface or body of particles. Within the framework of DIFA, a Gibbs-Duhem-type formula is introduced to treat Laplace pressure in multi-liquid-phase colloidal system and it obeys Young-Laplace equation. The model is thus capable to quantitatively study important capillarity related phenomena. Extensive computer simulations are performed to study the fundamental behavior of heterogeneous colloidal system. The role of Laplace pressure is revealed in determining the mechanical equilibrium of shape-anisotropic particles at fluid interfaces. In particular, it is found that the Laplace pressure plays a critical role in maintaining the stability of capillary bridges between close particles, which sheds light on a novel route to in situ firming compact but fragile colloidal microstructures via capillary bridges. Simulation results also show that competition between like-charge repulsion, dipole-dipole interaction and Brownian motion dictates the degree of aggregation of heterogeneously charged particles. Assembly and alignment of particles with magnetic dipoles under external field is studied. Finally, extended studies on the role of dipole-dipole interaction are performed for ferromagnetic and ferroelectric domain phenomena. The results reveal that the internal field generated by dipoles competes with external field to determine the dipole-domain evolution in ferroic materials.

Evolution of multivariant microstructures with anisotropic misfit: A phase field study

We study, in two dimensions, the effect of misfit anisotropy on microstructural evolution during precipitation of an ordered beta phase from a disordered alpha matrix; these phases have, respectively, 2- and 6-fold rotation symmetries. Thus, precipitation produces three orientational variants of beta phase particles, and they have an anisotropic (and crystallographically equivalent) misfit strain with the matrix. The anisotropy in misfit is characterized using a parameter t = epsilon(yy)/epsilon(xx), where epsilon(xx) and epsilon(yy) are the principal components of the misfit strain tensor. Our phase field, simulations show that the morphology of beta phase particles is significantly influenced by 1, the level of misfit anisotropy. Particles are circular in systems with dilatational misfit (t = 1), elongated along the direction of lower principal misfit when 0 < t < 1 and elongated along the invariant direction when - 1 <= t <= 0. In the special case of a pure shear misfit strain (t = - 1), the microstructure exhibits star, wedge and checkerboard patterns; these microstructural features are in agreement with those in Ti-Al-Nb alloys.

A phase field study of morphological instabilities in multilayer thin films

We studied the microstructural evolution of multiple layers of elastically stiff films embedded in an elastically soft matrix using a phase field model. The coherent and planar film/matrix interfaces are rendered unstable by the elastic stresses due to a lattice parameter mismatch between the film and matrix phases, resulting in the break-up of the films into particles. With an increasing volume fraction of the stiff phase, the elastic interactions between neighbouring layers lead to: (i) interlayer correlations from an early stage; (ii) a longer wavelength for the maximally growing wave; and therefore (iii) a delayed break-LIP. Further, they promote a crossover in the mode of instability from a predominantly anti-symmetric (in phase) one to a symmetric (out of phase) one. We have computed a stability diagram for the most probable mode of break-up in terms of elastic modulus Mismatch and Volume fraction. We rationalize our results in terms of the initial driving force for destabilization, and corroborate our conclusions using simulations in elastically anisotropic systems.

Phase field study of precipitate growth: Effect of misfit strain and interface curvature

We have used phase field simulations to study the effect of misfit and interfacial curvature on diffusion-controlled growth of an isolated precipitate in a supersaturated matrix. Treating our simulations as computer experiments, we compare our simulation results with those based on the Zener–Frank and Laraia–Johnson–Voorhees theories for the growth of non-misfitting and misfitting precipitates, respectively. The agreement between simulations and the Zener–Frank theory is very good in one-dimensional systems. In two-dimensional systems with interfacial curvature (with and without misfit), we find good agreement between theory and simulations, but only at large supersaturations, where we find that the Gibbs–Thomson effect is less completely realized. At small supersaturations, the convergence of instantaneous growth coefficient in simulations towards its theoretical value could not be tracked to completion, because the diffusional field reached the system boundary. Also at small supersaturations, the elevation in precipitate composition matches well with the theoretically predicted Gibbs–Thomson effect in both misfitting and non-misfitting systems.

Precipitate growth with composition-dependent diffusivity: Comparison between theory and phase field simulations

We consider the growth of an isolated precipitate when the matrix diffusivity depends on the composition. We have simulated precipitate growth using the Cahn-Hilliard model, and find good agreement between our results and those from a sharp interface theory for systems with and without a dilatational misfit. With misfit, we report (and rationalize) an interesting difference between systems with a constant diffusivity and those with a variable diffusivity in the matrix.

