Interactions between columnar solidification and segregation: a comparison of the predictions of the CAFE model with in-situ observations

International audienceA two-dimensional (2D) cellular automaton (CA) - finite element (FE) model has been proposed to simulate the solidification of binary alloys. The time evolution of maps of temperature, composition and fraction of solid are simulated while accounting for the undercooling of the growing structure. The solidification experiment of a Gallium-5wt%Indium alloy developed by Yin and Koster [1-2] is shown to provide a good benchmark for comparison with predictions of the model. Observed and simulated time evolutions of the development of the grain structure and the macrosegregation can be directly compared, together with mesosegregation such as segregated channels. These channels differ from freckle-type segregation described in the literature. They form as a result of the dynamics of the columnar growth front and its interaction with the fluid and solute flows. Comparisons of the predictions of the CAFE model with a purely macroscopic FE model also reveal the influence of accounting for the growth undercooling in numerical modeling of solidification

Simulation of solidification grain structures with a multiple diffusion length scales model

International audienceA cellular automaton (CA) - finite element (FE) model is presented for the prediction of micro-and macrosegregation based on solute diffusion. On the one hand an open microsegregation model is implemented. It applies to each solidifying CA cell, i.e. a representative elementary volume of the mushy zone. Diffusion in the solid and in the extradendritic liquid are modeled with analytical expressions for two length scales based on the primary and secondary dendrite arm spacing and assuming cylindrical geometries representative of the dendritic network. On the other hand an unstructured and anisotropic FE mesh adaptation is used. The FE mesh is generated based on an error estimation method of the average composition field. Mesh refinement takes place in regions located ahead of the mushy zone growth front where diffusion layers are built up due to segregation. As a result, the diffusion length scale outside the envelopes of mushy zones (i.e., in the intergranular liquid that surrounds the envelopes of the grains) is directly captured. Numerical implementations of the coupling between the CA and FE methods being validated by comparison with the predictions of other models, simulations are compared with experimental results in Al-Cu alloys; thus demonstrating the capability of the model to predict segregation based on the coupling between several length scales

Temperature-based energy solver coupled with tabulated thermodynamic properties – Application to the prediction of macrosegregation in multicomponent alloys

International audienceWe present a new algorithm for solving energy balance in phase change problems, particularly in solidification with macrosegregation. The algorithm is based on a nonlinear temperature evaluation using the average enthalpy which is provided by (i) tabulated phase transformation paths and (ii) tabulated phase properties. The compatibility of this method with tabulations using a thermodynamic database, allows simulating solidification at equilibrium with multiple phase transformations for binary and multicomponent alloys. The method has been validated and applied to three-dimensional cases with macrosegregation: a binary Sn–3 wt.% Pb alloy and a ternary Fe–2 wt.% C–30 wt.% Cr alloy. For the latter case, predictions include composition maps for C and Cr due to thermosolutal instability leading to freckle formation and the subsequent distributions of liquid, BCC, FCC, M7C3 and Cementite phases. Compared with a previously published enthalpy method, the temperature-based energy solver shows similar accuracy and faster computational time

3D CAFE simulation of a macrosegregation benchmark experiment

International audienceA macrosegregation benchmark experiment is simulated using a three dimensional (3D) Cellular Automaton (CA) - Finite Element (FE) model. It consists of a Sn - 3 wt% Pb alloy solidified in a rectangular cavity. Thanks to tabulated thermodynamic properties and solidification paths with temperature and composition, the effect of natural convection and macrosegregation on cooling curves is correctly predicted. Nucleation parameters are adjusted so that the simulated grain structure correlates with the real grain structure. Although macrosegregation is well predicted, this is not the case for freckles yet observed in the solidified sample

Modelling of Columnar-to-Equiaxed and Equiaxed-to- Columnar Transitions in Ingots Using a Multiphase Model

International audienceWe present a new method to handle a representative elementary volume (REV) with a mixture of columnar and equiaxed grains in ingot castings in the framework of an Eulerian volume averaged model. The multiscale model is based on a previously established fully equiaxed model. It consists of a three-phase (extra-granular liquid, intra-granular liquid and solid) grain-growth stage coupled with a two-phase (solid and liquid) macroscopic transport stage accounting for grain and nuclei movement. In this context, we take into account the formation of a columnar structure and its development using a simplified front-tracking method. Columnar solidification is coupled with the growth of equiaxed grains ahead of the columnar front. The particularity of the model is the treatment of concurrent growth of mixed columnar and equiaxed structures only in the volumes that contain the columnar front. Everywhere else, the structure is considered either fully columnar or fully equiaxed. This feature allows for reasonable computational times even in industrial size castings, while describing the solutal and mechanical blocking phenomena responsible for the Columnar-to-Equiaxed Transition. After a validation of the model, we discuss the numerical results for a 6.2-ton industrial steel ingot by comparison with experimental measurements. Final maps for macrosegregation and grain structures size and morphology are analysed. Furthermore, we quantify the impact of nuclei formation through fragmentation along the columnar front on the result. An attempt at predicting the occurrence of the Equiaxed-to-Columnar Transition in the later phases of the process is also made

