Dilatant shear bands in solidifying metals

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Gourlay, C.M., Dahle, A.K., Nature 445 (2007).


dilatancy, shear, granular media


Figure 1.
Figure 2.
Figure 3.

The authors study the microstructure of partially solidified alloys under shear. During the solidification of a metallic alloy, it has been shown that after nucleation, crystals are initially dispersed in the liquid and the material behaves as a suspension. As the crystals grow, the volume fraction of solid, <math>f_s</math> increases, and at a critical value <math>f_s^{Coh}</math>, there is a sharp increase in viscosity due to the formation of a loose solid. As the metal continues to solidify, partial cohesion between solids develops, allowing the solid to transmit shear, compressive, and tensile strains. Although metals at high volume fraction have been studied extensively, metals at relatively low volume fractions (<math>f_s^{Coh} \leq f_s \leq 0.5</math>) have not. This paper deals with dilatancy in solidifying metal alloys in this low volume fraction regime.

In the main set of experiments, an Mg alloy was deformed during solidification using a four-bladed vane. Figure 1 shows the torque versus vane response; it shows an increase in torque to a peak value, then a sharp decrease, and finally deformation continues at a lower torque than the initial torque. Figure 2 is a macrograph of one-quarter of the cross-section of the sample, and it shows a porous band just outside the radius of the vane. The authors note that the torque-vane curve shown in Figure 1 and the shear band shown in Figure 2 are characteristic of compacted cohesionless granular material. Compacted granular materials exhibit Reynolds dilatancy - that is, they expand when sheared because particles must increase the space between themselves in order to rearrange.

It is thus shown that