Ch7 Mechanical Properties

1

Chapter 7:

MECHANICAL PROPERTIES

Chapter Outline

Terminology for Mechanical Properties The Tensile Test: Stress-Strain Diagram Properties Obtained from a Tensile Test True Stress and True Strain The Bend Test for Brittle Materials Hardness of Materials

3

Questions to Think About• 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?

• Ceramic Materials: What special provisions/tests are made for ceramic materials?

4

Stress-Strain Test

specimen

machine

5

Tensile Test

6

Important Mechanical Properties from a Tensile Test

• Young's Modulus: This is the slope of the linear portion of the stress-strain curve, it is usually specific to each material; a constant, known value.

• Yield Strength: This is the value of stress at the yield point, calculated by plotting young's modulus at a specified percent of offset (usually offset = 0.2%).

• Ultimate Tensile Strength: This is the highest value of stress on the stress-strain curve.

• Percent Elongation: This is the change in gauge length divided by the original gauge length.

Terminology Load - The force applied to a material during

testing. Strain gage or Extensometer - A device used for

measuring change in length (strain). Engineering stress - The applied load, or force,

divided by the original cross-sectional area of the material.

Engineering strain - The amount that a material deforms per unit length in a tensile test.

8

F

bonds stretch

return to initial

1. Initial 2. Small load 3. Unload

Elastic means reversible.

F

Linear- elastic

Non-Linear-elastic

Elastic Deformation

9

1. Initial 2. Small load 3. Unload

Plastic means permanent.

F

linear elastic

linear elastic

plastic

planes still sheared

F

elastic + plastic

bonds stretch & planes shear

plastic

Plastic Deformation (Metals)

10

Typical stress-strain behavior for a metal showing elastic and plastic deformations, the proportional limit P and the yield strength σy, as determined using the 0.002 strain offset method (where there

is noticeable plastic deformation). P is the gradual elastic to plastic transition.

11

Plastic Deformation (permanent)

• From an atomic perspective, plastic deformation corresponds to the breaking of bonds with original atom neighbors and then reforming bonds with new neighbors.

• After removal of the stress, the large number of atoms that have relocated, do not return to original position.

• Yield strength is a measure of resistance to plastic deformation.

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

• Localized deformation of a ductile material during a tensile test produces a necked region. • The image shows necked region in a fractured sample

14

Permanent Deformation• Permanent deformation for metals is

accomplished by means of a process called slip, which involves the motion of dislocations.

• Most structures are designed to ensure that only elastic deformation results when stress is applied.

• A structure that has plastically deformed, or experienced a permanent change in shape, may not be capable of functioning as intended.

15

tensile stress,

engineering strain,

y

p = 0.002

Yield Strength, y

tensile stress,

engineering strain,

Elastic initially

Elastic+Plastic at larger stress

permanent (plastic) after load is removed

pplastic strain

Stress-Strain Diagram

Strain ( ) (L/Lo)41

2

3

5

Stre

ss (

F/A

)

Elastic Region

PlasticRegion

StrainHardening Fracture

ultimatetensile strength

Slop

e=E

Elastic region slope =Young’s (elastic) modulus yield strengthPlastic region ultimate tensile strength strain hardening fracture

necking

yieldstrength

UTS

y

εEσ

εσE

12

y

ε εσ

E

Stress-Strain Diagram (cont)

• Elastic Region (Point 1 –2) - The material will return to its original shape after the material is unloaded( like a rubber band). - The stress is linearly proportional to the strain in this region.

εEσ : Stress(psi)E : Elastic modulus (Young’s Modulus) (psi) : Strain (in/in)

σ

ε- Point 2 : Yield Strength : a point where permanent deformation occurs. ( If it is passed, the material will no longer return to its original length.)

εσE or

• Strain Hardening - If the material is loaded again from Point 4, the curve will follow back to Point 3 with the same Elastic Modulus (slope). - The material now has a higher yield strength of Point 4. - Raising the yield strength by permanently straining the material is called Strain Hardening.


