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Materials Data Book 2003 Edition

Cambridge University Engineering Department

PHYSICAL CONSTANTS IN SI UNITS Absolute zero of temperature Acceleration due to gravity, g Avogadro’s number, N A Base of natural logarithms, e Boltzmann’s constant, k Faraday’s constant, F Universal Gas constant, R Permeability of vacuum, µo Permittivity of vacuum, εo Planck’s constant, h Velocity of light in vacuum, c Volume of perfect gas at STP

– 273.15 °C 9. 807 m/s2 6.022x1026 /kmol 2.718 1.381 x 10–26 kJ/K 9.648 x 107 C/kmol 8.3143 kJ/kmol K 1.257 x 10–6 H/m 8.854 x 10–12 F/m 6.626 x 10–37 kJ/s 2.998 x 108 m/s 22.41 m3/kmol

CONVERSION OF UNITS Angle, θ Energy, U Force, F Length, l Mass, M Power, P Stress, σ Specific Heat, Cp Stress Intensity, K Temperature, T Thermal Conductivity, λ Volume, V Viscosity, η

1 rad See inside back cover 1 kgf 1 lbf 1 ft 1 inch 1Å 1 tonne 1 lb See inside back cover See inside back cover 1 cal/g.°C 1 ksi in 1 °F 1 cal/s.cm.oC 1 Imperial gall 1 US gall 1 poise 1 lb ft.s

57.30 ° 9.807 N 4.448 N 304.8 mm 25.40 mm 0.1 nm 1000 kg 0.454 kg

4.188 kJ/kg.K 1.10 MPa m 0.556 K 4.18 W/m.K 4.546 x 10–3 m3 3.785 x 10–3 m3 0.1 N.s/m2 0.1517 N.s/m2

1

CONTENTS Page Number Introduction Sources

3 3 I. FORMULAE AND DEFINITIONS

Stress and strain Elastic moduli Stiffness and strength of unidirectional composites Dislocations and plastic flow Fast fracture Statistics of fracture Fatigue 7 Creep Diffusion Heat flow

4 4 5 5 6 6 7 8 8

II. PHYSICAL AND MECHANICAL PROPERTIES OF MATERIALS Melting temperature Density Young’s modulus Yield stress and tensile strength Fracture toughness Environmental resistance Uniaxial tensile response of selected metals and polymers

9 10 11 12 13 14 15

III. MATERIAL PROPERTY CHARTS Young’s modulus versus density Strength versus density Young’s modulus versus strength Fracture toughness versus strength Maximum service temperature Material price (per kg)

16 17 18 19 20 21

IV. PROCESS ATTRIBUTE CHARTS Material-process compatibility matrix (shaping) Mass Section thickness Surface roughness Dimensional tolerance Economic batch size

22 23 23 24 24 25

2 V. CLASSIFICATION AND APPLICATIONS OF ENGINEERING MATERIALS Metals: ferrous alloys, non-ferrous alloys Polymers and foams Composites, ceramics, glasses and natural materials

26 27 28

VI. EQUILIBRIUM (PHASE) DIAGRAMS Copper – Nickel Lead – Tin Iron – Carbon Aluminium – Copper Aluminium – Silicon Copper – Zinc Copper – Tin Titanium-Aluminium Silica – Alumina

29 29 30 30 31 31 32 32 33

VII. HEAT TREATMENT OF STEELS TTT diagrams and Jominy end-quench hardenability curves for steels

34

VIII. PHYSICAL PROPERTIES OF SELECTED ELEMENTS Atomic properties of selected elements Oxidation properties of selected elements

36 37

3

INTRODUCTION The data and information in this booklet have been collected for use in the Materials Courses in Part I of the Engineering Tripos (as well as in Part II, and the Manufacturing Engineering Tripos). Numerical data are presented in tabulated and graphical form, and a summary of useful formulae is included. A list of sources from which the data have been prepared is given below. Tabulated material and process data or information are from the Cambridge Engineering Selector (CES) software (Educational database Level 2), copyright of Granta Design Ltd, and are reproduced by permission; the same data source was used for the material property and process attribute charts. It must be realised that many material properties (such as toughness) vary between wide limits depending on composition and previous treatment. Any final design should be based on manufacturers’ or suppliers’ data for the material in question, and not on the data given here.

