Engineering Materials vol 2 Part 16 pot

366 Engineering Materials 2 (c) Describe the solidification of an alloy of eutectic composition, and the resulting structure. (d) Compare and contrast this with the formation of a eutectoid structure. 4.6 A hypothetical equilibrium diagram between two elements A and B shows the following features: A has three solid allotropic forms with change temperatures of 800°C and 1150°C and melts at 1980°C. These form solid solutions α , β and γ containing B, α being the low-temperature one. An intermediate compound A 2 B 3 melts at 1230°C. It has a limited solid solubility for A, forming solid solution ε and no solid solubility for B. B melts at 800°C and has negligible solid solubility for A. Eutectic reactions: at 1000°C, liquid (55% B) → β (25% B) + ε (60% B) at 650°C, liquid (90% B) → A 2 B 3 + B. Peritectic reaction at 1300°C: γ (8% B) + liquid (35% B) → β (15% B). Eutectoid reaction at 600°C: β (12% B) → α (5% B) + ε (65% B). Peritectoid reaction at 300°C: α (3% B) + ε (69% B) → δ (40% B). Fig. A1.53. Teaching yourself phase diagrams 367 At 0°C the solubilities of B in A and A in A 2 B 3 are negligible and the δ phase extends from 35% to 45% B. All percentages given are by weight. The atomic weight of B is twice that of A. Draw the equilibrium diagram assuming all phase boundaries are straight lines. For an alloy containing 30% B describe the changes that occur as it is cooled from 1600°C to 0°C. Give the proportions of phases present immediately above and immediately below each temperature at which a reaction occurs. Answers to questions: part 4 4.1 Between about 11.5 and 13.0 GPa or 1.14 × 10 5 − 1.28 × 10 5 atm. 4.2 (a) See (Fig. A1.54). (b) Two-phase region. (c) α (copper-rich solid) and β (the compound CuZn). (d) W Zn ≈ 33%, W Zn ≈ 48%. (e) Very roughly, 50–50; more precisely: wt% of wt% of . α β = − − = 48 40 40 33 8 7 4.3 The solid which first appears on cooling is higher in nickel. Repeated directional remelting and solidification “zones” the copper up to the end of the bar, and leaves most of the bar increasingly pure in nickel. Fig. A1.54. 368 Engineering Materials 2 Fig. A1.55. (a) 1. (b) 2. (c) 1. 4.4 (a) AlTi, Al 3 Ti. (b) See Fig. A1.55. (c) 1680°C. (d) 980°C to 1010°C. 4.5 (a) 11.7 wt% Si, 577°C. (b) One phase at 1000°C, two phases at 400°C. (c) See pp. 337, 339. (d) Eutectoid structure produced by the decomposition of a solid phase, not a liquid. 4.6 A 2 B 3 contains 32 2132 75 % × ×+× = B by weight. Hence equilibrium diagram is as given in Fig A1.56. On cooling 30% B mixture from 1600°C: at 1397°C, solidifica- tion commences by separation of γ crystals. Just above 1300°C 22 27 (= 81.5%) liquid (35% B) + 5 27 (= 18.5%) γ (8% B). At 1300°C, all γ + some liquid form β in peritectic reaction. Just below 1300°C 15 20 (= 75%) liquid (35% B) + 5 20 (= 25%) β (15% B). 1300°C → 1000°C, more β separates. Just above 1000°C 5 30 (= 17%) liquid (55% B) + 25 30 (= 83%) β (25% B). At 1000°C all liquid forms β and ε in eutectic reaction. Just below 1000°C 5 35 (= 14.3%) ε (60% B) + 30 35 (= 85.7%) β (25% B). 1000°C → 600°C, β Teaching yourself phase diagrams 369 Fig. A1.56. precipitates ε and ε precipitates β . Just above 600°C 18 53 (= 34%) ε (65% B) + 35 53 (= 66%) β (12% B). At 600°C all β forms α and ε in eutectoid reaction. Just below 600°C 25 60 (= 42%) ε (65% B) + 35 60 (= 58%) α (5% B). 600°C → 300°C, α precipitates ε and ε precipitates α . Just above 300°C 27 66 (= 41%) ε (69% B) + 39 66 (= 59%) α (3% B). At 300°C all ε and some α form δ in peritectoid reaction. Just below 300°C 27 37 (= 73%) δ (40% B) + 10 37 (= 27%) α (3% B). 300°C → 0°C, amount of α decreases and δ increases. At 0°C 30 35 (= 86%) δ (35% B) + 5 35 (= 14%) α (0% B). 