a lattice parameter nm a crack length mm A availability J A1 eutectoid temperature °C A3 first ferrite temperature °C Acm first Fe3C temperature °C b Burgers vector nm c height of c.p.h.
Trang 1Fig A1.56.
precipitates ε and ε precipitates β Just above 600°C 18 ( = 34%) ε (65% B) + 35 ( = 66%) β (12% B) At 600°C all β forms α and ε in eutectoid reaction Just below 600°C 25 ( = 42%) ε (65% B) + 35 ( = 58%) α (5% B) 600°C → 300°C, α precipitates ε and ε precipitates α Just above 300°C 27 ( = 41%) ε (69% B) + 39 ( = 59%) α (3% B).
At 300°C all ε and some α form δ in peritectoid reaction Just below 300°C 27 (= 73%) δ (40% B) + 10 ( = 27%) α (3% B) 300°C → 0°C, amount of α decreases and δ increases At 0°C 30 ( = 86%) δ (35% B) + 5
35 ( = 14%) α (0% B).
Trang 2Appendix 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)
A1 eutectoid temperature (°C)
A3 first ferrite temperature (°C)
Acm first Fe3C 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)
g acceleration due to gravity on the Earth’s surface (m s−2)
G shear modulus (GPa)
G Gibbs function (J)
Gc toughness (kJ m−2)
∆H latent heat of transformation (J)
I second moment of area of structural section (mm4)
k ratio of Csolid/Cliquid on phase diagram (dimensionless)
k Boltzmann’s constant (J K−1)
k shear yield strength (MPa)
KIC fracture toughness (MPa m1/2)
Trang 3Symbol Meaning(units)
m Weibull modulus (dimensionless)
M bending moment (N m)
MF martensite finish temperature (°C)
MS martensite start temperature (°C)
n time exponent for slow crack-growth (dimensionless)
p pressure (Pa)
Pf failure probability (dimensionless)
PS 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)
Te equilibrium temperature (K)
Tg glass temperature (K)
Tm melting temperature (K)
∆T thermal shock resistance (K)
ν velocity (m s−1)
V volume (m3)
V volume fraction (dimensionless)
WA weight % (dimensionless)
Wf free work (J)
XA 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)
εf (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)
σc (nominal) compressive strength (MPa)
σr modulus of rupture (MPa)
σTS (nominal) tensile strength (MPa)
σy (nominal) yield strength (MPa)
Greek letters are used to label the phases on phase diagrams.
Trang 4Summary of principal formulae and magnitudes
Chapter 3 and Teaching yourself phase diagrams: phase diagrams
Composition is given by
WA=
weight of A weight of A weight of B+ ×100
in weight %, and by
XA=
atoms (mols) of A atoms (mols) of A atoms (mols) of B + × 100
in atom (mol) %.
WA+ WB = 100%; XA+ XB = 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
Cs=
l
01 −( )exp1− −
Cs = concentration of impurities in refined solid; C0 = average impurity concentration;
k = Csolid/Cliquid; x = distance from start of bar; l = zone length.
Chapter 5: Driving forces
Driving force for solidification
Wf = −∆G =
T m (T m T).
∆H = latent heat of solidification; Tm= absolute melting temperature; T = actual
tem-perature (absolute).
Driving force for solid-state phase change
Wf = −∆G =
T e ( ).T e T
∆H = latent heat of transformation; T = equilibrium temperature (absolute).
Trang 5Chapter 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* =
2γSLT
H T T
m m
∆ ( )− .
γSL = solid–liquid interfacial energy; Tm = 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
σy∝ ε3 2s/ C1 2 / .
C = solute concentration; εs= mismatch parameter.
Work-hardening
σy∝ εn.
ε = true strain; n = constant.
Chapter 14: Metal processing
Forming pressure
No friction
p = σ
Trang 6Sticking friction
pf =
σy
w x d
1 + ( 2) −
/
σy = 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
σTS=
K
a m
IC
KIC= fracture toughness; am= size of widest microcrack (crack width for surface crack; crack half-width for buried crack).
Modulus of rupture
σr=
6
2
M
bd
r
Mr = bending moment to cause rupture; b = width of beam; d = depth of beam Compressive strength
σc ≈ 15σTS,
σc =
CK
a
IC
π .
C = constant (≈15); a = average crack size.
Thermal shock resistance
∆T = σTS/E α.
E = Young’s modulus; α = linear coefficient of thermal expansion.
˙ εss= Aσnexp(− /Q RT).
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
Ps(V ) =
V V
m
σ σ
Trang 7
ln ln 1 ln ln
P
V
s
σ σ
Ps= survival probability of component; V = volume of component; σ = tensile stress on component; V0= volume of test sample; σ0= stress that, when applied to test sample,
gives Ps= 1/e (= 0.37); m = Weibull modulus.
Failure probability
Pf= 1 − Ps.
Slow crack-growth
σ
σTS
(test)
=
n
t
t
σ = strength of component after time t; σTS = strength of component measured over
time t(test); n = slow crack-growth exponent.
Chapter 19: Ceramics processing
Sintering
d
ρ
t
C
a n Q RT
= 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(aT) =
C T T
1 1 0
( ) .
