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

For equilibrium conditions and a Nb-80 wt% W alloy, 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, the
Identify which of the following oxides when added to BaTiO3 are likely to exhibit 100% solid solubility:(a) SrTiO3;(b) CaTiO3;(c) ZnTiO3;(d) BaZrO3. All of these oxides have a perovskite crystal structure.
Figure 10-21 shows the cooling curve for a Nb-W alloy. Determi ne (a) The liquidus temperature; (b) The solidus temperature; (c) t he freezing range; (d) The pouring temperature; (e) The superheat; (f) The local solidification time; (g) The total solidification time; and (h) The composition
Cooling curves are shown in Figure 10-22 for several M o-V alloys. Based on these curves, construct the Mo-V phase diagram?
Suppose 1 at% of the following elements is added to copper (forming a separate alloy with each element) without exceeding the solubility limit. Which one would be expected to give the higher strength alloy? Are any of the alloying elements expected to have unlimited solid solubility in copper? (a)
Suppose 1 at% of the following elements is added to aluminum (forming a separate alloy with each element) without exceeding the solubility limit. Which one would be expected to give the smallest reduction in electrical conductivity? Are any of the alloy elements expected to have unlimited solid
Which of the following oxides is expected to have the largest solid solubility in Al2O3? (a) Y2O3; (b) Cr2O3; (c) Fe2O3.
Determine the degrees of freedom under the following conditions: (a) Tl-20 wt% Pb at 325 °C and 400 °C; (b) Tl-40 wt% Pb at 325 °C and 400 °C; (c) Tl-90 wt% Pb at 325 °C and 400 °C. Refer to the phase diagram in Figure 10-8(d).
Determine the composition range in which the Tl-Pb alloy at 350 °C is (a) Fully liquid; (b) Fully solid;
Determine the liquidus temperature, solidus temperature, and freezing range for the following MgO-FeO ceramic compositions. (a) MgO-25 wt% FeO; (b) MgO-45 wt% FeO; (c) MgO-65 wt% FeO; (d) MgO-80 wt% FeO.
Consider a Pb-15% Sn alloy. During solidification, determine (a) The composition of the first solid to form; (b) The liquids temperature, solidus temperature, solvus temperature, and freezing range of the alloy; (c) The amounts and compositions of each phase at 260 °C; (d) The amounts and
Consider an Al-12% Mg alloy (Figure 11-29). During solidification, determine (a) The composition of the first solid to form; (b) The liquidus temperature, solidus temperature, solvus temperature, and freezing range of the alloy; (c) The amounts and compositions of each phase at 525 ˚C; (d) The
Consider a Pb-35% Sn alloy. Determine (a) If the alloy is hypoeutectic or hypereutectic; (b) The composition of the first solid to form during solidification; (c) The amounts and compositions of each phase at 184 ˚C; (d) The amounts and compositions of each phase at 182 ˚C; (e) The amounts and
Consider a Pb-70% Sn alloy. Determine (a) If the alloy is hypoeutectic or hypereutectic; (b) The composition of the first solid to form during solidification; (c) The amounts and compositions of each phase at 184 ˚C; (d) The amounts and compositions of each phase at 182 ˚C; (e) The amounts and
(a) Sketch a typical eutectic phase diagram, with components A and B having similar melting points. B is much more soluble in A (maximum = 15%) than A is in B (maximum = 5%), and the eutectic composition occurs near 40% B. The eutectic temperature is 2/3 of the melting point. Label the axes of the
The copper-silver phase diagram is shown in Figure 11-30. Copper has a higher melting point than silver. Refer to the silver-rich solid phase as gamma (Î³) and the copper-rich solid phase as delta (Î´). Denote the liquid as L.Figure 11-30 A phase diagram for elements A and B
Calculate the total % β and the % eutectic micro constituent at room temperature for the following lead-tin alloys: 10% Sn, 20% Sn, 50% Sn, 60% Sn, 80% Sn, and 95% Sn. Using Figure, plot the strength of the alloys versus the % β and the % eutectic and explain your graphs.
Consider an Al-4% Si alloy (Figure 11-19). Determine (a) If the alloy is hypoeutectic or hypereutectic; (b) The composition of the first solid to form during solidification; (c) The amounts and compositions of each phase at 578 ˚C; (d) The amounts and compositions of each phase at 576 ˚C; (e) The
Consider an Al-25% Si alloy. (See Figure 11-19.) Determine (a) If the alloy is hypoeutectic or hypereutectic; (b) The composition of the first solid to form during solidification; (c) The amounts and compositions of each phase at 578 ˚C; (d) The amounts and compositions of each phase at 576
Write the eutectic reaction that occurs, including the compositions of the three phases in equilibrium, and calculate the amount of α and β in the eutectic micro constituent in the Mg-Al system (Figure 11-29).
