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Questions and Problems • 231

7.15

7.16

(b)

7.17

7.18

and in a [101] direction, and is initiated at an applied tensile stress of 1.1 MPa (160 psi), compute the critical resolved shear stress. A single crystal of a metal that has the FCC crystal structure is oriented such that a tensile stress is applied parallel to the [110] direction. If the critical resolved shear stress for this material is 1.75 MPa, calculate the magnitude(s) of applied stress(es) necessary to cause slip to occur on the (111) plane in each of the [110], [101] and [011] directions. (a) A single crystal of a metal that has the BCC crystal structure is oriented such that a tensile stress is applied in the [010] direction. If the magnitude of this stress is 2.75 MPa, compute the resolved shear stress in the [111] direction on each of the (110) and (101) planes. On the basis of these resolved shear stress values, which slip system(s) is (are) most favorably oriented? Consider a single crystal of some hypothetical metal that has the FCC crystal structure and is oriented such that a tensile stress is applied along a [102] direction. If slip occurs on a (111) plane and in a [101] direction, compute the stress at which the crystal yields if its critical resolved shear stress is 3.42 MPa. The critical resolved shear stress for iron is 27 MPa (4000 psi). Determine the maximum possible yield strength for a single crystal of Fe pulled in tension.

Deformation by Twinning 7.19 List four major differences between deformation by twinning and deformation by slip relative to mechanism, conditions of occurrence, and final result. Strengthening by Grain Size Reduction 7.20 Briefly explain why small-angle grain boundaries are not as effective in interfering with the slip process as are high-angle grain boundaries. 7.21 Briefly explain why HCP metals are typically more brittle than FCC and BCC metals. 7.22 Describe in your own words the three strengthening mechanisms discussed in this chapter (i.e., grain size reduction, solid-solution streng-

thening, and strain hardening). Be sure to explain how dislocations are involved in each of the strengthening techniques. 7.23 (a) From the plot of yield strength versus (grain diameter)⫺1/2 for a 70 Cu–30 Zn cartridge brass, Figure 7.15, determine values for the constants s0 and ky in Equation 7.7. (b) Now predict the yield strength of this alloy when the average grain diameter is 1.0 ⫻ 10⫺3 mm. 7.24 The lower yield point for an iron that has an average grain diameter of 5 ⫻ 10⫺2 mm is 135 MPa (19,500 psi). At a grain diameter of 8 ⫻ 10⫺3 mm, the yield point increases to 260 MPa (37,500 psi). At what grain diameter will the lower yield point be 205 MPa (30,000 psi)? 7.25 If it is assumed that the plot in Figure 7.15 is for noncold-worked brass, determine the grain size of the alloy in Figure 7.19; assume its composition is the same as the alloy in Figure 7.15. Solid-Solution Strengthening 7.26 In the manner of Figures 7.17b and 7.18b, indicate the location in the vicinity of an edge dislocation at which an interstitial impurity atom would be expected to be situated. Now briefly explain in terms of lattice strains why it would be situated at this position. Strain Hardening 7.27 (a) Show, for a tensile test, that %CW ⫽ a

⑀ b ⫻ 100 ⑀⫹1

if there is no change in specimen volume during the deformation process (i.e., A0l0 ⫽ Adld). (b) Using the result of part (a), compute the percent cold work experienced by naval brass (the stress–strain behavior of which is shown in Figure 6.12) when a stress of 400 MPa (58,000 psi) is applied. 7.28 Two previously undeformed cylindrical specimens of an alloy are to be strain hardened by reducing their cross-sectional areas (while maintaining their circular cross sections). For one specimen, the initial and deformed radii are 16 mm and 11 mm, respectively. The second specimen, with an initial radius of 12 mm,

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232 • Chapter 7 / Dislocations and Strengthening Mechanisms must have the same deformed hardness as the first specimen; compute the second specimen’s radius after deformation. 7.29 Two previously undeformed specimens of the same metal are to be plastically deformed by reducing their cross-sectional areas. One has a circular cross section, and the other is rectangular; during deformation the circular cross section is to remain circular, and the rectangular is to remain as such. Their original and deformed dimensions are as follows:

Original dimensions Deformed dimensions

Circular (diameter, mm)

Rectangular (mm)

