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Essentials of Materials Science and Engineering 3rd edition Donald R. Askeland, Wendelin J. Wright - Solutions

The following data were collected from a 12-mm-diameter test specimen of magnesium (l0 = 30.00 mm):After fracture, the total length was 32.61 mm, and the diameter was 11.74 mm. Plot the engineering stress-strain curve and calculate (a) The 0.2% offset yield strength; (b) The tensile strength; (c)
The following data were collected from a test specimen of cold-rolled and annealed brass. The specimen had an initial gage length l0 of 35 mm and an initial cross sectional area A0 of 10.5 mm2?(a) Plot the engineering stress-strain curve and the true stress-strain curve. Since the instantaneous
Consider the tensile stress-strain diagrams in Figure 6-28 labeled 1 and 2 and answer the following questions. These diagrams are typical of metals. Consider each part as a separate question that has no relationship to previous parts of the question?Figure 6 - 28 Stress - strain curves for Problem
A bar of Al2O3 that is 0.25 in. thick, 0.5 in. wide, and 9 in. long is tested in a three-point bending apparatus, with the supports located 6 in. apart. The deflection of the center of the bar is measured as a function of the applied load. The data are shown below. Determine the flexural strength
A three-point bend test is performed on a block of ZrO2 that is 8 in. long, 0.50 in. wide, and 0.25 in. thick and is resting on two supports 4 in. apart. W hen a force of 400 lb is applied, the specimen deflects 0.037 in. and breaks. Calculate (a) The flexural strength; and (b) The flexural
A three-point bend test is performed on a block of silicon carbide that is 10 cm long, 1.5 cm wide, and 0.6 cm thick and is resting on two supports 7.5 cm apart. The sample breaks when a deflection of 0.09 mm is recorded. The flexural modulus for silicon carbide is 480 GPa. Assume that no plastic
A thermosetting polymer containing glass beads is required to deflect 0.5 mm when a force of 500 N is applied. The polymer part is 2 cm wide, 0.5 cm thick, and 10 cm long. If the flexural modulus is 6.9 GPa, determine the minimum distance between the supports. Will the polymer fracture if its
A force of 100,000 N is applied to an iron bar with a cross-sectional area of 10 mm × 20 mm and having a yield strength of 400 MPa and a tensile strength of 480 MPa. Determine (a) Whether the bar will plastically deform; and (b) Whether the bar will experience necking.
The flexural modulus of alumina is 45 × 106 psi and its flexural strength is 46,000 psi. A bar of alumina 0.3 in. thick, 1.0 in. wide, and 10 in. long is placed on supports 7 in. apart. Determine the amount of deflection at the moment the bar breaks, assuming that no plastic deformation occurs?
When a 3000-kg load is applied to a 10-mm-diameter ball in a Brinell test of a steel, an indentation of 3.1 mm is produced. Estimate the tensile strength of the steel?
The elastic modulus of a metallic glass is determined to be 95 GPa using nanoindentation testing with a diamond Berkovich tip. The Poisson's ratio of the metallic glass is 0.36. The unloading stiffness as determined from the load displacement data is 5.4 × 105 N/m. The maximum load is 120 mN. What
The following data were obtained from a series of Charpy impact tests performed on four steels, each having a different manganese content. Plot the data and determine(a) The transition temperature of each (defined by the mean of the absorbed energies in the ductile and brittle regions); and(b) The
Plot the transition temperature versus manganese content using the data in the previous problem and discuss the effect of manganese on the toughness of steel. What is the minimum manganese allowed in the steel if a part is to be used at 0ºC?
The following data were obtained from a series of Charpy impact tests performed on four ductile cast irons, each having a different silicon content. Plot the data and determine(a) The transition temperature of each (defined by the mean of the absorbed energies in the ductile and brittle regions);
FCC metals are often recommended for use at low temperatures, particularly when any sudden loading of the part is expected. Explain?
A steel part can be made by powder metallurgy (compacting iron powder particles and sintering to produce a solid) or by machining from a solid steel block. Which part is expected to have the higher toughness? Explain.
A number of aluminum-silicon alloys have a structure that includes sharp-edged plates of brittle silicon in the softer, more ductile aluminum matrix. Would you expect these alloys to be notch-sensitive in an impact test? Would you expect these alloys to have good toughness? Explain your answers.
A load versus displacement diagram is show n in Figure 6-29 for a metallic glass. A metallic glass is a non-crystalline (amorphous) metal. The sample was tested in compression. Therefore, even through the load and displacement values are plotted as positive, the sample length w as shortened during
A force of 20,000 N will cause a 1 cm × 1 cm bar of magnesium to stretch from 10 cm to 10.045 cm. Calculate the modulus of elasticity, both in GPa and psi?
