Mechanical Properties. ISSUES TO ADDRESS. • 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?. - PowerPoint PPT Presentation
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Chapter 6 - 1 ISSUES TO ADDRESS... • 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 does permanent deformation occur? What materials are most resistant to permanent deformation? • Toughness and ductility: What are they and how do we measure them? Mechanical Properties
Transcript
Chapter 6 - 1
ISSUES TO ADDRESS...
• 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 does permanent deformation occur? What materials are most resistant to permanent deformation?
• Toughness and ductility: What are they and how do we measure them?
Mechanical Properties
Chapter 6 - 2
Stress has units: N/m2 or lbf/in2
Engineering Stress• Shear stress, :
Area, A
Ft
Ft
Fs
F
F
Fs
= Fs
Ao
• Tensile stress, :
original area before loading
Area, A
Ft
Ft
=Ft
Ao2f
2m
Nor
in
lb=
Chapter 6 - 3
Stress and Strain
Stress: Force per unit area arising from applied load.
Tension, compression, shear, torsion or any combination.
Stress = σ = force/area
Strain: ε – physical deformation response of amaterial to stress, e.g., elongation.
Chapter 6 - 4
• Simple tension: cable
Common States of Stress
Ao = cross sectional
area (when unloaded)
FF
o F
A
o
FsA
M
M Ao
2R
FsAc
• Torsion (a form of shear): drive shaftSki lift (photo courtesy P.M. Anderson)
Chapter 6 - 5
(photo courtesy P.M. Anderson)Canyon Bridge, Los Alamos, NM
Elastic Deformation1. Initial 2. Small load 3. Unload
F
bonds stretch
return to initial
F
Linear- elastic
Non-Linear-elastic
Chapter 6 - 9
Plastic means permanent!
Plastic Deformation (Metals)
F
linear elastic
linear elastic
plastic
1. Initial 2. Small load 3. Unload
planes still sheared
F
elastic + plastic
bonds stretch & planes shear
plastic
Chapter 6 -
1. Elastic Materials
Return to the their original shape when the applied load is removed.
Unloading
P
Loading
Chapter 6 -
2. Plastic Materials
No deformation is observed up to a certain limit. Once the load passes this limit, permanent deformartions are observed.
δ
P
Limit
Plastic deformation
UnloadingLoadin
g
Chapter 6 - 12
Stress-Strain Testing
• Typical tensile test machine
Adapted from Fig. 6.3, Callister 7e. (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.)
specimenextensometer
• Typical tensile specimen
Adapted from Fig. 6.2,Callister 7e.
gauge length
Chapter 6 - 13
Linear Elastic Properties
• Modulus of Elasticity, E: (also known as Young's modulus)
• Hooke's Law:
= E
Linear- elastic
E
F
Fsimple tension test
Chapter 6 - 14
• Hooke's Law: σ = E ε (linear elastic behavior)
Copper sample (305 mm long) is pulled in tension with stress of 276 MPa. If deformation is elastic, what is elongation?
Example: Hooke’s Law
E Ell
0
l
l0
E
l (276MPa)(305mm)
110x103MPa0.77mm
For Cu (polycrystalline), E = 110 GPa.
Hooke’s law involves axial (parallel to applied tensile load) elastic deformation.
F
Fsimple tension test
Axial strain
Width strain
Chapter 6 - 15
Elastic Deformation
Elastic means reversible!
F
Linear- elastic
Non-Linear-elastic
2. Small load
F
bonds stretch
1. Initial 3. Unload
return to initial
Chapter 6 - 16
Poisson's ratio,
• Poisson's ratio, :
Units:E: [GPa] or [psi]: dimensionless > 0.50 density increases
< 0.50 density decreases (voids form)
L
-
L
metals: ~ 0.33ceramics: ~ 0.25polymers: ~ 0.40
Chapter 6 - 17
Mechanical Properties• Slope of stress strain plot (which is
proportional to the elastic modulus) depends on bond strength of metal
Adapted from Fig. 6.7, Callister 7e.
Chapter 6 - 18
• Elastic Shear modulus, G:
G
= G
Other Elastic Properties
simpletorsiontest
M
M
• Special relation for isotropic materials:
2(1 )EG
Chapter 6 - 19
MetalsAlloys
GraphiteCeramicsSemicond
PolymersComposites
/fibers
E(GPa)
Based on data in Table B2,Callister 7e.Composite data based onreinforced epoxy with 60 vol%of alignedcarbon (CFRE),aramid (AFRE), orglass (GFRE)fibers.
Young’s Moduli: Comparison
109 Pa
0.2
8
0.6
1
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
4
6
10
20
40
6080
100
200
600800
10001200
400
Tin
Cu alloys
Tungsten
<100>
<111>
Si carbide
Diamond
PTFE
HDPE
LDPE
PP
Polyester
PSPET
CFRE( fibers) *
GFRE( fibers)*
GFRE(|| fibers)*
AFRE(|| fibers)*
CFRE(|| fibers)*
Chapter 6 - 20
(at lower temperatures, i.e. T < Tmelt/3)Plastic (Permanent) Deformation
• Simple tension test:
engineering stress,
engineering strain,
Elastic+Plastic at larger stress
permanent (plastic) after load is removed
p
plastic strain
Elastic initially
Adapted from Fig. 6.10 (a), Callister 7e.
