Two-phase modelling of hot tearing in aluminium alloys using a semi-coupled method

Hot tearing is one of the most severe defects observed in castings, e.g. in billets or sheet ingots of aluminum alloys produced by DC casting. It is due to both tensile strains and a lack of interdendritic feeding in the mushy zone. In order to predict this phenomenon at the scale of an entire casting, the two-phase averaged conservation equations for mass and momentum must be solved in the mushy (i.e. mixed solid and liquid) region of the material. In recent contributions, M'Hamdi et al [1] proposed a strongly coupled resolution scheme for this set of equations. The solution of the problem was obtained using a rheological model established by Ludwig et al [2] and that captures the partially cohesive nature of the mushy alloy. In the present contribution, the problem is addressed using a slightly different approach. The same rheological model (i.e. saturated porous media treatment) is used, but the influence of the liquid pressure is neglected at this stage. This assumption allows for a weakly coupled resolution scheme in which the mechanical problem is first solved alone using ABAQUS™ and user subroutines. Then the pressure in the liquid phase is calculated separately accounting for the viscoplastic deformation of the porous solid skeleton and solidification shrinkage. This is done with a code previously developed for porosity calculations, and that uses a refined mesh in the mushy zone [3]. This semi-coupled method was implemented and its numerical convergence studied from the point of view of both time step and mesh size. Guidelines for selecting these numerical parameters as well as the conditions under which the semi-coupled method may be applied are provided. The model was then applied to three cases, i.e. two tensile tests conducted on mushy alloys [4, 5] and the casting of an entire billet [6]. Experimental data was indeed available concerning these problems prior to the present work. This information was used for the validation of the thermal and mechanical models that were setup to describe these different cases. The results of the semi-coupled approach were also used to describe in more details these different castings. First of all, the numerical study of the mushy zone tearing test [5] proved helpful for distinguishing different fracture modes. The role of the high strain rate applied to the mushy alloy in this case was also outlined. Another tensile test, referred to as the rig test [4], was successfully modeled in the present framework. The numerical results could be used to quantify the redistribution of strain in the mushy sample. As a consequence, intrinsic properties of the material, such as its ductility, could be extracted from the results. This study also gave further insight about the conditions under which tearing occurs in the samples. Finally, the semi-coupled method was used to study the DC casting process. In this case, a real process performed under realistic conditions for the production of an industrial scale billet was modeled. As it is more complex and difficult to characterize experimentally, the conditions for hot tearing formation are less accessible. However, the isotherm velocity, the strain, the strain rate and the liquid pressure could be described reasonably accurately. It was thus possible to correlate experimental observations of the hot tear with various calculated indicators of hot tearing susceptibility. Even with this information, it remains difficult to formulate new hot tearing criteria because all the indicators follow a similar trend during the casting and their respective contributions can thus not be distinguished. The present work showed that the level of accuracy and detail that can be reached using two-phase models with appropriate materials properties and boundary conditions is satisfactory. It is indeed possible to model the relevant phenomena (heat flow, solid deformation and liquid feeding) at the scale of an entire casting. The variation of the different simulated fields can be described down to a scale of the order of a few millimeters. In that sense, this approach is one important aspect required to build a multiscale model for the problem of hot tearing. It is expected that coupling such a method with granular models (which cover length scales from a few microns to a few centimeters [7]) will allow for a more complete description of the phenomena at hand. In the future, the development of such a multiscale numerical tool may prove to be the most efficient way towards quantitative predictions of hot tearing formation in real solidification processes.