Combined modelling of solidification and visco-plasticity

During solidification of some alloys equiaxed grains form, grow and move. Small grains are carried with the melt flow, while with further growth grains often sink down and sediment. At a certain dense packing, they form a coherent network with intergranu- lar/interdendritic liquid. Such a semi-solid slurry is known to have visco-plastic flow behavior. In addition, thermal contraction leads to a deformation of the solidifying part. In order to describe these phenomena it is suggested to combined three simulation ap- proaches in the present project proposal: (i) a modeling approach which describes growth and sedimentation of crystals, (ii) a modeling approach which describes the me- chanical behavior of the sedimented layer (visco-plasticity) and (iii) a modeling ap- proach to describe the thermal contraction of the cast part. Recent developments de- scribe the combined modelling of fluid/gas flow and deformation of solids (FSI: fluid- structure interaction), e.g. gas flow in exhaust pipes). The present project proposal tar- gets at an even more complicated case namely the combination of flow with defor- mations in a solid not via a given surface (as in FSI) but through an a priory unknown volume, the two phase mushy zone.

The main purpose of the present project was to explore the modeling potential of a two-phase volume-average formulation to simulate solidification problems. These typically contemplate (i) the convective transport of solidifying equiaxed crystals through an alloy melt, (ii) formation of a coherent viscoplastic structure above an arbitrary solid fraction, and (iii) deformation of the mush due to shrinkage, convection or due to the application of external loads. A considerable amount of research has been conducted on melt convection with solid-phase transport during solidification, and numerous models have been proposed in the literature in this respect. They are usually intended to the suspensions regime (i.e., melt containing a relatively low amount of crystals) and the rheology of the flow is mainly dictated by the trans-porting character of the liquid phase. However, at a critical solid fraction, the rheology of the flow changes completely. The crystals become fully connected and the mush exhibits a solid-like behavior. This is where strength development of the material increases substantially. Furthermore, at high temperatures, it is known that metallic alloys become dynamic structures that experience deformation in response to thermal or mechanical strains. Modeling such distinct rheological behavior, however, is a complex task that is generally replaced with not so accurate alternative approaches. The main goal of this project was to integrate the constitutive equations that replicate the viscoplastic behavior of the mush into a general solidification model. After achieving a robust mathematical formulation that combined both regimes in a finite-volume solver, the model was tested in different configurations, ranging from cavity setups to industry-relevant continuous casting processes (such as the twin-roll casting). First, simple configurations have been selected to assess the capacity of the model in test cases where the semi-solid dynamics are not significant and the flow behavior is easier to understand. A comprehensive description of the different stages of the solidification process has been presented and details concerning the flow within the viscoplastic regime have been also discussed. Twin-roll casting is an important technology that produces thin strips directly from melt, where the solidifying shells are subjected to hot rolling before reaching the roll nip. In such cases, the deformation of the mush is critical in the final microstructure of the cast product and so the viscoplastic regime must be considered in computational models. With the improved model, it was possible to explain the flow dynamics, as well as the origin of macrosegregation patterns in products, originated from this technology. The results compared well with experimental findings reported in the literature. Furthermore, optimal process windows have been predicted where cast strips retained minimal macrosegregation deviations.