370 Engineering Materials 2 Appendix 2 Symbols and formulae List of principal symbols Symbol Meaning(units) Note: Multiples or sub-multiples of basic units indicate the unit suffixes normally used in materials data. a lattice parameter (nm) a crack length (mm) A availability (J) A 1 eutectoid temperature (°C) A 3 first ferrite temperature (°C) A cm first Fe 3 C temperature (°C) b Burgers vector (nm) c height of c.p.h. unit cell (nm) C concentration (m −3 ) CCR critical cooling rate (°C s −1 ) DP degree of polymerisation (dimensionless) E Young’s modulus of elasticity (GPa) f force (N) F force (N) g acceleration due to gravity on the Earth’s surface (m s −2 ) G shear modulus (GPa) G Gibbs function (J) G c toughness (kJ m −2 ) H hardness (GPa) ∆H latent heat of transformation (J) I second moment of area of structural section (mm 4 ) k ratio of C solid /C liquid on phase diagram (dimensionless) k Boltzmann’s constant (J K −1 ) k shear yield strength (MPa) K IC fracture toughness (MPa m 1/2 ) L liquid phase Symbols and formulae 371 Symbol Meaning(units) m mass (kg) m Weibull modulus (dimensionless) M bending moment (N m) M F martensite finish temperature (°C) M S martensite start temperature (°C) n time exponent for slow crack-growth (dimensionless) p pressure (Pa) P f failure probability (dimensionless) P S survival probability (dimensionless) q activation energy per atom (J) Q activation energy per mole (kJ mol −1 ) r* critical radius for nucleation (nm) R universal gas constant (J K −1 mol −1 ) T absolute temperature (K) T e equilibrium temperature (K) T g glass temperature (K) T m melting temperature (K) ∆T thermal shock resistance (K) ν velocity (m s −1 ) V volume (m 3 ) V volume fraction (dimensionless) W A weight % (dimensionless) W f free work (J) X A mol % (dimensionless) α linear coefficient of thermal expansion (MK −1 ) γ energy of interface (J m −2 ) or tension of interface (N m −1 ) δ elastic deflection (mm) ε true (logarithmic) strain (dimensionless) ε f (nominal) strain after fracture; tensile ductility (dimensionless) ε . ss steady-state tensile strain-rate in creep (s −1 ) η viscosity (P, poise) ν Poisson’s ratio (dimensionless) ρ density (Mg m −3 ) σ true stress (MPa) σ c (nominal) compressive strength (MPa) σ r modulus of rupture (MPa) σ TS (nominal) tensile strength (MPa) σ y (nominal) yield strength (MPa) Greek letters are used to label the phases on phase diagrams. 372 Engineering Materials 2 Summary of principal formulae and magnitudes Chapter 3 and Teaching yourself phase diagrams: phase diagrams Composition is given by W A = weight of A weight of A weight of B+ × 100 in weight %, and by X A = atoms (mols) of A atoms (mols) of A atoms (mols) of B+ × 100 in atom (mol) %. W A + W B = 100%; X A + X B = 100%. Three-phase reactions Eutectic: L a α + β Eutectoid: β a α + γ Peritectic: L + α a β Peritectoid: A + B a δ Chapter 4: Zone refining C s = Ck kx l 0 11 ( )exp .−− −             C s = concentration of impurities in refined solid; C 0 = average impurity concentration; k = C solid /C liquid ; x = distance from start of bar; l = zone length. Chapter 5: Driving forces Driving force for solidification W f = −∆G = −− ∆H T TT m m ( ). ∆H = latent heat of solidification; T m = absolute melting temperature; T = actual tem- perature (absolute). Driving force for solid-state phase change W f = −∆G = −− ∆H T TT e e ( ). ∆H = latent heat of transformation; T e = equilibrium temperature (absolute). Symbols and formulae 373 Chapter 6: Kinetics of diffusive transformations Speed of interface ν ∝ e −q/kT ∆T. q = activation energy per atom; k = Boltzmann’s constant; T = absolute temperature; ∆T = difference between interface temperature and melting or equilibrium temperature. Chapter 7: Nucleation Nucleation of solids from liquids: critical radius for homogeneous and heterogeneous nucleation r* = 2 γ SL T HT T m m ∆ ( ) . − γ SL = solid–liquid interfacial energy; T m = absolute melting temperature; ∆H = latent heat of solidification; T = actual temperature (absolute). Chapter 8: Displacive transformations Overall rate of diffusive transformation ∝ no. of nuclei × speed of interface. Chapter 10: The light alloys Solid solution hardening σ y ∝ ε s C 32 12// . C = solute concentration; ε s = mismatch parameter. Work-hardening σ y ∝ ε n . ε = true strain; n = constant. Chapter 14: Metal processing Forming pressure No friction p f = σ y . 