Transition of the mushy zone from continuous liquid films to a coherent solid

Abstract

While studies of solidification microstructures have focused mainly on the tips of the dendrites, the last stage solidification is equally important from the point of view of defect formation (porosity, hot tearing), mechanical strength build-up and precipitation of phases. In particular, the transition from continuous liquid films to a coherent solid in low concentration alloys is of crucial importance for hot tearing formation, and more generally speaking for liquid feeding ability and coherency development. Based on a fairly recent theoretical model of coalescence which will be recalled briefly, new results obtained for a population of equiaxed grains will be presented. A granular-type model based on a Voronoi tessellation has been used for the description of the gradual disappearance of liquid films and the clustering of equiaxed grains. This percolation-type approach has been used then to calculate the pressure drop in the mushy zone on the assumptions of a Poiseuille flow in between the grains and a Kirchhoff model for the connectivity of the liquid films including the Losses associated with solidification shrinkage (i.e, PKL model). Comparison with a standard average pressure drop calculation based on Carman-Kozeny's relationship will be presented.-1 -

A granular model of equiaxed mushy zones: Formation of a coherent solid and localization of feeding

“…The 2-dimensional (2D) solidification model has been developed initially by Mathier and Rappaz [12] and was further improved by Vernède and Rappaz [13]. It will only be briefly summarised here.…”

“…The justification of using a Poiseuille flow approximation, which supposes a no-slip condition at the boundaries, whereas a flow normal to the solid-liquid boundary is compensating shrinkage is given in [13]. A weak formulation of equations (5) and (6) …”

“…The normal n to the interface along which v l is projected is pointing toward the liquid. Integration of the mass conservation for an incompressible flow (div(v l ) = 0) over the width of a channel leads to [13]:…”

“…As for the work of Mathier et al and Vernède et al [12,13], the present contribution considers a random network of grains for the calculation of solidification and feeding in a gobular mushy zone. It goes beyond the latest work of Vernède et al in several ways:…”

“…In a first part, we briefly present the granular model of solidification and liquid feeding, outlining the improvements made with respect to our previous model [13]. In the following section, localisation of feeding and cluster formation during solidification are shown and analysed.…”