[email protected] engr-45_lec-15_metal_mechprop-2.ppt 1 bruce mayer, pe engineering-45:...

[email protected] • ENGR-45_Lec-15_Metal_MechProp-2.ppt1

Bruce Mayer, PE Engineering-45: Materials of Engineering

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engineering 45

Mechanical Mechanical Properties of Properties of

Metals (2)Metals (2)



Learning Goals.1 – Mech PropsLearning Goals.1 – Mech Props

STRESS and STRAIN: • What they are and why they are they used

instead of LOAD and DEFORMATION

ELASTIC Behavior• How much deformation occurs when Loads

are SMALL?

• Which materials deform least



Learning Goals.2 – Mech PropsLearning Goals.2 – Mech Props

PLASTIC Behavior• Determine the point at which Dislocations

cause PERMANENT deformation

• Which materials are most resistant to Permanent Deformation

TOUGHNESS and DUCTILITY• What they are

• How to Measure them



Properties of Solid MaterialsProperties of Solid Materials

Mechanical: Characteristics of materials displayed when forces and/or torques are applied to them.

Physical: Characteristics of materials that relate to the interaction of materials with various forms of energy.

Chemical: Material characteristics that relate to the structure of a material.

Dimensional: Size, shape, and finish



Material PropertiesMaterial Properties Chemical Physical Mechanical Dimensional

Composition Melting Point Tensile properties Standard Shapes

Microstructure Thermal Toughness Standard Sizes

Phases Magnetic Ductility Surface Texture

Grain Size Electrical Fatigue Stability

Corrosion Optical Hardness Mfg. Tolerances

Crystallinity Acoustic Creep

Molecular Weight Gravimetric Compression

Flammability



Recall ELASTIC DeformationRecall ELASTIC Deformation Apply/Remove a SMALL Force-Load to a Specimen

1. Initial 3. Unload

return to initial

2. SMALL load

bonds stretch

F

• F Force Load

(lb or N) Deformation in

Response to the Load (in or m)

F

Linear- elastic

Non-Linear-elastic

ELASTIC means REVERSIBLE



Recall PLASTIC DeformationRecall PLASTIC Deformation Apply/Remove a LARGE Force Load to a Specimen

PLASTIC means PERMANENT

1. Initial 3. Unload

PlanesStillSheared

& planes

2. LARGE load

bonds stretch

shear

F

elastic+plasticplastic

F

linear elastic

linear elastic

plastic



Plastic Deformation Plastic Deformation -- Simple Tension Test (Temperature <Tmelt/3)

TensileStress,

engineering strain,

Elastic+Plastic at larger stress

Elastic initially

permanent (plastic) after load is removed

P

plastic strain

Elastic Recovery



YIELD Strength, YIELD Strength, yy Define YIELD Strength as the Stress at Which

NOTICEABLE Plastic Deformation Occurs• Define NOTICEABLE as 0.2% → P = 0.002 (0.2%)

tensi

le s

tress

,

engineering strain, P = 0.002

y σy ≡ Yield Strength

• For Matl’s WithOUt a well Defined Yield Pt σy = σ(ε = 0.2%)

For a 2” gage-length• ΔL = 2”•0.002

= 0.004” (0.1 mm)



Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibersPolymers

Yield

str

en

gth

, y (M

Pa)

PVC

Ha

rd t

o m

ea

sure,

si

nce in

ten

sion

, fr

actu

re u

sually

occu

rs b

efo

re y

ield

.

Nylon 6,6

LDPE

70

20

40

6050

100

10

30

200

300

400500600700

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

Ha

rd t

o m

ea

sure

, in

cera

mic

matr

ix a

nd

ep

oxy m

atr

ix c

om

posi

tes,

sin

ce

in

ten

sion

, fr

actu

re u

sually

occu

rs b

efo

re y

ield

.HDPEPP

humid

dryPC

PET

¨ Room T values

Based on data in Table B4,Callister 6e.a = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & tempered

Yield Strength: ComparisonYield Strength: Comparison

y,ceramics >> y,metals >> y,polymers



TENSILE/ULTIMATE Strength TENSILE/ULTIMATE Strength Define TENSILE/ULTIMATE Strength (TS/σu)

as the MAX-σ Point on the σ-ε Curve

• Metals: occurs when noticeable NECKING starts

• Ceramics: occurs when CRACK PROPAGATION starts

• Polymers: occurs when POLYMER BACKBONES are aligned and about to break

engineering strain

en

gin

eeri

ng

str

ess

y

TS



Room T valuesSi crystal<100>

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibersPolymers

Ten

sile

str

en

gth

, TS

(MPa

)

PVC

Nylon 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

PP

PC PET

20

3040

20003000

5000

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 fib

C 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: ComparisonTensile Strength: Comparison

TSceramics TSmetals TScomp >>TSpolymers



Ductility → Strain at Fracture Ductility → Strain at Fracture At Tensile Fracture Define Ductility

in Terms of ELONGATION

Lo LfAo Af

Plastic Strain AtTensile Failure

100%

o

of

L

LLEL

Engineering tensile strain,

Engineering tensile stress,

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

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



Ductility → Strain at Fracture Ductility → Strain at Fracture Alternative Definition

is Reduction of Area

Lo LfAo Af

RA Ductility

100%

o

fo

A

AARA

Note: %RA and %EL Tend to Be Quite Comparable• Reason: crystal slip

does not change material VOLUME.

• %RA < %EL possible if internal voids form in neck.