Calculate the total amount of α and β and the amount of each micro constituent in a Pb-50% Sn alloy at 182 ˚C. What fraction of the total α in the alloy is contained in the eutectic micro constituent?
Figure 11-31 shows a cooling curve for a Pb-Sn alloy. Determine (a) The pouring temperature; (b) The superheat; (c) The liquidus temperature; (d) The eutectic temperature; (e) The freezing range; (f) The local solidification time; (g) The total solidification time; and (h) The composition of the
Figure 11-32 shows a cooling curve for an Al-Si alloy and Figure 11-19 shows the binary phase diagram for this system. Determine (a) The pouring temperature; (b) The superheat; (c) The liquidus temperature; (d) The eutectic temperature; (e) The freezing range; (f) The local solidification time; (g)
See Figure 11-19 and draw the cooling curves, including appropriate temperatures, expected for the following Al-Si alloys. (a) Al-4% Si; (b) Al-12.6% Si; (c) Al-25% Si; and (d) Al-65% Si.
Cooling curves are obtained for a series of Cu-Ag alloys (Figure 11-33). Use this data to produce the Cu-Ag phase diagram. The maximum solubility of Ag in Cu is % and the maximum solubility of Cu in Ag is 8.8%. The solubilities at room temperature are near zero.
The binary phase diagram for the silver (Ag) and germanium (Ge) system is shown in Figure 11-34.Figure 11-34 The silver-germanium phase diagram (for Problem 11-35). (a) Schematically draw the phase diagram, and label the phases present in each region of the diagram. Denote Î± as the
The copper-silver phase diagram is shown in Figure 11-30. Copper has a higher melting point than silver.Figure 11-35 A phase diagram for elements A and B (for Problem 11-36). (a) Is copper element A or element B as labeled in the phase diagram? (b) Schematically draw the phase diagram and label all
A hypothetical phase diagram is shown in Figure 11-26.(a) Are there any inter metallic compounds present? If so, identify them and determine whether they are stoichiometric or nonstoichiometric.
The Cu-Zn phase diagram is shown in Figure 11-27.(a) Are any inter metallic compounds present? If so, identify them and determine whether they are stoichiometric or nonstoichiometric.
The Al-Li phase diagram is shown in Figure 11-28.(a) Are any inter metallic compounds present? If so, identify them and determine whether they are stoichiometric or nonstoichiometric. Determine the formula for each compound.(b) Identify the three-phase reactions by writing down the temperature, the
(a) Determine the critical nucleus size r* for homogeneous nucleation for precipitation of phase β in a matrix of phase α.(b) Plot the total free energy change ΔG as a function of the radius of the precipitate.(c) Comment on the value of r* for homogeneous nucleation for solid-state
Suppose that age hardening is possible in the Al-Mg system (see Figure12-10.)(a) Recommend an following alloys; and artificial age-hardening heat treatment for each of the(b) Compare the amount of the β precipitate that forms from your treatment of each alloy: (i) Al-4% Mg (ii) Al-6% Mg (iii)
An Al-2.5% Cu alloy is solution-treated, quenched, and over aged at 230 ˚C to produce a stable microstructure. If the θ precipitates as spheres with a diameter of 9000 Å and a density of 4.26 g/cm3, determine the number of precipitate particles per cm3. (See Figure 12-5)
Based on the principles of age hardening of Al-Cu alloys, rank the following Al-Cu alloys from highest to lowest for maximum yield strength achievable by age hardening and longest to shortest time required at 190 ˚C to achieve the maximum yield strength: Al-2 wt% Cu, Al-3 wt% Cu, and Al-4 wt% Cu.
Figure 12-31 shows a hypothetical phase diagram. Determine whether each of the following alloys might be good candidates for age hardening, and explain your answer. For those alloys that might be good candidates, describe the heat treatment required, including recommended temperatures. (a) A-10%
For an Fe-0.35% C alloy, determine(a) The temperature at which austenite first begins to transform on cooling;(b) The primary micro constituent that forms;(c) The composition and amount of each phase present at 728 ˚C;(d) The composition and amount of each phase present at 726 ˚C; and(e) The
For an Fe-1.15%C alloy, determine (a) The temperature at which austenite first begins to transform on cooling; (b) The primary micro constituent that forms; (c) The composition and amount of each phase present at 728 ˚C; (d) The composition and amount of each phase present at 726 ˚C; and (e) The
Determine the constants c and n in Equation 12-2 that describe the rate of crystallization of polypropylene at 140 ˚C. (See Figure 12-30.)