SOURCES Cambridge Engineering Selector software (CES 4.1), 2003, Granta Design Limited, Rustat House, 62 Clifton Rd, Cambridge, CB1 7EG M F Ashby, Materials Selection in Mechanical Design, 1999, Butterworth Heinemann M F Ashby and D R H Jones, Engineering Materials, Vol. 1, 1996, Butterworth Heinemann M F Ashby and D R H Jones, Engineering Materials, Vol. 2, 1998, Butterworth Heinemann M Hansen, Constitution of Binary Alloys, 1958, McGraw Hill I J Polmear, Light Alloys, 1995, Elsevier C J Smithells, Metals Reference Book, 6th Ed., 1984, Butterworths Transformation Characteristics of Nickel Steels, 1952, International Nickel

4

I. FORMULAE AND DEFINITIONS STRESS AND STRAIN

σt =

F A

σn =

F Ao

 l   lo 

ε t = ln 

ν =−

l −lo lo

σ t = true stress σ n = nominal stress ε t = true strain ε n = nominal strain

F = normal component of force Ao = initial area A = current area l o = initial length l = current length Poisson’s ratio,

εn =

lateral strain longitudinal strain

Young’s modulus E = initial slope of σ t − εt curve = initial slope of σ n − ε n curve. Yield stress σ y is the nominal stress at the limit of elasticity in a tensile test. Tensile strength σ ts is the nominal stress at maximum load in a tensile test. Tensile ductility ε f is the nominal plastic strain at failure in a tensile test. The gauge length of the specimen should also be quoted. ELASTIC MODULI G=

E 2 (1 +ν )

K=

E 3 (1− 2ν )

For polycrystalline solids, as a rough guide, Poisson’s Ratio

ν≈

1 3

Shear Modulus

G≈

3 E 8

Bulk Modulus

K ≈ E

These approximations break down for rubber and porous solids.

5 STIFFNESS AND STRENGTH OF UNIDIRECTIONAL COMPOSITES E II = V f E f + ( 1 − V f ) E m

 V f 1− V f E⊥ =  +  Ef Em 

   

−1

σ ts = V f σ ff + ( 1 − V f ) σ m y E II = composite modulus parallel to fibres (upper bound) E ⊥ = composite modulus transverse to fibres (lower bound) V f = volume fraction of fibres E f = Young’s modulus of fibres

E m = Young’s modulus of matrix σ ts = tensile strength of composite parallel to fibres

σ ff = fracture strength of fibres

σm y = yield stress of matrix DISLOCATIONS AND PLASTIC FLOW

The force per unit length F on a dislocation, of Burger’s vector b , due to a remote shear stress τ , is F = τ b . The shear stress τ y required to move a dislocation on a single slip plane is

τy =

cT bL

where T = line tension (about 1 G b 2 , where G is the shear modulus) 2

L = inter-obstacle distance c = constant ( c ≈ 2 for strong obstacles, c < 2 for weak obstacles) The shear yield stress k of a polycrystalline solid is related to the shear stress τ y required to move a dislocation on a single slip plane: k ≈ 32 τ y . The uniaxial yield stress σ y of a polycrystalline solid is approximately σ y = 2 k , where k is the shear yield stress. Hardness H (in MPa) is given approximately by: H ≈ 3 σ y . Vickers Hardness HV is given in kgf/mm2, i.e. HV = H / g , where g is the acceleration due to gravity.

6 FAST FRACTURE K = Y σ

The stress intensity factor, K :

πa

Fast fracture occurs when K = K IC In plane strain, the relationship between stress intensity factor K and strain energy release rate G is: K =

EG 1 −ν 2

≈

(as ν

EG

2

≈ 0.1 ) K IC =

Plane strain fracture toughness and toughness are thus related by:

E GIC 1 −ν 2

≈

E GIC

2

“Process zone size” at crack tip given approximately by: r p =

K IC

π σ2f

Note that KIC (and GIC ) are only valid when conditions for linear elastic fracture mechanics apply (typically the crack length and specimen dimensions must be at least 50 times the process zone size). In the above: σ = remote tensile stress a = crack length Y = dimensionless constant dependent on geometry; typically Y ≈ 1 K IC = plane strain fracture toughness; G IC = critical strain energy release rate, or toughness; E = Young’s modulus ν = Poisson’s ratio σ f = failure strength STATISTICS OF FRACTURE  Weibull distribution, Ps (V) = exp  