Three-dimensional modeling of a thermal dendrite using the phase field method with automatic anisotropic and unstructured adaptive finite element meshing

International audienceDendritic growth is computed with automatic adaptation of an anisotropic and unstructured finite element mesh. The energy conservation equation is formulated for solid and liquid phases considering an interface balance that includes the Gibbs-Thomson effect. An equation for a diffuse interface is also developed by considering a phase field function with constant negative value in the liquid and constant positive value in the solid. Unknowns are the phase field function and a dimensionless temperature, as proposed by [1]. Linear finite element interpolation is used for both variables, and discretization stabilization techniques ensure convergence towards a correct non-oscillating solution. In order to perform quantitative computations of dendritic growth on a large domain, two additional numerical ingredients are necessary: automatic anisotropic unstructured adaptive meshing [2,[3] and parallel implementations [4], both made available with the numerical platform used (CimLib) based on C++ developments. Mesh adaptation is found to greatly reduce the number of degrees of freedom. Results of phase field simulations for dendritic solidification of a pure material in two and three dimensions are shown and compared with reference work [1]. Discussion on algorithm details and the CPU time will be outlined

Numerical tensile test on a mushy zone sample

International audienceTime sequences of 3D images of an Al-Cu alloy in the mushy state are obtained using in situ and real-time X-ray microtomography during a tensile test. Surface meshes of phase interfaces are built from these images with the help of a Marching Cubes algorithm. The signed distance to the surface meshes is then computed on a finite element mesh of the volume of the phases. These signed distance functions enable to track the interfaces between the phases in an implicit way. A numerical representation of the real microstructure is thus obtained, allowing to perform a numerical tensile test which is compared with the experimental tensile test. Results retrieve the general dynamic behaviour of the strain field evolution and opens promising perspectives for further interpretations of experimental results based on numerical simulations

Study of hot tearing through ingot bending test: thermomechanical and solute transport analysis

International audienceHot tearing is one of the critical defects in cast products. It takes place close to the end of solidification, typically for solid fraction between 0.9 and 1.0, when the material is subjected to deformation based on tensile stress. In this study, a hot tearing experiment, so-called "bending test", is carried out in which a cast ingot is deformed by an external tool before the ingot is fully solidified. To analyze the experiment, two types of thermomechanical simulation are performed. The first one is a classical thermomechanical approach in which the mushy zone (composed of liquid and solid phases) is considered as a homogenized material so that a unique velocity field is solved for [1, 2]. Through stress-strain analyses, macroscopic hot tearing criteria found in literature are then evaluated [3]. The second type is an effective "two phase" modelling approach in which the liquid and solid velocity fields are computed separately in the mushy zone [4]. It allows simulating solute transport phenomena leading to macrosegregation induced by deformation shrinkage and advection. The effect of micro- and macro-segregation on hot tearing sensitivity is then discusse

Study of hot tearing and macrosegregation through ingot bending test and its numerical simulation

International audienceIngot bending tests are performed on the already formed solid shell of a 450 kg solidifying ingot. It is designed in order to be representative of two defects occurring during secondary cooling in steel continuous casting: hot tearing and macrosegregation. Ingots show the defects which result from the application of bending. In order to understand the different physical phenomena, finite element numerical modelling of the test has been developed, using two different approaches. A first approach consists of a 3D finite element thermomechanical simulation. Hot tearing criteria, based on strain, strain rate and two values for solid fraction are then evaluated. It is demonstrated that such a strain based criterion has an excellent capability to predict the formation of hot tears. A second approach consists of a 2D planar finite element simulation in the median section of the ingot. A two-phase formulation is used, in which the velocity of the liquid and solid phases are distinguished. The simulation shows how solutes are redistributed through the ingot under the effect of bending. Solute-depleted and enriched regions are well reproduced, but peak values of macrosegregation are underestimated