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Class Homework 2  
 
  ALLOY SEGREGATION IN CAST STRUCTURES

Homework Problem # 2 Due Wednesday September 11

2 pages maximum including plots

All of the alloys cast in the week of September 2 belong to a eutectic system, either Al - Cu, Al - Si, or Al - Mg.

Given the segregation scenario within dendrites as described on pages 73 - 75 in your notes (similar to what was discussed in class on September 4), and using the relationship derived under conditions where no solid state diffusion occurs but where sufficient liquid mixing maintains a uniform liquid composition, CS= kCo[1/(1 - f)]1-k where CSis the variable composition in weight percent of the solute element, k is the equilibrium distribution coefficient (ratio of solidus composition / liquidus composition, k = CS/ CL,at the liquidus temperature of alloy) , Co is the alloy composition, and f is the fraction transformed from liquid to solid. See illustration below.
 
 
 
  1. Using the phase diagrams supplied, estimate the k values in each of the following binary alloys, Al - 6% Si, Al - 7% Mg and Al - 4% Cu.
  2. Using these k values and the maximum solubilities given by the phase diagrams, determine the fraction of liquid remaining when the dendrite surface composition reaches the solubility limit of the respective binary diagram (see sketch above; at the eutectic temperature when the outer layer of the dendrite is at the point of maximum solubility). It should be understood that this liquid represents the remaining amount that will transform to the eutectic product.
  3. Using the lever rule, estimate the equilibrium amount of liquid which would undergo the eutectic reaction in each alloy. Is this lesser or greater than that calculated in b? Discuss briefly.
  4. Compute and plot the segregation profiles (CSvs.f) within the dendrite arms (from the center to the outside edge defined by the maximum solubility) for Mg in the binary Al - 7% Mg alloy, for Si in the binary Al - 6% Si alloy,and for Cu in the binary Al - 4% Cu alloy. Put these on one plot.

INCLUDE ALL YOUR CALCULATIONS

These three binary alloys are similar to three of the alloys poured in the week of Sept. 2. Analysis of the castings poured will continue in the weeks of Sept 9 and 16. Segregation in the fourth hypereutectic Al - Si alloy would be similar to that in the Al - 6 Si alloy