MSE 3300-Lecture Note 10-Chapter 06 Mechanical Properties of Metals 2

8/18/2019 MSE 3300-Lecture Note 10-Chapter 06 Mechanical Properties of Metals 2

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MSE 3300 / 5300 UTA Spring 2015 Lecture 10 -

Lecture 10. Mechanical Properties

of Metals (2)Learning Objectives

After this lecture, you should be able to do the following:

1. Understand elastic and plastic deformation.

2. Given an engineering stress–strain diagram, determine (a) the

modulus of elasticity, (b) the yield stress, and (c) the tensile strength and

(d) estimate the percentage elongation (ductility).

3. Understand (a) measures of energy capacity of materials (resilience

and toughness) and (b) hardness.

Reading

• Chapter 6: Mechanical Properties of Metals (6.6–6.12)

Multimedia• Tensile tests: https://www.youtube.com/watch?v=ZwTF_-JZgt8;

https://www.youtube.com/watch?v=67fSwIjYJ-E;

https://www.youtube.com/watch?v=K28WiL21Sgs

1


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1. Elastic Deformation

• Elastic deformation is nonpermanent: when the applied load is released, the

piece returns to its original shape (not breaking atomic bonds).

• Hooke’s Law

E [Pa]: Modulus of elasticity, or Young’s modulus

2

Linear elastic deformation Nonlinear elastic deformation


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2. Plastic Deformation

• Plastic deformation is irreversible.

• Elastic deformation of metals: up to strain of about 0.005

• Beyond this point, the stress is no longer proportional to strain, and plastic

deformation occurs.

• Breaking of bonds with original atom neighbors and reformation of bonds with

new neighbors.

3

Mechanisms

• Crystalline solids: slip

(Section 7.2)

• Noncrystalline solids:

viscous flow mechanism

(Section 12.10)


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MSE 3300 / 5300 UTA Spring 2015 Lecture 10 - 4

Elastic means reversible!

Elastic Deformation

2. Small load

F

δ

bondsstretch

1. Initial 3. Unload

return to

initial

F

δ

Linear-

elastic

Non-Linear- elastic


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Plastic means permanent!

Plastic Deformation (Metals)

F

δ linearelastic

linearelastic

δ plastic

1. Initial 2. Small load 3. Unload

planesstillsheared

F

δ elastic + plastic

bondsstretch& planesshear

δ plastic


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(at lower temperatures, i.e. T < T melt /3)

Plastic (Permanent) Deformation

• Simple tension test:

engineering stress,σ

engineering strain, e

Elastic+Plasticat larger stress

e p

plastic strain

Elasticinitially

Adapted from Fig. 6.10 (a),

Callister & Rethwisch 9e.

permanent (plastic)after load is removed


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Yield Strength, σ y

7

• Yield strength: The stress level at which plastic deformation begins, or

yielding occurs.

P: Proportional limit

(onset of plastic

deformation at the

microscopic level

Strain offset of 0.002


Yield point phenomenon

* Yield stress for nonlinear elastic deformation

(Figurer 6.6): stress required to produce

some amount of strain (e.g., ε=0.005)


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• Stress at which noticeable plastic deformation has

occurred.when e p = 0.002


σ y = yield strength

Note: for 2 inch sample

e = 0.002 = ∆z /z

∴ ∆z = 0.004 in

Adapted from Fig. 6.10 (a),


tensile stress,σ

engineering strain, e

σ y

e p = 0.002



Room temperaturevalues

Based on data in Table B.4,


a = annealed

hr = hot rolledag = aged

cd = cold drawn

cw = cold worked

qt = quenched & tempered

Yield Strength : ComparisonGraphite/Ceramics/Semicond

Metals/ Alloys

Composites/fibers

Polymers

Y i e l d s

t r e n g

t h ,

σ y

( M P a

)

PVC

H a r d

t o m e a s u r e

,

s i n c e

i n t e n s

i o n ,

f r a c

t u r e u s u a

l l y o c c u r s

b

e f o r e y

i e l d

.

