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physics
thermodynamics
Materials Science and Engineering An Introduction 8th edition William D. Callister Jr., David G. Rethwisch - Solutions
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.
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?
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,
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 cold-worked yield strength in excess of 250 MPa (36,250 psi) and a ductility of at least 12%EL are desired. Furthermore, the
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
What is the magnitude of the maximum stress that exists at the tip of an internal crack having a radius of curvature of 2.5 × 10-4 mm (10-5 in.) and a crack length of 2.5 × 10-2 mm (10-3 in.) when a tensile stress of 170 MPa (25,000 psi) is applied?
A structural component in the form of a wide plate is to be fabricated from a steel alloy that has a plane strain fracture toughness of 77.0 MPa √m (70.1 ksi √in.) and a yield strength of 1400 MPa (205,000 psi). The flaw size resolution limit of the flaw detection apparatus is 4.0 mm (0.16
Following is tabulated data that were gathered from a series of Charpy impact tests on a ductile cast iron.(a) Plot the data as impact energy versus temperature. (b) Determine a ductile-to-brittle transition temperature as that temperature corresponding to the average of the maximum and minimum
Following is tabulated data that were gathered from a series of Charpy impact tests on a tempered 4140 steel alloy.(a) Plot the data as impact energy versus temperature. (b) Determine a ductile-to-brittle transition temperature as that temperature corresponding to the average of the maximum and
A fatigue test was conducted in which the mean stress was 50 MPa (7250 psi) and the stress amplitude was 225 MPa (32,625 psi). (a) Compute the maximum and minimum stress levels. (b) Compute the stress ratio. (c) Compute the magnitude of the stress range.
A cylindrical 1045 steel bar (Figure 8.34) is subjected to repeated compression-tension stress cycling along its axis. If the load amplitude is 22,000 N (4950 lbf), compute the minimum allowable bar diameter to ensure that fatigue failure will not occur. Assume a factor of safety of 2.0.
An 8.0 mm (0.31 in.) diameter cylindrical rod fabricated from a red brass alloy (Figure 8.34) is subjected to reversed tension-compression load cycling along its axis. If the maximum tensile and compressive loads are + 7500 N (1700 lbf) and - 7500 N (- 1700 lbf), respectively, determine its fatigue
A 12.5 mm (0.50 in.) diameter cylindrical rod fabricated from a 2014-T6 alloy (Figure 8.34) 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 × 107 cycles. Assume that the stress
The fatigue data for a brass alloy are given as follows:(a) Make an S-N plot (stress amplitude versus logarithm cycles to failure) using these data. (b) Determine the fatigue strength at 5 × 105 cycles. (c) Determine the fatigue life for 200 MPa.
Suppose that the fatigue data for the brass alloy in Problem 8.18 were taken from torsional tests, and that a shaft of this alloy is to be used for a coupling that is attached to an electric motor operating at 1500 rpm. Give the maximum torsional stress amplitude possible for each of the following
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 0.25 mm (0.01 in.) and having a tip radius of curvature of 1.2 × 10-3 mm (4.7 × 10-5 in.) when a stress of 1200 MPa (174,000
The fatigue data for a ductile cast iron are given as follows:(a) Make an S-N plot (stress amplitude versus logarithm cycles to failure) using these data. (b) What is the fatigue limit for this alloy? (c) Determine fatigue lifetimes at stress amplitudes of 230 MPa (33,500 psi) and 175 MPa (25,000
Suppose that the fatigue data for the cast iron in Problem 8.20 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 750 revolutions per minute. Give maximum lifetimes of continuous driving that
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 below; the frequency is the same for all three tests.Rank the fatigue lifetimes of these three specimens from the longest to the
Cite five factors that may lead to scatter in fatigue life data.
Briefly explain the difference between fatigue striations and beach marks both in terms of (a) size and (b) origin.
List four measures that may be taken to increase the resistance to fatigue of a metal alloy.
Give the approximate temperature at which creep deformation becomes an important consideration for each of the following metals: nickel, copper, iron, tungsten, lead, and aluminum.
The following creep data were taken on an aluminum alloy at 400°C (750°F) and a constant stress of 25 MPa (3660 psi). Plot the data as strain versus time, then determine the steady-state or minimum creep rate. Note: The initial and instantaneous strain is not included.
A specimen 750 mm (30 in.) long of an S-590 alloy is to be exposed to a tensile stress of 80 MPa (11,600 psi) at 815°C (1500°F). Determine its elongation after 5000 h. Assume that the total of both instantaneous and primary creep elongations is 1.5 mm (0.06 in.).
