Mesoscopic modeling of spacing and grain selection in columnar dendritic solidification: Envelope versus phase-field model

We investigate and assess the capability of the mesoscopic envelope model of dendritic solidification to represent the growth of columnar dendritic structures. This is done by quantitative comparisons to phase-field simulations in two dimensions. While the phase-field model resolves the detailed growth morphology at the microscale, the mesoscopic envelope model describes a dendritic grain by its envelope. The envelope growth velocities are calculated by an analytical dendrite-tip model and matched to the numerical solution of the solute concentration field in the vicinity of the envelope. The simplified representation of the dendrites drastically reduces the calculation time compared to phase field. Larger ensembles of grains can therefore be simulated. We show that the mesoscopic envelope model accurately reproduces the evolution of the primary branch structure, the undercooling of the dendrite tips, and the solidification path in the columnar mushy zone. We further show that it can also correctly describe the transient adjustments of primary spacing, both by spacing increase due to elimination of primary branches and by spacing reduction due to tertiary rebranching. Elimination and tertiary rebranching are also critical phenomena for the evolution of grain boundaries between columnar grains that have a different crystallographic orientation with respect to the temperature gradient. We show that the mesoscopic model can reproduce the macroscopic evolution of such grain boundaries for small and moderate misorientation angles, i.e., up to 30°. It is therefore suitable for predicting the texture of polycrystalline columnar structures. We also provide guidelines for the calibration of the main parameters of the mesoscopic model, required to obtain reliable predictions.ANR-11-LABX-0008/11-LABX-0008 - DAMAS - Design des Alliages Métalliques pour Allègement des Structures (2011) - German Space Agency DLR under Contract FKZ 50WM144

Modélisation par champ de phases de la croissance de la ferrite allotriomorphe dans les aciers Fe-C-Mn

The growth of allotriomorphic ferrite plays a major role in the formation of martensite bands in Dual-Phase steels. We have thus developed a phase field model to study the ferritic growth in different ternary Fe-C-X alloys, incorporating two necessary features. First, we have paid a particular attention to recover the different growth regimes due to the huge difference between the diffusion rates of Cand X substitutional species. Our calculations have exhibited a transition from fast paraequilibrium to slow orthoequilibrium in good agreement with experimental measurements in the literature. Second, austenite grain boundaries have been included in the model because they can conterbalance the manganese segregation bands, as shown in our calculations. Indeed, our results show that the bands can be broken bythe wetting of ferrite along the austenite grain boundaries, provided that the segregation is below a threshold value, and provided that the grain boundary energies are sufficiently highLa ferrite allotriomorphe est une des morphologies de la ferrite dont la répartition spatiale influe fortement sur les propriétés mécaniques dans les aciers dual-phase. En fonction des traitements qu'ils subissent, la ferrite peut s'y répartir suivant les bandes de ségrégation en manganèse, issues de l'étape de solidification. Pour établir le rôle que joue le processus de croissance de la ferrite allotriomorphe sur la mise en place de la structure en bandes, nous avons développé un modèle de champ de phases possédant deux spécificités originales, imposées par le problème. D'une part, ce modèle est capable de reproduire les différents régimes cinétiques observés dans les alliages ternaires Fe-C-X, pilotés par la présence concomittante du carbone diffusant rapidement,et d'un élément substitutionnel X diffusant lentement. Nous avons ainsi mis en évidence la transition d'un régime initial rapide de paraéquilibre vers une croissance lente en orthoéquilibre, en bon accord avec des résultats expérimentaux de la littérature. D'autre part, notre modèle incorpore de manière économe la présence des joints de grains austénitiques, dont le rôle dans l'élimination des structures en bande est souligné par nos calculs. Nous observons ainsi qu'il existe un seuil d'intensité deségrégation en manganèse en dessous duquel le mouillage de la ferrite le long des joints de grain de plus grande énergie peut contrecarrer la croissance dans les bandes ségrégées négativemen

Phase field modeling of allotriomorphic ferrite growth in Fe-C-Mn steels

La ferrite allotriomorphe est une des morphologies de la ferrite dont la répartition spatiale influe fortement sur les propriétés mécaniques dans les aciers dual-phase. En fonction des traitements qu'ils subissent, la ferrite peut s'y répartir suivant les bandes de ségrégation en manganèse, issues de l'étape de solidification. Pour établir le rôle que joue le processus de croissance de la ferrite allotriomorphe sur la mise en place de la structure en bandes, nous avons développé un modèle de champ de phases possédant deux spécificités originales, imposées par le problème. D'une part, ce modèle est capable de reproduire les différents régimes cinétiques observés dans les alliages ternaires Fe-C-X, pilotés par la présence concomittante du carbone diffusant rapidement,et d'un élément substitutionnel X diffusant lentement. Nous avons ainsi mis en évidence la transition d'un régime initial rapide de paraéquilibre vers une croissance lente en orthoéquilibre, en bon accord avec des résultats expérimentaux de la littérature. D'autre part, notre modèle incorpore de manière économe la présence des joints de grains austénitiques, dont le rôle dans l'élimination des structures en bande est souligné par nos calculs. Nous observons ainsi qu'il existe un seuil d'intensité deségrégation en manganèse en dessous duquel le mouillage de la ferrite le long des joints de grain de plus grande énergie peut contrecarrer la croissance dans les bandes ségrégées négativementThe growth of allotriomorphic ferrite plays a major role in the formation of martensite bands in Dual-Phase steels. We have thus developed a phase field model to study the ferritic growth in different ternary Fe-C-X alloys, incorporating two necessary features. First, we have paid a particular attention to recover the different growth regimes due to the huge difference between the diffusion rates of Cand X substitutional species. Our calculations have exhibited a transition from fast paraequilibrium to slow orthoequilibrium in good agreement with experimental measurements in the literature. Second, austenite grain boundaries have been included in the model because they can conterbalance the manganese segregation bands, as shown in our calculations. Indeed, our results show that the bands can be broken bythe wetting of ferrite along the austenite grain boundaries, provided that the segregation is below a threshold value, and provided that the grain boundary energies are sufficiently hig

Three-dimensional mesoscopic modeling of equiaxed dendritic solidification in a thin sample: effect of convection flow

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

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