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physics
modern physics

Materials Science and Engineering An Introduction 9th edition William D. Callister Jr., David G. Rethwisch - Solutions

The following tabulated data were gathered from a series of Charpy impact tests on a commercial low-carbon steel alloy.Temperature (°C) _______________ Impact Energy (J)50 ................................................. 7640 ................................................. 7630
What is the maximum carbon content possible for a plain carbon steel that must have an impact energy of at least 200 J at (50(C?
A fatigue test was conducted in which the mean stress was 70 MPa (10,000 psi), and the stress amplitude was 210 MPa (30,000 psi).(a) Compute the maximum and minimum stress levels.(b) Compute the stress ratio.(c) Compute the magnitude of the stress range?
A cylindrical bar of ductile cast iron is subjected to reversed and rotating-bending tests; test results (i.e., S-N behavior) are shown in Figure 8.20. If the bar diameter is 9.5 mm, determine the maximum cyclic load that may be applied to ensure that fatigue failure will not occur. Assume a factor
A cylindrical 4340 steel bar is subjected to reversed rotating-bending stress cycling, which yielded the test results presented in Figure 8.20. If the maximum applied load is 5,000 N, compute the minimum allowable bar diameter to ensure that fatigue failure will not occur. Assume a factor of safety
A cylindrical 2014-T6 aluminum alloy bar is subjected to compression-tension stress cycling along its axis; results of these tests are shown in Figure 8.20. If the bar diameter is 12.0 mm, calculate the maximum allowable load amplitude (in N) to ensure that fatigue failure will not occur at 107
Estimate the theoretical fracture strength of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped surface crack of length 0.5 mm (0.02 in.) and a tip radius of curvature of 5 × 10-3 mm (2 × 10-4 in.), when a stress of 1035 MPa (150,000 psi) is
A cylindrical rod of diameter 6.7 mm fabricated from a 70Cu-30Zn brass alloy is subjected to rotating-bending load cycling; test results (as S-N behavior) are shown in Figure 8.20. If the maximum and minimum loads are +120 N and -120 N, respectively, determine its fatigue life. Assume that the
A cylindrical rod of diameter 14.7 mm fabricated from a Ti-5Al-2.5Sn titanium alloy (Figure 8.20) is subjected to a repeated tension-compression load cycling along its axis. Compute the maximum and minimum loads that will be applied to yield a fatigue life of 1.0 × 106 cycles. Assume that data in
The fatigue data for a brass alloy are given as follows:Stress Amplitude (MPa) ______________ Cycles to Failure170 ..................................................... 3.7 × 104148 ..................................................... 1.0 × 105130
Suppose that the fatigue data for the brass alloy in Problem 8.22 were taken from bending-rotating tests and that a rod of this alloy is to be used for an automobile axle that rotates at an average rotational velocity of 1800 revolutions per minute. Give the maximum bending stress amplitude
The fatigue data for a steel alloy are given as follows:Stress Amplitude [MPa (ksi)] __________ Cycles to Failure470 (68.0) ................................... 104440 (63.4) ............................... 3 × 104390 (56.2) ..................................... 105350 (51.0)
Suppose that the fatigue data for the steel alloy in Problem 8.24 were taken for bending-rotating tests and that a rod of this alloy is to be used for an automobile axle that rotates at an average rotational velocity of 600 revolutions per minute. Give the maximum lifetimes of continuous driving
Three identical fatigue specimens (denoted A, B, and C) are fabricated from a nonferrous alloy. Each is subjected to one of the maximum-minimum stress cycles listed in the following table; the frequency is the same for all three tests.(a) Rank the fatigue lifetimes of these three specimens from the
If the specific surface energy for aluminum oxide is 0.90 J/m2, then using data in Table 12.5, compute the critical stress required for the propagation of an internal crack of length 0.40 mm?
The following creep data were taken on an aluminum alloy at 480°C (900°F) and a constant stress of 2.75 MPa (400 psi). Plot the data as strain versus time, then determine the steady-state or minimum creep rate. The initial and instantaneous strain is not included.