Nylon 6,6

LDPE

70

20

40

6050

100

10

30

200

300

400

500600700

1000

2000

Tin (pure)

Al (6061) a

Al (6061) ag

Cu (71500) hr Ta (pure) Ti (pure) a Steel (1020) hr

Steel (1020) cd Steel (4140) a

Steel (4140) qt

Ti (5Al-2.5Sn) a W (pure)

Mo (pure) Cu (71500) cw

H a r d

t o m e a s u r e ,

i n c e r a m

i c m a

t r i x a n

d e p o x y m a

t r i x c o m p o s

i t e s ,

s i n c e

i n t e n s

i o n , f r

a c

t u r e u s u a

l l y o c c u r s

b e

f o r e y

i e l d

.

H DPE PP

humid

dry

PC

PET

¨


10/33MSE 3300 / 5300 UTA Spring 2015 Lecture 10 -

VMSE: Virtual Tensile Testing

10



Tensile Strength, TS

• Metals: occurs when noticeable necking starts.

• Polymers: occurs when polymer backbone chains are aligned and about to break.

• Tensile strength: Maximumstress on engineering

stress-strain curve;

maximum stress that can be

sustained by the structure in

tension

• If this stress is applied,fracture will result.

s t r e s s

strain

Necking

TS

F = Fracture or ultimate

strength

Neck acts as stress

concentrator; fractureoccurs at the neck.

M = Tensile strength (TS )



Tensile Strength: Comparison

Si crystal

Graphite/Ceramics/Semicond

Metals/ Alloys

Composites/fibers

Polymers

T e n s

i l e

s t

r e n g

t h ,

T S

( M P a

)

PVC

Nylon 6,6

10

100

200300

1000

Al (6061) a

Al (6061) ag

Cu (71500) hr

Ta (pure) Ti (pure) a

Steel (1020)

Steel (4140) a

Steel (4140) qt

Ti (5Al-2.5Sn) a W (pure)

Cu (71500) cw

L DPE

PP

PC PET

20

3040

2000

3000

5000

Graphite

Al oxide

Concrete

Diamond

Glass-soda

Si nitride

H DPE

wood ( fiber)

wood(|| fiber)

1

GFRE (|| fiber)

GFRE ( fiber)

C FRE (|| fiber)

C FRE ( fiber)

A FRE (|| fiber)

A FRE( fiber)

E-glass fib C fibers Aramid fib

Based on data in Table B4,


a = annealed

hr = hot rolled

ag = aged

cd = cold drawncw = cold worked

qt = quenched & tempered

AFRE, GFRE, & CFRE =

aramid, glass, & carbon

fiber-reinforced epoxy

composites, with 60 vol%

fibers.

Room temperaturevalues


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Example Problem 6.3

13

Determine the following:

(a) Modulus of elasticity

(b) Yield strength at a strain

offset of 0.002

(c) The maximum load that can

be sustained by a cylindrical

specimen having a diameterof 12.8 mm (0.05 in)

(d) The change in length of a

specimen originally 250 mm

long that is subjected to a

tensile stress of 345 MPa


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Ductility

14

S t r e s s

Strain

• Ductility: Measure of the degree

of plastic deformation that hasbeen sustained at fracture

• Brittle: little or not plastic

deformation (approximately, a

fracture strain < 5%)

• Ductility usually increases with

temperature.

• Percent elongation

• Percent reduction in area

1. It indicates the degree to which a structure will deform plastically before fracture

2. It specifies the degree of allowable deformation during fabrication operations


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• Plastic tensile strain at failure:

Ductility

• Another ductility measure: 100x A

A ARA%

o

fo-

=

x 100L

LLEL%

o

of-

=

Lf Ao Af Lo

Engineering tensile strain, e

E ngineering

tensile

stress,σ

smaller %EL

larger %EL


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Table 6.2: Mechanical Properties

of Several Metals

16


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Stress-strain behavior for iron at

three temperatures

17


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Measures of Energy Capacity 1:

Resilience

18

S t r e s s

Strain

• Resilience: Capacity of a material to absorbenergy when it is deformed elastically and

then, upon, unloading, to have the energy

recovered.