• Tensile Strength (Point 3) - The largest value of stress on the diagram is called Tensile Strength(TS) or Ultimate Tensile Strength (UTS) - It is the maximum stress which the material can support without breaking.• Fracture (Point 5) - If the material is stretched beyond Point 3, the stress decreases as necking and non-uniform deformation occur. - Fracture will finally occur at Point 5.



The stress-strain curve for an aluminum alloy.

21

• Stress-strain behavior found for some steels with yield point phenomenon.

22

T

E

N

S

I

L

E

P

R

O

P

E

R

T

I

E

S

23

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibersPolymers

Yiel

d st

reng

th,

y (M

Pa)

PVC

Hard

to m

easu

re,

since

in te

nsion

, fra

ctur

e us

ually

occ

urs b

efor

e yie

ld.

Nylon 6,6

LDPE

70

20

40

6050

100

10

30

200300400500600700

1000

2000

Tin (pure)

Al (6061)a

Al (6061)ag

Cu (71500)hrTa (pure)Ti (pure)aSteel (1020)hr

Steel (1020)cdSteel (4140)a

Steel (4140)qt

Ti (5Al-2.5Sn)aW (pure)

Mo (pure)Cu (71500)cw

Hard

to m

easu

re,

in c

eram

ic m

atrix

and

epo

xy m

atrix

com

posit

es, s

ince

in te

nsion

, fra

ctur

e us

ually

occ

urs b

efor

e yie

ld.

HDPEPP

humid

dryPCPET

¨ Room T valuesa = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & tempered

Yield Strength: Comparison

24

• After yielding, the stress necessary to continue plastic deformation in metals increases to a maximum point (M) and then decreases to the eventual fracture point (F).• All deformation up to the maximum stress is uniform throughout the tensile sample. • However, at max stress, a small constriction or neck begins to form.• Subsequent deformation will be confined to this neck area.• Fracture strength corresponds to the stress at fracture.

Region between M and F:• Metals: occurs when noticeable necking starts.• Ceramics: occurs when crack propagation starts.• Polymers: occurs when polymer backbones are aligned and about to break.

Tensile Strength, TS

25

In an undeformed thermoplastic polymer tensile sample, (a)the polymer chains are randomly oriented. (b)When a stress is applied, a neck develops as chains become aligned locally. The neck continues to grow until the chains in the entire gage length have aligned. (c)The strength of the polymer is increased

26

Room T valuesSi crystal

<100>

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibersPolymers

Tens

ile s

treng

th, T

S (MPa

)

PVCNylon 6,6

10

100

200300

1000

Al (6061)a

Al (6061)agCu (71500)hr

Ta (pure)Ti (pure)aSteel (1020)

Steel (4140)a

Steel (4140)qt

Ti (5Al-2.5Sn)aW (pure)

Cu (71500)cw

LDPE

PPPC PET

20

3040

200030005000

Graphite

Al oxide

Concrete

Diamond

Glass-soda

Si nitride

HDPE

wood( fiber)

wood(|| fiber)

1

GFRE(|| fiber)

GFRE( fiber)

CFRE(|| fiber)

CFRE( fiber)

AFRE(|| fiber)

AFRE( fiber)

E-glass fibC fibersAramid fib

Based on data in Table B4, Callister 6e.

a = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & temperedAFRE, GFRE, & CFRE =aramid, glass, & carbonfiber-reinforced epoxycomposites, with 60 vol%fibers.

Tensile Strength: Comparison

27

• Tensile stress, : • Shear stress, :

Area, A

Ft

Ft

FtAo

original area before loading

Area, A

Ft

Ft

Fs

F

FFs

FsAo

Stress has units: N/m2 or lb/in2

Engineering Stress

28

VMSE

http://www.wiley.com/college/callister/0470125373/vmse/strstr.htmhttp://www.wiley.com/college/callister/0470125373/vmse/index.htm

Example 1Tensile Testing of Aluminum Alloy

Convert the change in length data in the table to engineering stress and strain and plot a stress-strain curve.

