Janin Eiken

Phase-field simulation of microstructure formation in technical castings - A self-consistent homoenthalpic approach to the micro-macro problem

Performing microstructure simulation of technical casting processes suffers from the strong interdependency between latent heat release due to local microstructure formation and heat diffusion on the macroscopic scale: local microstructure formation depends on the macroscopic heat fluxes and, in turn, the macroscopic temperature solution depends on the latent heat release, and therefore on the microstructure formation, in all parts of the casting. A self-consistent homoenthalpic approximation to this micro-macro problem is proposed, based on the assumption of a common enthalpy-temperature relation for the whole casting which is used for the description of latent heat production on the macroscale. This enthalpy-temperature relation is iteratively obtained by phase-field simulations on the microscale, thus taking into account the specific morphological impact on the latent heat production. This new approach is discussed and compared to other approximations for the coupling of the macroscopic heat flux to complex microstructure models. Simulations are performed for the binary alloy Al-3at%Cu, using a multiphase-field solidification model which is coupled to a thermodynamic database. Microstructure formation is simulated for several positions in a simple model plate casting, using a one-dimensional macroscopic temperature solver which can be directly coupled to the microscopic phase-field simulation tool.

Upgrading CALPHAD to microstructure simulation: the phase-field method

Abstract By amending the time and space evolution of interfaces to the CALPHAD Gibbsian phase descriptions, the phase-field method now makes realistic microstructure simulations possible. This combination allows incorporating more than one century of accumulated experimental information, consistently synthesized in the thermodynamic and kinetic CALPHAD databases, into multicomponent, multiphase, 3-dimensional microstructure evolution simulations. It represents a large step in materials design and a call for creative contributions from a growing interdisciplinary community. The approach is illustrated by steel and magnesium alloy microstructure simulations.

Phase-field simulation of microstructure formation in technical magnesium alloys

Abstract A phase-field model is presented which is specially tailored for engineering-oriented application. It addresses multiphase, multicomponent alloys and considers lattice specific crystallographic anisotropy. Versatile application examples to magnesium alloys demonstrate the models capability of handling important aspects of microstructure formation during solidification. Thermodynamic data is derived from a Calphad database for the Mg – Al – Zn – Ca – Mn system. First, orientation selection and texture evolution is studied under directional growth conditions. A new approach is proposed to model the anisotropy of the hexagonal close-packed magnesium phase. Subsequently, grain structure formation is simulated for technical Mg – Al-based alloys under equiaxed growth conditions. It is shown how the cooling rate and the addition of specific alloy elements affect the grain size. Finally, the solidification path and its effect on the precipitation of the secondary phase MgAl has been investigated.

Numerical solution of the phase-field equation with minimized discretization error

Phase-field models are gaining importance as application-oriented tools for alloy and process optimization. In this context, numerical performance plays an essential role, but is often difficult to reconcile with accuracy. The numerical solution of the phase-field equation based on finite differences inherently implies a discretization error which may strongly bias the simulation results. A direct correlation between the accuracy of the finite-difference solution and the number of numerical cells resolving the diffuse interface profile has been observed. This presents a problem, because high numbers of interface cells are unfavorable for computational performance. To overcome the problem, an improved numerical solution of the phase-field equation is proposed, which allows obtaining highly accurate results with three or four interface cells only. The solution takes advantage of the a priori knowledge of the phase-field profile, determined by the choice of the potential function in the free energy functional. This knowledge enables an almost exact quantification and compensation of the error evoked by the discrete nature of the grid spacing and interface width. Benchmark simulations demonstrate the significant gain in both accuracy and numerical efficiency

Towards a metadata scheme for the description of materials – the description of microstructures

Abstract The property of any material is essentially determined by its microstructure. Numerical models are increasingly the focus of modern engineering as helpful tools for tailoring and optimization of custom-designed microstructures by suitable processing and alloy design. A huge variety of software tools is available to predict various microstructural aspects for different materials. In the general frame of an integrated computational materials engineering (ICME) approach, these microstructure models provide the link between models operating at the atomistic or electronic scales, and models operating on the macroscopic scale of the component and its processing. In view of an improved interoperability of all these different tools it is highly desirable to establish a standardized nomenclature and methodology for the exchange of microstructure data. The scope of this article is to provide a comprehensive system of metadata descriptors for the description of a 3D microstructure. The presented descriptors are limited to a mere geometric description of a static microstructure and have to be complemented by further descriptors, e.g. for properties, numerical representations, kinetic data, and others in the future. Further attributes to each descriptor, e.g. on data origin, data uncertainty, and data validity range are being defined in ongoing work. The proposed descriptors are intended to be independent of any specific numerical representation. The descriptors defined in this article may serve as a first basis for standardization and will simplify the data exchange between different numerical models, as well as promote the integration of experimental data into numerical models of microstructures. An HDF5 template data file for a simple, three phase Al-Cu microstructure being based on the defined descriptors complements this article.

