The "virtual cast house", development of a process chain model of aluminium direct chill casting of tailored products (VIRCAST)

EPFL has developed and improved an experimental set-up for studying hot tearing formation in transparent alloys. The experiment has been improved by means of controllable displacement engine and dye.

A software tool, which allows to couple new models with existing software, is delivered to industrial partners of the project. The new models address hot tears prediction, as-cast microstructure modelling and homogenisation/precipitation physics. The coupling with existing commercial software is performed in the form of so-called weak coupling. The data used as input to the new models are usually 2D or 3D (two or three dimensional) simulation results such as temperature, fraction of solid, stress, etc. provided by the various software used by the industrial partners of the project. The software-coupling concept is based on: - A specific binary file format. This specific file format ensures the compatibility between the different commercial software used by the VIRCAST partners and the new models; - Converting functions which link result files produced by existing commercial software with input files for the new models; - Reading/writing functions, which link the new models with their input and output ascci files. The software: - Allows direct visualization of 2D or 3D macro results provided by the various software used by the industrial partners of the project. - Accepts as input data various formats, process the data using the models developed in the other workpackages, and output the results in specific formats; - Allows direct visualization of hot-tearing prediction maps and as-cast microstructures.

IFE, in collaboration with Calcom, has implemented the SINTEF/INPG two-phase model for thermally induced deformations and shrinkage induced flow in a 2D axisymmetric solution domain relevant for DC casting. The new modelling tool is referred to as TearSim. Its finite element program code is assembled from building blocks that have been separately implemented and validated by comparing the numerical solution for simplified validation examples with analytical solutions.

An interface dedicated to as-cast microstructure prediction is available in the VIRCAST software tool. The interface allows pre-processing the pseudo-front tracking model developed at EPFL for the description of as-cast microstructures. The graphical interface allows reading the following model inputs: - Temperature or heat extraction rate as a function of time; - The phase diagram (primary phase only for now): - The initial field of solid fraction; - The diffusion coefficient in the various phases; - The volumetric specific heat; - The volumetric latent heat; - The Gibbs-Thomson coefficient; - The symmetry order of the crystal (4 for aluminium); - The relative stiffness of the surface tension; - The total simulation time. The user will be able to visualize the following specific results: - Concentration maps at various times; - Solid fraction maps at various times; - Temperature evolution; - Evolution of the solid fraction in the calculation domain; - Maps of the fractions of secondary phases (not yet implemented); - Solidification path.

EPFL and CALCOM have derived a transient version of EPFL/Calcom�s hot tearing criterion. Input to this criterion has been obtained from temperature and stress/strain field modelling using Calcosoft and ABAQUS. The model has been implemented in the form of a new software module, which has been applied to study hot tearing formation during DC casting of aluminium.

An interface dedicated to hot tearing prediction is available in the VIRCAST software tool. Two models developed at EPFL are considered: a thermal and a mechanical criterion: - In the thermal criterion, the maximum strain rate sustainable by the mush at the root of the dendrites is computed for a given cavitation depression. The inverse of this quantity yields the hot tearing sensitivity. This criterion can be implemented in pure thermal models. - In the mechanical criterion, the pressure drop due to the solidification shrinkage and to the deformation undergone by the mush (given by the strain rate perpendicular to the thermal gradient) is computed. The larger the pressure drop, the more prone the alloy to develop cracks. This criterion can be implemented in thermo-mechanical models. The interface allows to read the required model inputs and to visualize the typical results. The results to be displayed are: - Thermal criterion: -- Maximum strain rate sustainable by the mushy zone, epsmax [1/s]; -- Hot cracking sensitivity, 1/epsmax [s]. - Mechanical criterion: -- Pressure drop in the mushy zone [Pa]; -- Hot cracking index: 1 or 0 [-].