374 Engineering Materials 2 Sticking friction p f = σ y wx d 1 2 () .+ −       / σ y = yield strength; w = width of forging die; x = distance from centre of die face; d = distance between dies. Chapter 17: Ceramic strengths Sample subjected to uniform tensile stress Tensile strength σ TS = K a m IC π . K IC = fracture toughness; a m = size of widest microcrack (crack width for surface crack; crack half-width for buried crack). Modulus of rupture σ r = 6 2 M bd r . M r = bending moment to cause rupture; b = width of beam; d = depth of beam. Compressive strength σ c ≈ 15 σ TS , σ c = CK a IC π . C = constant (≈15); a = average crack size. Thermal shock resistance ∆T = σ TS /E α . E = Young’s modulus; α = linear coefficient of thermal expansion. ˙ exp( ). εσ ss n AQRT=−/ ε . ss = steady-state tensile strain rate; A, n = constants; σ = tensile stress; Q = activation energy for creep; R = universal gas constant; T = absolute temperature. Chapter 18: Statistics of fracture Weibull distribution P s (V ) = exp −                 V V m 00 σ σ Symbols and formulae 375 or ln ln ln ln . 1 00 P V V m s             =+       σ σ P s = survival probability of component; V = volume of component; σ = tensile stress on component; V 0 = volume of test sample; σ 0 = stress that, when applied to test sample, gives P s = 1/e (= 0.37); m = Weibull modulus. Failure probability P f = 1 − P s . Slow crack-growth σ σ TS (test)       = n t t . σ = strength of component after time t; σ TS = strength of component measured over time t(test); n = slow crack-growth exponent. Chapter 19: Ceramics processing Sintering d d / ρ t C a QRT n exp( ).=− ρ = density; t = time; C, n = constants; a = particle size; Q = activation energy for sinter- ing; R = universal gas constant; T = absolute temperature. Glass forming η ∝ exp(Q/RT). η = viscosity; Q = activation energy for viscous flow. Chapter 20: Cements and concretes Hardening rate ∝ exp(–Q/RT). Q = activation energy for hardening reaction; R = universal gas constant; T = absolute temperature. Chapter 23: Mechanical behaviour of polymers Modulus: WLF shift factor log(a T ) = CT T CTT 11 0 210 ( ) . − +− [...]... Polyester 22 3, 22 4 Polyethylene 22 2, 22 4 Polyethyleneteraphthalate 22 1 Polyisoprene 21 6, 21 7, 24 7 Polymers 21 9 et seq case studies in 308 production, forming and joining 25 4 et seq properties 23 8 et seq structure 22 8 et seq Polymethylmethacrylate 22 2, 22 4, 24 6, 3 12 Polymorphism 16 Polypropylene 22 2, 22 4, 3 12 Polysilicon 95 Polystyrene 22 2, 22 4 Polytetrafluorethylene 22 2, 22 4 Polyvinylchloride 22 2, 22 4, 25 5... polymers 22 1, 22 6 Crystal growth 91 Crystal structure of ceramics 168 metals 14 polymers 23 3 Cupronickel 7 Dacron 22 1 Data for ceramics and glasses 163 , 165 composites 26 5 metals 11 polymers 22 4, 22 5 woods 27 8 Decomposition of polymers 24 6 Degree of polymerisation 22 8 Dendrites 65, 92, 3 52 Density of ceramics and glasses 164 foams 27 2 metals 12 polymers 22 4 woods 27 8 Design-limiting properties 28 9 Design... 