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Chapter 9: Problem 52

Compute the mass fractions of proeutectoid ferrite and pearlite that form in an iron-carbon alloy containing \(0.25 \mathrm{wt} \% \mathrm{C}\).

Short Answer

Expert verified
Answer: The mass fractions of proeutectoid ferrite and pearlite in the iron-carbon alloy containing 0.25 wt% C are 67.1% and 32.9% respectively.

Step by step solution

01

Identify the Eutectoid Composition and Temperature

Consulting the iron-carbon phase diagram, we can find that the eutectoid composition is approximately 0.76 wt% C, and the eutectoid temperature is around 727°C. This is the point where the phase transformation from austenite to a mixture of ferrite and cementite (pearlite) occurs.
02

Use the Lever Rule to Determine Mass Fractions

To determine the mass fractions of proeutectoid ferrite and pearlite, we will use the lever rule applied to the iron-carbon phase diagram. Since the alloy composition (0.25 wt% C) is to the left of the eutectoid composition (0.76 wt% C), the alloy consists of proeutectoid ferrite and pearlite. The lever rule formula is: Mass fraction = \frac{Length (opposite side)}{Total length} We will first compute the mass fraction of proeutectoid ferrite: Mass fraction of proeutectoid ferrite = \(\frac{(0.76-0.25)}{(0.76-0)}\)^\) Mass fraction of proeutectoid ferrite = 0.671 Next, we will compute the mass fraction of pearlite: Mass fraction of pearlite = 1 - Mass fraction of proeutectoid ferrite = 1 - 0.671 = 0.329
03

Discuss Results and Microstructure

The mass fractions of proeutectoid ferrite and pearlite in the given iron-carbon alloy containing 0.25 wt% C are: - Proeutectoid ferrite: 67.1% - Pearlite: 32.9% The microstructure of this alloy consists of continuous proeutectoid ferrite with pearlite islands distributed throughout. At the eutectoid temperature of 727°C, the alloy will have a mixture of proeutectoid ferrite and pearlite formed by the decomposition of austenite.

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Most popular questions from this chapter

Is it possible to have an iron-carbon alloy for which the mass fractions of total cementite and pearlite are \(0.039\) and 0.417, respectively? Why or why not?

The mass fractions of total ferrite and total cementite in an iron-carbon alloy are \(0.88\) and \(0.12\), respectively. Is this a hypoeutectoid or hypereutectoid alloy? Why?

(a) What is the distinction between hypoeutectoid and hypereutectoid steels? (b) In a hypoeutectoid steel, both eutectoid and proeutectoid ferrite exist. Explain the difference between them. What will be the carbon concentration in each?

For a copper-silver alloy of composition 25 \(\mathrm{wt} \% \mathrm{Ag}-75 \mathrm{wt} \% \mathrm{Cu}\) and at \(775^{\circ} \mathrm{C}\left(1425^{\circ} \mathrm{F}\right)\), do the following: (a) Determine the mass fractions of \(\alpha\) and \(\beta\) phases. (b) Determine the mass fractions of primary \(\alpha\) and eutectic microconstituents. (c) Determine the mass fraction of eutectic \(\alpha\).

(a) Briefly describe the phenomenon of coring and why it occurs. (b) Cite one undesirable consequence of coring.
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