Materials Science and Engineering

William D. Callister, David G. Rethwisch

Chapter 10 Phase Transformations: Development of Microstructure and Alteration of Mechanical Properties - all with Video Answers

Educators

Chapter Questions

01:02

Problem 1

Name the two stages involved in the formation of particles of a new phase. Briefly describe each.

Hunza Gilgit

Numerade Educator

01:49

(a) Rewrite the expression for the total free energy change for nucleation (Equation 10.1) for the case of a cubic nucleus of edge length $a$ (instead of a sphere of radius $r$ ). Now differentiate this expression with respect to $a$ (per Equation 10.2) and solve for both the critical cube edge length, $a^{*}$, and $\Delta G^{*}$.
(b) Is $\Delta G^{*}$ greater for a cube or a sphere? Why?

Manik Pulyani

Numerade Educator

01:14

Problem 3

If ice homogeneously nucleates at $-40^{\circ} \mathrm{C}$, calculate the critical radius given values of $-3.1 \times$ $10^{8} \mathrm{~J} / \mathrm{m}^{3}$ and $25 \times 10^{3} \mathrm{~J} / \mathrm{m}^{2}$, respectively, for the, latent heat of fusion and the surface free energy.

Manik Pulyani

Numerade Educator

01:02

Problem 4

(a) For the solidification of nickel, calculate the critical radius $r^{*}$ and the activation free energy $\Delta G^{*}$ if nucleation is homogeneous. Values for the latent heat of fusion and surface free energy are $-2.53 \times 10^{9} \mathrm{~J} / \mathrm{m}^{3}$ and $0.255 \mathrm{~J} / \mathrm{m}^{2}$, respectively. Use the supercooling value found in Table 10.1.
(b) Now, calculate the number of atoms found in a nucleus of critical size. Assume a lattice parameter of $0.360 \mathrm{~nm}$ for solid nickel at its melting temperature.

Manik Pulyani

Numerade Educator

01:08

Problem 5

(a) Assume for the solidification of nickel (Problem 10.4) that nucleation is homogeneous and that the number of stable nuclei is $10^{6}$ nuclei per cubic meter. Calculate the critical radius and the number of stable nuclei that exist at the following degrees of supercooling: 200 and $300 \mathrm{~K}$.
(b) What is significant about the magnitudes of these critical radii and the numbers of stable nuclei?

Manik Pulyani

Numerade Educator

01:31

Problem 6

For some transformation having kinetics that obey the Avrami equation (Equation 10.17), the parameter $n$ is known to have a value of $1.5 .$ If the reaction is $25 \%$ complete after $125 \mathrm{~s}$, howlong (total time) will it take the transformation to go to $90 \%$ completion?

Manik Pulyani

Numerade Educator

01:56

Problem 7

Compute the rate of some reaction that obeys Avrami kinetics, assuming that the constants $n$ and $k$ have values of $2.0$ and $5 \times 10^{-4}$, respectively, for time expressed in seconds.

Manik Pulyani

Numerade Educator

01:32

Problem 8

It is known that the kinetics of recrystallization for some alloy obeys the Avrami equation, and that the value of $n$ in the exponential is $5.0$. If, at some temperature, the fraction recrystallized is $0.30$ after $100 \mathrm{~min}$, determine the rate of recrystallization at this temperature.

Manik Pulyani

Numerade Educator

01:33

Problem 9

It is known that the kinetics of some transformation obeys the Avrami equation and that the value of $k$ is $2.6 \times 10^{-6}$ (for time in minutes). If the fraction recrystallized is $0.65$ after $120 \mathrm{~min}$, determine the rate of this transformation.

Manik Pulyani

Numerade Educator

01:24

Problem 10

10 The kinetics of the austenite-to-pearlite transformation obeys the Avrami relationship. Using the fraction transformed-time data given here, determine the total time required for $95 \%$ of the austenite to transform to pearlite.
\begin{tabular}{cc}
\hline Fraction Transformed & Time $(s)$ \\
\hline $0.2$ & 280 \\
\hline $0.6$ & 425 \\
\hline
\end{tabular}

Manik Pulyani

Numerade Educator

01:52

Problem 11

recrystallization at $350^{\circ} \mathrm{C}$ of a previously deformed aluminum are tabulated here. Assuming that the kinetics of this process obey the Avrami relationship, determine the fraction recrystallized after a total time of $116.8 \mathrm{~min}$.
\begin{tabular}{cc}
\hline Fraction Recrystallized & Time (min) \\
\hline $0.30$ & $95.2$ \\
\hline $0.80$ & $126.6$ \\
\hline
\end{tabular}

