lecture # 6 mechanical properties of metals intended learning outcomes: after the end of this...

Lecture # 6Mechanical Properties of Metals

• Intended learning Outcomes:• After the end of this lecture the student should

be able to:• Define stress –strain relation.• State Hooke’s law.• Modules of elasticity .• Tensile strength ,percent elongation ,Ductility• Hardness and the different tests methods for

measuring it.

TENSION TESTS:

4

• Tensile stress, s: • Shear stress, t:

Area, A

Ft

Ft

FtAo

original area before loading

Area, A

Ft

Ft

Fs

F

F

Fs

FsAo

Stress has units:

N/m2 or lb/in2

ENGINEERING STRESS

5

• Simple tension: cable

o

FA

• Simple shear:

Ao = cross sectional Area (when unloaded)

FF

o

FsA

Note: t = M/AcR here.

COMMON STATES OF STRESS

M

M Ao

2R

FsAc

ϵ= Strain.Io= original length Ii= instantaneous lengthΔI= deformation elongation or change in length

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• Tensile strain: • Lateral strain:

• Shear strain:

/2

/2

/2 -

/2

/2

/2

L/2L/2

Lowo

Lo

L L

wo

= tan Strain is alwaysdimensionless.

ENGINEERING STRAIN

• Typical tensile specimen

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• Other types of tests: --compression: brittle materials (e.g., concrete) --torsion: cylindrical tubes, shafts.

gauge length

(portion of sample with reduced cross section)=

• Typical tensile test machine

load cell

extensometerspecimen

moving cross head

Adapted from Fig. 6.2, Callister 6e.

Adapted from Fig. 6.3, Callister 6e. (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.)

STRESS-STRAIN TESTING

STRESS–STRAIN BEHAVIORFor most metals that are stressed in tension and at relatively low levels, stress and strain are proportional to each other through the relationship:

ELASTIC DEFORMAT ION

• Modulus of Elasticity, E: (also known as Young's modulus)

• Hooke's Law:

= E

Linear- elastic

1E

F

Fsimple tension testUnits:

E: [GPa] or [psi]

Elastic Deformation

Linear Behavior

Behavior of most metals (E)

Non Linear Elastic Behavior

(Secant and Tangent Modulus)

Eg: Gray cast iron ,concrete,polymers

EXAMPLE:1

A piece of copper originally 305 mm (12 in.) long is pulled in tension with astress of 276 MPa (40,000 psi). If the deformation is entirely elastic, what willbe the resultant elongation?

MECHA NICAL BEHAVIOR of META LS

Typical stress–strain behavior for a metal showingelastic and plastic deformations, the proportional limitP, and the yield strengthy, as determined using the 0.002 strain offset method.

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• Simple tension test:

(at lower temperatures, T < Tmelt/3)

tensile stress,

engineering strain,

Elastic initially

Elastic+Plastic at larger stress

permanent (plastic) after load is removed

pplastic strain

PLASTIC (PERMANENT) DEFORMATION

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• Stress at which noticeable plastic deformation has occurred.

when ep = 0.002 tensile stress,

engineering strain,

y

p = 0.002

YIELD STRENGTH, sy

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Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibersPolymers

Yie

ld s

trength

, y

(MPa)

PVC

Ha

rd t

o m

ea

su

re,

sin

ce in t

ensio

n, fr

actu

re u

sually o

ccurs

befo

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

su

re,

in c

era

mic

matr

ix a

nd e

poxy m

atr

ix c

om

posites, sin

ce

in

tensio

n, fr

actu

re u

sually o

ccurs

befo

re y

ield

.HDPEPP

humid

dryPC

PET

¨

Room T values

y(ceramics) >>y(metals) >> y(polymers)

YIELD STRENGTH: COMPARISON

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• Maximum possible engineering stress in tension.

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

Adapted from Fig. 6.11, Callister 6e.

TENSILE STRENGTH, TS

strain

engin

eeri

ng

str

ess

TS

Typical response of a metal

Example 2:From the tensile stress–strain behavior for the brass specimen shown in the following Figure determine the following:(a) The modulus of elasticity.(b) The yield strength at a strain offset of 0.002.(c) The maximum load that can be sustained by a cylindrical specimen havingan original diameter of 12.8 mm (0.505 in.).(d) The change in length of a specimen originally 250 mm (10 in.) long that issubjected to a tensile stress of 345 MPa (50,000 psi).