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We give an overview of contributions made to the computational phase-field modelling of alloy solidification from the University of Leeds as part of the LiME project (EPSRC Advanced Manufacturing Hub in Liquid Metal Engineering). The broader look at the more salient features from our research allows the individual contributions to be seen in a wider context than can be seen from each contribution separately. We begin with a general introduction to phase-field and then reference the numerical issues that arise from the solution of the model before outlining contributions to phase-field modelling that we found most interesting or significant. These range from controlling and developing interface-width independent modelling; controlling morphology in both single and multiphase settings; generalising from single to multiphase models; and creating a thermodynamically consistent framework for modelling entropy flow and thereby postulating a temperature field consistent with the concepts of, and applicable in, multiphase and density-dependent settings.

Al-Ni alloys (for Ni −1. Analysis of historical results from the literature indicates that such surface Ni-enhancement may have been present, but overlooked, in other experiments on Al-rich Al-Ni droplets.

An analysis of the stability of a dendrite against a small perturbation to the tip velocity is presented for alloy systems at low undercooling. We find that above a critical concentration, dendritic growth may become unstable below a critical undercooling, offering a potential explanation of spontaneous grain refinement in these systems. This accords well with a number of experimental studies of alloy systems at low undercooling. The model is illustrated with reference to the system Ni-Cu.

The Fourier thermal conduction model is subject to a pathological anomaly in that it predicts an infinite velocity of propagation for heat. A finite propagation velocity can be introduced by adding a hyperbolic relaxation term to the conventional model. We show that in high-speed pulsed laser melting experiments, ignoring the hyperbolic nature of thermal conduction may lead to the surface temperature being seriously underestimated. We also develop a model of dendritic growth within a hyperbolic conduction framework. It is found that stable dendritic growth is only possible if the growth velocity is less than half the thermal wave velocity, C.

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%.

Traditionally, models of intergranular pressure solution have assumed that grain boundary diffusion, probably through an adsorbed water layer, is the rate-limiting process (Weyl, 1959; Rutter, 1976). However, observations by Heald (1956, 1965) and experiments by Cecil and Heald (1971) show that the presence of clays may strongly inhibit the growth of secondary quartz. Under these circumstances, silica precipitation kinetics may also be important in determining the pressure solution rate. A model of quartz pressure solution including the rate of silica precipitation kinetics is developed, and strain rate equations are derived for a compacting sediment. Laboratory data for the precipitation constant k_, for quartz, indicate that precipitation kinetics should not be important in determining the rate of pressure solution in clean quartz sand. However, an estimate of the in situ value of k_ for the Dogger Beta formation, made from the data of Fuchtbauer (1983), suggests that in a geological setting, k_ may be much smaller than under laboratory conditions. In consequence, it is asserted that silica precipitation kinetics may influence the rate of quartz pressure solution when secondary quartz growth is inhibited.