A polymer bar's dimensions are 1 in. × 2 in. × 15 in. The polymer has a modulus of elasticity of 600,000 psi. What force is required to stretch the bar elastically from 15 in. to 15.25 in.?
An aluminum plate 0.5 cm thick is to withstand a force of 50,000 N with no permanent deformation. If the aluminum has a yield strength of 125 MPa, what is the minimum width of the plate?
A steel cable 1.25 in. in diameter and 50-ft long is to lift a 20-ton load. What is the length of the cable during lifting? The modulus of elasticity of the steel is 30 × 106 psi?
(a) Carbon nanotubes are one of the stiffest and strongest materials known to scientists and engineers. Carbon nanotubes have an elastic modulus of 1.1 TPa (1 TPa = 1012 Pa). If a carbon nanotube has a diameter of 15 nm, determine the engineering stress sustained by the nanotube when subjected to a
Derive the expression ε = ln(1 + e), where ε is the true strain and e is the engineering strain. This expression is not valid after the onset of necking?
Alumina (Al2O3) is a brittle ceramic with low toughness. Suppose that fibers of silicon carbide (SiC), another brittle ceramic with low toughness, could be embedded within thes alumina. Would doing this affect the toughness of the ceramic matrix composite? Explain.
A cyclical load of 1500 lb is to be exerted at the end of a 10-in.-long aluminum beam (Figure 7-17). The bar must survive for at least 106 cycles. What is the minimum diameter of the bar?
A cylindrical acetal polymer bar 20-cm-long and 1.5 cm in diameter is subjected to a vibrational load at a frequency of 500 vibrations per minute, with a load of 50 N. How many hours will the part survive before breaking?
Suppose that we would like a part produced from the acetal polymer shown in Figure 7-27 to survive for one million cycles under conditions that provide for equal compressive and tensile stresses. What is the fatigue strength, or maximum stress amplitude, required? What are the maximum stress, the
A fatigue test is conducted on an aluminum alloy at a frequency of 100 Hz. If the number of cycles is 107, how much time will this fatigue test take? How much time would it take if this test were conducted for 108 cycles?
The manufacturer of a product that is subjected to repetitive cycles has specified that the product should be removed from service when any crack reaches 15% of the critical crack length required to cause fracture.Consider a crack that is initially 0.02 mm long in a material with a fracture
A material containing cracks of initial length 0.010 mm is subjected to alternating tensile stresses of 25 and 125 MPa for 350,000 cycles. The material is then subjected to alternating tensile and compressive stresses of 250 MPa. How many of the larger stress amplitude cycles can be sustained
A ceramic matrix composite contains internal flaws as large as 0.001 cm in length. The plane strain fracture toughness of the composite is 45 MPa(m, and the tensile strength is 550 MPa. Will the stress cause the composite to fail before the tensile strength is reached? Assume that f = 1.
An aluminum alloy that has a plane strain fracture toughness of 25,000 psi(in. fails when a stress of 42,000 psi is applied. Observation of the fracture surface indicates that fracture began at the surface of the part. Estimate the size of the flaw that initiated fracture. Assume that f = 1.1?
A ceramic part for a jet engine has a yield strength of 75,000 psi and a plane strain fracture toughness of 5,000 psi(in. To be sure that the part does not fail, we plan to ensure that the maximum applied stress is only one third of the yield strength. We use a nondestructive test that will detect
The manufacturer of a product that is subjected to repetitive cycles has specified that the product should be removed from service when any crack reaches 15% of the critical crack length required to cause fracture.Consider a crack that is initially 0.02 mm long in a material with a fracture
Assume that the critical stress intensity factor or fracture toughness for partially stabilized zirconia is 10 MPa(m. If there is a plate of this ceramic with a sharp edge notch 100 μm deep and subjected to a stress of 300 MPa, will this plate be able to withstand this stress?
A cylindrical tool steel specimen that is 6 in. long and 0.25 in. in diameter rotates as a cantilever beam and is to be designed so that failure never occurs. Assuming that the maximum tensile and compressive stresses are equal, determine the maximum load that can be applied to the end of the beam?
A 2-cm-diameter, 20-cm-long bar of an acetal polymer (Figure 7-27) is loaded on one end and is expected to survive one million cycles of loading, with equal maximum tensile and compressive stresses, during its lifetime. What is the maximum permissible load that can be applied?