For a cylindrical S-590 alloy specimen (Figure 8.31) originally 10 mm (0.40 in.) in diameter and 500 mm (20 in.) long, what tensile load is necessary to produce a total elongation of 145 mm (5.7 in.) after 2,000 h at 730°C (1350°F)? Assume that the sum of instantaneous and primary creep
If the specific surface energy for soda-lime glass is 0.30 J/m2, using data contained in Table 12.5, compute the critical stress required for the propagation of a surface crack of length 0.05 mm.
If a component fabricated from an S-590 alloy (Figure 8.30) is to be exposed to a tensile stress of 300 MPa (43,500 psi) at 650°C (1200°F), estimate its rupture lifetime.
A cylindrical component constructed from an S-590 alloy (Figure 8.30) has a diameter of 12 mm (0.50 in.). Determine the maximum load that may be applied for it to survive 500 h at 925°C (1700°F).
From Equation 8.19, if the logarithm of εÝs is plotted versus the logarithm of σ, then a straight line should result, the slope of which is the stress exponent n. Using Figure 8.31, determine the value of n for the S-590 alloy at 925°C, and for the initial (i.e., lower temperature) straight
(a) Estimate the activation energy for creep (i.e., Qc in Equation 8.20) for the S-590 alloy having the steady-state creep behavior shown in Figure 8.31. Use data taken at a stress level of 300 MPa (43,500 psi) and temperatures of 650°C and 730°C. Assume that the stress exponent n is independent
Steady-state creep rate data are given below for nickel at 1000°C (1273 K):If it is known that the activation energy for creep is 272,000 J/mol, compute the steady-state creep rate at a temperature of 850°C (1123 K) and a stress level of 25 MPa (3625 psi).
Steady-state creep data taken for a stainless steel at a stress level of 70 MPa (10,000 psi) are given as follows:If it is known that the value of the stress exponent n for this alloy is 7.0, compute the steady-state creep rate at 1250 K and a stress level of 50 MPa (7250 psi).
Cite three metallurgical/processing techniques that are employed to enhance the creep resistance of metal alloys.
A polystyrene component must not fail when a tensile stress of 1.25 MPa (180 psi) is applied. Determine the maximum allowable surface crack length if the surface energy of polystyrene is 0.50 J/m2 (2.86 × 10-3 in.-lbf/in.2). Assume a modulus of elasticity of 3.0 GPa (0.435 × 106 psi).
A specimen of a 4340 steel alloy having a plane strain fracture toughness of 45 MPa √m (41 ksi √in.) is exposed to a stress of 1000 MPa (145,000 psi). Will this specimen experience fracture if it is known that the largest surface crack is 0.75 mm (0.03 in.) long? Why or why not? Assume that the
Some aircraft component is fabricated from an aluminum alloy that has a plane strain fracture toughness of 35 MPa √m (31.9 ksi √in.). It has been determined that fracture results at a stress of 250 MPa (36,250 psi) when the maximum (or critical) internal crack length is 2.0 mm (0.08 in.). For
Suppose that a wing component on an aircraft is fabricated from an aluminum alloy that has a plane strain fracture toughness of 40 MPa √m (36.4 ksi √in.). It has been determined that fracture results at a stress of 365 MPa (53,000 psi) when the maximum internal crack length is 2.5 mm (0.10
A large plate is fabricated from a steel alloy that has a plane strain fracture toughness of 55 MPa √m (50 ksi √in.). If, during service use, the plate is exposed to a tensile stress of 200 MPa (29,000 psi), determine the minimum length of a surface crack that will lead to fracture. Assume a
Calculate the maximum internal crack length allowable for a 7075-T651 aluminum alloy (Table 8.1) component that is loaded to a stress one half of its yield strength. Assume that the value of Y is 1.35.
(a) For the thin-walled spherical tank discussed in Design Example 8.1, on the basis of critical crack size criterion [as addressed in part (a)], rank the following polymers from longest to shortest critical crack length: nylon 6,6 (50% relative humidity), polycarbonate, poly(ethylene
An S-590 alloy component (Figure 8.32) must have a creep rupture lifetime of at least 100 days at 500°C (773 K). Compute the maximum allowable stress level.
Consider an S-590 alloy component (Figure 8.32) that is subjected to a stress of 200 MPa (29,000 psi). At what temperature will the rupture lifetime be 500 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 80 MPa (11,600 psi) at 700°C (973 K).
Consider an 18-8 Mo stainless steel component (Figure 8.35) that is exposed to a temperature of 500°C (773 K). What is the maximum allowable stress level for a rupture lifetime of 5 years? 20 years?