Manik Pulyani

Numerade Educator

01:44

Problem 12

(a) From the curves shown in Figure $10.11$ and using Equation 10.18, determine the rate of recrystallization for pure copper at the several temperatures.
(b) Make a plot of $\ln ($ rate) versus the reciprocal of temperature (in $\mathrm{K}^{-1}$ ), and determine the activation energy for this recrystallization process. (See Section 5.5.)
(c) By extrapolation, estimate the length of time required for $50 \%$ recrystallization at room temperature, $20^{\circ} \mathrm{C}(293 \mathrm{~K})$.

Manik Pulyani

Numerade Educator

01:04

Problem 13

Determine values for the constants $n$ and $k$ (Equation 10.17) for the recrystallization of copper (Figure 10.11) at $119^{\circ} \mathrm{C}$.

Manik Pulyani

Numerade Educator

01:08

Problem 14

In terms of heat treatment and the development of microstructure, what are two major limitations of the iron-iron carbide phase diagram?

Hunza Gilgit

Numerade Educator

01:32

Problem 15

(a) Briefly describe the phenomena of superheating and supercooling.
(b) Why do these phenomena occur?

Hunza Gilgit

Numerade Educator

01:37

Problem 16

Suppose that a steel of eutectoid composition is cooled to $675^{\circ} \mathrm{C}\left(1250^{\circ} \mathrm{F}\right)$ from $760^{\circ} \mathrm{C}\left(1400^{\circ} \mathrm{F}\right)$ in less than $0.5 \mathrm{~s}$ and held at this temperature.
(a) How long will it take for the austenite-topearlite reaction to go to $50 \%$ completion? To $100 \%$ completion?
(b) Estimate the hardness of the alloy that has completely transformed to pearlite.

Manik Pulyani

Numerade Educator

02:18

Problem 17

Briefly cite the differences among pearlite, bainite, and spheroidite relative to microstructure and mechanical properties.

Manik Pulyani

Numerade Educator

00:50

Problem 18

What is the driving force for the formation of spheroidite?

Hunza Gilgit

Numerade Educator

01:31

Problem 19

Using the isothermal transformation diagram for an iron-carbon alloy of eutectoid composition (Figure $10.22$ ), specify the nature of the final microstructure (in terms of microconstituents present and approximate percentages of each) of a small specimen that has been subjected to the following time-temperature treatments. In each case assume that the specimen begins at $760^{\circ} \mathrm{C}$ $\left(1400^{\circ} \mathrm{F}\right)$ and that it has been held at this temperature long enough to have achieved a complete and homogeneous austenitic structure.
(a) Cool rapidly to $350^{\circ} \mathrm{C}\left(660^{\circ} \mathrm{F}\right)$, hold for $10^{3} \mathrm{~s}$, then quench to room temperature.
(b) Rapidly cool to $625^{\circ} \mathrm{C}\left(1160^{\circ} \mathrm{F}\right)$, hold for $10 \mathrm{~s}$, then quench to room temperature.(c) Rapidly cool to $600^{\circ} \mathrm{C}\left(1110^{\circ} \mathrm{F}\right)$, hold for $4 \mathrm{~s}$, rapidly cool to $450^{\circ} \mathrm{C}\left(840^{\circ} \mathrm{F}\right)$, hold for $10 \mathrm{~s}$, then quench to room temperature.
(d) Reheat the specimen in part (c) to $700^{\circ} \mathrm{C}$ $\left(1290^{\circ} \mathrm{F}\right)$ for $20 \mathrm{~h}$.
(e) Rapidly cool to $300^{\circ} \mathrm{C}\left(570^{\circ} \mathrm{F}\right)$, hold for $20 \mathrm{~s}$, then quench to room temperature in water. Reheat to $425^{\circ} \mathrm{C}\left(800^{\circ} \mathrm{F}\right)$ for $10^{3}$ s and slowly cool to room temperature.
(f) Cool rapidly to $665^{\circ} \mathrm{C}\left(1230^{\circ} \mathrm{F}\right)$, hold for $10^{3} \mathrm{~s}$, then quench to room temperature.
(g) Rapidly cool to $575^{\circ} \mathrm{C}\left(1065^{\circ} \mathrm{F}\right)$, hold for $20 \mathrm{~s}$, rapidly cool to $350^{\circ} \mathrm{C}\left(660^{\circ} \mathrm{F}\right)$, hold for $100 \mathrm{~s}$, then quench to room temperature.
(h) Rapidly cool to $350^{\circ} \mathrm{C}\left(660^{\circ} \mathrm{F}\right)$, hold for $150 \mathrm{~s}$, then quench to room temperature.