15.2 11.4

125 ⫻ 175 75 ⫻ 200

Which of these specimens will be the hardest after plastic deformation, and why? 7.30 A cylindrical specimen of cold-worked copper has a ductility (%EL) of 25%. If its coldworked radius is 10 mm (0.40 in.), what was its radius before deformation? 7.31 (a) What is the approximate ductility (%EL) of a brass that has a yield strength of 275 MPa (40,000 psi)? (b) What is the approximate Brinell hardness of a 1040 steel having a yield strength of 690 MPa (100,000 psi)? 7.32 Experimentally, it has been observed for single crystals of a number of metals that the critical resolved shear stress ␶crss is a function of the dislocation density ␳D as tcrss ⫽ t0 ⫹ A2rD where ␶0 and A are constants. For copper, the critical resolved shear stress is 2.10 MPa (305 psi) at a dislocation density of 105 mm⫺2. If it is known that the value of A for copper is 6.35 ⫻ 10⫺3 MPa # mm (0.92 psi # mm), compute tcrss at a dislocation density of 107 mm⫺2. Recovery Recrystallization Grain Growth 7.33 Briefly cite the differences between recovery and recrystallization processes. 7.34 Estimate the fraction of recrystallization from the photomicrograph in Figure 7.21c.

7.35 Explain the differences in grain structure for a metal that has been cold worked and one that has been cold worked and then recrystallized. 7.36 (a) What is the driving force for recrystallization? (b) For grain growth? 7.37 (a) From Figure 7.25, compute the length of time required for the average grain diameter to increase from 0.01 to 0.1 mm at 500⬚C for this brass material. (b) Repeat the calculation at 600⬚C. 7.38 The average grain diameter for a brass material was measured as a function of time at 650⬚C, which is shown in the following table at two different times: Time (min)

Grain Diameter (mm)

30 90

3.9 ⫻ 10⫺2 6.6 ⫻ 10⫺2

(a) What was the original grain diameter? (b) What grain diameter would you predict after 150 min at 650⬚C? 7.39 An undeformed specimen of some alloy has an average grain diameter of 0.040 mm. You are asked to reduce its average grain diameter to 0.010 mm. Is this possible? If so, explain the procedures you would use and name the processes involved. If it is not possible, explain why. 7.40 Grain growth is strongly dependent on temperature (i.e., rate of grain growth increases with increasing temperature), yet temperature is not explicitly given as a part of Equation 7.9. (a) Into which of the parameters in this expression would you expect temperature to be included? (b) On the basis of your intuition, cite an explicit expression for this temperature dependence. 7.41 An uncold-worked brass specimen of average grain size 0.008 mm has a yield strength of 160 MPa (23,500 psi). Estimate the yield strength of this alloy after it has been heated to 600⬚C for 1000 s, if it is known that the value of ky is 12.0 MPa # mm1/2 (1740 psi # mm1/2).

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Design Problems • 233 Spreadsheet Problem 7.1SS For crystals having cubic symmetry, generate a spreadsheet that will allow the user to de-

termine the angle between two crystallographic directions, given their directional indices.

DESIGN PROBLEMS Strain Hardening Recrystallization 7.D1 Determine whether it is possible to cold work steel so as to give a minimum Brinell hardness of 225, and at the same time have a ductility of at least 12%EL. Justify your decision. 7.D2 Determine whether it is possible to cold work brass so as to give a minimum Brinell hardness of 120 and at the same time have a ductility of at least 20%EL. Justify your decision. 7.D3 A cylindrical specimen of cold-worked steel has a Brinell hardness of 250. (a) Estimate its ductility in percent elongation. (b) If the specimen remained cylindrical during deformation and its original radius was 5 mm (0.20 in.), determine its radius after deformation. 7.D4 It is necessary to select a metal alloy for an application that requires a yield strength of at least 345 MPa (50,000 psi) while maintaining a minimum ductility (%EL) of 20%. If the metal may be cold worked, decide which of the following are candidates: copper, brass, and a 1040 steel. Why? 7.D5 A cylindrical rod of 1040 steel originally 15.2 mm (0.60 in.) in diameter is to be cold

