熔焊原理-4.3 Microsegregation and Banding

4.3 Microsegregation and Banding

4.3.1 Microsegregation

Solute redistribution during solidification results in microsegregation across cells or dendrite arms. The analysis of solute redistribution during the directional solidification of a liquid metal (Section 4.1) can be applied to solute redistribution during the solidification of an intercellular or interdendritic liquid during welding (or casting).The total volume of material in directional solidification (Figures 4.3-4.5) is now a volume element in a cell or a dendrite arm, as shown in Figure4.13. Within the volume element the S/L interface is still planar even though the overall structure is cellular or dendritic. The volume element covers the region from the centerline of the cell or dendrite arm to the boundary between cells or dendrite arms. Solidification begins in the volume element when the tip of the cell or dendrite arm reaches the volume element.

Figure 4.13 V olume elements for microsegregation analysis:

(a) cellular solidification; (b) dendritic solidification.

Figure 4.14 Microsegregation profiles across cells or dendrite arms: (a) k < 1; (b) k > 1.

The case of the equilibrium partition ratio k < 1 is shown in Figure 4.14a. No

segregation occurs when diffusion is complete in both the liquid and solid. This requires that D L t >> l2 and that D S t >> l2, where l is now half the cell or dendrite arm spacing (the length of the volume element).Segregation is worst with complete diffusion in the liquid but no diffusion in the solid. This requires that D L t >> l2 and that D S t << l2. Segregation is intermediate with limited diffusion in the liquid and no diffusion in the solid. When this occurs, there is a clear concentration minimum at the centerline of the cell or dendrite arm. Usually, there is some diffusion in the solid and the concentration minimum may not always be clear. The case of k > 1 is shown in Figure4.14b. The segregation profiles are opposite to those of k < 1.

Consider the case of a eutectic phase diagram, which is common among aluminum alloys. Assume complete liquid diffusion and no solid diffusion. As shown in Figure 4.15, the solid composition changes from kC0to C SM, the maximum possible solute content in the solid, when the eutectic temperature T E is reached. The remaining liquid at this point has the eutectic composition C E and, therefore, solidifies as solid eutectic at T E. The fraction of eutectic, f E, can be calculated from Equation (4.13) with f L= f E and T = T E, that is,

(4.19)

Figure 4.15 Solute redistribution during solidification with complete diffusion in liquid and no diffusion in solid: (a) eutectic phase diagram; (b) composition profiles in liquid and solid.