INPG has designed and performed shear experiments using the tensile rheometer with Al-Cu and 5083 Aluminium alloys at various strain rates and various solid fractions. Tests have also been carried out non-isothermally during solidification. Moreover, INPG has designed a drained oedometric compression apparatus, and tested it initially with Sn-Pb alloys. Various compression rates and temperatures have been investigated. The apparatus has been modified to allow tests to be carried out with Al alloys. These tests have been performed with Al-Cu alloys. In addition, a tensile test apparatus that allows straining the alloy during solidification has been developed.

A model based on a granular dynamics approach has been developed in order to describe the nucleation, growth and movement of groups of grains in the DC casting process. The outputs of the model consist in the local average grain density, grain size, secondary dendrite arm spacing, and grain morphology at the outlet of the product. Moreover, the numerical tool, which has been developped, allows a new way to analyse the history of the grains in the DC-casting of aluminium process. This model can also provide the local grain density as an input to the as-cast microstructure model developed at EPFL. The grain density determines to a large extent the morphology of the grains and thus the repartition of intermetallic phases.

A simple 1D model describing the evolution of a primary precipitate and the one of the surrounding matrix with a prescribed micro segregation during the homogenisation has been established. The occurrence of growth of secondary precipitates is allowed in the matrix on a second frame. The equilibrium conditions are prescribed through thermodynamic data obtained from thermodynamical calculations. The evolution of either the chemical composition of the matrix and the primary and secondary precipitates is driven by diffusion processes. To describe the model, the input data are the respective size of the primary precipitate and the size of the surrounding matrix, the number of secondary precipitates and the geometrical distance between these �nuclei�. The physical input are the thermodynamic data for the different temperatures, the chemical composition of the primary precipitates and the matrix, and the diffusion data. The temperature law is assigned. The output of the model are the evolution of the primary precipitates (size and chemical composition) and the chemical composition of the matrix.

The pseudo-front tracking model used to describe the formation of microstructure during solidification also applies to homogenisation. This 2-dimensional model can describe the evolution of the primary precipitates, which formed in the interdendritic regions during solidification. The model predicts the amount and the type of primary precipitates as a function of temperature and solute distribution in the matrix during homogenisation. It is based on the assumptions of diffusion controlled phase transformations and local equilibrium at the interfaces. The equilibrium conditions are obtained either by direct calls to the phase diagram software Thermo-Calc or from tabulated phase diagrams. The model is presently operational for multicomponent alloys in the direct coupling mode and for binary alloys in the tabulation mode. Comparisons with experimental data have been performed but remain limited if not coupled to a precipitation model. A preliminary coupled version of the present homogenisation model with the INPL precipitation model has been developed and applied to the 3003 alloys for a 1D geometry. Results are promising, although the extension of the coupled model to 2D would require the development of optimisation methods to reduce the computation time.

INPG has developed a new internal variable constitutive model for the rheological behavior of the mushy zone that takes into account solid skeleton volume change and strain hardening for high solid fractions and small strains. The equations have been formulated such that they can be incorporated in SINTEF/INPGs two-phase model.

A numerical model based on a pseudo-front tracking method has been developed in order to describe the formation of the microstructure during solidification of multicomponent systems. This two-dimensional model can simulate the growth of individual dendritic or globulo-dendritic grains in a selected zone of a casting. The model provides a direct simulation of the grain morphology evolution and microsegregation patterns. The method is based on the resolution of the solute diffusion equations including the effect of interface curvature. The calculations are performed from the knowledge of the average local concentrations at the end of solidification and of the local thermal history. These quantities are obtained by measurement or from a macroscopic calculation on the scale of the casting. The pseudo-front tracking model has been extended to describe the formation of the secondary phases in the interdendritic regions, after the temperature for eutectic or peritectic phases has been reached. Considering the effect of back-diffusion and cooling, the model can predict the type, the amount and the spatial distribution of the secondary phases. The model is coupled to the phase diagram software Thermo-Calc, allowing therefore applications to complex alloys. During the project the model is validated against experimental data for 3xxx and 5xxx series alloys. This comprehensive microstructure model can be used to perform predictive simulations of as-cast microstructures as a function of alloy composition and cooling conditions. Comparisons with 3xxx and 5xxx series alloys are presently underway.