worked by drawing; the circular cross section will be maintained during deformation. A cold-worked tensile strength in excess of 840 MPa (122,000 psi) and a ductility of at least 12%EL are desired. Furthermore, the final diameter must be 10 mm (0.40 in.). Explain how this may be accomplished. 7.D6 A cylindrical rod of copper originally 16.0 mm (0.625 in.) in diameter is to be cold worked by drawing; the circular cross section will be maintained during deformation. A coldworked yield strength in excess of 250 MPa (36,250 psi) and a ductility of at least 12%EL are desired. Furthermore, the final diameter must be 11.3 mm (0.445 in.). Explain how this may be accomplished. 7.D7 A cylindrical 1040 steel rod having a minimum tensile strength of 865 MPa (125,000 psi), a ductility of at least 10%EL, and a final diameter of 6.0 mm (0.25 in.) is desired. Some 7.94 mm (0.313 in.) diameter 1040 steel stock, which has been cold worked 20%, is available. Describe the procedure you would follow to obtain this material. Assume that 1040 steel experiences cracking at 40%CW.

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386 • Chapter 10 / Phase Transformations 10.4 (a) For the solidification of iron, calculate the critical radius r* and the activation free energy ⌬G* if nucleation is homogeneous. Values for the latent heat of fusion and surface free energy are ⫺1.85 ⫻ 109 J/m3 and 0.204 J/m2, 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 0.292 nm for solid iron at its melting temperature. 10.5 (a) Assume for the solidification of iron (Problem 10.4) that nucleation is homogeneous, and the number of stable nuclei is 106 nuclei per cubic meter. Calculate the critical radius and the number of stable nuclei that exist at the following degrees of supercooling: 200 K and 300 K. (b) What is significant about the magnitudes of these critical radii and the numbers of stable nuclei? 10.6 For some transformation having kinetics that obey the Avrami equation (Equation 10.17), the parameter n is known to have a value of 1.7. If, after 100 s, the reaction is 50% complete, how long (total time) will it take the transformation to go to 99% completion? 10.7 Compute the rate of some reaction that obeys Avrami kinetics, assuming that the constants n and k have values of 3.0 and 7 ⫻ 10⫺3, respectively, for time expressed in seconds. 10.8 It is known that the kinetics of recrystallization for some alloy obey the Avrami equation and that the value of n in the exponential is 2.5. If, at some temperature, the fraction recrystallized is 0.40 after 200 min, determine the rate of recrystallization at this temperature. 10.9 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: Fraction Transformed 0.2 0.8

Time (s) 12.6 28.2

10.10 The fraction recrystallized–time data for the recrystallization at 600⬚C of a previously

deformed steel are tabulated here. Assuming that the kinetics of this process obey the Avrami relationship, determine the fraction recrystallized after a total time of 22.8 min. Fraction Recrystallized

Time (min)

0.20 0.70

13.1 29.1

10.11 (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 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⬚C (293 K). 10.12 Determine values for the constants n and k (Equation 10.17) for the recrystallization of copper (Figure 10.11) at 102⬚C. Metastable versus Equilibrium States 10.13 In terms of heat treatment and the development of microstructure, what are two major limitations of the iron–iron carbide phase diagram? 10.14 (a) Briefly describe the phenomena of superheating and supercooling. (b) Why do these phenomena occur? Isothermal Transformation Diagrams 10.15 Suppose that a steel of eutectoid composition is cooled to 550⬚C (1020⬚F) from 760⬚C (1400⬚F) in less than 0.5 s and held at this temperature. (a) How long will it take for the austeniteto-pearlite reaction to go to 50% completion? To 100% completion? (b) Estimate the hardness of the alloy that has completely transformed to pearlite. 10.16 Briefly cite the differences between pearlite, bainite, and spheroidite relative to microstructure and mechanical properties. 10.17 What is the driving force for the formation of spheroidite?

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Questions and Problems • 387 10.18 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⬚C (1400⬚F) and that it has been held at this temperature long enough to have achieved a complete and homogeneous austenitic structure.

(g) Rapidly cool to 575⬚C (1065⬚F), hold for 20 s, rapidly cool to 350⬚C (660⬚F), hold for 100 s, then quench to room temperature. (h) Rapidly cool to 250⬚C (480⬚F), hold for 100 s, then quench to room temperature in water. Reheat to 315⬚C (600⬚F) for 1 h and slowly cool to room temperature. 10.19 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) Cool rapidly to 700⬚C (1290⬚F), hold for 104 s, then quench to room temperature.

(a) 100% fine pearlite

(b) Reheat the specimen in part (a) to 700⬚C (1290⬚F) for 20 h.

