CHAPTER 6: MECHANICAL PROPERTIES ISSUES TO ADDRESS... • Stress and strain: What are they and why are they used instead of load and deformation? • Elastic behavior: When loads are small, how much deformation occurs? What materials deform least? • Plastic behavior: At what point do dislocations cause permanent deformation? What materials are most resistant to permanent deformation? • Toughness and ductility: What are they and how do we measure them? Chapter 6- 1

Chapter 6- 2

6.1 Introduction

• Mechanical properties: strength,hardness,ductility,stiffness. • ASTM: American society for testing and materials

Chapter 6- 3

Elastic Deformation 1. Initial

2. Small load

3. Unload

bonds stretch return to initial

 F

F

Linearelastic

Elastic means reversible!



Non-Linearelastic Chapter 6- 4

Plastic Deformation (Metals) 1. Initial

2. Small load bonds stretch & planes shear elastic + plastic

3. Unload planes still sheared plastic

F F Plastic means permanent!

linear elastic

linear elastic

plastic



displacement Chapter 6- 5

6.2 Concepts of Stress and Strain

• A load applied in three ways: Fig 6.1 1.tension 2.compression3.shear Tension Tests: Fig 6.2 and Fig 6.3

Chapter 6- 6

Chapter 6- 7

Stress-Strain Testing • Typical tensile test machine

extensometer

• Typical tensile specimen

specimen

Adapted from Fig. 6.2, Callister 7e.

gauge length

Adapted from Fig. 6.3, Callister 7e. (Fig. 6.3 is taken from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons, New York, 1965.)

Chapter 6- 8

Engineering Stress • Tensile stress, :

• Shear stress, :

Ft

Ft Area, A

Area, A

Ft Ft lb f N = 2 or = 2 in m Ao original area before loading

F Fs

Fs Fs =  Ao

F

 Stress has units: N/m2 or lbf/in2

Ft

Chapter 6- 9

Common States of Stress • Simple tension: cable

F

F

A o = cross sectional area (when unloaded)

F   Ao



• Torsion (a form of shear): drive shaft

M

Ac M

Fs

Ski lift

(photo courtesy P.M. Anderson)



Ao Fs   Ao

2R

Note:  = M/AcR here.

Chapter 6- 10

OTHER COMMON STRESS STATES (1) • Simple compression:

Ao

Canyon Bridge, Los Alamos, NM (photo courtesy P.M. Anderson)

Balanced Rock, Arches National Park (photo courtesy P.M. Anderson)

F  Ao

Note: compressive structure member ( < 0 here).

Chapter 6- 11

OTHER COMMON STRESS STATES (2) • Bi-axial tension:

Pressurized tank (photo courtesy P.M. Anderson)

• Hydrostatic compression:

Fish under water

 > 0 z > 0

(photo courtesy P.M. Anderson)

h< 0 Chapter 6- 12

Engineering Strain • Tensile strain:

• Lateral strain: /2

   Lo

wo

• Shear strain:

L L  wo

Lo

L /2

  = x/y = tan 

x 90º - 

y 90º

Strain is always dimensionless.

Adapted from Fig. 6.1 (a) and (c), Callister 7e.

Chapter 6- 13

Shear and Torsional Tests τ = F/A0 shear stress

 1  cos 2   (6.4a ) 2    sin 2   '   sin  cos      (6.4b)  2 

 '   cos 2    

Adapted from Fig. 7.9, Callister 6e. (Fig. 7.9 is from C.F. Elam, The

Distortion of Metal Crystals,

Oxford University Press, London, 1935.)

Chapter 6- 14

6.3 Stress-Strain Behavior

1.σ = Eε (6.5) E:modulus of elasticity or Young’s modulus(GPa)

2.Elastic deformation:stress and strain are proportional 3.The greater the modulus, the stiffer the material.

Chapter 6- 15

Chapter 6- 16

Chapter 6- 17

Chapter 6- 18

Mechanical Properties • Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal

dF   E    dr 

r0

Adapted from Fig. 6.7, Callister 7e.