• %EL is More Common Than %RA



Desirable Mechanical Properties Desirable Mechanical Properties

Without Considering Such Factors Cost, Weight, Weldability, etc., The Typically Desired Combination of Strength and Ductility• HIGH σy

• HIGH %EL

σy, is the Mechanical DESIGN PARAMETER, not The Ultimate Strength• YIELDING

permanently deforms (bends) Structures; typically rendering them NON-functional



Resilience → Energy Storage Resilience → Energy Storage Consider the σ·ε

Product

Now• F•δL has Units of

ENERGY (J)

• A•L has Units of Volume (cu-m)

Let U → J/m3

LA

LF

L

L

A

F

Next Consider the σ-ε Curve in the Elastic Range

d

dU

dε



Resilience cont.Resilience cont. In The Elastic Range

the Material Stretches and then Returns to the Original Size

Thus Define Resilience, Ur, as the REVERSIBLE Energy Storage• Ur → Area under σ·ε

curve in elastic Rng

In the Elastic Range

y

dU r

002.0

EddE

E

yy

y

&

so0.002&

Then the Ur Integral

EU

EdEU

yr

E

r

y

y

2

22

0

2

0



ToughnessToughness

smaller toughness- unreinforced polymers

Engineering tensile strain,

, E

ngin

eeri

ng

Tensi

le S

tress

smaller toughness (ceramics)

larger toughness (metals, some composites)

An Extension of RESILIENCE Beyond the Elastic Range to Plastic-Flow & Fracture

A Measure of the TOTAL Energy-per-Vol Absorbance Capability of a Material to the Total Plastic-Def. Area under the σ-ε curve



TRUE Stress & StrainTRUE Stress & Strain Engineering Stress

oAF • F Applied Pull

• Ao Original Area

But the Specimen NECKS-DOWN, Reducing the Area• So the TRUE Stress

• Ai Instantaneous Area = f(σ) or f(ε)

iT AF



TRUE Stress & Strain contTRUE Stress & Strain cont Engineering Strain

oLL In the Instantaneous

Case (see Rt)

• Integrating

''' P Pti xdx d

i

i

o

T

LLT

L

Li

x

xdxd

0'ln

''0

L0

Li

Thus

oiT

oiT

LL

LL

ln

lnln

Original (UnLoaded)

Load at Instant “i”



Engineering/True Stress/StrainEngineering/True Stress/Strain

For Strain

1ln

ln

ln

T

o

o

oiT

L

LL

LL

Now Assume Constant Material VOLUME

iioo LAL A )1(

)1(

; and

;

but ;

T

o

o

o

i

oi

o

i

o

i

ooo

iT

i

ooi

iT

L

LL

L

L

LLL

L

L

L

L

A

F

LA

FL

L

LAA

A

F



Plastic Behavior → Plastic Behavior → --

Typical Metal

Stress

Strain

True Stress - Strain Curve

Engineering Stress - Strain Curve

Ultimate Tensile Strength

Fracture

Fracture



Typ. Work-Hardening ParametersTyp. Work-Hardening Parameters For Most Metals, True Stress Increases

in the Plastic Range (not ElastoPlastic)• The Material “Hardens” as it is WORKED

Log (true plastic strain,)

Log

(tru

e st

ress

, )

MP

a

1.00.100.0100.0010

K

n

necking

fracture

nplasTplasT K ,,

KyLog intercept 01Note )(:

slope



Strain-HardeningStrain-Hardening

K Work-Hardening Prefactor in MPa or Ksi n Work-Hardening Exponent (unitless)

Material Yield Stress(MPa)

UltimateStress (MPa)

ElasticModulus(MPa)

K(MPa)

n

1020 Steel 300 420 207000 530 0.264340 Steel 400 600 207000 640 0.152024 Al Alloy 350 400 72000 690 0.16304 Stainless Steel 210 550 185000 1275 0.4570/30 Brass 75 300 110000 900 0.49



Elastic RecoveryElastic Recovery When a material is

released prior to fracture:• Some of the total

energy is stored elastically

• Some is absorbed by the plastic deformation

• The plastic deformation energy represents the lattice strains.

The elastic energy will be recovered once the material is released• i.e., the material

will unstretch



Elastic Recovery cont.Elastic Recovery cont.

Elastic Energy, Ur

13

2

To determine the amount that the material recovers:1. draw a line

PARALLEL to the elastic modulus line that goes back to the strain axis

2. The difference in strains provides the recovered length

3. The area under this line is the recovered energy



HardnessHardness

Short Definition = Resistance to Penetration

Metals HandBook

"Resistance of metal to plastic deformation, usually by indentation. However, the term may also refer to stiffness or temper, or to resistance to scratching,

abrasion, or cutting. It is the property of a metal, which gives it the ability to resist being permanently, deformed (bent, broken, or have its shape changed), when a load is applied. The greater the hardness of the metal, the

greater resistance it has to deformation.



Hardness, cont.Hardness, cont. Hardness Resistance to Plastic Indentation LARGE Hardness Indicates Properties:

• Resistance to plastic deformation or cracking when loaded in COMPRESSION

• Better Wear Resistance

e.g., 10mm sphere

apply known force (1 to 1000 kg)

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



WhiteBoard WorkWhiteBoard Work



Elastic Strain RECOVERYElastic Strain RECOVERY

Ur

ParallelLines

When a Post-Yield Load is Removed the Material Recovers along a Line PARALLEL to the initial ELASTIC extension Line

[email protected] engr-45_lec-15_metal_mechprop-2.ppt 1 bruce mayer, pe engineering-45:...

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characteristics of materials

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noticeable plastic deformation

f f force load

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