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Transcript of Fundamentals of Material Scienceeng.modern-academy.edu.eg/e-learning/mech/MNF 212 Lecture/7... ·...
Fundamentals of Material Science
CHAPTER 7
Mechanical Properties
Fundamentals of Material Science Dr. Gamal Abdou
Behavior Of Material Under
Mechanical Loads = Mechanical Properties.
• Stress and strain:
• What are they and why are they used instead of load and
deformation
• Elastic behavior:
• Recoverable Deformation of small magnitude
• Plastic behavior:
• Permanent deformation We must consider which materials
are most resistant to permanent deformation?
• Toughness and ductility:
• Defining how much energy that a material can take before
failure. How do we measure them?
• Hardness:
• How we measure hardness and its relationship to material
strength
•(i) Tensile strength
•(ii) Hardness
•(iii) Impact strength
• (iv) fatigue
•(v) Creep
3
Fundamental Mechanical Properties
Comparison of Units: SI and Engineering Common
Unit SI Eng. Common
Force Newton (N) Pound-force (lbf)
Area mm2 or m2 in2
Stress Pascal (N/m2) or MPa (106 pascals) psi (lbf/in2) or Ksi (1000 lbf/in2)
Strain (Unitless!) mm/mm or m/m in/in
Conversion Factors SI to Eng. Common Eng. Common to SI
Force N*4.448 = lbf Lbf*0.2248 = N
Area I mm2*645.16 = in2 in2 *1.55x10-3 = mm2
Area II m2 *1550 = in2 in2* 6.452x10-4 = m2
Stress I - a Pascal * 1.450x10-4 = psi psi * 6894.76 = Pascal
Stress I - b Pascal * 1.450x10-7 = Ksi Ksi * 6.894 x106 = Pascal
Stress II - a MPa * 145.03 = psi psi * 6.89x 10-3 = MPa
Stress II - b MPa * 1.4503 x 10-1= Ksi Ksi * 6.89 = MPa
One other conversion: 1 GPa = 103 MPa
• Simple tension: cable
Note: = M/AcR here. Where M is the “Moment” Ac shaft area & R shaft radius
Common States of Stress
Ao = cross sectional
area (when unloaded)
FF
o
s =F
A
o
=Fs
A
ss
M
M Ao
2R
FsAc
• Torsion (a form of shear): drive shaftSki lift (photo courtesy
P.M. Anderson)
(photo courtesy P.M. Anderson)Canyon Bridge, Los Alamos, NM
o
s =F
A
• Simple compression:
Note: compressive
structure member
(s < 0 here).(photo courtesy P.M. Anderson)
OTHER COMMON STRESS STATES (1)
Ao
Balanced Rock, Arches National Park
• Bi-axial tension: • Hydrostatic compression:
Pressurized tank
s < 0h
(photo courtesy
P.M. Anderson)
(photo courtesy
P.M. Anderson)
OTHER COMMON STRESS STATES (2)
Fish under water
sz > 0
sq > 0
• Tension Test
– Strength
– Ductility
– Toughness
– Elastic Modulus
– Strain-hardening capability
• Test Specimen
– Usually solid and round
– Original Gauge length lo– Cross-sectional area Ao
Tension
4
• Tensile stress, s: • Shear stress, :
Area, A
Ft
Ft
s =Ft
Aooriginal area
before loading
Area, A
Ft
Ft
Fs
F
F
Fs
=Fs
Ao
Stress has units:
N/m2 or lb/in2
ENGINEERING STRESS
8
• Tensile strain: • Lateral strain:
• Shear strain:q/2
/2
/2 - q
q/2
/2
/2
L/2L/2
Lowo
=
Lo
L =L
wo
= tan q Strain is always
dimensionless.
ENGINEERING STRAIN
Linear: Elastic Properties
• Modulus of Elasticity, E:(also known as Young's modulus)
• Hooke's Law:
s = E s
Linear-
elastic
E
Units:
E: [GPa] or [psi]
s: in [Mpa] or [psi]
: [m/m or mm/mm] or [in/in]
F
Ao/2
L/2
Lowo
Here: The Black
Outline is Original,
Green is after
application of load
Stress-Strain: Testing Uses Standardized methods
developed by ASTM for Tensile Tests it is ASTM E8
• 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 (ASTM A-bar)
Adapted from
Fig. 6.2,
Callister 7e.
gauge length
- During Tensile Testing,
Instantaneous load and displacement is measured
These load / extension graphs depend on the size of the specimen.
E.g. if we carry out a tensile test on a specimen having a cross-sectional area
twice that of another, you will require twice the load to produce the same
elongation.
LOAD vs. EXTENSION PLOTS
The Force .vs. Displacement plot will be the same shape as the
Eng. Stress vs. Eng. Strain plot
Raw Data Obtained
Load, PfDeformation
Load
,P
(kN
)Total Elongation
Uniform Deformation
X
Maximum
Load, Pmax
Elastic
Elongation, L (mm)
• Stress-strain curves
– Linear elastic: elongation in the specimen that is
proportional to the applied load.
– Engineering stress: the ratio of the applied load P,
to the original cross-sectional area, Ao, of the
specimen.
• Engineering stress equation: σ = P/Ao
• Engineering strain equation: e = (l-lo)/lo
• Yield Stress: the stress at which permanent
(plastic) deformation occurs.
• Permanent (plastic) deformation: stress and
strain are no longer proportional.