Chapter 6- 19

Chapter 6- 20

6.5 ELASTIC PROPERTIES of Materials

• Modulus of Elasticity, E:



• Hooke's Law:

=E

F

E

(also known as Young's modulus)

1

Linearelastic



L

Units: E: [GPa] or [psi]

 -

1

F simple tension test

Chapter 6- 21

Chapter 6- 22

• Poisson’s ratio

y      

metals: ~ 0.33 ceramics: ~0.25 polymers: ~0.40



x

z



z

ν : dimensionless

• ν = 0.25 for isotropic materials • E = 2G(1+ν) (6.9) Chapter 6- 23

YOUNG’S MODULI: COMPARISON Metals Alloys 1200 1000 800 600 400

E(GPa)

200 100 80 60 40

109 Pa

Graphite Composites Ceramics Polymers /fibers Semicond Diamond

Tungsten Molybdenum Steel, Ni Tantalum Platinum Cu alloys Zinc, Ti Silver, Gold Aluminum Magnesium, Tin

Si carbide Al oxide Si nitride

Carbon fibers only

CFRE(|| fibers)*



Si crystal

Aramid fibers only



AFRE(|| fibers)*

Glass-soda

Glass fibers only

GFRE(|| fibers)* Concrete GFRE*

20 10 8 6 4 2 1 0.8 0.6 0.4 0.2

CFRE* GFRE( fibers)*

Graphite

Polyester PET PS PC

CFRE( fibers)* AFRE( fibers)*

Epoxy only

Eceramics > Emetals >> Epolymers Based on data in Table B2, Callister 6e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers.

PP HDPE PTFE LDPE

Wood( grain)

Chapter 6- 24

Chapter 6- 25

Chapter 6- 26

Plastic Deformation 6.6 Tensile Properties Yielding and Yield strength • Plastic deformation:the stress no longer proportional to strain, and permanent nonrecoverable • Yielding:plastic deformation begins

Chapter 6- 27

Chapter 6- 28

YIELD STRENGTH: COMPARISON Metals/ Alloys

200

Al (6061)ag Steel (1020)hr Ti (pure)a Ta (pure) Cu (71500)hr

100 70 60 50 40

Al (6061)a

30 20

10

Tin (pure)

¨

dry

PC Nylon 6,6 PET humid PVC PP HDPE

LDPE

Hard to measure,

300

in ceramic matrix and epoxy matrix composites, since in tension, fracture usually occurs before yield.

700 600 500 400

Ti (5Al-2.5Sn)a W (pure) Cu (71500)cw Mo (pure) Steel (4140)a Steel (1020)cd

since in tension, fracture usually occurs before yield.

1000

Composites/ fibers

Steel (4140)qt

Hard to measure,

Yield strength, y (MPa)

2000

Graphite/ Ceramics/ Polymers Semicond

y(ceramics) >>y(metals) >> y(polymers) Room T values Based on data in Table B4, Callister 6e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered

Chapter 6- 29

Tensile Strength, TS • Maximum stress on engineering stress-strain curve. Adapted from Fig. 6.11, Callister 7e.

TS

F = fracture or ultimate strength

engineering stress

y

Typical response of a metal

Neck – acts as stress concentrator

strain engineering strain • Metals: occurs when noticeable necking starts. • Polymers: occurs when polymer backbone chains are aligned and about to break.

Chapter 6- 30

Chapter 6- 31

345MPa

150

Chapter 6- 32

Chapter 6- 33

Ductility(延性)

• Ductility is a measure of the degree of plastic deformation that has been sustained at fracture. • Percent elongation or percent reduction in area （percent elongation）

（percent reduction in area）

 l f  l0    100 % EL    l  0    % RA    

A A A 0

0

f

   100   Chapter 6- 34

DUCTILITY, %EL L f  Lo x100 • Plastic tensile strain at failure: %EL  Lo Engineering tensile stress,  Adapted from Fig. 6.13,

smaller %EL (brittle if %EL5%)

Ao

Af

Lf

Callister 6e.

Engineering tensile strain, 

• Another ductility measure:

% RA 

Ao  Af Ao

x100

• Note: %RA and %EL are often comparable. --Reason: crystal slip does not change material volume. --%RA > %EL possible if internal voids form in neck. Chapter 6- 35

Chapter 6- 36

Chapter 6- 37

Temperature effect on the stress-strain behavior

Chapter 6- 38

Resilience:彈性能 The capacity of a material to absorb energy when it is deformed elastically and then, unloading, to have this energy recovered.