Consider the tensile stress-strain diagrams in Figure 8 - 20 labeled 1 and 2 and answer the following questions. These curves are typical of metals. Consider each part as a separate question that has no relationship to previous parts of the question.Figure 8 - 20 Stress - strain curves (for Problem
A 3105 aluminum bar is reduced from a 1 in. diameter, to a 0.8-in. diameter, to a 0.6 in. diameter, to a final 0.4 in. diameter. Determine the % CW and the properties after each step of the process. Calculate the total percent cold work. Note 3105 designates a particular of aluminum alloy?
We want a Cu-30% Zn brass plate originally 1.2 in. thick to have a yield strength greater than 50,000 psi and a % elongation of at least 10%. What range of final thicknesses must be obtained?
A 3105 aluminum plate previously cold worked 20% is 2 in. thick. It is then cold worked further to 1.3 in. Calculate the total percent cold work and determine the final properties of the plate. Note: 3105 designates a particular aluminum alloy?
We want to draw a 0.3-in.-diameter copper wire having a yield strength of 20,000 psi into 0.25-in.-diameter wire.(a) Find the draw force, assuming no friction;(b) Will the drawn wire break during the drawing process? Show why.
A 3105 aluminum wire is to be drawn to give a 1-mm-diameter wire having a yield strength of 20,000 psi. 3105 designates a particular aluminum alloy. (a) Find the original diameter of the wire; (b) Calculate the draw force required; and (c) Determine whether the as-drawn wire will break during the
Samples of cartridge brass (Cu-30% Zn) were cold-rolled and then annealed for one hour. The data shown in the table below were obtained.(a) Plot the yield strength and grain size as a function of annealing temperature on the same graph, Use two vertical axes, one for hardness and one for grain
The following data were obtained when a cold-worked metal was annealed.(a) Estimate the recovery, recrystallization, and grain growth temperatures;(b) Recommend a suitable temperature for a stress-relief heat treatment;(c) Recommend a suitable temperature for a hot-working process; and(d) Estimate
A plot of true stress versus true strain for a metal. For total imposed strains of Îµ = 0.1, 0.2, 0.3 and 0.4, determine the elastic and plastic components of the strain. The modulus of elasticity of the metal is 100 G Pa.Figure 8 - 22 true stress versus true strain curve for a metal
The following data were obtained when a cold-worked metal was annealed.(a) Estimate the recovery, recrystallization, and grain growth temperatures;(b) Recommend a suitable temperature for obtaining a high-strength, high-electrical- conductivity wire;(c) Recommend a suitable temperature for a hot
Consider the tensile stress-strain diagrams labeled 1 and 2 in Figure 8 - 20 and answer the following questions. These diagrams are typical of metals. Consider each part as a separate question that has no relationship to previous parts of the question.Figure 8 - 20 Stress-strain curves (for Problem
Using the data in Table 8 - 3, plot the recrystallization temperature versus the melting temperature of each metal, using absolute temperatures (Kelvin). Measure the slope and compare with the expected relationship between these two temperature. Is our approximation a good one?
We wish to produce a 0.3 in. thick plate of 3105 aluminum having a tensile strength of at least 25,000 psi and a % elongation of at least 5%. The original thickness of the plate is 3 in. The maximum cold work in each step is 80%. Describe the cold working and annealing steps required to make this
We wish to produce a 0.2-in.-diameter wire of copper having a minimum yield strength of 60,000 psi and a minimum % elongation of 5%. The original diameter of the rod is 2 in. and the maximum cold work in each step is 80%. Describe the cold working and annealing steps required to make this product.
A 0.505-in.-diameter metal bar with a 2-in. gage length I0 is subjected to a tensile test. The following measurement are made in the plastic region:Determine the strain-hardening exponent for the metal. Is the metal most likely to be FCC, BCC, or HCP? Explain?
A 1.5-cm-diameter metal bar with a 3-cm gage length I0 is subjected to a tensile test. The following measurements are made:Determine the strain-hardening coefficient for the metal. Is the metal most likely to be FCC, BCC, or HCP? Explain.
A true stress-true strain curve is shown is Figure 8 - 22.Determine the strain-hardening exponent for the metal?
Shows a plot of the natural log of the true stress versus the natural log of the true strain for a Cu-30% Zn sample tested in tension. Only the plastic portion of the stress-strain curve is shown. Determine the strength coefficient K and the work-hardening exponent n?In (True strain) Figure 8 - 24
A Cu-30% Zn alloy tensile bar has a strain-hardening coefficient of 0.50. The bar, which has an initial diameter of 1 cm and an initial gage length of 3 cm, fails at an engineering stress of 120 MPa. At the moment of fracture, the gage length is 3.5 cm and the diameter is 0.926 cm. No necking
Why is undercooling required for solidification? Derive an equation showing the total free energy change as a function of undercooling when the nucleating solid has the critical nucleus radius r*?