Consider the sugar-water phase diagram of Figure 9.1.(a) How much sugar will dissolve in 1500 g water at 90°C (194°F)?
Is it possible to have a copper-zinc alloy that, at equilibrium, consists of an ε phase of composition 80 wt% Zn-20 wt% Cu, and also a liquid phase of composition 95 wt% Zn-5 wt% Cu? If so, what will be the approximate temperature of the alloy? If this is not possible, explain why.
A copper-nickel alloy of composition 70 wt% Ni-30 wt% Cu is slowly heated from a temperature of 1300°C (2370°F). (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
A 50 wt% Pb-50 wt% Mg alloy is slowly cooled from 700°C (1290°F) to 400°C (750°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 liquid
For an alloy of composition 74 wt% Zn-26 wt% Cu, cite the phases present and their compositions at the following temperatures: 850°C, 750°C, 680°C, 600°C, and 500°C.
Determine the relative amounts (in terms of mass fractions) of the phases for the alloys and temperatures given in Problem 9.8. Problem 9.8. (a) 90 wt% Zn-10 wt% Cu at 400°C (750°F) (b) 75 wt% Sn-25 wt% Pb at 175°C (345°F) (c) 55 wt% Ag-45 wt% Cu at 900°C (1650°F) (d) 30 wt% Pb-70 wt% Mg at
A 1.5-kg specimen of a 90 wt% Pb-10 wt% Sn alloy is heated to 250°C (480°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 either by
A magnesium-lead alloy of mass 5.5 kg consists of a solid α phase that has a composition that is just slightly below the solubility limit at 200°C (390°F). (a) What mass of lead is in the alloy? (b) If the alloy is heated to 350°C (660°F), how much more lead may be dissolved in the α phase
A 90 wt% Ag-10 wt% Cu alloy is heated to a temperature within the β + liquid phase region. If the composition of the liquid phase is 85 wt% Ag, determine: (a) The temperature of the alloy (b) The composition of the β phase (c) The mass fractions of both phases
A 30 wt% Sn-70 wt% Pb alloy is heated to a temperature within the α + liquid phase region. If the mass fraction of each phase is 0.5, estimate: (a) The temperature of the alloy (b) The compositions of the two phases
For alloys of two hypothetical metals A and B, there exist an α, A-rich phase and a β, B-rich phase. From the mass fractions of both phases for two different alloys provided in the table below, (which are at the same temperature), determine the composition of the phase
At 500°C (930°F), what is the maximum solubility (a) of Cu in Ag? (b) Of Ag in Cu?
A hypothetical A-B alloy of composition 55 wt% B-45 wt% A at some temperature is found to consist of mass fractions of 0.5 for both α and β phases. If the composition of the β phase is 90 wt% B-10 wt% A, what is the composition of the α phase?
Is it possible to have a copper-silver alloy of composition 50 wt% Ag-50 wt% Cu, which, at equilibrium, consists of α and β phases having mass fractions Wα = 0.60 and Wβ = 0.40? If so, what will be the approximate temperature of the alloy? If such an alloy is not possible, explain why.
For 11.20 kg of a magnesium-lead alloy of composition 30 wt% Pb-70 wt% Mg, is it possible, at equilibrium, to have α and Mg2Pb phases having respective masses of 7.39 kg and 3.81 kg? If so, what will be the approximate temperature of the alloy? If such an alloy is not possible, explain why.
Derive Equations 9.6a and 9.7a, which may be used to convert mass fraction to volume fraction, and vice versa.
Determine the relative amounts (in terms of volume fractions) of the phases for the alloys and temperatures given in Problem 9.8a, b, and c. Below are given the approximate densities of the various metals at the alloy temperatures:Problem 9.8 (a) 90 wt% Zn-10 wt% Cu at 400°C (750°F) (b) 75
(a) Briefly describe the phenomenon of coring and why it occurs. (b) Cite one undesirable consequence of coring.
It is desirable to produce a copper-nickel alloy that has a minimum non cold-worked tensile strength of 350 MPa (50,750 psi) and a ductility of at least 48%EL. Is such an alloy possible? If so, what must be its composition? If this is not possible, then explain why.
A 45 wt% Pb-55 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 0.65 and 0.35. Determine the
Briefly explain why, upon solidification, an alloy of eutectic composition forms a microstructure consisting of alternating layers of the two solid phases.
What is the difference between a phase and a micro constituent?
Cite three variables that determine the microstructure of an alloy.
Is it possible to have a copper-silver alloy in which the mass fractions of primary β and total β are 0.68 and 0.925, respectively, at 775°C (1425°F)? Why or why not?
