Particle Dynamic Simulation of Semi-Solid Metal Rheology
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Particle Dynamic Simulation of Semi-Solid Metal Rheology Andrew M. Mullis School of Materials, University of Leeds, Leeds LS2 9JT, UK. ABSTRACT Models of semi-solid processing currently utilise constitutive equations to describe slurry rheology. However, using the techniques of molecular dynamics it may be possible to go beyond this approach to obtain direct relationships between applied shear rates, the resultant microstructural changes and rheology. The results of a simple molecular dynamics simulation of semi-solid flow within a Couette rheometer are presented and compared with experimental data for the system Sn -15% Pb. We find that the model correctly predicts the apparent viscosity under steady state conditions, up to solid fractions of ≈ 40%. Introduction The rheology of semi-solid metal slurries is extremely complex in nature, being both shearthinning and thixotropic. This complexity is a serious obstacle to the development of process models of semi-solid forming operations. Within such process models the conventional way of dealing with this complex rheological response is by means of constitutive equations[1, 2, 3], that is semi-empirical equations that relate the apparent viscosity of the semi-solid, ηr, to physical and process variables such as the shear rate, γ& , the solid fraction, fs, and cooling rate, C. While such models have enabled significant progress to be made in the modelling of semi-solid flow, this approach has limitations. In particular, most of these formulations contain fitting parameters which can only be determined by performing rheological experiments. In general, these parameters will vary with alloy composition, restricting the applicability of the constitutive equation. Moreover, this type of approach gives only indirect insight into the physical nature of the processes occurring at the microstructural level which are controlling the rheology of the semi-solid. In this paper we will discuss the application of the techniques of molecular dynamic modelling as a direct link between the interactions of individual solid particles within the fluid to the rheology of the bulk semi-solid. One of the problems encountered in discussing the rheology of complex structured fluids is that the viscosity is not necessarily well defined. That is, the value of the viscosity,η, may depend not only upon the shear and shear history of the fluid, but also upon the nature of measurement being made. Such fluids are termed non-viscometric. Within the context of the current discussion we define viscosity in terms of the response of an idealised Couette rheometer. The Couette rheometer consists of two (long) flat plates of area A, separated by a distance d. One of these plates is free to translate at velocity V while the other is fixed. If the fluid between the plates has a non-zero viscosity the motion of the upper plate creates a force F on the lower plate, wherein we define the shear rate and viscosity as
γ& =
V d
(1) AA7.18.1
and
η=
F . Aγ&
(2)
For a particulate suspension in which direct stres
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