Chapter 5, Problem 5.62P

(a)

To determine

The amount of alpha and gamma phases at temperature $750\text{°C}$ .

Answer to Problem 5.62P

The amount of alpha and gamma phases at temperature $750\text{°C}$ are $0\%$ and $100\%$ respectively.

Explanation of Solution

  

Figure 5.4b

Figure drawn below shows the detailed view of microstructure above and below the eutectoid temperature of $727\text{°C}$ .

  

Figure 2

At $750\text{°C}$ , the alloy is in single phase austenite (gamma) region, therefore, the gamma percentage is $100\%$ and the alpha percentage is $0\%$ .

Conclusion:

Therefore, the amount of alpha and gamma phases at temperature $750\text{°C}$ are $0\%$ and $100\%$ respectively.

(b)

To determine

The amount of alpha and gamma phases at temperature $728\text{°C}$ .

Answer to Problem 5.62P

The amount of alpha and gamma phases at temperature $728\text{°C}$ are $23\%$ and $77\%$ respectively.

Explanation of Solution

Formula used:

The expression for the alpha percentage is given as,

  $\%\alpha =\left(\frac{x_{\gamma }-x_o}{x_{\gamma }-x_a}\right)\times 100$

Here, $x_{\gamma }$ is the solubility of the gamma, $x_o$ is the solubility of the reference material, and $x_a$ is the solubility of the solubility of the cubic iron.

The expression for the gamma percentage is given as,

  $\%\gamma =\left(\frac{x_o-x_a}{x_{\gamma }-x_a}\right)\times 100$

Calculation:

The alpha percentage can be calculated as,

  $\begin{array}{c}\%\alpha =\left(\frac{x_{\gamma }-x_o}{x_{\gamma }-x_a}\right)\times 100\\ \%\alpha =\left(\frac{0.77-0.60}{0.77-0.022}\right)\times 100\\ \%\alpha =23\%\end{array}$

The gamma percentage can be calculated as,

  $\begin{array}{c}\%\gamma =\left(\frac{x_o-x_a}{x_{\gamma }-x_a}\right)\times 100\\ \%\gamma =\left(\frac{0.60-0.022}{0.77-0.022}\right)\times 100\\ \%\gamma =77\%\end{array}$

Conclusion:

Therefore, the amount of alpha and gamma phases at temperature $728\text{°C}$ are $23\%$ and $77\%$ respectively.

(c)

To determine

The amount of alpha and gamma phases at temperature $726\text{°C}$ .

Answer to Problem 5.62P

The amount of alpha and gamma phases at temperature $726\text{°C}$ are $91\%$ and $0\%$ respectively.

Explanation of Solution

At $726\text{°C}$ the alloy is in two phases alpha and ${\text{Fe}}_{\text{3}}\text{C}$ field. At this moment no gamma phase is present.

Formula used:

The expression for the alpha percentage is given as,

  $\%\alpha =\left(\frac{x_{\gamma }-x_o}{x_{\gamma }-x_a}\right)\times 100$

Calculation:

The alpha percentage can be calculated as,

  $\begin{array}{c}\%\alpha =\left(\frac{x_{\gamma }-x_o}{x_{\gamma }-x_a}\right)\times 100\\ \%\alpha =\left(\frac{6.67-0.60}{6.67-0.022}\right)\times 100\\ \%\alpha =91\%\end{array}$

Conclusion:

Therefore, the amount of alpha and gamma phases at temperature $726\text{°C}$ are $91\%$ and $0\%$ respectively.