A specimen 975 mm (38.4 in.) long of an S-590 alloy (Figure 8.32) is to be exposed to a tensile stress of 300 MPa (43,500 psi) at 730°C (1350°F). Determine its elongation after 4.0 h. Assume that the total of both instantaneous and primary creep elongations is 2.5 mm (0.10 in.)?
For a cylindrical S-590 alloy specimen (Figure 8.31) originally 14.5 mm (0.57 in.) in diameter and 400 mm (15.7 in.) long, what tensile load is necessary to produce a total elongation of 52.7 mm (2.07 in.) after 1150 h at 650°C (1200°F)? Assume that the sum of instantaneous and primary creep
A cylindrical component 50 mm long constructed from an S-590 alloy (Figure 8.32) is to be exposed to a tensile load of 70,000 N. What minimum diameter is required for it to experience an elongation of no more than 8.2 mm after an exposure for 1,500 h at 650(C? Assume that the sum of instantaneous
A cylindrical specimen 13.2 mm in diameter of an S-590 alloy is to be exposed to a tensile load of 27,000 N. At approximately what temperature will the steady-state creep be 10-3 h-1?
If a component fabricated from an S-590 alloy (Figure 8.31) is to be exposed to a tensile stress of 100 MPa (14,500 psi) at 815°C (1500°F), estimate its rupture lifetime?
A cylindrical component constructed from an S-590 alloy (Figure 8.31) has a diameter of 14.5 mm (0.57 in.). Determine the maximum load that may be applied for it to survive 10 h at 925°C (1700°F)?
A cylindrical component constructed from an S-590 alloy (Figure 8.31) is to be exposed to a tensile load of 20,000 N. What minimum diameter is required for it to have a rupture lifetime of at least 100 h at 925(C?
AnMgO component must not fail when a tensile stress of 13.5 MPa (1960 psi) is applied. Determine the maximum allowable surface crack length if the surface energy of MgO is 1.0 J/m2. Data found in Table 12.5 may prove helpful?
Steady-state creep rate data are given in the following table for a nickel alloy at 538(C (811 K):(2 (h-1) _____________ ((MPa)10-7 ........................ 22.0106 .......................... 36.1Compute the stress at which the steady-state creep is 10-5 h(1(also at 538(C)?
Steady-state creep rate data are given in the following table for some alloy taken at 200°C (473 K):s (h-1) __________________ ( [MPa (psi)]2.5 × 10-3 .......................... 55 (8000)2.4 × 10-2 ........................ 69 (10,000)If it is known that the activation energy for creep is
Steady-state creep data taken for an iron at a stress level of 140 MPa (20,000 psi) are given here:s (h-1) ________________ T (K)6.6 × 10-4 ..................... 10908.8 × 10-2 ..................... 1200If it is known that the value of the stress exponent n for this alloy is 8.5, compute the
(a) Using Figure 8.31 compute the rupture lifetime for an S-590 alloy that is exposed to a tensile stress of 400 MPa at 815oC.(b) Compare this value to the one determined from the Larson-Miller plot of Figure 8.33, which is for this same S-590 alloy?
