Direct Simulation of a Solidification Benchmark Experiment

International audienceA solidification benchmark experiment is simulated using a three-dimensional cellular automaton-finite element solidification model. The experiment consists of a rectangular cavity containing a Sn-3 wt pct Pb alloy. The alloy is first melted and then solidified in the cavity. A dense array of thermocouples permits monitoring of temperatures in the cavity and in the heat exchangers surrounding the cavity. After solidification, the grain structure is revealed by metallography. X-ray radiography and inductively coupled plasma spectrometry are also conducted to access a distribution map of Pb, or macrosegregation map. The solidification model consists of solutions for heat, solute mass, and momentum conservations using the finite element method. It is coupled with a description of the development of grain structure using the cellular automaton method. A careful and direct comparison with experimental results is possible thanks to boundary conditions deduced from the temperature measurements, as well as a careful choice of the values of the material properties for simulation. Results show that the temperature maps and the macrosegregation map can only be approached with a three-dimensional simulation that includes the description of the grain structure

Application of Inverse Methods to the Estimation of Boundary Conditions and Properties

Inverse methods can be used in solidification and related processes for the estimation of boundary conditions or physical properties of materials. For heat flow problems, these methods are based upon a minimisation of the errors between calculated and measured temperatures at given locations and times of the space-time domain, the calculated values being obtained from a numerical solution of the heat flow equation. In the present case, a maximum a posteriori technique has been implemented into a finite element code. This method is then applied to several situations for the determination of : i) the time-dependent heat-transfer coefficient at the surface of a steel rod which has been water-cooled after induction heating (non-stationary situation) ; ii) the space-dependent heat flow at the surface of a direct chill cast aluminium slab (stationary situation) ; and iii) the temperature-dependent thermal conductivity of aluminium-silicon alloys. In this latter case, the influence of the silicon concentration on the thermal conductivity is clearly revealed

Experimental and Numerical Modeling of Segregation in Metallic Alloys

International audienceElectromagnetic levitation (EML) has been used as an experimental technique for investigating the effect of the nucleation and cooling rate on segregation and structure formation in metallic alloys. The technique has been applied to aluminum-copper alloys. For all samples, the primary phase nucleation has been triggered by the contact of the levitated droplet with an alumina plate at a given undercooling. Based on the recorded temperature curves, the heat extraction rate and the nucleation undercooling for the primary dendritic and the secondary eutectic structures have been determined. Metallurgical characterizations have consisted of composition measurements using a scanning electron microscope (SEM) equipped with energy dispersive X-ray spectrometry and the analysis of SEM images. The distribution maps drawn for the composition, the volume fraction of the eutectic structure, and the dendrite arm spacing (DAS) reveal strong correlations. Analysis of the measurements with the help of a cellular-automaton (CA)-finite-element (FE) model is also proposed. The model involves a new coupling scheme between the CA and FE methods and a segregation model accounting for diffusion in the solid and liquid phases. Extensive validation of the model has been carried out on a typical equiaxed grain configuration, i.e., considering the free growth of a mushy zone in an undercooled melt. It demonstrates its capability of dealing with mass exchange inside and outside the envelope of a growing primary dendritic structure. The model has been applied to predict the temperature curve, the segregation, and the eutectic volume fraction obtained upon single-grain nucleation and growth from the south pole of a spherical domain with and without triggering of the nucleation of the primary solid phase, thus simulating the solidification of a levitated droplet. Predictions permit a direct interpretation of the measurements

Relationship between solidification microstructure and hot cracking susceptibility for continuous casting of low-carbon and high-strength low-alloyed steels: A phase-field study

