Modeling of percolation of globular-equiaxed grains in Al-Cu alloys

A new mesoscopic model able to describe percolation of globular-equiaxed grains, highly relevant for hot tearing formation in castings, has been developed. This model is inspired from the granular model of Sistaninia et al. [1-5] that considers polyhedral grains based on a Voronoi tessellation of space. In the new mesoscopic model, the set of tetrahedra that define the grains are further subdivided into smaller tetrahedra called columns and solute diffusion is considered in both the solid and liquid phases. This allows to obtain smoother shapes of the grains and to better describe a progressive coalescence of the grains. In addition, it gives the possibility of having liquid pockets in the last-stage solidification (which is not possible in the case of polyhedral grains) and thus correctly describe the solid fraction at which the grain structure is percolated. The shape of the grains has first been validated with a multiphase-field method. The relevant microstructural features, such as the percolation state of an Al-Cu alloy, were then deduced from the model. This information will then be used to refine the 3D granular models of Sistaninia et al. [1-5] which account for stress development and liquid feeding, in order to create more advanced predictive tools for hot tearing formation.

Mesoscopic Modeling and Experimental Investigations of the Last-Stage Solidification of Globular-Equiaxed Grains in Metallic Alloys

Christophe Mondoux

Hot tearing is a major defect of solidification processes and welding. It occurs in metallic alloys while they are in the semi-solid state and is caused by a lack of liquid feeding in the mushy zone to compensate solid network openings due to tensile and shear strains. These strains are localized in the thin liquid films that remain at grain boundaries. Therefore, it is important to know when the solid grains coalesce and percolate to form a fully coherent solid, i.e., when the material can transmit stresses and strains but also withstand thermal contraction without rupture. Coalescence is defined as the disappearance of a liquid film in between two distinct grains, forming a solid grain boundary, while percolation is defined as the gradual transition of isolated grains or clusters surrounded by a continuous liquid film to a continuous solid network across a domain, even if some liquid regions remain. If the simulation of hot tearing has to account for localization of strains and liquid feeding, it is mandatory to use a granular approach. Two previous theses done recently at EPFL have developed such granular models of hot tearing, first in 2D (PhD of S. Vernède) and then in 3D (PhD of M. Sistaninia). However, these models have used a Voronoi tessellation for the description of globular microstructures in which equiaxed grains were approximated by polygons and polyhedra, respectively. From the experimental point of view, an innovative method, based on the Bridgman furnace principle, has been developed. The standard Bridgman furnace has been substantially modified in order to obtain the desired globular-equiaxed grain structure and reduce macrosegregation in the quenched sample. This modified furnace has been characterized then in terms of thermal measurements and observed final grain size. The samples obtained with the modified Bridgman furnace were then observed post-mortem by ex situ X-ray tomography. In addition, X-ray tomography experiments under similar conditions have been performed in situ with the laser-heated furnace installed on the TOMCAT synchrotron beam line at PSI. A postprocessing analysis of the principal curvature distribution (ISD plots) was performed on both ex situ and in situ observations for various compositions of inoculated Al-Cu alloys. The ISD plots of the X-ray tomography observations indicated the formation of liquid cylinders along triple line and, at a more advanced solidification stage, the formation of liquid pocket at quadruple vertices. From the modeling point of view, a new mesoscopic model has been developed both for 2D and 3D simulations. This model was inspired by the granular model developed by Phillon et al. that considers polyhedral grains based on a Voronoi tessellation of space, but allow to obtain smoother grain shapes and more progressive coalescence. After its validation with multiphase-field simulations, the mesoscopic model has been used to predict the various percolation transitions of the solid phase. In addition, by estimating the solid moment at which the liquid starts to form isolated pockets, it was possible to predict the temperature and solid fractions for which the mushy zone is most vulnerable to hot tearing. The simulations have been performed for various conditions and copper compositions, indicating the nominal compositions that are more sensitive to hot tearing. Finally, the 3D mesoscopic model predictions were compared with the X-ray tomography observations.

EPFL2015

A 3D Granular Model Of Equiaxed-Granular Solidification

Jean-Luc Desbiolles, André Phillion, Michel Rappaz

The solidification of an aluminum-copper alloy has been simulated in 3D using a granular model. Compared to previous similar 2D approaches for where only one phase is continuous, the extension to 3D allows for concurrent continuity of the solid and liquid phases. This concurrent continuity is a key factor in the formation of the solidification defect known as hot tearing. In this 3D model, grains are modeled as polyhedrons based on a Voronoi tessellation of a pseudo-random set of nucleation centers. Solidification within each polyhedron is calculated using a back-diffusion model. By performing a series of simulations over a range of grain sizes and cooling rates, the percolation of the solid grains is determined. The results, which indicate that the grain size and cooling rates play an important role in hot tear formation, constitute a basis on which feeding and deformation calculations will be carried out further.

Minerals, Metals & Materials Soc, 184 Thorn Hill Rd, Warrendale, Pa 15086-7514 Usa2009

Two-Phase Modeling of Hot Tearing in Aluminum Alloys: Applications of a Semicoupled Method

Vincent Mathier, Michel Rappaz, Stéphane Vernède

Hot tearing formation in both a classical tensile test and during direct chill (DC) casting of aluminum alloys has been modeled using a semicoupled, two-phase approach. Following a thermal calculation, the deformation of the mushy solid is computed using a compressive rheological model that neglects the pressure of the intergranular liquid. The nonzero expansion/compression of the solid and the solidification shrinkage are then introduced as source terms for the calculation of the pressure drop and pore formation in the liquid phase. A comparison between the simulation results and experimental data permits a detailed understanding of the specific conditions under which hot tears form under given conditions. It is shown that the failure modes can be quite different for these two experiments and that, as a consequence, the appropriate hot tearing criterion may differ. It is foreseen that a fully predictive theoretical tool could be obtained by coupling such a model with a granular approach. These two techniques do, indeed, permit coverage of the range of the length scales and the physical phenomena involved in hot tearing.

2009

Mesoscopic Modeling and Experimental Investigations of the Last-Stage Solidification of Globular-Equiaxed Grains in Metallic Alloys

Christophe Mondoux

EPFL2015