A specimen of a 4340 steel alloy with a plane strain fracture toughness of 54.8 MPa (50 ksi) is exposed to a stress of 1030 MPa (150,000 psi). Will this specimen experience fracture if the largest surface crack is 0.5 mm (0.02 in.) long? Why or why not? Assume that the parameter Y has a value of
An aircraft component is fabricated from an aluminum alloy that has a plane strain fracture toughness of 40 MPa (36.4 ksi). It has been determined that fracture results at a stress of 300 MPa (43,500 psi) when the maximum (or critical) internal crack length is 4.0 mm (0.16 in.). For this same
Suppose that a wing component on an aircraft is fabricated from an aluminum alloy that has a plane-strain fracture toughness of 26.0 MPa (23.7 ksi). It has been determined that fracture results at a stress of 112 MPa (16,240 psi) when the maximum internal crack length is 8.6 mm (0.34 in.). For this
A structural component is fabricated from an alloy that has a plane-strain fracture toughness of 62 Mα(m. It has been determined that this component fails at a stress of 250 MPa when the maximum length of a surface crack is 1.6 mm. What is the maximum allowable surface crack length (in mm) without
A large plate is fabricated from a steel alloy that has a plane strain fracture toughness of 82.4 MPa(m (75.0ksi(m). If the plate is exposed to a tensile stress of 345 MPa (50,000 psi) during service use, determine the minimum length of a surface crack that will lead to fracture. Assume a value of
A cylindrical metal bar is to be subjected to reversed and rotating-bending stress cycling. Fatigue failure is not to occur for at least 107 cycles when the maximum load is 250 N. Possible materials for this application are the seven alloys having S-N behaviors displayed in Figure 8.20. Rank these
An S-590 iron component (Figure 8.33) must have a creep rupture lifetime of at least 20 days at 650°C (923 K). Compute the maximum allowable stress level?
Consider an S-590 iron component (Figure 8.33) that is subjected to a stress of 55 MPa (8000 psi). At what temperature will the rupture lifetime be 200 h?
For an 18-8 Mo stainless steel (Figure 8.35), predict the time to rupture for a component that is subjected to a stress of 100 MPa (14,500 psi) at 600°C (873 K)?
Consider an 18-8 Mo stainless steel component (Figure 8.35) that is exposed to a temperature of 650°C (923 K). What is the maximum allowable stress level for a rupture lifetime of 1 year? 15 years?
Which type of fracture is associated with inter granular crack propagation? (A) Ductile (B) Brittle (C) Either ductile or brittle (D) Neither ductile nor brittle
Estimate the theoretical fracture strength (in MPa) of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped surface crack of length 0.25 mm that has a tip radius of curvature of 0.004 mm when a stress of 1060 MPa is applied.(A) 16,760 MPa(B) 8,380
A cylindrical 1045 steel bar (Figure 8.20) is subjected to repeated compression-tension stress cycling along its axis. If the load amplitude is 23,000 N, calculate the minimum allowable bar diameter (in mm) to ensure that fatigue failure will not occur. Assume a factor of safety of 2.0.(A) 19.4
Consider the sugar-water phase diagram of Figure 9.1.(a) How much sugar will dissolve in 1000 g of water at 80°C (176°F)?(b) If the saturated liquid solution in part (a) is cooled to 20°C (68°F), some of the sugar will precipitate out as a solid. What will be the composition of the saturated
Cite the phases that are present and the phase compositions for the following alloys:(a) 15 wt% Sn-85 wt% Pb at 100°C (212°F)(b) 25 wt% Pb-75 wt% Mg at 425°C (800°F)(c) 85 wt% Ag-15 wt% Cu at 800°C (1470°F)(d) 55 wt% Zn-45 wt% Cu at 600°C (1110°F)(e) 1.25 kg Sn and 14 kg Pb at 200°C
Is it possible to have a copper-silver alloy that, at equilibrium, consists of a β phase of composition 92 wt% Ag-8 wt% Cu and also a liquid phase of composition 76 wt% Ag-24 wt% Cu? If so, what will be the approximate temperature of the alloy? If this is not possible, explain why.
Is it possible to have a copper-silver alloy that, at equilibrium, consists of an α phase of composition 4 wt% Ag-96 wt% Cu and also a β phase of composition 95 wt% Ag-5 wt% Cu? If so, what will be the approximate temperature of the alloy? If this is not possible, explain why.