Manik Pulyani

Numerade Educator

01:28

Problem 20

Make a copy of the isothermal transformation diagram for an iron-carbon alloy of eutectoid composition (Figure $10.22$ ) and then sketch and label time-temperature paths on this diagram to produce the following microstructures:
(a) $100 \%$ coarse pearlite
(b) $50 \%$ martensite and $50 \%$ austenite
(c) $50 \%$ coarse pearlite, $25 \%$ bainite, and $25 \%$ martensite

Manik Pulyani

Numerade Educator

02:13

Problem 21

Using the isothermal transformation diagram for a $1.13$ wt $\%$ C steel alloy (Figure $10.39$ ), determine the final microstructure (in terms of just the microconstituents present) of a small specimen that has been subjected to the following timetemperature treatments. In each case assume that the specimen begins at $920^{\circ} \mathrm{C}\left(1690^{\circ} \mathrm{F}\right)$ and that it has been held at this temperature long enough to have achieved a complete and homogeneous austenitic structure.
(a) Rapidly cool to $250^{\circ} \mathrm{C}\left(480^{\circ} \mathrm{F}\right)$, hold for $10^{3} \mathrm{~s}$, then quench to room temperature.
(b) Rapidly cool to $775^{\circ} \mathrm{C}$ (1430^\circ), hold for $500 \mathrm{~s}$, then quench to room temperature.
(c) Rapidly cool to $400^{\circ} \mathrm{C}\left(750^{\circ} \mathrm{F}\right)$, hold for $500 \mathrm{~s}$, then quench to room temperature.
(d) Rapidly cool to $700^{\circ} \mathrm{C}\left(1290^{\circ} \mathrm{F}\right)$, hold at this temperature for $10^{5} \mathrm{~s}$, then quench to room temperature.
(e) Rapidly cool to $650^{\circ} \mathrm{C}\left(1200^{\circ} \mathrm{F}\right)$, hold at this temperature for $3 \mathrm{~s}$, rapidly cool to $400^{\circ} \mathrm{C}$ $\left(750^{\circ} \mathrm{F}\right)$, hold for $25 \mathrm{~s}$, then quench to room temperature.

Manik Pulyani

Numerade Educator

01:47

Problem 22

2 For parts a, c, d, f, and h of Problem $10.21$, determine the approximate percentages of the microconstituents that form.

Manik Pulyani

Numerade Educator

01:36

Problem 23

Make a copy of the isothermal transformation diagram for a 1.13 wt\% C iron-carbon alloy (Figure 10.39), and then on this diagram sketch and label time-temperature paths to produce the following microstructures:
(a) $6.2 \%$ proeutectoid cementite and $93.8 \%$ coarse pearlite
(b) $50 \%$ fine pearlite and $50 \%$ bainite
(c) $100 \%$ martensite
(d) $100 \%$ tempered martensite

Manik Pulyani

Numerade Educator

02:04

Problem 24

Name the microstructural products of eutectoid iron-carbon alloy $(0.76$ wt $\%$ C) specimens that are first completely transformed to austenite, then cooled to room temperature at the following rates:
(a) $1^{\circ} \mathrm{C} / \mathrm{s}$
(c) $50^{\circ} \mathrm{C} / \mathrm{s}$
(b) $20^{\circ} \mathrm{C} / \mathrm{s}$
(d) $175^{\circ} \mathrm{C} / \mathrm{s}$

Manik Pulyani

Numerade Educator

01:15

Problem 25

Figure $10.40$ shows the continuous-cooling transformation diagram for a $0.35 \mathrm{wt} \% \mathrm{C}$ ironcarbon alloy. Make a copy of this figure, and then sketch and label continuous-cooling curves to yield the following microstructures:
(a) Fine pearlite and proeutectoid ferrite
(b) Martensite
(c) Martensite and proeutectoid ferrite
(d) Coarse pearlite and proeutectoid ferrite
(e) Martensite, fine pearlite, and proeutectoid ferrite

Manik Pulyani

Numerade Educator

01:10

Problem 26

Cite two important differences between
continuous-cooling transformation diagrams for
plain carbon and alloy steels.