© The Minerals, Metals & Materials Society and ASM International 2013Hot cracking is one of the major defects in continuous casting of steels, frequently limiting the productivity. To understand the factors leading to this defect, microstructure formation is simulated for a low-carbon and two high-strength low-alloyed steels. 2D simulation of the initial stage of solidification is performed in a moving slice of the slab using proprietary multiphase-field software and taking into account all elements which are expected to have a relevant effect on the mechanical properties and structure formation during solidification. To account for the correct thermodynamic and kinetic properties of the multicomponent alloy grades, the simulation software is online coupled to commercial thermodynamic and mobility databases. A moving-frame boundary condition allows traveling through the entire solidification history starting from the slab surface, and tracking the morphology changes during growth of the shell. From the simulation results, significant microstructure differences between the steel grades are quantitatively evaluated and correlated with their hot cracking behavior according to the Rappaz-Drezet-Gremaud (RDG) hot cracking criterion. The possible role of the microalloying elements in hot cracking, in particular of traces of Ti, is analyzed. With the assumption that TiN precipitates trigger coalescence of the primary dendrites, quantitative evaluation of the critical strain rates leads to a full agreement with the observed hot cracking behavior. © 2013 The Minerals, Metals & Materials Society and ASM International

Columnar and Equiaxed Solidification of Al-7 wt.% Si Alloys in Reduced Gravity in the Framework of the CETSOL Project

International audienceDuring casting, often a dendritic microstructure is formed, resulting in a columnar or an equiaxed grain structure, or leading to a transition from columnar to equiaxed growth (CET). The detailed knowledge of the critical parameters for the CET is important because the microstructure affects materials properties. To provide unique data for testing of fundamental theories of grain and microstructure formation, solidification experiments in microgravity environment were performed within the European Space Agency Microgravity Application Promotion (ESA MAP) project Columnar-to-Equiaxed Transition in SOLidification Processing (CETSOL). Reduced gravity allows for purely diffusive solidification conditions, i.e., suppressing melt flow and sedimentation and floatation effects. On-board the International Space Station, Al-7 wt.% Si alloys with and without grain refiners were solidified in different temperature gradients and with different cooling conditions. Detailed analysis of the microstructure and the grain structure showed purely columnar growth for nonrefined alloys. The CET was detected only for refined alloys, either as a sharp CET in the case of a sudden increase in the solidification velocity or as a progressive CET in the case of a continuous decrease of the temperature gradient. The present experimental data were used for numerical modeling of the CET with three different approaches: (1) a front tracking model using an equiaxed growth model, (2) a three-dimensional (3D) cellular automaton–finite element model, and (3) a 3D dendrite needle network method. Each model allows for predicting the columnar dendrite tip undercooling and the growth rate with respect to time. Furthermore, the positions of CET and the spatial extent of the CET, being sharp or progressive, are in reasonably good quantitative agreement with experimental measurements

A three-dimensional cellular automation-finite element model for the prediction of solidification grain structures

International audienceA three-dimensional (3-D) model for the prediction of dendritic grain structures formed during solidification is presented. This model is built on the basis of a 3-D cellular automaton (CA) algorithm. The simulation domain is subdivided into a regular lattice of cubic cells. Using physically based rules for the simulation of nucleation and growth phenomena, a state index associated with each cell is switched from zero (liquid state) to a positive value (mushy and solid state) as solidification proceeds. Because these physical phenomena are related to the temperature field, the cell grid is superimposed to a coarser finite element (FE) mesh used for the solution of the heat flow equation. Two coupling modes between the microscopic CA and macroscopic FE calculations have been designed. In a so-called “weak” coupling mode, the temperature of each cell is simply interpolated from the temperature of the FE nodes using a unique solidification path at the macroscopic scale. In a “full” coupling mode, the enthalpy field is also interpolated from the FE nodes to the CA cells and a fraction of solid increment is computed for each mushy cell using a truncated Scheil microsegregation model. These fractions of solid increments are then fed back to the FE nodes in order to update the new temperature field, thus accounting for a more realistic release of the latent heat (i.e., the solidification path is no longer unique). Special dynamic allocation techniques have been designed in order to minimize the computation costs and memory size associated with a very large number of cells (typically 107 to 108). The potentiality of the CAFE model is demonstrated through the predictions of typical grain structures formed during the investment casting and continuous casting processes