HW-CH10 - 394 Clupter 10 t PhaseDiagrams ferrite phase in...

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Unformatted text preview: 394 - Clupter 10 t PhaseDiagrams' ferrite phase in addition to pearlite. 0n the other hand, pearlite and proeutectoid cementite constitute the microconstituents for hypereutectoid alloys—those with carbon contents in excess of the eutectoid composition. IMPORTANT TERMS AND CONCEPTS -—-—-—~m-*——-—-—._.—._~__—__ww—____—___fl_ Austenite Hypereutectoid alloy Phase Cementite Hypoeutectoid alloy Phase diagram Component Intermediate solid solution Phase equilibrium Congruent transformation Intermetallic compound Primary phase Equilibrium Invariant point Proeutectoid cementite Eutectic phase Isomorphous Proeutectoid ferrite Eutectic reaction Lever rule Solidus line Eutectic structure Liquidus line Solubility limit Eutectoid reaction Metastable Solvus line Ferrite Microconstituent System Free energy , Pearlite Terminal solid solution Gibbs phase rule Peritectic reaction Tie line ' RE F E R E N C E S m—————-——~—_._.—.wmm_fl____fl—WH_—__ ASM Handbook, Vol. 3, Alloy Phase Diagrams, ASM International, Materials Park, OH, 1992. ASM Handbook, Vol. 9, Metallography and Mi- crostructures. ASM International, Materials Park, OH, 2004. Bergeron, C. G. and S. H. Risbud. Introduction to Phase Equilibria in Ceramics, American Ce- ramic Society, Columbus, OH, 1984. Hansen, M. and K. Anderko, Constitution ofBinary Alloys, 2nd edition, McGraw-Hill, New York, 1958. First Supplement (R. P. Elliott), 1965. Sec— ond Supplement (F. A. Shunk), 1969. Reprinted by Genium Publishing Corp, Schenectady, NY. Kingery, W. D.. H. K. Bowen, and D. R. Uhlmann, Introduction to Ceramics, 2nd edition, Wiley, New York, 193'6. Chapter 7. Massalski, T. B., H. Okamoto, P. R. Subramanian, and L. Kacprzak (Editors), Binary Phase Dia- QUESTIONS AND PROBLEMS grams 2nd edition, ASM International, Mate- rials Park, OH, 1990. Three volumes Also on CD-ROM with updates Okamoto, H., Desk Handbook: Phase Diagrams for Binary Alloys, ASM International, Materials Park, OH, 2000. Petzow, G., Ternary Alloys A Comprehensive Com» pendiurn of Evaluated Constitutional Data and Phase Diagrams, Wiley, New York, 19884995. Fifteen volumes Phase Equilibria Diagrams (for Ceramists), Amer— ican Ceramic Society, Westerville, OH. In four- teen volumes, published between 1964 and 2005. Also on CD-ROM. Villars, P., A. Prince, and H. Okamoto (Editors), Handbook of Ternary Alloy Phase Diagrams, ASM International, Materials Park, OH, 1995. Ten volumes Also on CD-ROM. Additional problems and questions for this chapter may be found on both Student and Instructor Companion Sites at mwfley.com/college/calh3ter. Solubility Limit 10.1 Consider the. sugar-water phase diagram of Figure 10.1. (a) How much sugar will dissolvo in 1000 g of water at 30°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 liquid solution (in wt% sugar) at 20°C? (c) How much of the solid sugar will come out of solution upon cooling to 20“ C? i Micmstmcture 10.2 Cite three variables that determine the mi- crostructure of an alloy. One-Component ( or Unary) Phase Diagrams 10.3 Consider a specimen of ice that is at —15°C and 10 atm pressure. Using Figure 10.2, the pressure—temperature phase diagram for H20, determine the pressure to which the specimen must be raised or lowered to cause it (a) to melt. and (b) to sublime. Binary lsomorphour System: 10.4 Given here are the solidus and liquidus tem- peratures for the copper—gold system. Con- struct the phase diagram for this system and label each region. Camposifiqn Solidus Liquidus (19:96 An) Temperature (0 C) Temperature {° C} 0 1085 1085 20 1019 1042 40 972 996 60 934 945 80 91 l 911 90 928 942 95 974 984 00 1064 1064 H Interpretation of Phase Diagram 1' Binary lsomorphour Systems) ( Binary Eutectic Systems) (Equilibrium Diagrams Having Intermediate Phases or Compoands) 10.5 10.6 Cite the phases that are present and the phase compositions for the following alloys: (9) 25 wt% Pia—75 wt% Mg at 425°C (800°F) (h) 55 wt% Zn—45 wt% Cu at 600°C (1110°F) (c) 7.6 lmen and 144.4 lbtn Zn at 600°C (11 10°F) ((1) 4.2 mol Cu and 1.1 mol Ag at 900°C (1650°F) Is it possible to have a copper—silver alloy that, at equilibrium, consists of an a: phase of composition 4 wt % Ag—96 wt% Cu, and also a ,6 phase of composition 95 wt% Ag—S wt% Cu? If so, what will be the approximate tem- perature of the alloy? If this is not possible, explain why. Questions and Problems 'I 395 10.7 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? 01) What is the composition of this solid phase? (c) At what temperature does the liquid so- lidify? (d) What is the composition of this last re- maining liquid phase? 10.8 Determine the relative amounts (in terms of mass fractions) of the phases for the alloys and temperatures given in Problem 10.5. 