Example 1 SOLUTION

31

Engineering tensile strain,

Engineering tensile stress,

smaller %EL (brittle if %EL<5%)

larger %EL (ductile if %EL>5%)

• Another ductility measure: 100% xAAA

ARo

fo

• Ductility may be expressed as either percent elongation (% plastic strain at fracture) or percent reduction in area.• %AR > %EL is possible if internal voids form in neck.

Lo LfAo Af

100% xlll

ELo

of

Ductility, %ELDuctility is a measure of the plastic deformation that has been sustained at fracture:

A material that suffers very little plastic deformation is brittle.

32

ToughnessLower toughness: ceramics

Higher toughness: metals

Toughness is the ability to absorb energy up to fracture (energy per unit volume of material).

A “tough” material has strength and ductility.

Approximated by the area under the stress-straincurve.

• Energy to break a unit volume of material• Approximate by the area under the stress-strain curve.

21

smaller toughness- unreinforced polymers

Engineering tensile strain,

Engineering tensile stress,

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

Toughness

34

Linear Elastic Properties

Modulus of Elasticity, E: (Young's modulus)

• Hooke's Law: = E

• Poisson's ratio: metals: ~ 0.33 ceramics: ~0.25 polymers: ~0.40

Linear- elastic

1E

Units:E: [GPa] or [psi]: dimensionless

F

Fsimple tension test

x

y

35

Engineering Strain

Strain is dimensionless.

36

Axial (z) elongation (positive strain) and lateral (x and y) contractions (negative strains) in response to an imposed tensile stress.

True Stress and True Strain True stress The load divided by the actual cross-sectional

area of the specimen at that load. True strain The strain calculated using actual and not

original dimensions, given by εt ln(l/l0).

•The relation between the true stress-true strain diagram and engineering stress-engineering strain diagram. •The curves are identical to the yield point.

38

Stress-Strain Results for Steel Sample

Example 2: Young’s Modulus - Aluminum Alloy

From the data in Example 1, calculate the modulus of elasticity of the aluminum alloy.

• Use the modulus to determine the length after deformation of a bar of initial length of 50 in.

• Assume that a level of stress of 30,000 psi is applied.

Example 2: Young’s Modulus - Aluminum Alloy - continued

410.2

8

0.61

Magnesium,Aluminum

Platinum

Silver, Gold

Tantalum

Zinc, Ti

Steel, NiMolybdenum

Graphite

Si crystal

Glass -soda

Concrete

Si nitrideAl oxide

PC

Wood( grain)

AFRE( fibers)*

CFRE *GFRE*

Glass fibers only

Carbon fibers only

Aramid fibers only

Epoxy only

0.4

0.8

2

46

10

20

406080100

200

6008001000

1200

400

Tin

Cu alloys

Tungsten

<100><111>

Si carbide

Diamond

PTF E

HDPE

LDPE

PP

PolyesterPSPET

CFRE( fibers)*

GFRE( fibers)*

GFRE(|| fibers)*

AFRE(|| fibers)*

CFRE(|| fibers)*

MetalsAlloys

GraphiteCeramicsSemicond

Polymers Composites/fibers

E(GPa)

Eceramics > Emetals >> Epolymers

109 Pa Composite data based onreinforced epoxy with 60 vol%of aligned carbon (CFRE),aramid (AFRE), or glass (GFRE)fibers.

Young’s Moduli: Comparison

Example 3: True Stress and True Strain Calculation

Compare engineering stress and strain with true stress and strain for the aluminum alloy in Example 1 at (a) the maximum load. The diameter at maximum load is 0.497 in. and at fracture is 0.398 in.Example 3 SOLUTION

large hardening

small hardening

unlo

adre

load

y 0y 1

Strain Hardening

T C T n“true” stress (F/A) “true” strain: ln(L/Lo)

hardening exponent: n=0.15 (some steels) to n=0.5 (some copper)

An increase in y due to plastic deformation.

44

Strain Hardening (n, K or C values)

T C T n“true” stress (F/A) “true” strain: ln(L/Lo)

hardening exponent: n=0.15 (some steels) to n=0.5 (some copper)

47

Mechanical Behavior - Ceramics

• The stress-strain behavior of brittle ceramics is not usually obtained by a tensile test.1. It is difficult to prepare and test

specimens with specific geometry.2. It is difficult to grip brittle materials without

fracturing them.3. Ceramics fail after roughly 0.1% strain;

specimen have to be perfectly aligned.