A 50 wt% Ni-50 wt% Cu alloy is slowly cooled from 1400°C (2550°F) to 1200°C (2190°F). (a) At what temperature does the first solid phase form? (b) What is the composition of this solid phase? (c) At what temperature does the liquid solidify? (d) What is the composition of this last remaining
A copper-zinc alloy of composition 75 wt% Zn-25 wt% Cu is slowly heated from room temperature. (a) At what temperature does the first liquid phase form? (b) What is the composition of this liquid phase? (c) At what temperature does complete melting of the alloy occur? (d) What is the composition of
16For an alloy of composition 52 wt% Zn-48 wt% Cu, cite the phases present and their mass fractions at the following temperatures: 1000°C, 800°C, 500°C, and 300°C.
A 2.0-kg specimen of an 85 wt% Pb-15 wt% Sn alloy is heated to 200°C (390°F); at this temperature it is entirely an α-phase solid solution (Figure 9.8). The alloy is to be melted to the extent that 50% of the specimen is liquid, the remainder being the α phase. This may be accomplished by
A magnesium-lead alloy of mass 7.5 kg consists of a solid α phase that has a composition just slightly below the solubility limit at 300°C (570°F).(a) What mass of lead is in the alloy?(b) If the alloy is heated to 400°C (750°F), how much more lead may be dissolved in the α phase without
At 100°C, what is the maximum solubility of the following: (a) Pb in Sn (b) Sn in Pb
Consider 2.5 kg of a 80 wt% Cu-20 wt% Ag copper-silver alloy at 800(C. How much copper must be added to this alloy to cause it to completely solidify 800(C?
A 65 wt% Ni-35 wt% Cu alloy is heated to a temperature within the α + liquid-phase region. If the composition of the α phase is 70 wt% Ni, determine: (a) The temperature of the alloy (b) The composition of the liquid phase (c) The mass fractions of both phases
A 40 wt% Pb-60 wt% Mg alloy is heated to a temperature within the α + liquid-phase region. If the mass fraction of each phase is 0.5, then estimate:(a) The temperature of the alloy(b) The compositions of the two phases in weight percent(c) The compositions of the two phases in atom percent
A copper-silver alloy is heated to 900(C and is found to consist of α and liquid phases. If the mass fraction of the liquid phase is 0.68 determine(a) The composition of both phases, in both weight percent and atom percent, and(b) The composition of the alloy, in both weight percent and atom
A hypothetical A-B alloy of composition 40 wt% B-60 wt% A at some temperature is found to consist of mass fractions of 0.66 and 0.34 for the α and β phases, respectively. If the composition of the α phase is 13 wt% B-87 wt% A, what is the composition of the β phase?
Is it possible to have a copper-silver alloy of composition 20 wt% Ag-80 wt% Cu that, at equilibrium, consists of α and liquid phases having mass fractions Wα = 0.80 and WL = 0.20? If so, what will be the approximate temperature of the alloy? If such an alloy is not possible, explain why.
For 5.7 kg of a magnesium-lead alloy of composition 50 wt% Pb-50 wt% Mg, is it possible, at equilibrium, to have α and Mg2Pb phases with respective masses of 5.13 and 0.57 kg? If so, what will be the approximate temperature of the alloy? If such an alloy is not possible, then explain why.
Determine the relative amounts (in terms of volume fractions) of the phases for the alloys and temperatures given in Problems 9.10a, b, and d. The following table gives the approximate densities of the various metals at the alloy temperatures:Metal............................Temperature
It is desirable to produce a copper-nickel alloy that has a minimum non-cold-worked tensile strength of 380 MPa (55,000 psi) and a ductility of at least 45%EL. Is such an alloy possible? If so, what must be its composition? If this is not possible, then explain why.
A 60 wt% Pb-40 wt% Mg alloy is rapidly quenched to room temperature from an elevated temperature in such a way that the high-temperature microstructure is preserved. This microstructure is found to consist of the α phase and Mg2Pb, having respective mass fractions of 0.42 and 0.58. Determine the
Is it possible to have a magnesium-lead alloy in which the mass fractions of primary α and total α are 0.60 and 0.85, respectively, at 460°C (860°F)? Why or why not?
For 2.8 kg of a lead-tin alloy, is it possible to have the masses of primary β and total β of 2.21 and 2.53 kg, respectively, at 180°C (355°F)? Why or why not?
