Simulation of the Rheology of Semisolid Alloys by Using a Two-phase Flow Approach
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Simulation of the Rheology of Semisolid Alloys by Using a Two-phase Flow Approach A. Ludwig, M. Wu, T. Hofmeister Foundry-Institute of the Technical University Aachen, Intzestr. 5 D-52056 Aachen, Germany ABSTRACT Semisolid alloys exhibit a shear rate history dependent flow behavior. The increasing interest on numerical modeling of thixo-casting processes makes it quite important to understand the flow behavior of semisolids. Its apparent viscosity is the key parameter for the numerical models. In this paper a two phase approach is used to investigate the rheology of semisolid alloys. It is assumed that both, liquid and solid phase, can be regarded as interpenetrating continua with its own viscosity. Thus, each phase is thought to behave as a Newtonian fluid. The simulation results show that the rheology of the two-phase flow is determined by the interaction between the solid and the liquid, i.e. the momentum exchange between the two phases. Non-Newtonian flow behavior of the solid-liquid mixture is predicted although both phases are considered as Newtonian fluids. INTRODUCTION The viscosity of a semisolid alloy is the most crucial parameter in modeling the thixocasting process. An engineering viscometer as shown in Figure 1 is traditionally used to determine the apparent viscosity of a semisolid [1,2]. The semisolid slurry is pressed through a capillary tube with constant volume flow rate. When the flow comes to a steady state, the pressure drop along the tube is measured. Following [1], the apparent viscosity of a solidliquid mixture is proportional to the measured pressure drop and inversely proportional to the steady state flow rate. Additionally, only geometrical factors are needed [1]. It is often found that the measured viscosity of a semisolid varies over a very wide range, depending on grain structure, fraction of solid, and other process parameters. In order to gain a deeper understanding of the above described measuring technique a closer look to the thixotropic rheology of semisolid materials is needed. When an alloy that normally solidifies dendritically is vigorously stirred during solidification, the dendritic structure can be Figure 1. Capillary Viscosimeter [1]
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broken up and be replaced by a more-or-less spherical structure (Figure 2) [3]. The semisolid slurry injected into a thixo-casting die has nearly spherical solid particles suspended in a liquid matrix [4]. Based on this fact, a two-phase approach is used to investigate the flow behavior of the semisolid alloy and thus, to achieve understanding of the shear-rate history dependent Figure 2. Rheological behavior of a volume rheology. The applied two phase model was element of semisolid material. previously used to study the microstructure formation and segregation phenomena in equiaxed solidifying shape castings [5-9]. NUMERICAL MODEL The semi-solid slurry is characterized by two phases: liquid and solid. In the two-phase flow model it is assumed that both liquid and solid are described as two inter-penetrating r r Newtonian continua. T
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