Find the mold constant B and exponent n in Chvorinov's rule using the following data and a log-log plot.
A 2-in. cube solidifies in 4.6 min. Assume that n = 2. Calculate(a) The mold constant in Chvorinov's rule; and(b) The solidification time for a 0.5 in. ( in. ( 6 in. bar cast under the same conditions.
A 5-cm-diameter sphere solidifies in 1050 s. Calculate the solidification time for a 0.3 cm ( 10 cm ( 20 cm plate cast under the same conditions. Assume that n = 2?
Find the constants B and n in Chvorinov's rule by plotting the following data on a log-log plot:Casting dimensions (in.)Solicitation time (min)0.5 ( 8 ( 12......................3.482 ( 8 ( 10.........................15.782.5 cube............................10.171 ( 4 (
A 3-in.-diameter casting was produced. The times required for the so lid-liquid interface to reach different distances beneath the casting surface were measured and are shown in the following table:Distance from Surface (in.) Time
An aluminum alloy plate with dimensions 20 cm × 10 cm × 2 cm needs to be cast with a secondary dendrite arm spacing of 10-2 cm. (See Figure 9-6.) What mold constant B is required (assume n = 2)?
Find the constants k and m relating the secondary dendrite arm spacing to the local solidification time by plotting the following data on a log-log plot: Solidification Time (s) SDAS
A cooling curve is shown in Figure 9-20. Determine(a) The pouring temperature; (b) The solidification temperature; (c) The superheat; (d) The cooling rate, just before solidification begins; (e) The total solidification time; (f) The loc al solidification time; and (g) The probable identity of the
A cooling curve is shown in Figure 9 - 21. Determine (a) The pouring temperature; (b) The solidification temperature; (c) The superheat; (d) The cooling rate, just before solidification begins; (e) The total solidification time; (f) The loc al solidification time; and (g) The probable
Figure 9-22 shows the cooling curves obtained from several locations within a cylindrical aluminum casting. Determine the local solidification times and the SDAS at each location, then plot the tensile strength versus distance from the casting surface. Would you recommend that the casting be
Suppose that liquid nickel is undercooled until homogeneous nucleation occurs. Calculate(a) The critical radius of the nucleus required; and(b) The number of nickel atoms in the nucleus.Assume that the lattice parameter of the solid FCC nickel is 0.356 nm.
Calculate the volume, diameter, and height of the cylindrical riser required to prevent shrinkage in a 1 in. ( 6 in. casting if the H/D of the riser is 1.0?
Calculate the volume, diameter, and height of the cylindrical riser required to prevent shrinkage in a 4 in. × 10 in. × 20 in. casting if the H/D of the riser is 1.5?
Figure 9-23 shows a cylindrical riser attached to a casting. Compare the solidification times for each casting section and the riser and determine whether the riser will be effective?
A 4-in.-diameter sphere of liquid copper is allowed to solidify, producing a spherical shrinkage cavity in the center of the casting. Compare the volume and diameter of the shrinkage cavity in the copper casting to that obtained when a 4-in. sphere of liquid iron is allowed to solidify?
A 4-in. cube of a liquid metal is allowed to solidify. A spherical shrinkage cavity with a diameter of 1.49 in. is observed in the solid casting. Determine the percent volume change that occurs during solidification?
Molten copper at atmospheric pressure contains 0.01 wt% oxygen. The molten copper is placed in a chamber that is pumped down to 1 Pa to remove gas from the melt prior to pouring into the mold. Calculate the oxygen content of the copper melt after it is subjected to this degassing treatment?
Suppose that liquid iron is undercooled homogeneous nucleation occurs. Calculate. (a) The critical radius of the nucleus required; and (b) The number of iron atoms in the nucleus. Assume that the lattice parameter of the solid BCC iron is 2.92 Å.
Suppose that solid nickel was able to nucleate homogeneously with an undercooling of only 22 °C. How many atoms would have to group together spontaneously for this to occur? Assume that the lattice parameter of the solid FCC nickel is 0.356 nm?
Suppose that solid iron was able to nucleate homogeneously with an undercooling of only 15 °C. How many atoms would have to group together spontaneously for this to occur? Assume that the lattice parameter of the solid BCC iron is 2.92 Å.