10.9 A magnesium—lead alloy of mass 7.5 kg con- sists of a solid or 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 o: phase without exceeding the solu- bility limit of this phase? 10.10 A 40 wt% Pb—60 wt% Mg alloy is heated to a temperature within the a: + liquid-phase re- gion. If the mass fraction of each phase is 0.5, then estimate: (a) The temperature of the alloy 01) The compositions of the two phases 10.11 For alloys of two hypothetical metals A and B, there exist an a, A-rich phase and a ,8, B- rich phase. From the mass fractions of both phases for two different alloys provided in the table below, (which are at the same tem- perature). determine the composition of the phase boundary (or solubility limit) for both a and ,6 phases at this temperature. Alloy Fraction u Iii-action fl _ C (Imposition _ _ _Phase __ films: 70 wt% A—30 wt% 13 0.78 0.22 35 wt‘lfi: A—65 wt%_l§ 0.36 0.64 10.12 Is it possible to have a copper—silver alloy of composition 20 wt% Ag—80 wt% Cu that, at equilibrium, consists of u‘ and liquid phases having mass fractions W0, = 0.80 and W; = 0.20? If so, what will be the approximate 396 ' Chaplin-'10 l PhaseDiagrams temperature of the alloy? If such an alloy is not possible, explain why. 10.13 For 5.7 kg of a magnesium—lead alloy of com- position 50 wt% Pb—50 wt % Mg, is it possible, at equilibrium, to have a and Mgng 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. 10.14 Determine the relative amounts (in terms of volume fractions) of the phases for the alloys and temperatures given in Problems 10.531 and h. Given here are the approximate den- sities of the various metals at the alloy tem- peratures: Temperature Density Metal (“(2') __ (g/cm’) fin 600 8.68 g 425 1.68 Pb 425 10.96 Zn 600 6.67 Mechanical Properties of isomorphism Alloy: 10.15 It is desirable to produce a copper—nickel al- loy that has a minimum noncold-worked ten- sile 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. Development of Micmstrueture in Eutectic Alloys 10.16 Briefly explain why, upon solidification, an alloy of eutectic composition forms a mi- crostructure consisting of alternating layers of the two solid phases 10.17 Is it possible to have a magnesium—lead al- loy in which the mass fractions of primary or and total a are 0.60 and 0.85, respectively, at 460°C (860°F)? Why or why not? 10.18 For a lead—tin alloy of composition 80 wt% Sn—20 wt% Pb and at 180°C (355°F), do the following: {2) Determine the mass fractions of a and 6 phases. (1:) Determine the mass fractions of primary #9 and eutectic microconstituents. (1:) Determine the mass fraction of eutectic )3. 10.19 Consider the hypothetical eutectic phase di- agram for metals A and B, which is similar to that for the lead—tin system, Figure 10.8. As- sume that: (l) o: and ,6 phases exist at the A 'and B extremities of the phase diagram, re- spectively; (2) the eutectic composition is 36 wt% A—64 wt% B; and (3) the composition of the or phase at the eutectic temperature is 88 wt% A—12 wt% B. Determine the com- position of an alloy that will yield primary ,6 and total ,8 mass fractions of 0.367 and 0.768, respectively. 10.20 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 in- dicate their approximate compositions. 10.21 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 (l4?0°F), and 600°C (1100°F). Label all phases and in- dicate their approximate compositions. 10.22 The room-temperature tensile strengths of pure copper and pure silver are 209 MPa and 125 MPa, respectively. (a) Make a schematic graph of the room- temperature tensile strength versus com- position for all oomeSitions between pure copper and pure silver. (Hint: you may want to consult Sections 10.10 and 10.11, as well as Equation 10.24 in Prob- lem 10.36.) (b) On this same graph schematically plot tensile strength versus composition at 600°C. (c) Explain the shapes of these two' curves, as well as any differences between them. Eqm'fibnhm Diagram Hawhg Intermediate Phases or Compounds 10.23 Two intermetallic compounds, A3B and A33 , exist for elements A and B. If the composi- tions for A3B and AB; are 91.0 wt% A—9.0 wt% B and 53.0 wt% A—47.0 wt% B, respec- tively, and element A is zirconium, identify element B. Gangruent Phase Transformations Birmry Eutectic Systems Equilibrium Diagrams Having Intermediate Phase: or Compound: . Eutectoid and Penlecfic Reactions 10.24 Figure 10.40 is the tin-gold phase diagram, for which only single-phase regions are labeled. Specify temperature—composition points at which all eutectics, eutectoids, peri- tectics, and congruent phase transformations occur. Also, for each, write the reaction upon cooling. _ 10.25 Construct the hypothetical phase diagram for metals A and B between room temperature (20°C) and 