熔焊原理-4.3MicrosegregationandBanding

4.3 Microsegregation and Banding4.3.1 MicrosegregationSolute 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 duri ng the solidificati on of an in tercellular or in terde ndritic liquid duri ng weldi ng (or casting).The total volume of material in directional solidification (Figures 434.5) is now a volume element in a cell or a dendrite arm, as shown in Figure4.13. Within the volume eleme nt the S/L in terface is still pla nar eve n though the overall structure is cellular or den dritic. The volume eleme nt covers the regi on from the cen terl ine of the cell or den drite arm to the boun dary betwee n cells or den drite arms. Solidificati on beg ins in the volume eleme nt whe n the tip of the cell or den drite arm reachesthe volume eleme nt.canterline of collb oundary botwean cell&or dendrite arm element or dendrite arms(a)(b)Figure 4.14Microsegregation 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. Nocomplete liquid diffusion,no solid .diffusiondistanceJ 1limited liquid diffusion, nosolid qiffuskjn 一>(a) (b)Figure 4.13 Volume eleme nts for microsegregati on an alysis:(a) cellular solidification; (b) dendritic solidification.complete liquid & solid diffusiont( limited liquid diffusion, no solid.diffusion ACo kC..complete liquid & solid diffusioncomplete liquid ditfusion, o solid diffusoni /segregation occurs when diffusion is complete in both the liquid and solid. This2 2requires that DLt >> l and that D s t >> l , where l is now half the cell or dendrite arm spaci ng(the len gth of the volume eleme nt).Segregatio n is worst with complete2 diffusion in the liquid but no diffusion in the solid. This requires that D L t >> l and 2that D s t << l . Segregatio n is in termediate with limited diffusi on 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 concen trati on minimum may not always be clear. The case of k > 1 is show n in Figure4.14b. The segregation profiles are opposite to those of k < 1.Con sider the case of a eutectic phase diagram, which is com mon among aluminum alloys. Assume complete liquid diffusion and no solid diffusion. As shown in Figure 4.15, the solid composition changes from kC o to 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)* initia melt THs?rn&Jo>dE 段composition, CTeulectcTm T4.3.2 BandingIn addition to microsegregation, solute segregation can also occur as a result of growth rate fluctuations caused by thermal fluctuations. This phenomenon, shown in Figure 4.16, is known as banding. As shown, steady-state solidification occurs at the growth rate R 1. Whe n the growth rate is sudde nly in creased from R 1 to R 2, an extra amount of solute is rejected into the liquid at the S/L in terface, caus ing its solute content to rise. As a result, the material solidifies right after the in crease in the growth rate has a higher solute concen trati on tha n that before the in crease. The boun dary layer at R 2 is thinner tha n that at R 1 because, as men ti oned previously, the boun dary layer thick ness is about D L /R. The solute concen trati on eve ntually resumes its steady value if no further cha nges take place. If, however, the growth rate is the n decreased sudde nly from R 2 back to R 1, a smaller amount of solute is rejected into the liquid at the S/L in terface, caus ing its solute content to drop. As a result, the material solidifies right after the decrease in the growth rate has a lower solute concen trati on tha n that just before the decrease. In practice, the growth rate can vary as a result of thermal fluctuations during solidification caused by unstable fluid flow in the weld pool, and solute-rich and solute-depleted bands form side by side along the solidification path. When the flow carrying heat from the heat source and impinging on the growth front sudde nly speeds up, the growth rate is reduced and vice versa.R = R > RR R, R*Time, tFigure 4.16Formation of banding due to changes in the solidification rate R.«c■ib)■ ■ ■■ ■ i0 Fraction of Solid, tc soildeutecticwlume elementComplete LiqudDiffusiorCEConcentration C1I:: :::: ]4i ill! 2皿j *3 XIFigure 4.15 Solute redistribution during solidification with complete diffusion in liquid and no diffusi on in solid: (a) eutectic phase diagram; (b) compositi on profiles in liquid and solid.。