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