Chapter 10, Problem 10.84P

Interpretation Introduction

Interpretation:

Homogenization time for the given alloy at the specified temperature is to be calculated for the given SDAS values. Also, the value of the constant $c$ is to be calculated along with the assumptions made during the calculations.

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; thus, causing poor properties of the casting.

The removal of non-uniformity or segregations present in the alloy due to crystallization of it is known as homogenization. It is done by increasing the temperature of the alloy and equalizes the temperature of the alloy throughout which reduces the coring effect.

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

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

Here, SDAS is the secondary dendrite arm spacing, $D_s$ is the diffusion rate of the solute into the matrix and $c$ is a constant.