PERCOLATION APPROACH TO THE DESCRIPTION OF INTERDENDRITIC FEEDING AT THE FINAL STAGE OF SOLIDIFICATION OF METALS AND ALLOYS

Abstract

The paper examines the physical foundations of interdendritic feeding during the final stage of solidification of metals and alloys. It is shown that the efficiency of shrinkage compensation within the mushy zone is determined not only by the presence of residual liquid phase, but also by the conditions of its transport through the interdendritic space. Particular attention is paid to the role of permeability, local pressure gradients, morphology of liquid channels, and preservation of continuous feeding paths in ensuring the transport capacity of the liquid phase. The mechanisms of shrinkage and gas-shrinkage porosity formation are analyzed, and it is emphasized that the appearance of such defects is directly related to the degradation of the liquid feeding network at high solid fractions.

The study summarizes the influence of increasing solid fraction on the narrowing of interdendritic channels, reduction in permeability, localization of liquid flow, and growth of local hydraulic resistance. It is shown that, as the dendritic skeleton evolves toward a coherent solid framework, the liquid phase gradually loses its ability to form a continuous transport network. Under such conditions, even if some amount of liquid remains in the mushy zone, it may no longer participate in real feeding because of topological isolation. This circumstance indicates the limitations of conventional continuum approaches, which mainly operate with averaged characteristics such as permeability, pressure, or liquid fraction, but do not fully capture the structural transformation of the liquid network at the final stage of solidification.

To overcome these limitations, the applicability of the percolation approach is substantiated. Within this interpretation, the mushy zone is considered as a two-phase system in which the liquid phase acts as a transport network and the solid phase forms a constraining framework. It is argued that the loss of interdendritic feeding should be associated not with the complete disappearance of the liquid phase, but with the destruction of its global connectivity and the disappearance of a continuous feeding path. Thus, liquid-phase percolation is proposed as a physically meaningful criterion for feeding loss in the mushy zone. The obtained results confirm that the percolation-based interpretation provides a promising theoretical framework for further modeling of solidification processes, localization of feeding paths, and prediction of shrinkage-related defect formation in metallic castings.