323 et seq 379 380 Index Moduli of ceramics and glasses 164 , 177 composites 26 5, 26 6 foams 27 3 metals 12 polymers 22 4, 23 9 woods 27 8 Modulus of rupture 164 , 181 Monel 7, 12 Mould design 308 Moulding 20 0, 25 7 Mullite 173 Mylar 22 1 Neoprene 22 3 Network ceramics and glasses 167 Nickel-based alloys 7, 12 Nitriding 155 Normalisation of steels 113 Nucleation 68, 73, 77, 89 et seq Nylon 22 2, 22 4, 25 5, 3 12. .. Optimised materials 26 4, 27 0, 27 5 Pearlite 64, 115 et seq Peritectic 359 Peritectoid 380 Phase boundaries 18, 21 Phase diagrams 26 et seq., 326 case studies 34 et seq teach yourself 320 et seq Phase reactions 348 Phase transformations 46 et seq., 89 Phases 18, 25 , 323 Phenol-formaldehyde 22 3, 22 4 Plasticisers 25 6 Plumbers solder 34, 35 Polyacrylonitrile 22 1 Polybutadiene 22 3, 22 4 Polychloroprene 22 3, 22 4... Synthesis of polymers 25 4 Teach yourself phase diagrams 320 et seq Ternary alloy 25 , 327 Terylene 22 1 Thermal properties of ceramics and glasses 165 metals 13 polymers 22 5 Thermal shock resistance 166 , 1 82 Thermoplastics 22 0, 22 4, 23 0 Thermosets 22 0, 22 4 Time-dependent strength 189 Titanium-based alloys 10, 100, 103 Tobomorite gel 20 8 Traction engine 3 TTT curves 80, 98, 105, 110, 122 , 123 Undercooling 63,... Amorphous metals 96 polymers 23 6 structure 16 Anisotropy 26 6, 28 0, 316 Annealing 151 Atactic polymers 23 1 Austenite 114, 130, 355 Availability 50 Bain strain 84 Bakelite 22 1 Beryllium 100 Binary alloy 25 , 327 , 336 Boiler design 133 Bone 164 , 165 Borosilicate glass 1 62, 165 Boundaries 18 Boundary tension 22 Brass 7, 12, 3 42 Brick 163 , 20 1 Bronze 7, 12, 356 Carbide formers 129 Carbon equivalent 138 Carbon... and glasses 164 , 178 et seq composites 26 5, 26 7 foams 27 3 metals 12 polymers 22 4, 25 1 woods 27 7, 28 3 Structure of amorphous solids 16 ceramics and glasses 167 et seq compounds 16 metals 14 et seq polymers 22 8 et seq solid solutions 16, 322 381 Structural change 46 et seq Substitutional solutions 17 Sulphur 96 Surface energy and tension 21 Surface engineering 155 Superalloys 7, 12 Symbols 321 , 370 et... concrete 20 7 et seq production, forming and joining 194 et seq properties 164 , 177 et seq structures 167 , 174 et seq Cermets 164 , 20 3 CFRP 164 , 26 3 et seq., 317 Chain-folded crystals 23 3 Chemical reactions 47 Chemical vapour deposition 198 China 163 Coherent interfaces 20 , 83, 107 Cold drawing 24 8, 24 9 Columnar crystals 91, 144 Components 22 , 25 , 321 Composites 165 , 20 3, 21 5, 26 3 et seq case studies in 3 12. .. forming 25 7 Vibrations 314 Viscoelastic behaviour 24 2 Viscosity 198, 24 5 Vitreous ceramics 1 62, 174 Vulcanisation 24 7, 25 7 Weibull statistics 185 et seq Welding 136, 154, 303 Wheel design 303 Window design 190 Wood 27 7 et seq case study in 3 12 properties 28 0 structure 27 8 Work 46 Work hardening 110, 1 52 Working of metals 147 Zinc 12 Zirconia 163 , 164 , 169 , 20 2, 20 3 Zone refining 39 et seq 3 82 Index... in 3 12 et seq Composition 25 , 321 , 336 Compounds 17 Compression moulding 25 7, 25 9 Compressive strength 1 82, 21 3 Concentration 321 378 Index Constitution 22 , 30, 324 Constitution point 27 , 336, 337 Continuous casting 145 Conveyor drum design 29 6 Co-polymers 25 5 Copper-based alloys 6, 12, 30, 31, 356, 361 Corrosion 129 Cooling curves 333 Covalent ceramics 167 , 170 Crazing 24 8, 25 0 Creep of ceramics 183 . 35 Polyacrylonitrile 22 1 Polybutadiene 22 3, 22 4 Polychloroprene 22 3, 22 4 Polyester 22 3, 22 4 Polyethylene 22 2, 22 4 Polyethyleneteraphthalate 22 1 Polyisoprene 21 6, 21 7, 24 7 Polymers 21 9 et seq. case studies. joining 25 4 et seq. properties 23 8 et seq. structure 22 8 et seq. Polymethylmethacrylate 22 2, 22 4, 24 6, 3 12 Polymorphism 16 Polypropylene 22 2, 22 4, 3 12 Polysilicon 95 Polystyrene 22 2, 22 4 Polytetrafluorethylene. 95 Polystyrene 22 2, 22 4 Polytetrafluorethylene 22 2, 22 4 Polyvinylchloride 22 2, 22 4, 25 5 Porcelain 163 , 20 1 Porosity 43 Portland cement 163 , 20 8 Pottery 163 , 20 1 Powder methods 143, 145, 195 et seq. Precipitate