(b) 100% tempered martensite (c) 50% coarse pearlite, 25% bainite, and 25% martensite

(c) Rapidly cool to 600⬚C (1110⬚F), hold for 4 s, rapidly cool to 450⬚C (840⬚F), hold for 10 s, then quench to room temperature.

10.20 Using the isothermal transformation diagram for a 0.45 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 time–temperature treatments. In each case assume that the specimen begins at 845⬚C (1550⬚F) and that it has been held at

(d) Cool rapidly to 400⬚C (750⬚F), hold for 2 s, then quench to room temperature. (e) Cool rapidly to 400⬚C (750⬚F), hold for 20 s, then quench to room temperature. (f) Cool rapidly to 400⬚C (750⬚F), hold for 200 s, then quench to room temperature. 900

1600 800

A+F

A

1400

700 1200

A+P 600

P B 1000

500

A+B A

800

50%

400 M(start) 300

M(50%)

600

M(90%) 200

400

100

200

0 0.1

1

10

102 Time (s)

103

104

105

Temperature (°F)

Temperature (°C)

Figure 10.39 Isothermal transformation diagram for a 0.45 wt% C iron–carbon alloy: A, austenite; B, bainite; F, proeutectoid ferrite; M, martensite; P, pearlite. (Adapted from Atlas of TimeTemperature Diagrams for Irons and Steels, G. F. Vander Voort, Editor, 1991. Reprinted by permission of ASM International, Materials Park, OH.)

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388 • Chapter 10 / Phase Transformations this temperature long enough to have achieved a complete and homogeneous austenitic structure. (a) Rapidly cool to 250⬚C (480⬚F), hold for 103 s, then quench to room temperature. (b) Rapidly cool to 700⬚C (1290⬚F), hold for 30 s, then quench to room temperature. (c) Rapidly cool to 400⬚C (750⬚F), hold for 500 s, then quench to room temperature. (d) Rapidly cool to 700⬚C (1290⬚F), hold at this temperature for 105 s, then quench to room temperature. (e) Rapidly cool to 650⬚C (1200⬚F), hold at this temperature for 3 s, rapidly cool to 400⬚C (750⬚F), hold for 10 s, then quench to room temperature. (f) Rapidly cool to 450⬚C (840⬚F), hold for 10 s, then quench to room temperature. (g) Rapidly cool to 625⬚C (1155⬚F), hold for 1 s, then quench to room temperature. (h) Rapidly cool to 625⬚C (1155⬚F), hold at this temperature for 10 s, rapidly cool to 400⬚C (750⬚F), hold at this temperature for 5 s, then quench to room temperature. 10.21 For parts (a), (c), (d), (f), and (h) of Problem 10.20, determine the approximate percentages of the microconstituents that form.

10.22 Make a copy of the isothermal transformation diagram for a 0.45 wt% C iron–carbon alloy (Figure 10.39), and then sketch and label on this diagram the time–temperature paths to produce the following microstructures: (a) 42% proeutectoid ferrite and 58% coarse pearlite (b) 50% fine pearlite and 50% bainite (c) 100% martensite (d) 50% martensite and 50% austenite Continuous Cooling Transformation Diagrams 10.23 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) 200⬚C/s, (b) 100⬚C/s, and (c) 20⬚C/s. 10.24 Figure 10.40 shows the continuous cooling transformation diagram for a 1.13 wt% C iron–carbon 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 cementite (b) Martensite

Figure 10.40 Continuous cooling transformation diagram for a 1.13 wt% C iron–carbon alloy.

800 A

C

Temperature (°C)

