Chapter 10, Problem 10.88DP

Interpretation Introduction

Interpretation:

A process to cool the given Cu-Ni alloy to cool it more rapidly according to the given conditions is to be designed.

Concept Introduction:

Microsegregation is the nonuniform composition of the material formed between small dendrite arms over short distances due to nonequilibrium solidification. It is also known as interdendritic segregation or coring.

The crystal centers (dendrites) have higher melting point elements surrounded by regions of lower melting point elements. This results in the difference in the composition and properties of the solid phase from one region to another causing poor properties of the casting.

In castings, microsegregation can be removed using homogenization heat treatment which is a controlled heat flow process but in active manner. This reduces the time lapse between start and completion of the solidification process by reducing the distance within the casting material by increasing the temperature of the liquid melt around the liquidus curve region and therefore, decreasing the distance between the liquidus and solidus curves.

The formula to calculate the time $\left(t\right)$ of homogenization is:

  $t=c\frac{{\left(\text{SDAS}\right)}^2}{D_s}$   ......(1)

Here, $\text{SDAS}$ is the secondary dendrite arm spacing, $c$ is a constant, and $D_s$ is the rate of diffusion of solute in the matrix.