700°C given the following infor- mation: - ‘ 0 The melting temperature of metal A is 480°C. 0 The maximum solubility of B in A is 4 wt% B, which occurs at 420°C. 0 The solubility of B in A at room temper- ature is 0 wt% B. 0 One eutectic occurs at 420°C and 18 wt% B—82 wt% A. . A second eutectic occurs at 475°C and 42 wt% B—58 wt% A. Woman-id thlm 0 397 0 The intermetallic compound AB exists at a composition of 30 wt% 13—70 wt% A, and melts congruently at 525°C. 0 The melting temperature of metal B is 600°C. 0 The maximum solubility of A in B is 13 wt% A, which occurs at 475°C. - The solubility of A in B at room temper- ature is 3 wt% A. Ceramic Phase Diagrams 10.26 From Figure 10.24, the phase diagram for the MngAIZOg, system, it may be noted that the spine] solid solution exists over a range of compositions, which means that it is non- stoichiornetric at compositions other than 50 mol% MgO—SO mol % A1203. (:1) The maximum nonstoichiometry on the Alzog-rich side of the spine] phase field exists at about 2000°C (3630"F) corre- sponding to approximately 82 1110196 (92 Wt%) A1203. Determine the type of va- cancy defect that is produced and the percentage of vacancies that exist at this composition. (1)) The maximum nonstoichiometry on the MgO-rich side of the spine] phase field Figure 10.40 The tin—gold phase diagram. (Adapted with permission from Metals 1000 Handbook, 8th edition, Vol. 8, Melaliography, Structures and Phase Diagrams, American Society for Metals, Metals Park, OH, 1973.) Temperature (“C) m 8 400 (Sn) Composition (wt'ie Au) 398 ' Chaphr101PllaseDiagrams existsat about 2000°C (3630”F) corre- sponding to approximately 39 mol% (62 wt%) A1203. Determine the type of va- cancy defect that is produced and the percentage of vacancies that exist at this composition. The Gibbs Phase Rule 10.27 In Figure 10.41 is shown the pressure— temperature phase diagram for H20. Apply the Gibbs phase rule at points A, B, and C; that is, specify the number of degrees of free- dom at each of the points—that is, the num- ber of externally controllable variables that need be specified to completely define the system. The iron—Iron Carbide (Fe-Fe; C) Phase Diagram Development of Micmrtructure in iron—Carbon Alloys 10.28 What is the carbon concentration of an iron— carbon alloy for which the fraction of total eementite is 0.10? 10.29 Consider 3.5'kg of austenite containing 0.95 wt% C, cooled to below 727°C(1341°F). (a) What is the proeutcctoid phase? (b) How many kilograms each of total ferrite and eementite form? (c) How many kilograms each of pearlite and the proeutectoid phase form? (d) Schematicaliy sketch and label the result- ing microstructure. 10.30 Compute the mass fractions of proeutectoid ferrite and pearlite that form in an iron— carbon alloy containing 0.35 wt% C. 10.31 The mass fractions of total ferrite and total eementite in an iron—carbon alloy are 0.91 and 0.09, respectively. Is this a hypoeutectoid or hypereutectoid alloy? Why? 10.32 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 fer- rite form? 03) How many kilograms of eutectoid ferrite form? (c) How many kilograms of eementite form? 10.33 Is it possible to have an iron—carbon alloy for which the mass fractions of total eementite and proeutectoid ferrite are 0.057 and 0.36, respectively? Why or why not? 10.34 Compute the mass fraction of eutectoid cm mentite in an iron-carbon alloy that contains 1.00 wt% C. 10.35 The mass fraction of eutecroid ferrite in an iron—carbon alloy is 0.71. Onth'e 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. . 10.36 Often, the properties of multiphase alloys = may be approximated by the relationship E (alloy) = av. + Eng (1024) Figure 10.41 Logarithm pressure~versus-temperature phase diagram for H20. 1.0 Pressure (aim? 0.1 0.01 0.001 Temperature (°C) where E represents a specific property (mod- ulus of elasticity, hardness, etc). and V is the volume fraction. The subscripts a and {3 de- note the existingphases ormicroconstituents Employ this relationship to determine the ap- proximate Brinell hardness of a 99.75 wt% Pie—0.25 wt% C alloy. Assume Brinell hard- nesses of 80 and 280 for ferrite and pearlite. respectively, and that volume fractions may be approximated by mass fractions Questions and Problems 0 399 (a) What is the approximate eutectoid tem- perature of this alloy? (b) What is the proeutectoid phase when this alloy is cooled to a temperature just be- low the eutectoid? (c) Compute the relative amounts of the proeutectoid phase and pearlite. Assume that there are no alterations in the posi- tions of other phase boundaries with the addition of Mn. The Influence of Other Afloyfllg Element: 10.37 A steel alloy is known to contain 93.55 wt% Fe, 6.0 wt% Mn, and 0.35 wt% C. ...
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