Fig. 1 Schematic illustration of Bridgman solidification apparatus in superconductor magnet

Fig. 2 Longitudinal solidification structures of GCr18Mo steel specimen at various magnetic field intensities and growth speeds under temperature gradient of 104 K/cm

Fig. 3 Longitudinal microstructures near liquid/solid interfaces of GCr18Mo steel specimen at growth speed of 20 μm/s and various axial static magnetic field intensities under temperature gradient of 104 K/cm The solidification structures of GCr18Mo steel specimen at the growth speed of 5 μm/s under various temperature gradients are exhibited in Fig. 4. Larger columnar grains are generated along the longitudinal section of the specimens in the absence of a magnetic field. With increasing the temperature gradient, columnar grains become equiaxed grains at the growth speed of 5 μm/s under the 4 T axial static magnetic field. In addition, the dendrites are all regular at various temperature gradients without axial static magnetic field from the corresponding microstructures near the liquid/solid interface as displayed in Fig. 5. Columnar dendrites degenerate and transform into equiaxed dendrites as the temperature gradient increases with the 4 T axial static magnetic field.

Fig. 4 Longitudinal solidification structures of GCr18Mo steel specimen at growth speed of 5 μm/s and various temperature gradients without and with 4 T axial static magnetic field

Fig. 5 Longitudinal microstructures near liquid/solid interfaces of GCr18Mo steel specimen at growth speed of 5 μm/s and various temperature gradients without and with 4 T axial static magnetic field

Fig. 6 Cr contents for radial profiles in solid at 20 mm from the solid/liquid interface (indicated by the graph on the left) fabricated under temperature gradient of 104 K/cm with growth speeds of 10 μm/s a, 20 μm/s b

Fig. 7 Numerical simulation for TE magnetic effects in directionally solidified GCr18Mo steel under a 2 T axial static magnetic field: a geometry of computation domain; b computed TE current; c computed TE magnetic convection (c1, c2 and c3 show the direction and magnitudes of computed TE magnetic convection in x-y plane at different positions in mushy zone)

Fig. 8 Distribution of computed TE magnetic convection during directional solidification of GCr18Mo steel at various axial static magnetic field intensities under temperature gradient of 104 K/cm

Fig. 9 Distribution of computed TE magnetic convection at various temperature gradients during directional solidification of GCr18Mo steel under 4 T axial static magnetic field

Fig. 10 Schematics for TE magnetic effects during directional solidification of alloys under an axial static magnetic field On the other hand, numerous investigations have pointed out that a pronounced decrease in grain size can be obtained with increasing intensity of forced convection in the solidifying melt [27, 28]. Hellawell et al. [40] suggest that the flow transports the fragments from the interdendritic spacing to the region ahead of the solidification front. According to Hunt model [41], the advancing columnar solidification front stops as soon as the concentration of the equiaxed grains has reached a critical value. In the present work, from the numerical and estimation results, potential fragments of GCr18Mo steel originating from the mushy zone can be transported to the undercooled zone at the solidification front by TE magnetic convection (Fig. 10).

Fig. 11 Schematic illustration of grain refinement in GCr18Mo steel during directional solidification without and with axial static magnetic field