INPL has developed a numerical model calculating the secondary precipitates formation and evolution during the homogenisation thermal treatment of a multi-component alloy. The models of the physical mechanisms i.e. the nucleation, growth (and coarsening as a consequence) are based on classical law for nucleation, diffusion control for the growth. A coupling with the phase diagram software (Thermo-Calc) is realized and the effect of interface curvature on local equilibrium is included. The input of the model are the chemical composition of the solid solution (given either by experiments or by a calculation of the solidification microstructure), the thermodynamic and diffusion data, and some additional parameters of the model (density of nucleation sites, interface energy). Outputs of the model are the chemical composition of the matrix, the volume fraction of secondary precipitates, the mean size as well as the size distribution of precipitates at any time of the thermal treatment. The model is able to take into account variable concentration of the volume considered, and can thus be coupled to a homogenisation model. The model is validated against experimental data obtained on AA3003 alloy for well-controlled thermal treatments of the AA3003 alloy. Comparisons of overall precipitation kinetics as well as the evolution of size, density, and chemical composition of precipitates are conducted.

SINTEF and NTNU have developed a new technique for studying the formation of interdendritic bridging (coalescence) during solidification. The existence of such interdendritic bridges at various solid fractions is demonstrated experimentally in binary aluminium alloys. Small samples have been solidified and subsequently quenched in water close to the start of the eutectic reaction. Al-Cu samples with various amounts of eutectic have been investigated to assess the solid fraction corresponding to the onset of bridging. A thin polished section of an Al-12wt. %Mg sample has been deep etched to remove the quenched eutectic and investigated in a SEM. Interdendritic bridges have been shown to exist in fragments of the sample.

The microstructures evolutions have been largely investigated by the different partners and numerous data are available for two alloys chosen in the study (AA 3003 and AA3103). These data can be used for the further description of the microstructure for the forming process and are mainly data that allow comparisons between modelling and experiments. The procedures for the measurements used by the different partner were compared in a Round Robin test. The mechanisms associated with the microstructure evolution were defined for a large part of the thermal cycle (heating and during the temperature holding). The one during the further cooling have to be further investigated for a full knowledge of these mechanisms. The nature of the phases appearing on heating, the transformations of the intermetallic primary phases were established. A quantification of the initial microstructure was performed (Amount, size and shape factor distribution of primary precipitates, Chemical composition of precipitates, microsegregation, DAS). The following evolution were quantified during heating, maintain at temperatures and further cooling: - Primary precipitates evolution (amount, size, shape factor, number of particles, change in composition and structure). - Secondary precipitates (size, number of particles, chemical composition).

Using the phase field technique, EPFL has developed a mathematical model for coalescence between grains during solidification. The new model can be used for understanding the basic mechanism of coalescence, and for predicting the extent of bridging during solidification.

A numerical model based on a phase-field method has been developed in order to describe the formation of the primary solid phase in multicomponent systems. This two-dimensional model can simulate the growth of individual dendritic grains in a selected zone of a casting. The model provides a direct simulation of the grain morphology evolution and microsegregation patterns. The method is based on the resolution of the solute diffusion equations including the effects of interface curvature and attachment kinetics at the interface. The calculations are performed from the knowledge of the average local concentration at the end of solidification and of the local thermal history. These quantities are obtained from a macroscopic calculation on the scale of the casting. At present, the model is limited to binary systems but extension to multi-component systems might be considered in the future. This model is an alternative approach to the pseudo-front tracking method for the prediction of as-cast microstructures. It is intended to be used as a comparison tool. It may also offer shorter computation times than the pseudo-front tracking methods for purely dendritic microstructures.

SINTEF and INPG have developed a two-phase model by which the main mechanism for hot tearing formation, i.e., interdendritic melt flow caused by solidification shrinkage, and thermally induced deformation in the entirely solidified parts of the casting and in the solid phase within the cooler parts of the coherent mushy zone, are taken into account. This model will serve as a basis for new hot tearing criteria build on two-phase quantities.

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