600 A P 400

200 A

0 0.1

M

103

10 Time (s)

105

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448 • Chapter 11 / Applications and Processing of Metal Alloys 11.11 What is the chief difference between heattreatable and non-heat-treatable alloys? 11.12 Give the distinctive features, limitations, and applications of the following alloy groups: titanium alloys, refractory metals, superalloys, and noble metals. Forming Operations 11.13 Cite advantages and disadvantages of hot working and cold working. 11.14 (a) Cite advantages of forming metals by extrusion as opposed to rolling. (b) Cite some disadvantages. Casting 11.15 List four situations in which casting is the preferred fabrication technique. 11.16 Compare sand, die, investment, lost foam, and continuous casting techniques. Miscellaneous Techniques 11.17 If it is assumed that, for steel alloys, the average cooling rate of the heat-affected zone in the vicinity of a weld is 10⬚C/s, compare the microstructures and associated properties that will result for 1080 (eutectoid) and 4340 alloys in their HAZs. 11.18 Describe one problem that might exist with a steel weld that was cooled very rapidly. Annealing Processes 11.19 In your own words describe the following heat treatment procedures for steels and, for each, the intended final microstructure: full annealing, normalizing, quenching, and tempering. 11.20 Cite three sources of internal residual stresses in metal components. What are two possible adverse consequences of these stresses? 11.21 Give the approximate minimum temperature at which it is possible to austenitize each of the following iron–carbon alloys during a normalizing heat treatment: (a) 0.20 wt% C, (b) 0.76 wt% C, and (c) 0.95 wt% C.

11.22 Give the approximate temperature at which it is desirable to heat each of the following iron–carbon alloys during a full anneal heat treatment: (a) 0.25 wt% C, (b) 0.45 wt% C, (c) 0.85 wt% C, and (d) 1.10 wt% C. 11.23 What is the purpose of a spheroidizing heat treatment? On what classes of alloys is it normally used? Heat Treatment of Steels 11.24 Briefly explain the difference between hardness and hardenability. 11.25 What influence does the presence of alloying elements (other than carbon) have on the shape of a hardenability curve? Briefly explain this effect. 11.26 How would you expect a decrease in the austenite grain size to affect the hardenability of a steel alloy? Why? 11.27 Name two thermal properties of a liquid medium that will influence its quenching effectiveness. 11.28 Construct radial hardness profiles for the following: (a) A 50-mm- (2-in.-) diameter cylindrical specimen of an 8640 steel alloy that has been quenched in moderately agitated oil (b) A 75-mm- (3-in.-) diameter cylindrical specimen of a 5140 steel alloy that has been quenched in moderately agitated oil

(c) A 65-mm- 12 12 -in.-) diameter cylindrical specimen of an 8620 steel alloy that has been quenched in moderately agitated water (d) A 70-mm- 12 34 -in.-) diameter cylindrical specimen of a 1040 steel alloy that has been quenched in moderately agitated water.

11.29 Compare the effectiveness of quenching in moderately agitated water and oil by graphing, on a single plot, radial hardness profiles for 65-mm- 12 12-in.-) diameter cylindrical specimens of an 8630 steel that have been quenched in both media. Precipitation Hardening 11.30 Compare precipitation hardening (Section 11.9) and the hardening of steel by quenching

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Design Problems • 449 (c) How the mechanical properties change during the several heat treatment stages

and tempering (Sections 10.5, 10.6, and 10.8) with regard to the following: (a) The total heat treatment procedure (b) The microstructures that develop

11.31 What is the principal difference between natural and artificial aging processes?

DESIGN PROBLEMS Ferrous Alloys

phor bronze, lead, 6150 steel, 304 stainless steel, and C17200 beryllium copper.

Nonferrous Alloys 11.D1 The following is a list of metals and alloys: Plain carbon steel Magnesium Brass Zinc Gray cast iron Tool steel Platinum Aluminum Stainless steel Tungsten Titanium alloy Select from this list the one metal or alloy that is best suited for each of the following applications, and cite at least one reason for your choice: (a) The block of an internal combustion engine (b) Condensing heat exchanger for steam (c) Jet engine turbofan blades (d) Drill bit (e) Cryogenic (i.e., very low temperature) container (f) As a pyrotechnic (i.e., in flares and fireworks) (g) High-temperature furnace elements to be used in oxidizing atmospheres 11.D2 A group of new materials are the metallic glasses (or amorphous metals). Write an essay about these materials in which you address the following issues: (a) compositions of some of the common metallic glasses, (b) characteristics of these materials that make them technologically attractive, (c) characteristics that limit their utilization, (d) current and potential uses, and (e) at least one technique that is used to produce metallic glasses. 11.D3 Of the following alloys, pick the one(s) that may be strengthened by heat treatment, cold work, or both: R50250 titanium,AZ31B magnesium, 6061 aluminum, C51000 phos-

11.D4 A structural member 100 mm (4 in.) long must be able to support a load of 50,000 N (11,250 lbf) without experiencing any plastic deformation. Given the following data for brass, steel, aluminum, and titanium, rank them from least to greatest weight in accordance with these criteria. Alloy

