Markus Apel

2D and 3D phase-field simulations of lamella and fibrous eutectic growth

Abstract The coupled eutectic growth of binary alloys was studied by means of phase-field models or boundary integral methods for many years. The use of numerical methods discovered the remarkable variety of growth structures like lamellae or different kinds of oscillating modes. In this work, the multi-phase-field method which is generally valid for most kinds of transitions between multiple phases is applied to the eutectic growth problem. We simulated the directional solidification of a binary eutectic during the initial transient state in 2 and 3 dimensions. The chosen phase diagram of the eutectic alloy is asymmetric with a composition ratio between the two solid phases α and β of 0.82. The 2D simulations show stable lamella growth or unstable oscillating modes dependent on the number of β lamella specified by explicit seeding at the bottom of the calculation domain. The undercooling at the growth front is evaluated for different spacing and compared with the values obtained by the fundamental analysis for the steady-state growth via the Jackson and Hunt model. For the regular lamella growth, the undercooling evaluated from the phase-field simulations fits within 20% of the analytical values. 3D calculations show the fibrous growth structure. This is in agreement with the expectation because for small phase fractions of β the fibrous structure possesses a smaller total amount of surface energy compared with lamellas and therefore should be preferred. For a larger number of fibres, they tend to form a hexagonal arrangement which is usually observed by experiments.

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.

Towards integrative computational materials engineering of steel components

This article outlines on-going activities at the RWTH Aachen University aiming at a standardized, modular, extendable and open simulation platform for materials processing. This platform on the one hand facilitates the information exchange between different simulation tools and thus strongly reduces the effort to design/re-design production processes. On the other hand, tracking of simulation results along the entire production chain provides new insights into mechanisms, which cannot be explained on the basis of individual simulations. Respective simulation chains provide e.g. the basis for the determination of materials and component properties, like e.g. distortions, for an improved product quality, for more efficient and more reliable production processes and many further aspects. After a short introduction to the platform concept, actual examples for different test case scenarios will be presented and discussed.

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.

Parallelising computational microstructure simulations for metallic materials with OpenMP

This work focuses on the OpenMP parallelisation of an iterative linear equation solver and parallel usage of an explicit solver for the nonlinear phase-field equations. Both solvers are used in microstructure evolution simulations based on the phase-field method. For the latter one, we compare a graph based solution using OpenMP tasks to a first-come-first-serve scheduling using an OpenMP critical section. We discuss how the task solution might benefit from the introduction of OpenMP task dependencies. The concepts are implemented in the software MICRESS which is mainly used by material engineers for the simulation of the evolving material microstructure during processing.

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.

Phase-field modeling of the columnar-to-equiaxed transition in neopentylglycol-camphor alloy solidification

We have performed phase field simulations in order to explore the effect of equiaxed grain nucleation undercooling on the columnar to equiaxed transition CET in the NPG-DC alloy system. Our phase field model is based on the multiphase-field method. The simulation parameters are adapted to a microgravity experiment performed under purely diffusive growth conditions. The experimental investigation is made during the sounding rocket campaign TEXUS-47.

Phase-Field Simulation of Cooperative Growth of Pearlite

Cooperative growth of pearlite is simulated for eutectoid steel using the multi-phase field method. This allows to take into account diffusion of carbon not only in γ phase, but also in α phase. The lamellar spacing and growth velocity are estimated for different undercoolings and compared with experimental results from literature and theoretical results from analytical models. It is predicted, that diffusion in ferrite and growth of cementite from the ferrite increase the kinetics of pearlitic transformation by a factor of four as compared to growth from austenite only, which is assumed by the classical Zener-Hillert model. Further on the effect of stress due to inhomogeneous carbon distribution in austenite and due to transformation strain is discussed shortly.

Phase field modeling of rapid crystallization in the phase-change material AIST

We carry out phase field modeling as a continuum simulation technique in order to study rapid crystallization processes in the phase-change material AIST (Ag4In3Sb67Te26). In particular, we simulate the spatio-temporal evolution of the crystallization of a molten area of the phase-change material embedded in a layer stack. The simulation model is adapted to the experimental conditions used for recent measurements of crystallization rates by a laser pulse technique. Simulations are performed for substrate temperatures close to the melting temperature of AIST down to low temperatures when an amorphous state is involved. The design of the phase field model using the thin interface limit allows us to retrieve the two limiting regimes of interface controlled (low temperatures) and thermal transport controlled (high temperatures) dynamics. Our simulations show that, generically, the crystallization velocity presents a maximum in the intermediate regime where both the interface mobility and the thermal transport...

Mesoscopic modelling of columnar solidification

We used two complementary modeling approaches for the simulation of columnar growth in directional solidification of organic alloys: a phase-field model and a mesoscopic envelope model of dendritic growth. While the phase-field method captures the details of the dendritic structure and of the growth dynamics, the mesoscopic model approximates the complex dendritic morphology by its envelope. The envelope growth is deduced from the velocities of the dendrite tips, calculated by an analytical LGK-type tip model that is matched to the heat and concentration fields in the stagnant film around the envelope. The computational cost of the mesoscopic model is several orders of magnitude lower and can bridge the gap between phase-field and macroscopic models. We demonstrate the applicability of the mesoscopic model to columnar growth and discuss its possibilities and limitations by comparisons with phase-field simulations for the same conditions.