For constant stress:

∫

  Ps (V) = exp  − 

 σ −  V σo σ  σo

   

m

dV   Vo 

m   V     V o 

Ps = survival probability of component V = volume of component σ = tensile stress on component V o = volume of test sample

σ o = reference failure stress for volume Vo , which gives Ps = m = Weibull modulus

1 = 0 .37 e

7 FATIGUE

Basquin’s Law (high cycle fatigue):

∆σ N αf = C1 Coffin-Manson Law (low cycle fatigue):

∆ε pl N βf = C2 Goodman’s Rule. For the same fatigue life, a stress range ∆ σ operating with a mean stress σ m , is equivalent to a stress range ∆σ o and zero mean stress, according to the relationship: 

∆σ = ∆σ o 1 − 

σm   σ ts 

Miner’s Rule for cumulative damage (for i loading blocks, each of constant stress amplitude and duration Ni cycles):

∑ i

Ni N fi

= 1

Paris’ crack growth law: da = A ∆Kn dN In the above:

∆σ = stress range; ∆ε pl = plastic strain range; ∆K = tensile stress intensity range; N = cycles; N f = cycles to failure; α , β , C1 , C 2 , A, n = constants; a = crack length; σ ts = tensile strength. CREEP

Power law creep:

ε&ss = A σ n exp ( − Q / RT )

ε& ss = steady-state strain-rate Q = R = T = A, n

activation energy (kJ/kmol) universal gas constant absolute temperature = constants

8 DIFFUSION

D = Do exp ( − Q / RT )

Diffusion coefficient:

Fick’s diffusion equations:

J =−D

C = concentration x = distance t = time

dC dx

2

∂ C ∂C =D ∂t ∂ x2

and

J = diffusive flux D = diffusion coefficient (m2/s) Do = pre-exponential factor (m2/s) Q = activation energy (kJ/kmol) HEAT FLOW

Steady-state 1D heat flow (Fourier’s Law):

q = −λ

dT dx

∂ 2T ∂T =a ∂t ∂ x2 T = temperature (K) q = heat flux per second, per unit area (W/m2.s)

Transient 1D heat flow:

λ = thermal conductivity (W/m.K)

a = thermal diffusivity (m2/s)

For many 1D problems of diffusion and heat flow, the solution for concentration or temperature depends on the error function, erf :  C( x , t ) = f erf 

 x     2 D t   

or

 T ( x , t ) = f erf 

 x     2 a t   

A characteristic diffusion distance in all problems is given by x ≈ characteristic heat flow distance in thermal problems being x ≈ The error function, and its first derivative, are: X 2 exp − y 2 dy and erf ( X ) =

π

∫0

( )

D t , with the corresponding at .

d [ erf ( X )] = dX

2

π

(

exp − X 2

)

The error function integral has no closed form solution – values are given in the Table below. X

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

erf ( X )

0

0.11

0.22

0.33

0.43

0.52

0.60

0.68

0.74

X

0.9

1.0

1.1

1.2

1.3

1.4

1.5

∞

erf ( X )

0.80

0.84

0.88

0.91

0.93

0.95

0.97

1.0

9

II. PHYSICAL AND MECHANICAL PROPERTIES OF MATERIALS II.1 MELTING (or SOFTENING) TEMPERATURE, Tm All data are for melting points at atmospheric pressure. For polymers (and glasses) the data indicate the glass transition (softening) temperature, above which the mechanical properties rapidly fall. Melting temperatures of selected elements are given in section VIII. Tm (oC)

Tm (oC) 1

Metals Ferrous

Non-ferrous

Ceramics Glasses

Porous Technical

Composites Metal Polymer

Cast Irons High Carbon Steels Medium Carbon Steels Low Carbon Steels Low Alloy Steels Stainless Steels Aluminium Alloys Copper Alloys Lead Alloys Magnesium Alloys Nickel Alloys Titanium Alloys Zinc Alloys

