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A Phase Field Model for Grain Refinement in Deeply Undercooled Metallic Melts A.M. Mullis & R.F. Cochrane Department of Materials, University of Leeds, Leeds LS2 9JT, UK. ABSTRACT We present the results of phase field simulations of dendritic growth into pure undercooled melts, at growth velocities up to 35 m s-1. We find that, at low growth velocities, dendrite morphologies are broadly self-similar with increasing growth velocity. However, above ≈ 15 m s-1 the initiation of side-branching moves closer to the dendrite tip with increasing growth velocity. This appears to be related to the level of kinetic undercooling at the tip. Once sidebranch initiation begins to occur within 1-2 radii of the tip, profound morphological changes occur, leading to severe thinning of the dendrite trunk and ultimately repeated multiple tipsplitting. This process can be invoked to explain many of the observed features of spontaneous grain refinement in deeply undercooled metallic melts. 1. Introduction Spontaneous grain refinement in undercooled pure melts was first reported by Walker[1] in Ni. At a well defined undercooling, ∆T* = 140 - 150 K, Walker observed an abrupt transition from a coarse columnar grain structure to a fine equiaxed structure, with a reduction in grain size of at least one order of magnitude. Similar behaviour was found in Co, with a value for ∆T* of ≈ 180 K. This effect has subsequently been identified in other pure metals[2, 3] and in a range of alloy systems[4, 5, 6]. Measurement of dendrite growth velocity, V, in a number systems[7, 8, 9, 10] has revealed an apparent correlation between the velocity-undercooling relationship and grain refinement. Below ∆T*, growth velocity can be adequately represented by current dendrite growth models, with V ∝ ∆T β , where β ≈ 2.5. Above ∆T* the velocity-undercooling relationship is approximately linear. High speed (> 40000 fps) imaging of the recalescence front by Matson[11] has identified that the morphology of the solid-liquid interface may also change on passing through the grain refinement transition. Below ∆T*, an angular recalescence front is observed with well defined facets, which may be identified with the envelope of a primary dendrite trunk and its associated side-branches, while above ∆T* this gives way to a diffuse, spherical recalescence front. The observation of ‘branched dendritic’ fragments[12] in grain refined materials has lead to most theories for the origin of grain refinement to concentrate on dendritic fragmentation mechanisms. The most widely accepted such model is that due to Schwarz et al.[13]. Within their model grain refinement occurs if the local duration of interdendritic solidification, ∆tpl exceeds a time characteristic of dendritic break-up, ∆tbu. However, there are a number of apparently intractable problems with the Schwarz model. Firstly, by definition, a remelting process must occur post-recalescence and, as a consequence of this, the apparent correspondence of a break in the velocity-undercooling behaviour with the onset of grain refine