Chapter 6 - 21
• Stress where noticeable plastic deformation occurs.
When εp = 0.002
Yield Stress, σY
For metals agreed upon 0.2%
Note: for 2 in. sample
ε = 0.002 = Δz/z
Δz = 0.004 in
• P is the proportional limit where deviation from linear behavior occurs.
Strain off-set method for Yield Stress• Start at 0.2% strain (for most metals).• Draw line parallel to elastic curve (slope of E).• σY is value of stress where dotted line
crosses stress-strain curve (dashed line).
tensile stress,
Eng. strain, p = 0.002
Elastic recovery
PσY
Adapted from Fig. 6.10 (a), Callister 7e.
Chapter 6 - 22
• Yield-point phenomenon occurs when elastic plastic transition is abrupt.
Yield Points and σYS
For steels, take the avg. stress of lower yield point since less sensitive to testing methods.
No offset method required.
• In steels, this effect is seen when dislocations start to move and unbind for interstitial solute.
• Lower yield point taken as σY.
• Jagged curve at lower yield point occurs when solute binds dislocation and dislocation unbinding again, until work-hardening begins to occur.
Chapter 6 - 23
Room T values
Based on data in Table B4,Callister 7e.a = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & tempered
• Metals: occurs when noticeable necking starts.• Polymers: occurs when polymer backbone chains are aligned and about to break.
Adapted from Fig. 6.11, Callister 7e.
y
strain
Typical response of a metal
F = fracture or
ultimate
strength
Neck – acts as stress concentrator
eng
inee
ring
TS s
tres
s
engineering strain
• Maximum stress on engineering stress-strain curve.
Chapter 6 - 25
Tensile Strength : Comparison
Si crystal<100>
Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibers
Polymers
Ten
sile
str
engt
h, T
S
(MP
a)
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
Room Temp. valuesBased on data in Table B4,Callister 7e.a = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & temperedAFRE, GFRE, & CFRE =aramid, glass, & carbonfiber-reinforced epoxycomposites, with 60 vol%fibers.
Chapter 6 -
• Plastic tensile strain at failure:
Engineering tensile strain,
Engineering tensile stress,
smaller %EL (brittle if %EL<5%)
larger %EL (ductile if %EL>5%)
• Another ductility measure: %RA
Ao
Af
Ao
x100
• Note: %RA and %EL are often comparable. - Reason: crystal slip does not change material volume. - %RA > %EL possible if internal voids form in neck.
Lo LfAo Af
%EL
Lf L
o
Lo
x100
Ductility (%EL and %RA)
Adapted from Fig. 6.13, Callister 7e.
Chapter 6 - 27
• Energy to break a unit volume of material• Approximate by the area under the stress-strain curve.
Toughness
Brittle fracture: elastic energyDuctile fracture: elastic + plastic energy
very small toughness (unreinforced polymers)
Engineering tensile strain,
Engineering tensile stress,
small toughness (ceramics)
large toughness (metals)
Adapted from Fig. 6.13, Callister 7e.
Chapter 6 - 28
Resilience, Ur• Ability of a material to store energy
– Energy stored best in elastic region
If we assume a linear stress-strain curve this simplifies to
Adapted from Fig. 6.15, Callister 7e.
yyr2
1U
y dUr 0
Chapter 6 - 29
Elastic Strain Recovery
Adapted from Fig. 6.17, Callister 7e.
• Unloading in step 2 allows elastic strain to be recovered from bonds.• Reloading leads to higher YS, due to work-hardening already done
Chapter 6 - 30
Hardness• Resistance to permanently indenting the surface.• Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties.
e.g., 10 mm sphere
apply known force 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. 7.18.
Chapter 6 - 31
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
Chapter 6 - 32
Hardness: MeasurementTable 6.5
Chapter 6 - 33
True Stress & StrainNote: S.A. changes when sample stretched
• True stress
• True Strain
iT AF
oiT ln
1ln
1
T
T
Adapted from Fig. 6.16, Callister 7e.
Chapter 6 - 34
Hardening
• Curve fit to the stress-strain response:
T K T n
“true” stress (F/A) “true” strain: ln(L/Lo)
hardening exponent:n = 0.15 (some steels) to n = 0.5 (some coppers)
• An increase in y due to plastic deformation.
large hardening
small hardeningy 0
y 1
Chapter 6 - 35
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 2
1
2
1
n
xxs i
n
n
xx n
n
where n is the number of data points
Chapter 6 - 36
• Design uncertainties mean we do not push the limit.• Factor of safety, N
Ny
working
Often N isbetween1.2 and 4
• Example: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below. Use a factor of safety of 5.
Design or Safety Factors
4
0002202 /d
N,
5
Ny
working
1045 plain
carbon steel: y = 310 MPa
TS = 565 MPa
F = 220,000N
d
Lo
d = 0.067 m = 6.7 cm
Chapter 6 - 37
• 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).
• Toughness: The energy needed to break a unit volume of material.
• Ductility: The plastic strain at failure.
Summary
• Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches y.