1130 1289 1380 1480 1382 1375 475 982 322 447 1435 1477 375

-

1250 1478 1514 1526 1529 1450 677 1082 328 649 1466 1682 492

Borosilicate Glass (*) Glass Ceramic (*) Silica Glass (*) Soda-Lime Glass (*) Brick Concrete, typical Stone Alumina Aluminium Nitride Boron Carbide Silicon Silicon Carbide Silicon Nitride Tungsten Carbide

450 563 957 442 927 927 1227 2004 2397 2372 1407 2152 2388 2827

-

602 1647 1557 592 1227 1227 1427 2096 2507 2507 1412 2500 2496 2920

Aluminium/Silicon Carbide CFRP GFRP

525

Bamboo (*) Cork (*) Leather (*) Wood, typical (Longitudinal) (*) Wood, typical (Transverse) (*)

77 77 107 77 77

-

Polymers Elastomer

Thermoplastic

Thermoset

-

102 102 127 102 102

– 73 – 73 – 83 – 78 – 48 – 73 – 123 88 –9 27 44 142 143 – 25 68 85 – 18 – 25 74 120 75 107

n/a n/a n/a

– 63 – 23 – 78 – 63 – 43 – 23 – 73 128 107 77 56 205 199 – 15 80 165 –8 – 15 110 160 105 123

Polymer Foams Flexible Polymer Foam (VLD) (*) Flexible Polymer Foam (LD) (*) Flexible Polymer Foam (MD) (*) Rigid Polymer Foam (LD) (*) Rigid Polymer Foam (MD) (*) Rigid Polymer Foam (HD) (*)

- 627 n/a n/a

Natural

Butyl Rubber (*) EVA (*) Isoprene (IR) (*) Natural Rubber (NR) (*) Neoprene (CR) (*) Polyurethane Elastomers (elPU) (*) Silicone Elastomers (*) ABS (*) Cellulose Polymers (CA) (*) Ionomer (I) (*) Nylons (PA) (*) Polycarbonate (PC) (*) PEEK (*) Polyethylene (PE) (*) PET (*) Acrylic (PMMA) (*) Acetal (POM) (*) Polypropylene (PP) (*) Polystyrene (PS) (*) Polyurethane Thermoplastics (tpPU) (*) PVC Teflon (PTFE) Epoxies Phenolics Polyester

1

112 112 112 67 67 67

-

177 177 177 171 157 171

For full names and acronyms of polymers – see Section V. (*) glass transition (softening) temperature n/a: not applicable (materials decompose, rather than melt) (Data courtesy of Granta Design Ltd)

10

II.2

DENSITY, ρ

ρ (Mg/m3)

ρ (Mg/m3) 1

Metals Ferrous

Non-ferrous

Ceramics Glasses

Porous Technical

Composites Metal Polymer

Cast Irons High Carbon Steels Medium Carbon Steels Low Carbon Steels Low Alloy Steels Stainless Steels Aluminium Alloys Copper Alloys Lead Alloys Magnesium Alloys Nickel Alloys Titanium Alloys Zinc Alloys

7.05 7.8 7.8 7.8 7.8 7.6 2.5 8.93 10 1.74 8.83 4.4 4.95

-

7.25 7.9 7.9 7.9 7.9 8.1 2.9 8.94 11.4 1.95 8.95 4.8 7

Borosilicate Glass Glass Ceramic Silica Glass Soda-Lime Glass Brick Concrete, typical Stone Alumina Aluminium Nitride Boron Carbide Silicon Silicon Carbide Silicon Nitride Tungsten Carbide

2.2 2.2 2.17 2.44 1.9 2.2 2.5 3.5 3.26 2.35 2.3 3 3 15.3

-

2.3 2.8 2.22 2.49 2.1 2.6 3 3.98 3.33 2.55 2.35 3.21 3.29 15.9

Aluminium/Silicon Carbide CFRP GFRP

2.66 1.5 1.75

-

2.9 1.6 1.97

Bamboo Cork Leather Wood, typical (Longitudinal) Wood, typical (Transverse)

0.6 0.12 0.81 0.6 0.6

-

0.8 0.24 1.05 0.8 0.8

Polymers Elastomer

Thermoplastic

Thermoset

Butyl Rubber EVA Isoprene (IR) Natural Rubber (NR) Neoprene (CR) Polyurethane Elastomers (elPU) Silicone Elastomers ABS Cellulose Polymers (CA) Ionomer (I) Nylons (PA) Polycarbonate (PC) PEEK Polyethylene (PE) PET Acrylic (PMMA) Acetal (POM) Polypropylene (PP) Polystyrene (PS) Polyurethane Thermoplastics (tpPU) PVC Teflon (PTFE) Epoxies Phenolics Polyester