U

r



Linear elastic region:



y

  d 0

U

r

1   y y 2

Chapter 6- 39

Toughness(韌性)

• It is a measure of the ability of a material to absorb energy up to fracture. • Figure 6.13:the area under curve • Section 8.6 :impact fracture testing Charpy,Izod

Chapter 6- 40

Chapter 6- 41

Chapter 6- 42

LOADING RATE • Increased loading rate... --increases y and TS --decreases %EL

• Why? An increased rate gives less time for disl. to move past obstacles.

• Impact loading:



y

TS larger  TS

y

smaller 



sample

(Charpy)

--severe testing case --more brittle --smaller toughness Adapted from Fig. 8.11(a) and (b), Callister 6e. (Fig. 8.11(b) is adapted from H.W. Hayden, W.G. Moffatt, and J. Wulff, The

Structure and Properties of Materials, Vol. III, Mechanical Behavior, John Wiley and Sons, Inc. (1965) p. 13.)

final height

initial height

Chapter 6- 43

TOUGHNESS • Energy to break a unit volume of material • Approximate by the area under the stress-strain curve. (Figure 6.13) Engineering tensile stress, 

smaller toughness (ceramics) larger toughness (metals, PMCs) smaller toughnessunreinforced polymers

Engineering tensile strain, 

Chapter 6- 44

6.7 True Stress and Strain true stress



T



F

A

i

true strain



T

Al Al i

i

 

T

T

 ln l i

0 0

l

0

No Volume change

  1     ln1    Chapter 6- 45



 KT

n

T

n: strain hardening exponent

Chapter 6- 46

HARDENING • An increase in y due to plastic deformation.



large hardening

y 1 y

small hardening reload

unloa d

0



• Curve fit to the stress-strain response:

 

T  C T 　rue?stress (F/A)

n

hardening exponent: n=0.15 (some steels) to n=0.5 (some copper) 　rue?strain: ln(L/Lo) Chapter 6- 47

Table 6.4

Chapter 6- 48

Chapter 6- 49

6.8 Elastic Recovery after Plastic Deformation

Chapter 6- 50

6.10 Hardness •Hardness is a measure of a material’s resistance to localized plastic deformation.硬度是材料對局部塑性變形(如小凹痕刮痕) 抵抗能力之一種量測。 Hardness tests are performed more frequently than any other mechanical test for several reasons: 1.They are simple and inexpensive 2.The test is nondestructive 3.Other mechanical properties often may be estimated from hardness data, such as tensile strength(Fig 6.19)

Chapter 6- 51

HARDNESS • Resistance to permanently indenting the surface. • Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties. e.g., 10mm sphere

apply known force (1 to 1000g)

D most plastics

measure size of indent after removing load Smaller indents mean larger hardness.

d

brasses easy to machine Al alloys steels file hard

cutting tools

nitrided steels diamond

increasing hardness Adapted from Fig. 6.18, Callister 6e. (Fig. 6.18 is adapted from G.F. Kinney, Engineering Properties and Applications of Plastics, p. 202, John Wiley and Sons, 1957.)

Chapter 6- 52

Hardness: Measurement • Rockwell – No major sample damage – Each scale runs to 130 but only useful in range 20100. – Minor load 10 kg – Major load 60 (A), 100 (B) & 150 (C) kg • A = diamond, B = 1/16 in. ball, C = diamond

• HB = Brinell Hardness – TS (psia) = 500 x HB – TS (MPa) = 3.45 x HB Chapter 6- 53

Table 6.5

Chapter 6- 54

Table 6.6a

Chapter 6- 55

Table 6.6b

Chapter 6- 56

Hardness Conversion

Chapter 6- 57

Chapter 6- 58

Correlation between hardness and tensile strength

TS(MPa) = 3.45 × HB TS(psi) = 500 × HB

Fig 6.19 steels alloys

Chapter 6- 59

SUMMARY • Stress and strain: These are size-independent measures of load and displacement, respectively. • Elastic behavior: This reversible behavior often shows a linear relation between stress and strain. To minimize deformation, select a material with a large elastic modulus (E or G). • Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches y. • Toughness: The energy needed to break a unit volume of material. • Ductility: The plastic strain at failure. Note: For materials selection cases related to mechanical behavior, see slides 22-4 to 22-10.

Chapter 6- 60