• Modulus of resilience [J/m3] Measure of

the ability of material to store elastic energy;Strain energy per unit volume required to

stress a material from an unloaded state up

to the point of yielding

∫= y

d U r ε

ε σ 0


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Resilience, U r

• Ability of a material to store energy

– Energy stored best in elastic region

If we assume a linear

stress-strain curve this

simplifies to

Fig. 6.15, Callister &

Rethwisch 9e.

yyr2

1U eσ ≅

ey


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• Tensile toughness: Measure of the ability of the material to absorb energy

without fracture

• The area under the entire stress-strain curve up to fracture (Unit: J/m3)

• Fracture toughness: Material’s resistance to fracture when a crack (or other

defect) is present

Measures of Energy Capacity 2:

Toughness

Brittle fracture: elastic energy

Ductile fracture: elastic + plastic energy

very small toughness(unreinforced polymers)

Engineering tensile strain, e

Engineering

tensile

stress, σ

small toughness (ceramics)

large toughness (metals):

strength + ductility

∫= f

d U f ε

ε σ 0


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Measures of Energy Capacity:

Toughness

21

S t r e s s

Strain

∫= f

d U f ε

ε σ 0

Large toughness:

strength + ductility


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True Stress and Strain

22

Ai is the instantaneous cross-

sectional area.

(Corrected axial

stress in the neck)


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Elastic Strain Recovery

Fig. 6.17, Callister &

Rethwisch 9e.

S t r e

s s

Strain

3. Reapplyload

2. Unload

D

Elastic strain

recovery

1. Load

σ y o

σ y i


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Hardness

• Resistance to permanently indenting the surface (localized plastic

deformation).• Large hardness means:

-- resistance to plastic deformation or cracking in compression.

-- better wear properties.

e.g.,10 mm sphere

apply known force

measure size or depthof indent after removing load

d D Smaller indentsmean largerhardness.

increasing hardness

mostplastics

brasses Al alloys

easy to machinesteels file hard

cuttingtools

nitridedsteels diamond


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Hardness: MeasurementTable 6.5


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Hardening

• Curve fit to the stress-strain response:

σ T = K eT( )n

“true” stress (F / A) “true” strain: ln(/o)

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

• An increase in σ y due to plastic deformation.

σ

e

large hardening

small hardening σ y0

σ y1


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• Design uncertainties mean we do not push the limit.

• Factor of safety, N Often N isbetween

1.2 and 4

• Example: Calculate a diameter, d , to ensure that yield doesnot occur in the 1045 carbon steel rod below. Use a

factor of safety of 5.

Design or Safety Factors

5

1045 plaincarbon steel:

σ y = 310 MPa

TS = 565 MPa

F = 220,000N

d

Lo

d = 0.067 m = 6.7 cm


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Summary of Mechanical

Properties of Metals

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Summary

1. Elastic and plastic deformations

2. Engineering measures of strength: Yield strength,

tensile strength (TS)

3. Engineering measures of ductility

4. Engineering measures of energy capacity:resilience, toughness

5. Hardness

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Hardness: Measurement

• Rockwell – No major sample damage

– Each scale runs to 130 but only useful in range

20-100.

– 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


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True Stress & Strain

Note: S.A. changes when sample stretched

• True stress

• True strain


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Variability in Material Properties

• Elastic modulus is material property

• Critical properties depend largely on sample flaws

(defects, etc.). Large sample to sample variability.

• Statistics

– Mean

– Standard Deviation

where n is the number of data points

MSE 3300-Lecture Note 10-Chapter 06 Mechanical Properties of Metals 2

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