Steel contains 96% γ and 4% Fe3C at 800 ˚C. Estimate the carbon content of the steel.
Steel is heated until 40% austenite, with a carbon content of 0.5% forms. Estimate the temperature and the overall carbon content of the steel.
Steel is heated until 85% austenite, with a carbon content of 1.05%, forms. Estimate the temperature and the overall carbon content of the steel.
The carbon steels listed in the table below were soaked at 1000 ˚C for 1 hour to form austenite and were cooled slowly, under equilibrium conditions to room temperature. Refer to the Fe-Fe3C phase diagram to answer the following questions for each of the carbon steel compositions listed in the
A faulty thermocouple in a carburizing heat-treatment furnace leads to unreliable temperature measurement during the process. Microstructure analysis from the carburized steel that initially contained 0.2% carbon revealed that the surface had 93% pearlite and 7% primary Fe3C, while at a depth of
Compare the interlamellar spacing and the yield strength when eutectoid steel is isothermally transformed to pearlite at (a) 700 ˚C and (b) 600 ˚C.
Isothermally transformed eutectoid steel is found to have yield strength of 410 MPa. Estimate (a) The transformation temperature; and (b) The inter lamellar spacing in the pearlite.
Determine the required transformation temperature and micro constituent if eutectoid steel is to have the following hardness values: (a) HRC 38; (b) HRC 42; (c) HRC 48; and (d) HRC 52.
A steel containing 0.3% C is heated to various temperatures above the eutectoid temperature, held for 1 h, and then quenched to room temperature. Using Figure 12-32, determine the amount, composition, and hardness of any marten site that forms when the heating temperature is (a) 728 ˚C; (b) 750
A steel containing 0.95% C is heated to various temperatures above the eutectoid temperature, held for 1 h, and then quenched to room temperature. Using Figure 12-32, determine the amount and composition of any martensite that forms when the heating temperature is (a) 728 ˚C (b) 750 ˚C (c) 780
A steel microstructure contains 75% marten site and 25% ferrite; the composition of the marten site is 0.6% C. Using Figure 12-32, determine (a) The temperature from which the steel was quenched and (b) The carbon content of the steel.
A steel containing 0.8% C is quenched to produce all marten site. Estimate the volume change that occurs, assuming that the lattice parameter of the austenite is 3.6 Å. Does the steel expand or contract during quenching?
In eutectic alloys, the eutectic micro constituent is generally the continuous one, but in the eutectoid structures, the primary micro constituent is normally continuous. By describing the changes that occur with decreasing temperature in each reaction, explain why this difference is expected.
Determine the constants c and n in the Avrami relationship (Equation 12-2) for the transformation of austenite to pearlite for a 1050 steel. Assume that the material has been subjected to an isothermal heat treatment at 600 ˚C and make a log-log plot of f versus t given the following
In a pearlitic 1080 steel, the cementite platelets are 4 × 10-5 cm thick, and the ferrite platelets are 14 × 10-5 cm thick. In a spheroidized 1080 steel, the cementite spheres are 4 × 10-3 cm in diameter. Estimate the total interface area between the ferrite and cementite in a cubic centimeter
Describe the microstructure present in a 1050 steel after each step in the following heat treatments: (a) Heat at 820 ˚C, quench to 650 ˚C and hold for 90 s, and quench to 25 ˚C; (b) Heat at 820 ˚C, quench to 450 ˚C and hold for 90 s, and quench to 25 ˚C; (c) Heat at 820 ˚C and quench to 25
Describe the microstructure present in a 10110 steel after each step in the following heat treatments: (a) Heat To 900 ˚C, quench to 400 ˚C and hold for 103 s, and quench to 25 ˚C; (b) Heat To 900 ˚C, quench to 600 ˚C and hold for 50 s, and quench to 25 ˚C; (c) Heat to 900 ˚C and quench to
Recommend appropriate isothermal heat treatments to obtain the following, including appropriate temperatures and times: (a). An isothermally annealed 1050 steel with HRC 23; (b). An isothermally annealed 10110 steel with HRC 40; (c). An isothermally annealed 1080 steel with HRC 38; (d). An
Compare the minimum times required to isothermally anneal the following steels at 600 ˚C. Discuss the effect of the carbon content of the steel on the kinetics of nucleation and growth during the heat treatment. (a) 1050; (b) 1080; and (c) 10110.
