0.25! "

Transcription

1 9.52 Compute the mass fractions of proeutectoid ferrite and pearlite that form in an iron carbon alloy containing 0.25 wt% C. The mass fractions of proeutectoid ferrite and pearlite that form in a 0.25 wt% C iron-carbon alloy are considered in this problem. From Equation 9.20 W p C 0 '! ! And, from Equation 9.21 (for proeutectoid ferrite) W!' 0.76 " C 0 ' 0.76 "

2 9.54 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? In this problem we are given values of W α and W Fe3 C for an iron-carbon alloy (0.88 and 0.12, respectively), and then are asked to specify whether the alloy is hypoeutectoid or hypereutectoid. Employment of the lever rule for total α leads to W! 0.88 C Fe 3 C " C " C " Now, solving for C 0, the alloy composition, leads to C wt% C. hypereutectoid since C 0 is greater than 0.76 wt% C. Therefore, the alloy is

3 9.55 The microstructure of an iron-carbon alloy consists of proeutectoid ferrite and pearlite; the mass fractions of these microconstituents are 0.20 and 0.80, respectively. Determine the concentration of carbon in this alloy. We are asked in this problem to determine the concentration of carbon in an alloy for which W!' 0.20 and W p If we let C 0 ' equal the carbon concentration in the alloy, employment of the appropriate lever rule expression, Equation 9.20, leads to W p C 0 '! Solving for C 0 ' yields C 0 ' 0.61 wt% C.

4 9.56 Consider 2.0 kg of a 99.6 wt% Fe 0.4 wt% C alloy that is cooled to a temperature just below the eutectoid. (a) How many kilograms of proeutectoid ferrite form? (b) How many kilograms of eutectoid ferrite form? (c) How many kilograms of cementite form? In this problem we are asked to consider 2.0 kg of a 99.6 wt% Fe-0.4 wt% C alloy that is cooled to a temperature below the eutectoid. (a) Equation 9.21 must be used in computing the amount of proeutectoid ferrite that forms. Thus, W!' 0.76 " C 0 ' 0.76 " Or, (0.49)(2.0 kg) 0.98 kg of proeutectoid ferrite forms. (b) In order to determine the amount of eutectoid ferrite, it first becomes necessary to compute the amount of total ferrite using the lever rule applied entirely across the α + Fe 3 C phase field, as W! C Fe 3 C " C " " which corresponds to (0.94)(2.0 kg) 1.88 kg. Now, the amount of eutectoid ferrite is just the difference between total and proeutectoid ferrites, or 1.88 kg 0.98 kg 0.90 kg (c) With regard to the amount of cementite that forms, again application of the lever rule across the entirety of the α + Fe 3 C phase field, leads to W Fe3 C C 0! C " 0.40! C Fe3 C! C " 6.70! which amounts to (0.057)(2.0 kg) kg cementite in the alloy.

5 9.57 Compute the maximum mass fraction of proeutectoid cementite possible for a hypereutectoid iron carbon alloy. This problem asks that we compute the maximum mass fraction of proeutectoid cementite possible for a hypereutectoid iron-carbon alloy. This requires that we utilize Equation 9.23 with C 1 ' 2.14 wt% C, the maximum solubility of carbon in austenite. Thus, W Fe3 C' C 1 '! !

6 9.58 Is it possible to have an iron-carbon alloy for which the mass fractions of total ferrite and proeutectoid cementite are and 0.049, respectively? Why or why not? This problem asks if it is possible to have an iron-carbon alloy for which W α and W Fe3 C! In order to make this determination, it is necessary to set up lever rule expressions for these two mass fractions in terms of the alloy composition, then to solve for the alloy composition of each; if both alloy composition values are equal, then such an alloy is possible. The expression for the mass fraction of total ferrite is W! C Fe 3 C " C " C " Solving for this C 0 yields C wt% C. Now for W Fe3 C! we utilize Equation 9.23 as W Fe3 C' C 1 '! This expression leads to C 1 ' 1.05 wt% C. And, since C 0 C 1 ', this alloy is possible.

7 9.60 Compute the mass fraction of eutectoid ferrite in an iron-carbon alloy that contains 0.43 wt% C. In order to solve this problem it is necessary to compute mass fractions of total and proeutectoid ferrites, and then to subtract the latter from the former. To calculate the mass fraction of total ferrite, it is necessary to use the lever rule and a tie line that extends across the entire α + Fe 3 C phase field as W! C Fe 3 C " C " " Now, for the mass fraction of proeutectoid ferrite we use Equation 9.21 as W!' 0.76 " C 0 ' " 0.76 " And, finally, the mass fraction of eutectoid ferrite W α'' is just W α'' W α W α'

8 9.62 The mass fraction of eutectoid ferrite in an iron-carbon alloy is On the basis of this information, is it possible to determine the composition of the alloy? If so, what is its composition? If this is not possible, explain why. This problem asks whether or not it is possible to determine the composition of an iron-carbon alloy for which the mass fraction of eutectoid ferrite is 0.82; and if so, to calculate the composition. Yes, it is possible to determine the alloy composition; and, in fact, there are two possible answers. For the first, the eutectoid ferrite exists in addition to proeutectoid ferrite. For this case the mass fraction of eutectoid ferrite (W α'' ) is just the difference between total ferrite and proeutectoid ferrite mass fractions; that is W α'' W α W α' Now, it is possible to write expressions for W α (of the form of Equation 9.12) and W α' (Equation 9.21) in terms of C 0, the alloy composition. Thus, W!" C Fe3 C " C 0 " 0.76 " C 0 And, solving for C 0 yields C wt% C. 6.70! C ! 0.022! 0.76! C For the second possibility, we have a hypereutectoid alloy wherein all of the ferrite is eutectoid ferrite. Thus, it is necessary to set up a lever rule expression wherein the mass fraction of total ferrite is Therefore, W! C Fe 3 C " C 0 And, solving for C 0 yields C wt% C " C "

9 9.66 A steel alloy is known to contain 93.8 wt% Fe, 6.0 wt% Ni, and 0.2 wt% 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. (a) From Figure 9.34, the eutectoid temperature for 6.0 wt% Ni is approximately 650 C (1200 F). (b) From Figure 9.35, the eutectoid composition is approximately 0.62 wt% C. Since the carbon concentration in the alloy (0.2 wt%) is less than the eutectoid (0.62 wt% C), the proeutectoid phase is ferrite. (c) Assume that the α (α + Fe 3 C) phase boundary is at a negligible carbon concentration. Modifying Equation 9.21 leads to W!' 0.62 " C 0 ' 0.62 " " Likewise, using a modified Equation 9.20 W p C 0 '! !