Yield Strength [MPa (ksi)]

Brass Steel Aluminum Titanium

415 860 310 550

(60) (125) (45) (80)

Density (g/cm3) 8.5 7.9 2.7 4.5

11.D5 Discuss whether it would be advisable to hot work or cold work the following metals and alloys on the basis of melting temperature, oxidation resistance, yield strength, and degree of brittleness: tin, tungsten, aluminum alloys, magnesium alloys, and a 4140 steel. Heat Treatment of Steels 11.D6 A cylindrical piece of steel 25 mm (1.0 in.) in diameter is to be quenched in moderately agitated oil. Surface and center hardnesses must be at least 55 and 50 HRC, respectively. Which of the following alloys will satisfy these requirements: 1040, 5140, 4340, 4140, and 8640? Justify your choice(s). 11.D7 A cylindrical piece of steel 75 mm (3 in.) in diameter is to be austenitized and quenched such that a minimum hardness of 40 HRC is to be produced throughout the entire piece. Of the alloys 8660, 8640, 8630, and 8620, which will qualify if the quenching medium is (a) moderately agitated water and (b) moderately agitated oil? Justify your choice(s).

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450 • Chapter 11 / Applications and Processing of Metal Alloys

Precipitation Hardening 11.D14 Copper-rich copper–beryllium alloys are precipitation hardenable. After consulting the portion of the phase diagram shown in Figure 11.30, do the following:

Composition (at% Be) 0

5

10

15

20 Liquid

1000 +L

866°C Temperature (°C)

11.D8 A cylindrical piece of steel 38 mm 1112 in. 2 in diameter is to be austenitized and quenched such that a microstructure consisting of at least 80% martensite will be produced throughout the entire piece. Of the alloys 4340, 4140, 8640, 5140, and 1040, which will qualify if the quenching medium is (a) moderately agitated oil and (b) moderately agitated water? Justify your choice(s). 11.D9 A cylindrical piece of steel 90 mm 13 12 in. 2 in diameter is to be quenched in moderately agitated water. Surface and center hardnesses must be at least 55 and 40 HRC, respectively. Which of the following alloys will satisfy these requirements: 1040, 5140, 4340, 4140, 8620, 8630, 8640, and 8660? Justify your choices. 11.D10 A cylindrical piece of 4140 steel is to be austenitized and quenched in moderately agitated oil. If the microstructure is to consist of at least 50% martensite throughout the entire piece, what is the maximum allowable diameter? Justify your answer. 11.D11 A cylindrical piece of 8640 steel is to be austenitized and quenched in moderately agitated oil. If the hardness at the surface of the piece must be at least 49 HRC, what is the maximum allowable diameter? Justify your answer. 11.D12 Is it possible to temper an oil-quenched 4140 steel cylindrical shaft 100 mm (4 in.) in diameter so as to give a minimum tensile strength of 850 MPa (125,000 psi) and a minimum ductility of 21%EL? If so, specify a tempering temperature. If this is not possible, then explain why. 11.D13 Is it possible to temper an oil-quenched 4140 steel cylindrical shaft 12.5 mm (0.5 in.) in diameter so as to give a minimum yield strength of 1000 MPa (145,000 psi) and a minimum ductility of 16%EL? If so, specify a tempering temperature. If this is not possible, then explain why.

800



 +

1

~620°C 600

 +

2

400

0 (Cu)

1

2

3

4

Composition (wt% Be)

Figure 11.30 The copper-rich side of the copper–beryllium phase diagram. [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 2, T. B. Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]

(a) Specify the range of compositions over which these alloys may be precipitation hardened. (b) Briefly describe the heat-treatment procedures (in terms of temperatures) that would be used to precipitation harden an alloy having a composition of your choosing, yet lying within the range given for part (a). 11.D15 A solution heat-treated 2014 aluminum alloy is to be precipitation hardened to have a minimum tensile strength of 450 MPa (65,250 psi) and a ductility of at least 15%EL. Specify a practical precipitation heat treatment in terms of temperature and time that would give these mechanical characteristics. Justify your answer. 11.D16 Is it possible to produce a precipitationhardened 2014 aluminum alloy having a minimum tensile strength of 425 MPa (61,625 psi) and a ductility of at least 12%EL? If so, specify the precipitation heat treatment. If it is not possible, explain why.