Rheological behavior of the mushy zone at small strains

The modeling of the hot-tearing phenomena at the end of solidification requires the development of specific constitutive equations for the mushy zone. The presence of liquid films in the solid-liquid mixture has important consequences on the rheological behavior of the mushy zone. This aspect is particularly treated in order to propose a constitutive equation for the mushy zone in the low strain region. Starting from the behavior of the fully solid material, the mush is modeled as a porous medium saturated with liquid with partial cohesion. The cohesion of the mush is treated as an internal variable for which an evolution equation is proposed. Experimental data on a Sn-Pb model alloy both in the fully solid state and in the mushy state are used in order to study the advantages and the limitations of the proposed constitutive equation.