0.9 0.945 0.93 0.92 1.23 1.02 1.3 1.01 0.98 0.93 1.12 1.14 1.3 0.939 1.29 1.16 1.39 0.89 1.04 1.12 1.3 2.14 1.11 1.24 1.04

-

0.92 0.955 0.94 0.93 1.25 1.25 1.8 1.21 1.3 0.96 1.14 1.21 1.32 0.96 1.4 1.22 1.43 0.91 1.05 1.24 1.58 2.2 1.4 1.32 1.4

Flexible Polymer Foam (VLD) Flexible Polymer Foam (LD) Flexible Polymer Foam (MD) Rigid Polymer Foam (LD) Rigid Polymer Foam (MD) Rigid Polymer Foam (HD)

0.016 0.038 0.07 0.036 0.078 0.17

-

0.035 0.07 0.115 0.07 0.165 0.47

Polymer Foams

Natural

1 For full names and acronyms of polymers – see Section V (Data courtesy of Granta Design Ltd).

11

II.3

YOUNG’S MODULUS, E E (GPa)

E (GPa) 1

Metals Ferrous

Non-ferrous

Ceramics Glasses

Porous Technical

Composites Metal Polymer

Cast Irons High Carbon Steels Medium Carbon Steels Low Carbon Steels Low Alloy Steels Stainless Steels Aluminium Alloys Copper Alloys Lead Alloys Magnesium Alloys Nickel Alloys Titanium Alloys Zinc Alloys

165 200 200 200 201 189 68 112 12.5 42 190 90 68

-

180 215 216 215 217 210 82 148 15 47 220 120 95

Borosilicate Glass Glass Ceramic Silica Glass Soda-Lime Glass Brick Concrete, typical Stone Alumina Aluminium Nitride Boron Carbide Silicon Silicon Carbide Silicon Nitride Tungsten Carbide

61 64 68 68 10 25 6.9 215 302 400 140 300 280 600

-

64 110 74 72 50 38 21 413 348 472 155 460 310 720

81 69 15

-

100 150 28

15 0.013 0.1 6 0.5

-

20 0.05 0.5 20 3

Aluminium/Silicon Carbide CFRP GFRP

Polymers Elastomer

Thermoplastic

Thermoset

Butyl Rubber EVA Isoprene (IR) Natural Rubber (NR) Neoprene (CR) Polyurethane Elastomers (elPU) Silicone Elastomers ABS Cellulose Polymers (CA) Ionomer (I) Nylons (PA) Polycarbonate (PC) PEEK Polyethylene (PE) PET Acrylic (PMMA) Acetal (POM) Polypropylene (PP) Polystyrene (PS) Polyurethane Thermoplastics (tpPU) PVC Teflon (PTFE) Epoxies Phenolics Polyester

0.001 0.01 0.0014 0.0015 0.0007 0.002 0.005 1.1 1.6 0.2 2.62 2 3.5 0.621 2.76 2.24 2.5 0.896 2.28 1.31 2.14 0.4 2.35 2.76 2.07

-

0.002 0.04 0.004 0.0025 0.002 0.003 0.02 2.9 2 0.424 3.2 2.44 4.2 0.896 4.14 3.8 5 1.55 3.34 2.07 4.14 0.552 3.075 4.83 4.41

Flexible Polymer Foam (VLD) Flexible Polymer Foam (LD) Flexible Polymer Foam (MD) Rigid Polymer Foam (LD) Rigid Polymer Foam (MD) Rigid Polymer Foam (HD)

0.0003 0.001 0.004 0.023 0.08 0.2

-

0.001 0.003 0.012 0.08 0.2 0.48

Polymer Foams

Natural Bamboo Cork Leather Wood, typical (Longitudinal) Wood, typical (Transverse)

1 For full names and acronyms of polymers – see Section V (Data courtesy of Granta Design Ltd) .

12

II.4

YIELD STRESS, σy, AND TENSILE STRENGTH, σts