Methods of segregation analysis applied to simulated multicomponent multiphase microstructures

Abstract Advanced microstructure simulation models can predict solute segregation in 2D and 3D space, which often leads to outputs of large arrays of concentration values with a multitude of detailed information that hinders straightforward evaluations. The target of this study is to establish a common evaluation method for both simulation results and experimental data as a standard for quantitative comparison and validation. For this purpose, a methodology is adopted from experimental segregation analysis to transform the multi-dimensional data into meaningful 1D segregation profiles, which can easily be plotted and discussed. As an application example, a directional solidification experiment on an AZ31 magnesium alloy is selected and the solidification process is simulated using the phase-field method. The subsequently obtained 1D segregation profiles are compared to measured segregation profiles. As part of the study, two common sorting methods are evaluated with respect to their applicability to recover the general segregation behavior and the solidification path, as well as to handle numerical noise.

Eutectic morphology evolution and Sr-modification in Al-Si based alloys studied by 3D phase-field simulation coupled to Calphad data

The mechanical properties of Al-Si cast alloys are mainly controlled by the morphology of the eutectic silicon. Phase-field simulations were carried out to study the evolution of the multidimensional branched eutectic structures in 3D. Coupling to a Calphad database provided thermodynamic data for the multicomponent multiphase Al-Si-Sr-P system. A major challenge was to model the effect of the trace element Sr. Minor amounts of Sr are known to modify the silicon morphology from coarse flakes to fine coral-like fibers. However, the underlying mechanisms are still not fully understood. Two different in literature most discussed mechanisms were modelled: a) an effect of Sr on the growth kinetics of eutectic silicon and b) the formation of Al2Si2Sr on AlP particles, which consumes most potent nucleation sites and forces eutectic silicon to form with lower frequency and higher undercooling. The phase-field simulations only revealed a successful modification of the eutectic morphology when both effects acted in combination. Only in this case a clear depression of the eutectic temperature was observed. The required phase formation sequence L → fcc-(Al) → AlP → Al2Si2Sr → (Si) determines critical values for the Sr and P content.

A Multi-phase-field Approach for Solidification with Non-negligible Volumetric Expansion—Application to Graphite Growth in Nodular Cast Iron

Multi-phase field models have become powerful tools for prediction of microstructure evolution in technical alloys. Coupling to CALPHAD databases provides complex multicomponent multiphase thermodynamic data and diffusion matrices. Although many thermodynamic databases contain volume data, this information is by now hardly used for solidification, since a comprehensive modelling of volumetric expansion based on solid- and fluid-mechanics exceeds present computational capacities. A novel multicomponent multi-phase-field approach is presented which handles volumetric expansion in a simplified way. It assumes that temporary pressure caused by local expansion is instantaneously released by matter transport on a time scale much faster than diffusion. The new approach neglects any mechanical and kinetic aspects of expansion, but allows for a change in total volume and for thermodynamically consistent volume fractions. Moreover, expansion-driven matter fluxes and associated advective solute transport are considered. Application is illustrated by the example of spheroidal graphite growth in a hypoeutectic cast iron alloy.

Is There a Difference Between Dendrites of a Binary or a Ternary Alloy? Some Answers by Phase-Field Simulations

Dendritic growth is best understood for pure substances growing into a uniformly supercooled environment. Under certain assumptions the standard growth theory can be applied to the directional growth of dendrites in a binary alloy. To apply the theory to technical multicomponent alloys so called ‘binary equivalent’ or ‘pseudo-binary’ models have been proposed. The basic question of ‘Is there a difference between dendrites of a binary or ternary alloy?’ has only partially been answered. A phase-field model applied to a ternary Fe-C alloy with a third fictive component will be used in this paper to compare ternary and binary equivalent phase-field simulations focussing on different component diffusivities. Results for directional dendritic solidification indicate negligible and relevant differences with respect to micro-segregation and micro-structure.Copyright