On the basis of the photomicrograph (i.e., the relative...

On the basis of the photomicrograph (i.e., the relative amounts of the microconstituents) for the ironcarbon alloy shown in Figure $9.30$ and the $\mathrm{Fe}-\mathrm{Fe}_{3} \mathrm{C}$ phase diagram (Figure 9.24), estimate the composition of the alloy, and then compare this estimate with the composition given in the figure legend of Figure 9.30. Make the following assumptions: (1) The area fraction of each phase and microconstituent in the photomicrograph is equal to its volume fraction; (2) the densities of proeutectoid ferrite and pearlite are $7.87$ and $7.84 \mathrm{~g} / \mathrm{cm}^{3}$, respectively; and (3) this photomicrograph represents the equilibrium microstructure at $725^{\circ} \mathrm{C}$.

Key Concepts

Phase Diagram

A phase diagram is a graphical representation that shows the stability regions of different phases in an alloy system as a function of composition and temperature. It is crucial for understanding which phases will form under equilibrium conditions and for predicting how the microstructure of an alloy will evolve during heating or cooling processes.

Microstructure Analysis

Microstructure analysis involves the examination of a material's internal structure using tools like photomicrographs. This process provides insight into the size, shape, and distribution of different phases or constituents within the alloy, which in turn helps in assessing the material’s overall properties and behavior.

Lever Rule

The lever rule is a technique used in conjunction with phase diagrams to quantify the relative amounts of phases present within a two-phase region. By applying the lever rule, one can estimate the composition of an alloy by comparing the distances on the phase diagram corresponding to the overall alloy composition and the boundaries of each phase.

Equilibrium Microstructure

An equilibrium microstructure is one in which the phases present have been stabilized by allowing sufficient time for diffusion and phase transformation to occur at a given temperature. This concept is crucial when analyzing micrographs that represent a state of thermal equilibrium, ensuring that the observed phase fractions accurately reflect the predictions from the phase diagram.

Density and Area-to-Volume Fraction Relationship

When estimating the composition of an alloy from a photomicrograph, it is often assumed that the area fraction of each phase is equivalent to its volume fraction. However, because different phases can have different densities, adjustments sometimes need to be made to account for these differences in order to accurately determine the alloy’s overall composition.

Transcript

00:01 All right, guys, in order to solve this question, first of all, we have to look at the given data in the question.

00:08 That is row alpha is equal to 7 .87 grams per centimeter cube.

00:22 Then there is row p that is equal to 7 .84 grams per centimeter cube.

00:32 Then there is the temperature that is 725 degrees centigrade so from iron and iron carbide phase diagrams that is mentioned in figure 9 .24 and photomicrograph from figure 9 .30 we can see that 0 .38 weight percentage of carbon.

01:16 Steel having a microstructure consisting of pure light and pro -utectoid so the composition of this alloy is 99 .62 weight percentage of ferric and 0 .38 weight percentage of carbon so from from portion of the iron -irn -carbide phase diagram in figure 3 .1, we can find the value of c -alpha that is 0 .0 -22 and the value of c iron carbide f -e3c that is equal to 6 .70.

02:22 So calculating the mass fraction for alpha phase we will use this formula that is w a w alpha is equal to c f e 3c minus c nod divided by c f e 3c which is iron carbide minus c alpha alpha now we put all these values into the formula.

03:05 It becomes 6 .70 minus 0 .38 divided by 6 .70 minus 0 .022 is equal to 0 .946.

03:25 So this is the answer for w -alpha.

03:29 Now, calculating mass fraction for ferric carbide phase.

03:34 We will see that wfe3c is equal to 1 minus w alpha, that is 1 minus 0 .946, and the answer is 0 .054.

03:53 Now moving further towards step c, towards part c of the question, we use the liver rule in conjunction with a tie line that extends from the face boundary that is 0 .022 to the eutectoid composition that is 0 .76 in as much as pure light in the transformation product of austenite having this composition...

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