The Bend Test for Brittle Materials

Bend test - Application of a force to the center of a bar that is supported on each end to determine the resistance of the material to a static or slowly applied load.

Flexural strength or modulus of rupture -The stress required to fracture a specimen in a bend test.

Flexural modulus - The modulus of elasticity calculated from the results of a bend test, giving the slope of the stress-deflection curve.


The stress-strain behavior of brittle materials compared with that of more ductile materials


(a) The bend test often used for measuring the strength of brittle materials, and (b) the deflection δ obtained by bending

51

• Schematic for a 3-point bending test.

• Able to measure the stress-strain behavior and flexural strength of brittle ceramics.

• Flexural strength (modulus of rupture or bend strength) is the stress at fracture.

Flexural Strength

See Table 7.2 for more values.

23

• Room T behavior is usually elastic, with brittle failure.• 3-Point Bend Testing often used. --tensile tests are difficult for brittle materials.

FL/2 L/2

= midpoint deflection

cross sectionR

bd

rect. circ.

• Determine elastic modulus according to:

E

F

L3

4bd3 F

L3

12R4rect. cross

section

circ. cross

section

Fx

linear-elastic behavior

F

slope =

MEASURING ELASTIC MODULUS

24

• 3-point bend test to measure room T strength.F

L/2 L/2cross section

Rb

d

rect. circ.location of max tension

• Flexural strength:

rect. fs m

fail 1.5FmaxLbd2

FmaxLR3

xFFmax

max

• Typ. values:Material fs(MPa) E(GPa)Si nitrideSi carbideAl oxideglass (soda)

700-1000550-860275-550

69

30043039069

Data from Table 12.5, Callister 6e.

MEASURING STRENGTH

54

--brittle response (aligned chain, cross linked & networked case) --plastic response (semi-crystalline case)

Stress-Strain Behavior: Elastomers3 different responses:

A – brittle failureB – plastic failureC - highly elastic (elastomer)

initial: amorphous chains are kinked, heavily cross-linked.

final: chains are straight,

still cross-linked

0

20

40

60

0 2 4 6

(MPa)

8

x

x

x

elastomer

plastic failure

brittle failure

Deformation is reversible!

Hardness of Materials

Hardness test - Measures the resistance of a material to penetration by a sharp object.

Macrohardness - Overall bulk hardness of materials measured using loads >2 N.

Microhardness Hardness of materials typically measured using loads less than 2 N using such test as Knoop (HK).

Nano-hardness - Hardness of materials measured at 1–10 nm length scale using extremely small (~100 µN) forces.

56

Hardness• Hardness is a measure of a material’s resistance

to localized plastic deformation (a small dent or scratch).

• Quantitative hardness techniques have been developed where a small indenter is forced into the surface of a material.

• The depth or size of the indentation is measured, and corresponds to a hardness number.

• The softer the material, the larger and deeper the indentation (and lower hardness number).

57

• 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) measure size

of indent after removing load

dDSmaller indents mean larger hardness.

increasing hardness

most plastics

brasses Al alloys

easy to machine steels file hard

cutting tools

nitrided steels diamond

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.)

Hardness

58

Hardness Testers

60

Conversion of Hardness Scales

Also see: ASTM E140 - 07 Volume 03.01Standard Hardness Conversion Tables for Metals Relationship Among Brinell Hardness, Vickers Hardness, Rockwell Hardness, Superficial Hardness, Knoop Hardness, and Scleroscope Hardness

61

Correlation between Hardness and Tensile Strength

• Both hardness and tensile strength are indicators of a metal’s resistance to plastic deformation.

• For cast iron, steel and brass, the two are roughly proportional.

• Tensile strength (psi) = 500*BHR

63

• 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.

Summary

Ch7 Mechanical Properties

Documents

Transcript of Ch7 Mechanical Properties