For a lead-tin alloy of composition 80 wt% Sn-20 wt% Pb and at 180°C (355°F) do the following:(a) Determine the mass fractions of the α and β phases.(b) Determine the mass fractions of primary β and eutectic micro constituents.(c) Determine the mass fraction of eutectic β.
The microstructure of a copper-silver alloy at 775°C (1425°F) consists of primary α and eutectic structures. If the mass fractions of these two micro constituents are 0.73 and 0.27, respectively, determine the composition of the alloy.
What thermodynamic condition must be met for a state of equilibrium to exist?
A magnesium-lead alloy is cooled from 600(C to 450(C and is found to consist of primary Mg2Pb and eutectic micro constituents. If the mass fraction of the eutectic micro constituent is 0.28, determine the alloy composition.
Consider a hypothetical eutectic phase diagram for metals A and B that is similar to that for the lead-tin system (Figure 9.8). Assume that:(1) α and β phases exist at the A and B extremes of the phase diagram, respectively;(2) The eutectic composition is 36 wt% A-64 wt% B;(3) The composition of
For a 64 wt% Zn-36 wt% Cu alloy, make schematic sketches of the microstructure that would be observed for conditions of very slow cooling at the following temperatures: 900°C (1650°F), 820°C (1510°F), 750°C (1380°F), and 600°C (1100°F). Label all phases and indicate their approximate
For a 76 wt% Pb-24 wt% Mg alloy, make schematic sketches of the microstructure that would be observed for conditions of very slow cooling at the following temperatures: 575°C (1070°F), 500°C (930°F), 450°C (840°F), and 300°C (570°F). Label all phases and indicate their approximate
For a 52 wt% Zn-48 wt% Cu alloy, make schematic sketches of the microstructure that would be observed for conditions of very slow cooling at the following temperatures: 950°C (1740°F), 860°C (1580°F), 800°C (1470°F), and 600°C (1100°F). Label all phases and indicate their approximate
On the basis of the photomicrograph (i.e., the relative amounts of the micro constituents) for the lead-tin alloy shown in Figure 9.17 and the Pb-Sn phase diagram (Figure 9.8), estimate the composition of the alloy, and then compare this estimate with the composition given in the legend of Figure
The room-temperature tensile strengths of pure copper and pure silver are 209 and 125 MPa, respectively. (a) Make a schematic graph of the room-temperature tensile strength versus composition for all compositions between pure copper and pure silver. (Hint: You may want to consult Sections 9.10 and
Two intermetallic compounds, A3B and AB3, exist for elements A and B. If the compositions for A3B and AB3 are 91.0 wt% A-9.0 wt% B and 53.0 wt% A-47.0 wt% B, respectively, and element A is zirconium, identify element B.
An intermetallic compound is found in the aluminum-zirconium system that has a composition of 22.8 wt% Al-77.2 wt% Zr. Specify the formula for this compound.
An intermetallic compound is found in the gold-titanium system that has a composition of 58.0 wt% Au-42.0 wt% Ti. Specify the formula for this compound.
Consider a specimen of ice that is at -15°C and 10 atm pressure. Using Figure 9.2, the pressure-temperature phase diagram for H2O, determine the pressure to which the specimen must be raised or lowered to cause it (a) To melt and (b) To sublime.
Specify the liquids, solidus, and solves temperatures for the following alloys: (a) 30 wt% Ni-70 wt% Cu (b) 5 wt% Ag-95 wt% Cu (c) 20 wt% Zn-80 wt% Cu (d) 30 wt% Pb-70 wt% Mg (e) 3 wt% C-97 wt% Fe
Figure 9.36 is the tin-gold phase diagram, for which only single-phase regions are labeled. Specify temperature-composition points at which all eutectics, eutectoids, peritectics, and congruent phase transformations occur. Also, for each, write the reaction upon cooling.
