材料手册(剑桥大学工程系2003版)01

1

MaterialsData Book

2003 Edition

Cambridge University Engineering Department

2

PHYSICAL CONSTANTS IN SI UNITS

CONVERSION OF UNITS

1

CONTENTS

Introduction 3 Sources I. FORMULAE AND DEFINITIONS

Stress and strain Elastic moduli Stiffness and strength of unidirectional composites and plastic flow 5 Fast fracture Statistics of fracture Fatigue Creep Diffusion Heat flow II. PHYSICAL AND MECHANICAL PROPERTIES OF MATERIALS Melting temperature Density modulus 11 stress and tensile strength 12 toughness 13 resistance 14 Uniaxial tensile response of selected metals and polymers III. MATERIAL PROPERTY CHARTS modulus versus density 16 versus density 17 modulus versus strength 18 toughness versus strength 19 service temperature 20 price (per kg) 21 IV. PROCESS ATTRIBUTE CHARTS compatibility matrix (shaping) 22

Mass Section thickness roughness 24 tolerance 24 batch size 25 3 4 4

5 6 6 7 8

8 9 10 15 23 23

Dislocations 7

Young’s Yield Fracture Environmental

Young’s Strength Young’s Fracture Maximum Material

Material-process Surface Dimensional Economic

2

V. CLASSIFICATION AND APPLICATIONS OF ENGINEERING MATERIALS Metals: ferrous alloys, non-ferrous alloys 26 Polymers and foams 27 Composites, ceramics, glasses and natural materials 28

VI. EQUILIBRIUM (PHASE) DIAGRAMS Copper – Nickel 29 Lead – Tin 29 Iron – Carbon 30 Aluminium – Copper 30 Aluminium – Silicon 31 Copper – Zinc 31 Copper – Tin 32 Titanium-Aluminium 32 Silica – Alumina

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

VIII. PHYSICAL PROPERTIES OF SELECTED ELEMENTS

Atomic properties of selected elements 36 Oxidation properties of selected elements 37

33 34

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.

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

Fσt=

A

Fσn=

Ao

εt=ln l

o oεn=

lo

F = normal component of force Ao = initial area A = current area lo = initial length l = current length

σt = true stress σn = nominal stress εt = true strain

εn = nominal strain

Poisson’s ratio, ν=

lateralstrain

longitudinalstrain

Young’s modulus E = initial slope of σt εt curve = initial slope of σn εn curve.

Yield stress σy is the nominal stress at the limit of elasticity in a tensile test.

Tensile strength σts is the nominal stress at maximum load in a tensile test.

Tensile ductility εf 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

K=E 2(1+ν)3(1 2ν)

For polycrystalline solids, as a rough guide,

Poisson’s Ratio

ν≈

G≈

1

3

Shear Modulus

Bulk Modulus

3E 8

K≈E

These approximations break down for rubber and porous solids.

STIFFNESS AND STRENGTH OF UNIDIRECTIONAL COMPOSITES

5

EII=VfEf+(1 Vf)Em

Vf1 Vf

E⊥= +

EfEm

1

σts=Vfσff+(1 Vf)σmy

EII = composite modulus parallel to fibres (upper bound) E⊥ = composite modulus transverse to fibres (lower bound) Vf = volume fraction of fibres

Ef = Young’s modulus of fibres

Em= Young’s modulus of matrix

σts= tensile strength of composite parallel to fibres

σff = fracture strength of fibres

σmy = 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=τb. The shear stress τy required to move a dislocation on a single slip plane is

τy=

cT

where T = line tension (about Gb2, where G is the shear modulus)

2bL

L = inter-obstacle distance

c = constant (c≈2for strong obstacles, c<2 for weak obstacles)

The shear yield stress k of a polycrystalline solid is related to the shear stress τy required to

τ. move a dislocation on a single slip plane: k≈y

The uniaxial yield stress σy of a polycrystalline solid is approximately σy=2k, where k is the shear yield stress.

Hardness H (in MPa) is given approximately by: H≈3σy.

Vickers Hardness HV is given in kgf/mm2, i.e. HV=H/g, where g is the acceleration due to gravity.

6

FAST FRACTURE

The stress intensity factor, K: K=Yσ

a

Fast fracture occurs when K=KIC

In plane strain, the relationship between stress intensity factor K and strain energy release rate G is:

K=

EG1 ν2

≈

EG (as ν2≈0.1)

EG1 ν

2

Plane strain fracture toughness and toughness are thus related by: KIC=“Process zone size” at crack tip given approximately by: rp=

2KIC

≈

EGIC

πσ2f

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 KIC= plane strain fracture toughness;

GIC= critical strain energy release rate, or toughness; E = Young’s modulus ν = Poisson’s ratio σf = failure strength

STATISTICS OF FRACTURE

Weibull distribution, Ps(V)=exp

For constant stress: Ps(V)=exp

∫

σ

σV o σ σ o

m

m

dV Vo

V Vo

Ps = survival probability of component V = volume of component

σ = tensile stress on component Vo = volume of test sample

σo= reference failure stress for volume Vo , which gives Ps=

m = Weibull modulus =0.37

FATIGUE

7

Basquin’s Law (high cycle fatigue):

σNαf=C1

Coffin-Manson Law (low cycle fatigue):

εplNβf=C2

Goodman’s Rule. For the same fatigue life, a stress range σ operating with a mean stress σm,

is equivalent to a stress range σo and zero mean stress, according to the relationship:

σ= σo 1

σm

σts

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

∑

i

Paris’ crack growth law:

Ni

=1 Nfi

da

=A Kn dN

In the above:

σ = stress range;

εpl= plastic strain range;

K = tensile stress intensity range;

N = cycles;

Nf = cycles to failure;

α,β,C1,C2,A,n= constants; a = crack length; σts = tensile strength.

CREEP

&ss=Aσnexp( Q/RT) Power law creep: ε

&ss = steady-state strain-rate ε

Q = activation energy (kJ/kmol) R = universal gas constant T = absolute temperature A,n = constants

8

DIFFUSION

Diffusion coefficient: D=Doexp( Q/RT) Fick’s diffusion equations:

dC

J= D and

dx

C 2C =D

2 t x

C= concentration

x= distance t = time

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

T 2T

=a Transient 1D heat flow:

2 t x

T = temperature (K) q = heat flux per second, per unit area (W/m2.s)

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:

x x

or T(x,t)=f erf C(x,t)=f erf 2Dt 2at

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:

Dt, with the corresponding at.

erf(X)=

2

∫0

X

exp y2dy

()

and

d

[erf(X)]=dX

2

exp X2

(

)

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

X 0.7 0.8

erf(X)

0.11

0.22

0.33

0.43

0.52

0.60

0.68

0.74

X

erf(X)

本文来源：https://www.bwwdw.com/article/raum.html