For 6.70 kg of a magnesium-lead alloy, is it possible to have the masses of primary α and total α of 4.23 kg and 6.00 kg, respectively, at 460°C (860°F)? Why or why not?
For a copper-silver alloy of composition 25 wt% Ag-75 wt% Cu and at 775°C (1425°F) do the following: (a) Determine the mass fractions of α and β phases. (b) Determine the mass fractions of primary α and eutectic micro constituents. (c) Determine the mass fraction of eutectic α.
The microstructure of a lead-tin alloy at 180°C (355°F) consists of primary β and eutectic structures. If the mass fractions of these two micro constituents are 0.57 and 0.43, respectively, determine the composition of the alloy.
Consider the hypothetical eutectic phase diagram for metals A and B, which 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 extremities of the phase diagram, respectively; (2) the eutectic composition is 47 wt% B-53 wt% A; and (3) the
For an 85 wt% Pb-15 wt% Mg alloy, make schematic sketches of the microstructure that would be observed for conditions of very slow cooling at the following temperatures: 600°C (1110°F), 500°C (930°F), 270°C (520°F), and 200°C (390°F). Label all phases and indicate their approximate
For a 68 wt% Zn-32 wt% Cu alloy, make schematic sketches of the microstructure that would be observed for conditions of very slow cooling at the following temperatures: 1000°C (1830°F), 760°C (1400°F), 600°C (1110°F), and 400°C (750°F). Label all phases and indicate their approximate
For a 30 wt% Zn-70 wt% Cu alloy, make schematic sketches of the microstructure that would be observed for conditions of very slow cooling at the following temperatures: 1100°C (2010°F), 950°C (1740°F), 900°C (1650°F), and 700°C (1290°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 figure legend.
The room-temperature tensile strengths of pure lead and pure tin are 16.8 MPa and 14.5 MPa, respectively. (a) Make a schematic graph of the room-temperature tensile strength versus composition for all compositions between pure lead and pure tin. (b) On this same graph schematically plot tensile
Two intermetallic compounds, AB and AB2, exist for elements A and B. If the compositions for AB and AB2 are 34.3 wt% A-65.7 wt% B and 20.7 wt% A-79.3 wt% B, respectively, and element A is potassium, identify element B.
What is the principal difference between congruent and incongruent phase transformations?
The aluminum-neodymium 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 titanium-copper phase diagram for which only single-phase regions are labeled. Specify all temperature-composition points at which 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 temperatures of 600°C and 1000°C given the following information: ● The melting temperature of metal A is 940°C. ● The solubility of B in A is negligible at all temperatures. ● The melting temperature of metal B is
In Figure 9.38 is shown the pressure-temperature phase diagram for H2O. Apply the Gibbs phase rule at points A, B, and C; that is, specify the number of degrees of freedom at each of the points-that is, the number of externally controllable variables that need be specified to completely define the
Compute the mass fractions of α ferrite and cementite in pearlite.
(a) What is the distinction between hypoeutectoid and hypereutectoid steels? (b) In a hypoeutectoid steel, both eutectoid and proeutectoid ferrite exist. Explain the difference between them. What will be the carbon concentration in each?
What is the carbon concentration of an iron-carbon alloy for which the fraction of total ferrite is 0.94?
What is the proeutectoid phase for an iron-carbon alloy in which the mass fractions of total ferrite and total cementite are 0.92 and 0.08, respectively? Why?
Consider a specimen of ice that is at 210°C and 1 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.
Consider 1.0 kg of austenite containing 1.15 wt% C, 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 the
Consider 2.5 kg of austenite containing 0.65 wt% C, 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 the
Compute the mass fractions of proeutectoid ferrite and pearlite that form in an iron-carbon alloy containing 0.25 wt% C.
The microstructure of an iron-carbon alloy consists of proeutectoid ferrite and pearlite; the mass fractions of these two micro constituents are 0.286 and 0.714, respectively. Determine the concentration of carbon in this alloy.
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?
The microstructure of an iron-carbon alloy consists of proeutectoid ferrite and pearlite; the mass fractions of these micro constituents are 0.20 and 0.80, respectively. Determine the concentration of carbon in this alloy.
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?
Compute the maximum mass fraction of proeutectoid cementite possible for a hypereutectoid iron-carbon alloy.
Is it possible to have an iron-carbon alloy for which the mass fractions of total ferrite and proeutectoid cementite are 0.846 and 0.049, respectively? Why or why not?
Is it possible to have an iron-carbon alloy for which the mass fractions of total cementite and pearlite are 0.039 and 0.417, respectively? Why or why not?
At a pressure of 0.01 atm, determine (a) The melting temperature for ice, and (b) The boiling temperature for water.
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