Typical media used for quenching include air, brine (10% salt in water), water, and various oils. (a) Rank the four media in order of the cooling rate from fastest to slowest. (b) Describe a situation when quenching in air would be undesirable. (c) During quenching in liquid media, typically
We wish to produce a 1050 steel that has a Brinell hardness of at least 330 and an elongation of at least 15%.(a) Recommend a heat treatment, including appropriate temperatures, that permits this to be achieved. Determine the yield and tensile strengths that are obtained by this heat treatment.
We wish to produce a 1050 steel that has a tensile strength of at least 175,000 psi and a reduction in area of at least 50%. (a) Recommend a heat treatment, including appropriate temperatures, that permits this to be achieved. Determine the Brinell hardness number, % elongation, and yield strength
A 1030 steel is given an improper quench and temper heat treatment, producing a final structure composed of 60% marten site and 40% ferrite. Estimate the carbon content of the marten site and the austenitizing temperature that was used. What austenitizing temperature would you recommend?
A 1050 steel should be austenitized at 820 ˚C, quenched in oil to 25 ˚C, and tempered at 400 ˚C for an appropriate time. (a) What yield strength, hardness, and % elongation would you expect to obtain from this heat treatment? (See Figure 13-9) (b) Suppose the actual yield strength of the steel
A part produced from a low-alloy, 0.2% C steel has a microstructure containing ferrite, pearlite, bainite, and marten site after quenching. What microstructure would be obtained if we had used a 1080 steel? What microstructure would be obtained if we used a 4340 steel? [See Figure 13-14, 13-15, and
Fine pearlite and a small amount of marten site are found in quenched 1080 steel. What microstructure would be expected if we used a low-alloy, 0.2% C steel? What microstructure would be expected if we had used a 4340 steel? [See Figures 13-14, 13-15, and 13-16(b).]
Predict the phases formed when a bar of 1080 steel is quenched from slightly above the eutectoid temperature under the following conditions: (a) Oil (without agitation); (b) Oil (with agitation); (c) Water (with agitation); and (d) Brine (no agitation). Suggest a quenching medium if we wish to
We have found that a 1070 steel, when austenitized at 750 ˚C, forms a structure containing pearlite and a small amount of grain-boundary ferrite that gives acceptable strength and ductility. What changes in the microstructure, if any, would be expected if the 1070 steel contained an alloying
Using the TTT diagrams, compare the hardenabilities of 4340 and 1050 steals by determining the times required for the isothermal transformation of ferrite and pearlite (Fs, Ps, and Pf) to occur at 650 ˚C. [See Figures 13-8 and 13- 16(a)]
We would like to obtain a hardness of HRC 38 to 40 in quenched steel. What range of cooling rates would we have to obtain for the following steels? Are some steels inappropriate for achieving these levels of hardness? (See Figure 13-21 and Table 13-3) (a) 4340; (b) 8640; (c) 9310; (d) 4320; (e)
A steel part must have an as-quenched hardness of HRC 35 in order to avoid excessive wear rates during use. When the part is made from 4320 steel, the hardness is only HRC 32. Determine the hardness if the part were made under identical conditions, but with the following steels. Which, if any, of
Calculate the amounts of ferrite, cementite, primary micro constituent, and pearlite in the following steels: (a) 1015; (b) 1035; (c) 1095; and (d) 10130.
A part produced from a 4320 steel has a hardness of HRC 35 at a critical location after quenching. Determine (a) The cooling rate at that location, and (b) The microstructure and hardness that would be obtained if the part were made from a 1080 steel.
A 1080 steel is cooled at the fastest possible rate that still permits all pearlite to form. What is this cooling rate? What Jominy distance and hardness are expected for this cooling rate?
Determine the hardness and the microstructure at the center of a 1.5-in. diameter 1080 steel bar produced by quenching in (a) Unagitated oil; (b) Unagitated water; and (c) Agitated brine.
A 2-in.-diameter bar of 4320 steel is to have a hardness of at least HRC 35. What is the minimum severity of the quench (H coefficient)? What type of quenching medium would you recommend to produce the desired hardness with the least chance of quench cracking?
A steel bar is to be quenched in agitated water. Determine the maximum diameter of the bar that will produce a minimum hardness of HRC 40 if the bar is(a) 1050;(b) 1080;(c) 4320;(d) 8640; and(e) 4340.
The center of a 1-in.-diameter bar of 4320 steel has a hardness of HRC 40. Determine the hardness and microstructure at the center of a 2-in.-bar of 1050 steel quenched in the same medium.
A 1010 steel is to be carburized using a gas atmosphere that produces 1.0% C at the surface of the steel. The case depth is defined as the distance below the surface that contains at least 0.5% C. If carburizing is done at 1000 ˚C, determine the time required to produce a case depth of 0.01 in.