Phase-Field Simulation of Fusion Interface Events during Solidification of Dissimilar Welds: Effect of Composition Inhomogeneity

We investigate the events near the fusion interfaces of dissimilar welds using a phase-field model developed for single-phase solidification of binary alloys. The parameters used here correspond to the dissimilar welding of a Ni/Cu couple. The events at the Ni and the Cu interface are very different, which illustrate the importance of the phase diagram through the slope of the liquidus curves. In the Ni side, where the liquidus temperature decreases with increasing alloying, solutal melting of the base metal takes place; the resolidification, with continuously increasing solid composition, is very sluggish until the interface encounters a homogeneous melt composition. The growth difficulty of the base metal increases with increasing initial melt composition, which is equivalent to a steeper slope of the liquidus curve. In the Cu side, the initial conditions result in a deeply undercooled melt and contributions from both constrained and unconstrained modes of growth are observed. The simulations bring out the possibility of nucleation of a concentrated solid phase from the melt, and a secondary melting of the substrate due to the associated recalescence event. The results for the Ni and Cu interfaces can be used to understand more complex dissimilar weld interfaces involving multiphase solidification.

Metastable extension of the fluorite phase field in Y2O3---ZrO2 and its effect on grain growth

Pure Y2O3 and Y2O3---ZrO2 solid solutions have been prepared by melt atomization and by pyrolysis of nitrate solutions. Extended solubility is readily achieved in both techniques for the entire composition range investigated: melts with 0–30% ZrO2 and precursors with 0–50% ZrO2. However, solidification of under cooled droplets yields almost exclusively single phase powders with the structure of cubic yttria (D53). In contrast, the pyrolysis route leads to a sequence of metastable microstructures beginning with a nanocrystalline disordered fluorite-based (C1) solid solution. Further heating leads to the evolution of much larger (micron size) flake crystals with a {001} texture, concurrent with partial ordering of the oxygen ions to the sites occupied in the D53 structure. The driving force for ordering and the rate of grain growth decrease with increasing ZrO2 addition. Abrupt heating to high temperatures or electron irradiation can induce ordering without substantial grain growth. There is no significant reduction in porosity during the recrystallization, which with the other observations suggests that grain growth is driven by the free energy available for the ordering transformation from fluorite to the yttria structure. This route offers opportunities for single crystal thin film development at relatively low processing temperatures.

Metastable extension of the fluorite phase field in Y2O3---ZrO2 and its effect on grain growth

Pure Y2O3 and Y2O3-ZrO2 solid solutions have been prepared by melt atomization and by pyrolysis of nitrate solutions. Extended solubility is readily achieved in both techniques for the entire composition range investigated: melts with 0-30% ZrO2 and precursors with 0-50% ZrO2. However, solidification of under cooled droplets yields almost exclusively single phase powders with the structure of cubic yttria (D5(3)). In contrast, the pyrolysis route leads to a sequence of metastable microstructures beginning with a nanocrystalline disordered fluorite-based (C1) solid solution. Further heating leads to the evolution of much larger (micron size) flake crystals with a {001} texture, concurrent with partial ordering of the oxygen ions to the sites occupied in the D5(3) structure. The driving force for ordering and the rate of grain growth decrease with increasing ZrO2 addition. Abrupt heating to high temperatures or electron irradiation can induce ordering without substantial grain growth. There is no significant reduction in porosity during the recrystallization, which with the other observations suggests that grain growth is driven by the free energy available for the ordering transformation from fluorite to the yttria structure. This route offers opportunities for single crystal thin film development at relatively low processing temperatures.

Thermal Stability of Spherical Nanoporous Aggregates and Formation of Hollow Structures by Sintering-A Phase-Field Study

Nanoporous structures are widely used for many applications and hence it Is important to investigate their thermal stability. We study the stability of spherical nanoporous aggregates using phase-field simulations that explore systematically the effect of grain boundary diffusion, surface diffusion, and grain boundary mobility on the pathways for microstructural evolution. Our simulations for different combinations of surface and GB diffusivity and GB mobility show four distinct microstructural pathways en route to 100% density: multiple dosed pores, hollow shells, hollow shells with a core, and multiple interconnected pores. The microstructures from our simulations are consistent with experimental observations in several different systems. Our results have important implications for rational synthesis of hollow nanostructures or aggregates with open pores, and for controlling the stability of nanoporous aggregates that are widely used for many applications.

Creep behaviour of Fe3Al-based alloys in DO3 phase field

A study is made to bring out the effect of alloying with Cr, Ti or Mn on the creep behaviour of Fe3Al. Impression creep experiments have been carried out in the DO3 phase field. In all the alloys, power law creep behaviour is observed in the stress range covered. The stress exponent for steady state creep rate and the activation energy for creep indicate that the creep rate is controlled by the dislocation climb process. Among the alloying elements studied, addition of Ti is most effective in improving the creep resistance.