Hunza Gilgit

Numerade Educator

01:35

Problem 27

Briefly explain why there is no bainite transfor-
mation region on the continuous-cooling trans-
formation diagram for an iron–carbon alloy of

eutectoid composition.

Manik Pulyani

Numerade Educator

02:38

Problem 28

Name the microstructural products of 4340 alloy steel specimens that are first completely transformed to austenite, then cooled to room temperature at the following rates:
(a) $0.005^{\circ} \mathrm{C} / \mathrm{s}$
(b) $0.05^{\circ} \mathrm{C} / \mathrm{s}$
(c) $0.5^{\circ} \mathrm{C} / \mathrm{s}$
(d) $5^{\circ} \mathrm{C} / \mathrm{s}$

Hunza Gilgit

Numerade Educator

01:08

Problem 29

Briefly describe the simplest continuouscooling heat treatment procedure that would be used in converting a 4340 steel from one microstructure to another.
(a) (Martensite $+$ ferrite $+$ bainite) to
$($ martensite $+$ ferrite $+$ pearlite $+$ bainite $)$
(b) (Martensite + ferrite + bainite) to spheroidite
(c) (Martensite $+$ bainite $+$ ferrite) to tempered
martensite

Manik Pulyani

Numerade Educator

01:21

Problem 30

On the basis of diffusion considerations, explain why fine pearlite forms for the moderate cooling of austenite through the eutectoid temperature, whereas coarse pearlite is the product for relatively slow cooling rates.

Hunza Gilgit

Numerade Educator

01:50

Problem 31

Briefly explain why fine pearlite is harder and
stronger than coarse pearlite, which in turn is
harder and stronger than spheroidite.

Jerrah Biggerstaff

Numerade Educator

01:50

Problem 32

Briefly explain why fine pearlite is harder and
stronger than coarse pearlite, which in turn is
harder and stronger than spheroidite.

Jerrah Biggerstaff

Numerade Educator

02:12

Problem 33

Rank the following iron-carbon alloys and associated microstructures from the hardest to the softest:
(a) $0.25 \mathrm{wt} \% \mathrm{C}$ with coarse pearlite
(b) $0.80 \mathrm{wt} \% \mathrm{C}$ with spheroidite
(c) $0.25 \mathrm{wt} \% \mathrm{C}$ with spheroidite
(d) $0.80 \mathrm{wt} \% \mathrm{C}$ with fine pearlite.
Justify this ranking

Manik Pulyani

Numerade Educator

01:36

Problem 34

Briefly explain why the hardness of tempered
martensite diminishes with tempering time (at

constant temperature) and with increasing tem-
perature (at constant tempering time).

Manik Pulyani

Numerade Educator

02:12

Problem 35

Briefly describe the simplest heat treatment
procedure that would be used in converting a
0.76 wt% C steel from one microstructure to the
other, as follows:
(a) Martensite to spheroidite
(b) Spheroidite to martensite
(c) Bainite to pearlite
(d) Pearlite to bainite
(e) Spheroidite to pearlite
(f) Pearlite to spheroidite
(g) Tempered martensite to martensite
(h) Bainite to spheroidite

Manik Pulyani

Numerade Educator

01:45

Problem 36

(a) Briefly describe the microstructural difference
between spheroidite and tempered martensite.
(b) Explain why tempered martensite is much
harder and stronger.

Hunza Gilgit

Numerade Educator

01:28

Problem 37

Estimate Brinell hardnesses and ductilities
(%RA) for specimens of an iron–carbon alloy of
eutectoid composition that have been subjected
to the heat treatments described in parts (a)
through (h) of Problem 10.19.

Manik Pulyani

Numerade Educator

01:30

Problem 38

Estimate the Brinell hardnesses for specimens
of a 1.13 wt% C iron–carbon alloy that have been
subjected to the heat treatments described in
parts (a), (d), and (h) of Problem 10.21.

Manik Pulyani

Numerade Educator

02:17

Problem 39

Determine the approximate tensile strengths

and ductilities (%RA) for specimens of a eutec-
toid iron–carbon alloy that have experienced the

heat treatments described in parts (a) through
(d) of Problem 10.24.

Manik Pulyani

Numerade Educator