−
Trang 8C1, C2= constants; T1, T0= absolute temperatures.
Polymer viscosity
η1 η0
.
C T T
C T T
Chapter 25: Composites
Unidirectional fibre composites
Ec||= VfEf+ (1 − Vf)Em,
E V
E
V E
f
f
f m
c⊥
−
= + −
1
1
Ec|| = composite modulus parallel to fibres; Ec⊥ = composite modulus perpendicular to
fibres; Vf= volume fraction of fibres; Ef = Young’s modulus of fibres; Em = Young’s modulus of matrix.
σTS= V f f V
f
f y m
σ ( )+ 1− σ
σTS = tensile strength parallel to fibres; σf
f = fracture strength of fibres; σy m = yield strength of matrix.
Optimum toughness
Gc=
V f d
f f
s m
( )
8
2 σ σ
d = fibre diameter; σs m = shear strength of matrix.
Magnitudes of properties The listed properties lie, for most structural materials, in the ranges shown
(unfoamed) (polymer
matrix)
Trang 9Adhesives 204, 260
Age hardening see Precipitation hardening
Alexander Keilland oil platform 136
Alloy 15, 25, 321
Alumina 163, 164, 167
Aluminium-based alloys 8, 12, 100 et seq.,
347, 351
Amorphous
metals 96
polymers 236
structure 16
Anisotropy 266, 280, 316
Annealing 151
Atactic polymers 231
Austenite 114, 130, 355
Availability 50
Bain strain 84
Bakelite 221
Beryllium 100
Binary alloy 25, 327, 336
Boiler design 133
Bone 164, 165
Borosilicate glass 162, 165
Boundaries 18
Boundary tension 22
Brass 7, 12, 342
Brick 163, 201
Bronze 7, 12, 356
Carbide formers 129
Carbon equivalent 138
Carbon fibres see CFRP
Carburising 155
Case studies
in ceramics and glasses 190, 303
in design 296 et seq.
in phase diagrams 34 et seq.
in phase transformations 89 et seq.
in steels 133 et seq.
Casting 91, 121, 144 Casting defects 144 Cast iron 6, 12, 121 Catalysis 91, 93
C-curves see TTT curves Cellular solids 272 et seq.
Cellulose 224, 279
Cement and concrete 163, 207 et seq.
chemistry 207 strength 212 structure 210
Cementite 114 et seq., 355 Ceramics 161 et seq.
brittle fracture 180, 185 et seq.
case studies in 190, 303
cement and concrete 207 et seq.
production, forming and joining 194 et seq properties 164, 177 et seq.
structures 167, 174 et seq.
Cermets 164, 203
CFRP 164, 263 et seq., 317
Chain-folded crystals 233 Chemical reactions 47 Chemical vapour deposition 198 China 163
Coherent interfaces 20, 83, 107 Cold drawing 248, 249 Columnar crystals 91, 144 Components 22, 25, 321
Composites 165, 203, 215, 263 et seq.
case studies in 312 et seq.
Composition 25, 321, 336 Compounds 17
Compression moulding 257, 259 Compressive strength 182, 213 Concentration 321
Trang 10Constitution 22, 30, 324
Constitution point 27, 336, 337
Continuous casting 145
Conveyor drum design 296
Co-polymers 255
Copper-based alloys 6, 12, 30, 31, 356,
361
Corrosion 129
Cooling curves 333
Covalent ceramics 167, 170
Crazing 248, 250
Creep of ceramics 183
Critical nucleus 69
Cross-linked polymers 221, 226
Crystal growth 91
Crystal structure of
ceramics 168
metals 14
polymers 233
Cupronickel 7
Dacron 221
Data for
ceramics and glasses 163, 165
composites 265
metals 11
polymers 224, 225
woods 278
Decomposition of polymers 246
Degree of polymerisation 228
Dendrites 65, 92, 352
Density of
ceramics and glasses 164
foams 272
metals 12
polymers 224
woods 278
Design-limiting properties 289
Design methodology 291, 292
Diamond 164
Die casting 145
Differential thermal analysis 334
Diffusion bonding 204
Diffusion-controlled kinetics 63
Diffusive transformations 57 et seq.
Displacive transformations 76 et seq.
Driving force 46 et seq.
Duralumin 103
Dynamic equilibrium 61
Elastic constants see Moduli
Elastomers 221, 224, 232, 244 Energy-efficient forming 155 Enthalpy 52
Entropy 49 Epoxies 221, 224 Equiaxed crystals 92, 142 Equilibrium 28, 51, 61
Equilibrium diagrams 25 et seq case studies 34 et seq.
teach yourself 326 et seq Eutectics 35, 42, 114, 346 et seq Eutectoids 346 et seq.
Extrusion 258 Fatigue 298
Ferrite 114 et seq., 355
Ferrous alloys 6, 10 Failure probability 185 Failure analyses 133, 296 Fibres 260, 263
Foams 263, 272 Forging 147 Formica 223 Forming of 194
ceramics and glasses 194 et seq.
composites 264
metals 143 et seq.
polymers 254 et seq.
Formulae 372 et seq.