Microstructure and texture evolution during sub-transus thermomechanical processing of Ti-6Al-4V-0.1B alloy: part I. hot rolling in (alpha plus beta) phase field

In the current study, the evolution of microstructure and texture has been studied for Ti-6Al-4V-0.1B alloy during sub-transus thermomechanical processing. This part of the work deals with the deformation response of the alloy by rolling in the (alpha + beta) phase field. The (alpha + beta) annealing behavior of the rolled specimen is communicated in part II. Rolled microstructures of the alloys exhibit either kinked or straight alpha colonies depending on their orientations with respect to the principal rolling directions. The Ti-6Al-4V-0.1B alloy shows an improved rolling response compared with the alloy Ti-6Al-4V because of smaller alpha lamellae size, coherency of alpha/beta interfaces, and multiple slip due to orientation factors. Accelerated dynamic globularization for this alloy is similarly caused by the intralamellar transverse boundary formation via multiple slip and strain accumulation at TiB particles. The (0002)(alpha) pole figures of rolled Ti-6Al-4V alloy shows ``TD splitting'' at lower rolling temperatures because of strong initial texture. Substantial beta phase mitigates the effect of starting texture at higher temperature so that ``RD splitting'' characterizes the basal pole figure. Weak starting texture and easy slip transfer for Ti-6Al-4V-0.1B alloy produce simultaneous TD and RD splittings in basal pole figures at all rolling temperatures.

Phase Field Simulation of Equiaxed Microstructure Formation during Semi-solid Processing of A380 Al Alloy

A phase field modelling approach is implemented in the present study towards simulation of microstructure evolution during cooling slope semi solid slurry generation process of A380 Aluminium alloy. First, experiments are performed to evaluate the number of seeds required within the simulation domain to simulate near spherical microstructure formation, occurs during cooling slope processing of the melt. Subsequently, microstructure evolution is studied employing a phase field method. Simulations are performed to understand the effect of cooling rate on the slurry microstructure. Encouraging results are obtained from the simulation studies which are validated by experimental observations. The results obtained from mesoscopic phase field simulations are grain size, grain density, degree of sphericity of the evolving primary Al phase and the amount of solid fraction present within the slurry at different time frames. Effect of grain refinement also has been studied with an aim of improving the slurry microstructure further. Insight into the process has been obtained from the numerical findings, which are found to be useful for process control.

Phase-field elasticity model based on mechanical jump conditions

Computational models based on the phase-field method typically operate on a mesoscopic length scale and resolve structural changes of the material and furthermore provide valuable information about microstructure and mechanical property relations. An accurate calculation of the stresses and mechanical energy at the transition region is therefore indispensable. We derive a quantitative phase-field elasticity model based on force balance and Hadamard jump conditions at the interface. Comparing the simulated stress profiles calculated with Voigt/Taylor (Annalen der Physik 274(12):573, 1889), Reuss/Sachs (Z Angew Math Mech 9:49, 1929) and the proposed model with the theoretically predicted stress fields in a plate with a round inclusion under hydrostatic tension, we show the quantitative characteristics of the model. In order to validate the elastic contribution to the driving force for phase transition, we demonstrate the absence of excess energy, calculated by Durga et al. (Model Simul Mater Sci Eng 21(5):055018, 2013), in a one-dimensional equilibrium condition of serial and parallel material chains. To validate the driving force for systems with curved transition regions, we relate simulations to the Gibbs-Thompson equilibrium condition

A method for coupling the phase-field model based on a grand-potential formalism to thermodynamic databases

In this paper we derive an approach for the effective utilization of thermodynamic data in phase-field simulations. While the most widely used methodology for multi-component alloys is following the work by Eiken et al. (2006), wherein, an extrapolative scheme is utilized in conjunction with the TQ interface for deriving the driving force for phase transformation, a corresponding simplistic method based on the formulation of a parabolic free-energy model incorporating all the thermodynamics has been laid out for binary alloys in the work by Folch and Plapp (2005). In the following, we extend this latter approach for multi-component alloys in the framework of the grand-potential formalism. The coupling is applied for the case of the binary eutectic solidification in the Cr-Ni alloy and two-phase solidification in the ternary eutectic alloy (Al-Cr-Ni). A thermodynamic justification entails the basis of the formulation and places it in context of the bigger picture of Integrated Computational Materials Engineering. (C) 2015 Elsevier Ltd. All rights reserved.