A 1015 steel is to be carburized at 1050 ˚C for 2 h using a gas atmosphere that produces 1.2% C at the surface of the steel. Plot the percent carbon versus the distance from the surface of the steel. If the steel is slowly cooled after carburizing, determine the amount of each phase and micro
Estimate the AISI-SAE number for steels having the following microstructures:(a) 38% pearlite-62% primary ferrite;(b) 93% pearlite-7% primary cementite;(c) 97% ferrite-3% cementite; and(d) 86% ferrite-14% cementite.
A 1050 s eel is welded. After cooling, hard nesses in the heat-affected zone are obtained at various locations from the edge of the fusion zone. Determine the hard nesses expected at each point if a 1080 steel were welded under the same conditions. Predict the microstructure at each location in the
We wish to produce a martensitic stainless steel containing 17% Cr. Recommend a carbon content and austenitizing temperature that would permit us to obtain 100% marten site during the quench. What microstructure would be produced if the marten site were then tempered until the equilibrium phases
Occasionally, when an austenitic stainless steel is welded, the weld deposit may be slightly magnetic. Based on the Fe-Cr-Ni-C phase diagram [Figure 13-28(b)], what phase would you expect is causing the magnetic behavior? Why might this phase have formed? What could you do to restore the
Compare the eutectic temperatures of a Fe-4.3% C cast iron with a Fe-3.6% C- 2.1% Si alloy. Which alloy is expected to be more machinable and why?
A bar of a class 40 gray iron casting is found to have a tensile strength of 50,000 psi. Why is the tensile strength greater than that given by the class number? What is the diameter of the test bar?
Complete the following table:
Two samples of steel contain 93% pearlite. Estimate the carbon content of each sample if one is known to be hypo eutectoid and the other hypereutectoid.
In some cases, we may be more interested in the cost of a material per unit volume than in the cost per unit weight. Rework Table 14-1 to show the cost in terms of $/cm3 Does this change / alter the relationship between the different materials?
Determine the amount of Mg2Al3 (β) expected to form in a 5182-O aluminum alloy. (See Figure 14-2)
From the data in Table 14-6, estimate the ratio by which the yield strength of magnesium can be increased by alloying and heat treatment and compare with that of aluminum alloys.
Suppose a 24-in.-long round bar is to support a load of 400 lb without any permanent deformation. Calculate the minimum diameter of the bar if it is made from (a) AZ80A-T5 magnesium alloy and (b) 6061-T6 aluminum alloy. Calculate the weight of the bar and the approximate cost (based on pure Al and
A 10-m rod 0.5 cm in diameter must elongate no more than 2 mm under load. Determine the maximum force that can be applied if the rod is made from (a) Aluminum; (b) Magnesium; and (c) Beryllium.
Compare the percent increase in the yield strength of commercially pure annealed aluminum, magnesium, and copper by strain hardening. Explain the differences observed.
We would like to produce a quenched and tempered aluminum bronze containing 13% Al. Recommend a heat treatment, including appropriate temperatures. Calculate the amount of each phase after each step of the treatment.
Determine the specific strength of the following metals and alloys (use the densities of the major metal component as an approximation of the alloy density where required):Alloy/MetalTensile Strength (MPa)1100-H18 ................................... 1655182-O ......................................
Would you expect the fracture toughness of quenched and tempered aluminum bronze to be high or low? Would there be a difference in the resistance of the alloy to crack nucleation compared with crack growth? Explain.
The density of Ni3Al is 7.5 g/cm3. Suppose a Ni-5 wt% Al alloy is heat treated so that all of the aluminum reacts with nickel to produce Ni3Al. Determine the volume percent of the Ni3Al precipitate in the nickel matrix.
When steel is joined using arc welding, only the liquid fusion zone must be protected by a gas or flux. When titanium is welded, both the front and back sides of the welded metal must be protected. Why must these extra precautions be taken when joining titanium?
Both a Ti-15% V alloy and a Ti-35% V alloy are heated to the lowest temperature at which all β just forms. They are then quenched and reheated to 300°C. Describe the changes in microstructures during the heat treatment for each alloy, including the amount of each phase. What is the matrix and
Determine the specific yield strengths of the strongest Al, Mg, Cu, Ti, and Ni alloys. Use the densities of the pure metals, in lb/in.3, in your calculations. Try to explain their order.
Based on the phase diagrams, estimate the solubilities of Ni, Zn, Al, Sn, and Be in copper at room temperature. Are these solubilities expected in view of Hume-Rothery's conditions for solid solubility? Explain.

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