Figure 9.37 is a portion of the copper-aluminum phase diagram for which only single-phase regions are labeled. Specify temperature-composition points at which all eutectics, eutectoids, peritectics, and congruent phase transformations occur. Also, for each, write the reaction upon cooling.
Construct the hypothetical phase diagram for metals A and B between room temperature (20°C) and 700°C, given the following information: 1. The melting temperature of metal A is 480°C. 2. The maximum solubility of B in A is 4 wt% B, which occurs at 420°C. 3. The solubility of B in A at room
Specify the number of degrees of freedom for the following alloys: (a) 20 wt% Ni-80 wt% Cu at 1300(C (b) 71.9 wt% Ag-28.1 wt% Cu at 779(C (c) 52.7 wt% Zn-47.3 wt% Cu at 525(C (d) 81 wt% Pb-19 wt% Mg at 545(C (e) 1 wt% C-99wt% Fe at 1000(C
What is the proeutectoid phase for an iron-carbon alloy in which the mass fractions of total ferrite and total cementite are 0.86 and 0.14, respectively? Why?
Consider 3.5 kg of austenite containing 0.95 wt% C and cooled to below 727°C (1341°F). (a) What is the proeutectoid phase? (b) How many kilograms each of total ferrite and cementite form? (c) How many kilograms each of pearlite and the proeutectoid phase form? (d) Schematically sketch and label
Consider 6.0 kg of austenite containing 0.45 wt% C and cooled to less than 727°C (1341°F). (a) What is the proeutectoid phase? (b) How many kilograms each of total ferrite and cementite form? (c) How many kilograms each of pearlite and the proeutectoid phase form? (d) Schematically sketch and
On the basis of the photomicrograph (i.e., the relative amounts of the micro constituents) for the iron-carbon alloy shown in Figure 9.30 and the Fe-Fe3C phase diagram (Figure 9.24), estimate the composition of the alloy, and then compare this estimate with the composition given in the figure
On the basis of the photomicrograph (i.e., the relative amounts of the micro constituents) for the iron-carbon alloy shown in Figure 9.33 and the Fe-Fe3C phase diagram (Figure 9.24), estimate the composition of the alloy, and then compare this estimate with the composition given in the figure
Compute the mass fractions of proeutectoid ferrite and pearlite that form in an iron-carbon alloy containing 0.35 wt% C.
For a series of Fe-Fe3C alloys that have compositions ranging between 0.022 and 0.76 wt% C that have been cooled slowly from 1000(C, plot the following:(a) Mass fractions of proeutectoid ferrite and pearlite versus carbon concentration at 725(C(b) Mass fractions of ferrite and cementite versus
The mass fractions of total ferrite and total cementite in an iron-carbon alloy are 0.91 and 0.09, respectively. Is this a hypo eutectoid or hypereutectoid alloy? Why?
The microstructure of an iron-carbon alloy consists of proeutectoid cementite and pearlite; the mass fractions of these micro constituents are 0.11 and 0.89, respectively. Determine the concentration of carbon in this alloy.
Given here are the solidus and liquids temperatures for the copper-gold system. Construct the phase diagram for this system and label each region.
Consider 1.5 kg of a 99.7 wt% Fe-0.3 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?
Compute the maximum mass fraction of proeutectoid cementite possible for a hypereutectoid iron-carbon alloy. Discuss.
Is it possible to have an iron-carbon alloy for which the mass fractions of total cementite and proeutectoid ferrite are 0.057 and 0.36, respectively? Why or why not?
Is it possible to have an iron-carbon alloy for which the mass fractions of total ferrite and pearlite are 0.860 and 0.969, respectively? Why or why not?
Compute the mass fraction of eutectoid cementite in an iron-carbon alloy that contains 1.00 wt% C.
Compute the mass fraction of eutectoid cementite in an iron-carbon alloy that contains 0.87 wt% C.
The mass fraction of eutectoid cementite in an iron-carbon alloy is 0.109. 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.
The mass fraction of eutectoid ferrite in an iron-carbon alloy is 0.71. 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.

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