Use the data in Table 9 - 1 and the specific heat data given below to calculate the undercooling required to keep the dendritic fraction at 0.5 for each metal.Metal Specific heat [J/(cm3 ( K)]Bi.................1.27Pb.................1.47Cu.................3.48Ni.................4.75
Calculate the fraction of solidification that occurs dendritically when silver nucleates (a) At 10 °C undercooling; (b) At 100 °C undercooling; and (c) Homogeneously. The specific heat of silver is 3.25 J/(cm3 · °C).
Calculate the fraction of solidification that occurs dendritically when iron nucleates (a) At 10 °C undercooling; (b) At 100 °C undercooling; and (c) Homogeneously. The specific heat of iron is 5.78 J/(cm3 · °C).
Analysis of a nickel casting suggests that 28% of the solidification process occurred in a dendritic manner. Calculate the temperature at which nucleation occurred. The specific heat of nickel is 4.1 J/(cm3 · °C).
Natural diamond is formed approximately 120-200 km below the earth's surface under high pressure and high temperature conditions. Assuming that the average density of the earth is 5500 kg/m3, use this information and the unary phase diagram for C (Figure 10-17) to calculate the range of the earth's
(a) Determine the phases present, the compositions of each phase, and the amount of each phase in wt% for the following MgO-FeO ceramics at 2000 °C. (i) MgO-25 wt% FeO;(ii) MgO-45 wt% FeO;(iii) MgO-60 wt% FeO; (iv) MgO-80 wt% FeO. (b) Consider an alloy of 65 wt% Cu and 35 wt% Al. Calculate the
Consider a ceramic composed of 30 mol% MgO and 70 mol% FeO. Calculate the composition of the ceramic in wt%?
A Nb-60 wt% W alloy is heated to 2800 °C. Determine (a) The composition of the solid and liquid phases in both wt% and at%; (b) The amount of each phase in both wt% and at%; and (c) Assuming that the density of the solid is 16.05 g/cm3 and that of the liquid is 13.91 g/cm3, determine the amount
How many grams of nickel must be added to 500 grams of copper to produce an alloy that has a liquidus temperature of 1350 °C? What is the ratio of the number of nickel atoms to copper atoms in this alloy?
How many grams of nickel must be added to 500 grams of copper to produce an alloy that contains 50 wt% α at 1300 °C?
How many grams of MgO must be added to 1 kg of NiO to produce a ceramic that has a solidus temperature of 2200 °C?
How many grams of MgO must be added to 1 kg of NiO to produce a ceramic that contains 25 mol% solid at 2400 °C?
We would like to produce a solid MgO-FeO ceramic that contains equal mole percentages of MgO and FeO at 1200 °C. Determine the wt% FeO in the ceramic?
We would like to produce an MgO-FeO ceramic that is 30 wt% solid at 2000 °C. Determine the composition of the ceramic in wt%?
Based on Hume-Rothery's conditions, which of the following systems would be expected to display unlimited solid solubility? Explain. (a) Au-Ag; (b) Al-Cu; (c) Al-Au; (d) U-W; (e) Mo-Ta; (f) Nb-W; (g) Mg-Zn; (h) Mg-Cd.
Suppose a 1200-lb bath of a Nb-40 wt% W alloy is held at 2800 °C. How many pounds of tungsten can be added to the bath before any solid forms? How many pounds of tungsten must be added to cause the entire bath to be solid?
A fiber-reinforced composite material is produced, in which tungsten fibers are embedded in a Nb matrix. The composite is composed of 70 vol% tungsten. (a) Calculate the wt% of tungsten fibers in the composite; and (b) Suppose the composite is heated to 2600 °C and held for several years. What
Equal moles of MgO and FeO are combined and melted. Determine (a) The liquidus temperature, the solidus temperature, and the freezing range of the ceramic, and (b) Determine the phase(s) present, their composition(s), and their amount(s) at 1800 °C.
Suppose 75 cm3 of Nb and 45 cm3 of W are combined and melted. Determine (a) The liquidus temperature, the solidus temperature, and the freezing range of the alloy; and (b) Determine the phase(s) present, their composition(s), and their amount(s) at 2800 °C?
For equilibrium conditions and a MgO-65 wt% FeO ceramic, determine (a) The liquidus temperature; (b) The solidus temperature; (c) The freezing range; (d) The composition of the first solid to form during solidification; (e) The composition of the last liquid to solidify; (f) The phase(s) present,
Figure 10-20 shows the cooling curve for a NiO-MgO ceramic. Determine (a) The liquidus temperature; (b) The solidus temperature; (c) The freezing range; (d) The pouring temperature; (e) The superheat; (f) The local solidification time; (g) The total solidification time; and (h) The composition

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