Forsterite 173 Fracture strength of ceramics and glasses 164, 180 composites 267
metals 13 polymers 225, 248 woods 278 Fracture toughness of ceramics and glasses 164, 180 composites 265, 269
metals 13 polymers 225 woods 278 Free work 50 Germanium 39
GFRP 219, 263 et seq., 317
Gibbs’ function 53 Gibbs’ phase rule 341
Trang 11Glasses 161 et seq.
brittle fracture 185 et seq.
production, forming and joining 97,
198 et seq.
properties 177 et seq.
structure 167 et seq.
Glass fibres see GFRP
Glass temperature 225, 235, 239
Glass transition 239
Glassy metals 63, 97
Glaze bonding 204
Glazes 202
GP zones 106
Grain
boundaries 18
growth 55, 137
shape 20, 64
size 93
strengthening 153
Grains 20
Granite 164, 175
Graphite 121
Habit plane 83
Hammer design 139
Hardenability 125
Heat 48
Heat-affected zone 137
Heat flow 62
Heterogeneous nucleation 69, 90
Homogeneous nucleation 69
Hot isostatic pressing 196
Hot pressing 196
Hydrogen cracking 138
Hydroplastic forming 194, 201
Ice 41, 51, 89, 164, 303, 335
Incoherent interfaces 20, 107
Induction hardening 122
Injection moulding 257
Inoculants 93
Instability 50
Integrated circuits 94
Internal energy 47
Interstitial solutions 16
Intrinsic strength 178
Investment casting 146
Ion implantation 155
Ionic ceramics 167, 168
Iron-based alloys 5, 12 Isotactic polymers 231 Joining
of ceramics and glasses 204
of metals 154
of polymers 260 Jominy test 126
Kevlar fibres see KFRP
KFRP 219, 271
Kinetics 59 et seq.
Lead-tin alloys 12, 26, 34, 326 et seq.
Ledeburite 115 Lever rule 339
Light alloys 100 et seq.
Lignin 224, 279 Liquid phase sintering 197 Limestone 164
Linear polymers 220, 225 Machining 153
Magnesia 168
Magnesium-based alloys 100 et seq.
Martensite 83, 118, 134, 137, 140 Mechanical properties of
cement and concrete 212 et seq.
ceramics and glasses 164, 177 et seq composites 265 et seq.
foams 273
metals 12, 101, 118, 140 et seq.
polymers 224, 238 et seq.
woods 277 et seq.
Melt spinning 98 Memory alloys 87
Metals 3 et seq.
case studies in 133 et seq.
equilibrium diagrams for 25 et seq.
glassy 63, 97
light alloys 100 et seq.
production, forming and joining
143 et seq.
properties 12, 13, 101
steels 113 et seq.
structure 14 et seq.
Metastability 50 Microchips 39
Microstructure 323 et seq.
Trang 12Moduli of
ceramics and glasses 164, 177
composites 265, 266
foams 273
metals 12
polymers 224, 239
woods 278
Modulus of rupture 164, 181
Monel 7, 12
Mould design 308
Moulding 200, 257
Mullite 173
Mylar 221
Neoprene 223
Network ceramics and glasses 167
Nickel-based alloys 7, 12
Nitriding 155
Normalisation of steels 113
Nucleation 68, 73, 77, 89 et seq.
Nylon 222, 224, 255, 312
Offshore structures 303
Optimised materials 264, 270, 275
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 223, 224
Plasticisers 256
Plumbers solder 34, 35
Polyacrylonitrile 221
Polybutadiene 223, 224
Polychloroprene 223, 224
Polyester 223, 224
Polyethylene 222, 224
Polyethyleneteraphthalate 221
Polyisoprene 216, 217, 247
Polymers 219 et seq.
case studies in 308
production, forming and joining 254 et seq.
properties 238 et seq.
structure 228 et seq.
Polymethylmethacrylate 222, 224, 246, 312 Polymorphism 16
Polypropylene 222, 224, 312 Polysilicon 95
Polystyrene 222, 224 Polytetrafluorethylene 222, 224 Polyvinylchloride 222, 224, 255 Porcelain 163, 201
Porosity 43 Portland cement 163, 208 Pottery 163, 201
Powder methods 143, 145, 195 et seq.
Precipitate coarsening 54 Precipitation hardening 103, 108, 128 Production of
ceramics and glasses 194 et seq.
composites 264
metals 143 et seq.
polymers 254 et seq.
Properties of
cement and concrete 212 et seq.
composites 264 et seq.
ceramics and glasses 177 et seq.
foams 273 metals 101, 118
polymers 238 et seq.
woods 280 et seq.
Proportions of phases 338 Protein 224
Quenching and tempering 119 Radicals 230
Rain making 89
Rates of transformation see Kinetics
Rayon 254 Reaction bonding 197 Recovery 151 Recrystallisation 55, 151 Resins 221, 224
Reversibility 49 Rolling 150, 200 Salol 58 Sand casting 145 Sandstone 175 Sandwich panels 272, 318 Scale of structural features 14, 66 Seeding 91, 93
Segregation 93, 144 Semicoherent interfaces 20