/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 57 Compute the maximum mass fractio... [FREE SOLUTION] | 91影视

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Chapter 9: Problem 57

Compute the maximum mass fraction of proeutectoid cementite possible for a hypereutectoid iron-carbon alloy.

Short Answer

Expert verified
Answer: The maximum mass fraction of proeutectoid cementite in a hypereutectoid iron-carbon alloy is approximately 0.231 (23.1%).

Step by step solution

01

Understand the iron-carbon phase diagram and hypereutectoid alloys

Hypereutectoid iron-carbon alloys have a carbon content greater than the eutectoid composition (0.77 wt% C) and less than approximately 2.14 wt% C. In these alloys, proeutectoid cementite (Fe3C) forms before the eutectoid reaction occurs. After the eutectoid reaction, the remaining austenite is converted into pearlite, which is a mixture of ferrite (伪-Fe) and cementite (Fe3C).
02

Computation of maximum mass fraction of proeutectoid cementite

We need to find the maximum mass fraction of proeutectoid cementite for an iron-carbon alloy. In order to do this, we can use the lever rule. The lever-rule formula for mass fraction is given by: \(mx_{cementite} = \frac{C_{total} - C_{eutectoid}}{C_{cementite} - C_{eutectoid}}\) where, \(mx_{cementite}\) - mass fraction of proeutectoid cementite \(C_{total}\) - total carbon content of the alloy \(C_{eutectoid}\) - eutectoid carbon content (0.77 wt% C) \(C_{cementite}\) - composition of the cementite phase (6.7 wt% C)
03

Calculate the mass fraction for maximum proeutectoid cementite

Let's assume the total carbon content of our hypereutectoid alloy is the maximum, i.e., 2.14 wt% C. Now, we can plug these values into the lever rule formula for mass fraction: \(mx_{cementite} = \frac{2.14 - 0.77}{6.7 - 0.77}\) \(mx_{cementite} = \frac{1.37}{5.93}\) \(mx_{cementite} \approx 0.231\) The maximum mass fraction of proeutectoid cementite in a hypereutectoid iron-carbon alloy is approximately 0.231 (23.1%).

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Most popular questions from this chapter

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

For \(11.20 \mathrm{~kg}\) of a magnesium-lead alloy of composition \(30 \mathrm{wt} \% \mathrm{~Pb}-70 \mathrm{wt} \% \mathrm{Mg}\), is it possible, at equilibrium, to have \(\alpha\) and \(\mathrm{Mg}_{2} \mathrm{~Pb}\) phases having respective masses of \(7.39 \mathrm{~kg}\) and \(3.81 \mathrm{~kg}\) ? If so, what will be the approximate temperature of the alloy? If such an alloy is not possible, explain 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?

Construct the hypothetical phase diagram for metals \(A\) and \(B\) between temperatures of \(600^{\circ} \mathrm{C}\) and \(1000^{\circ} \mathrm{C}\) given the following information: \- The melting temperature of metal \(A\) is \(940^{\circ} \mathrm{C} .\) \- The solubility of \(\mathrm{B}\) in \(\mathrm{A}\) is negligible at all temperatures. \- The melting temperature of metal \(\mathrm{B}\) is \(830^{\circ} \mathrm{C}\). \- The maximum solubility of \(\mathrm{A}\) in \(\mathrm{B}\) is 12 wt \(\%\) A, which occurs at \(700^{\circ} \mathrm{C}\). \- At \(600^{\circ} \mathrm{C}\), the solubility of \(\mathrm{A}\) in \(\mathrm{B}\) is \(8 \mathrm{wt} \% \mathrm{~A}\). \- One eutectic occurs at \(700^{\circ} \mathrm{C}\) and \(75 \mathrm{wt} \%\) B- \(25 \mathrm{wt} \% \mathrm{~A}\) \- A second eutectic occurs at \(730^{\circ} \mathrm{C}\) and 60 \(\mathrm{wt} \% \mathrm{~B}-40 \mathrm{wt} \% \mathrm{~A}\). \- A third eutectic occurs at \(755^{\circ} \mathrm{C}\) and 40 \(\mathrm{wt} \%\) B-60 wt \(\% \mathrm{~A}\). \- One congruent melting point occurs at \(780^{\circ} \mathrm{C}\) and \(51 \mathrm{wt} \%\) B-49 wt \(\% \mathrm{~A}\). \- A second congruent melting point occurs at \(755^{\circ} \mathrm{C}\) and \(67 \mathrm{wt} \%\) B-33 wt \(\% \mathrm{~A}\). \- The intermetallic compound \(\mathrm{AB}\) exists at \(51 \mathrm{wt} \%\) B-49 wt \% A. \- The intermetallic compound \(\mathrm{AB}_{2}\) exists at \(67 \mathrm{wt} \%\) B-33 wt \(\% \mathrm{~A}\).

A steel alloy is known to contain \(93.8\) wt \(\%\) \(\mathrm{Fe}, 6.0 \mathrm{wt} \% \mathrm{Ni}\), and \(0.2 \mathrm{wt} \% \mathrm{C}\). (a) What is the approximate eutectoid temperature of this alloy? (b) What is the proeutectoid phase when this alloy is cooled to a temperature just below the eutectoid? (c) Compute the relative amounts of the proeutectoid phase and pearlite. Assume that there are no alterations in the positions of other phase boundaries with the addition of Ni.
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