Make a copy of the isothermal transformation diagram for a 1.13 wt% C iron–carbon alloy, 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

Using the isothermal transformation diagram for an iron–carbon alloy of eutectoid composition , 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 C (1400 F) and that it has been held at this temperature long enough to have achieved a complete and homogeneous austenitic structure.

(a) Cool rapidly to $700^{\circ} \mathrm{C}\left(1290^{\circ} \mathrm{F}\right)$, hold for $10^4 \mathrm{~s}$, then quench to room temperature.

(b) Reheat the specimen in part (a) to $700^{\circ} \mathrm{C}$ (1290°F) for $20 \mathrm{~h}$.

(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) Cool rapidly to $400^{\circ} \mathrm{C}\left(750^{\circ} \mathrm{F}\right)$, hold for $2 \mathrm{~s}$, then quench to room temperature.

(e) Cool rapidly to $400^{\circ} \mathrm{C}\left(750^{\circ} \mathrm{F}\right)$, hold for $20 \mathrm{~s}$, then quench to room temperature.

(f) Cool rapidly to $400^{\circ} \mathrm{C}\left(750^{\circ} \mathrm{F}\right)$, hold for $200 \mathrm{~s}$, then quench to room temperature.

The microstructure of an iron–carbon alloy consists of proeutectoid cementite and pearlite; the mass fractions of these microconstituents are 0.11 and 0.89, respectively. Determine the concentration of carbon in this alloy.

(a) What is an isothermal transformation in the solid state? (b) Draw an isothermal transformation diagram for a plain-carbon eutectoid steel and indicate the various decomposition products on it. How can such a diagram be constructed by a series of experiments?

Cooling curves are shown in Figure 10-26 for several Mo-V alloys. Based on these curves, construct the Mo-V phase diagram.

Plot the yield and tensile strengths of the ratio of coarse to fine pearlite as a function of carbon composition according to Table $12$-$1$.

Which of the following polymers would be suitable for the fabrication of cups to contain hot coffee: polyethylene, polypropylene, poly(vinyl chloride), PET polyester, and polycarbonate. Why?

Estimate the Brinell hardnesses for specimens of a 0.45 wt% C iron–carbon alloy that have been subjected to the heat treatments described.

Let $\mathbf{F}(x, y, z)=\left(e^{x} \sin y\right) \mathbf{i}+\left(e^{x} \cos y\right) \mathbf{j}+z^{2} \mathbf{k}.$ Evaluate the integral $\int_{\mathbf{c}} \mathbf{F} \cdot d \mathbf{s},$ where $\mathbf{c}(t)=\left(\sqrt{t}, t^{3}, \exp \sqrt{t}\right), 0 \leq t \leq 1.$

Describe the characteristics of
(a) an alloy,
(b) pearlite,
(c) austenite,
(d) martensite, and
(e) cementite.

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.

Rapidly cool to $625^{\circ} \mathrm{C}\left(1160^{\circ} \mathrm{F}\right)$, hold for $10 \mathrm{~s}$, then quench to room temperature.

The kinetics of the austenite-to-pearlite transformation obey 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:

Briefly explain why there is no bainite transformation region on the continuous-cooling transformation diagram for an iron–carbon alloy of eutectoid composition.

(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. (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.