• Ultimate tensile strength (UTS): the maximum
engineering stress
Tension
The Engineering Stress - Strain curve
Divided into 2 regions
ELASTIC PLASTIC
Tensile Testing
(a)(b)
18
Ductile vs Brittle Failure
Very
Ductile
Moderately
DuctileBrittle
Fracture
behavior:
Large Moderate
(%EL)=100%
Small
• Ductile
fracture is usually
desirable!
• Classification:
Ductile:
warning before
fracture, as increasing
is required for crack
growth
Brittle:
No
warning
19
Ductile vs. Brittle Failure
cup-and-cone fracture brittle fracture
Elastic and Plastic behavior
All materials deform when subjected to an external load.
Up to a certain load the material will recover its original
dimensions when the load is released. This is known as
elastic behavior.
The load up to which the materials remains elastic is the
elastic limit. The deformation or strain produced within the
elastic limit is proportional to the load or stress. This is
known as Hook’s Law , Stress Strain or Stress = E*Strain.
E is known as the Elastic Modulus.
When the load exceeds the elastic limit, the deformation
produced is permanent. This is called plastic deformation.
Hook’s law is no longer valid in the plastic region.
Tensile Properties
In many other metals and alloys the yield point is not
distinct (Curve 2, Fig. b). In such cases, a line parallel to the
linear region is drawn at a strain = 0.002 (0.2%) and its
intercept on the plastic region is taken as the yield stress
(Fig. b). This is called 0.2% Proof stress.
The stress at the maximum load is called ultimate tensile
strength (UTS).
The strain up to UTS is the uniform plastic strain. Beyond
this the cross sectional area reduces and necking takes
place.
The fracture strain ef = (Lf - Lo)/Lo, where Lf is the length
after fracture, is taken as the measure of Ductility.
Tensile Properties
EL = Elastic limit, up to which Hook’s Law (Stress Strain)
is valid. The material comes back to original shape when theload is released.
Elastic limit is difficult to determine. The proportional limit,
PL, the load at which the curve deviates from linearity, is
taken as the elastic portion.
The slope of the linear region is the Young’s Modulus or
Elastic Modulus (E).
Loading beyond PL produces permanent or plastic
deformation. The onset point of plastic deformation is known
as Yield stress (YS).
In some materials like mild steel the yield point is prominent
(Curve 1 in Fig. b)
Poisson’s ratio
A tensile force in the x direction produces an extension along
thatand
The
axis while it produces contraction along the transverse yz axis.
ratio of the lateral to axial strain is the Poisson's ratio, .
For most metals it is around 0.33
y z
= = x
• Modulus of Elasticity, E:(also known as Young's modulus)
10
• Hooke's Law:
s = E
• Poisson's ratio, :
metals: ~ 0.33
ceramics: ~0.25
polymers: ~0.40
= L
L
1-
F
Fsimple tension test
s
Linear- elastic
1
E
Units:
E: [GPa] or [psi]
: dimensionless
LINEAR ELASTIC PROPERTIES
• Elastic Shear
modulus, G:
12
1
G
= G
• Elastic Bulk
modulus, K:
P= -KVVo
P
V
1-K
Vo
• Special relations for isotropic materials:
P
P P
M
M
G =
E
2(1 ) K =
E
3(1 2)
simple
torsion
test
pressure
test: Init.
vol =Vo.
Vol chg.
= V
OTHER ELASTIC PROPERTIES
True-Stress and True-Strain
• True-stress: ratio of the load, P, to the
instantaneous cross-sectional area, A, of the
specimen.
• True-strain: the sum of all the instantaneous
engineering strains.
– True-stress equation: σ = P/A
– True-strain equation: e = ln(l/lo)
True Stress-Strain Curve
Since the engineering stress-strain curve is based on
original area, it descends after maximum load as the load
bearing ability of the sample decreases due to reduction in
area.
The true stress-strain curve (blue) however, continues
to go up till fracture as it is based on the actual area.
True Stress & StrainNote: Stressed Area changes when sample is deformed
(stretched)
• True stress
• True Strain
iT AF=s
oiT llln=
=
s=s
1ln
1
T
T
Adapted from Fig. 6.16,
Callister 7e.
• An increase in sy due to plastic deformation.
22
• Curve fit to the stress-strain response:
s
large hardening
small hardeningu
nlo
ad
relo
ad
sy 0
sy 1
sT = C T
n
“true” stress (F/A) “true” strain: ln(L/Lo)
hardening exponent: n=0.15 (some steels) to n=0.5 (some copper)
HARDENING
Construction of Stress-Strain Curves
• The stress-strain curve can be
represented by the equation: σ = Ken
– K = strength coefficient
– n = strain hardening exponent
• Specific energy: energy-per-unit
volume of the material deformed.
• Ductility: extent of plastic deformation that
the material undergoes before fracture.
• Two measures of ductility:
– Total elongation: (lf-lo)/lo x 100%
– Reduction of Area: (Ao-Af)/Ao x 100%
Ductility
• Plastic tensile strain at failure:
20
Engineering tensile strain,
Engineering
tensile
stress, s
smaller %EL
(brittle if %EL<5%)
larger %EL
(ductile if
%EL>5%)
• Another ductility measure:
%AR =
Ao A f
Ao
x100
• Note: %AR and %EL are often comparable.
--Reason: crystal slip does not change material volume.
--%AR > %EL possible if internal voids form in neck.
Lo LfAo
Af
%EL =
L f Lo
Lo
x100
Adapted from Fig. 6.13,
Callister 6e.
Mechanical Properties of some commonly used materials
Material E, GPa YS, MPa UTS, MPa %Elong. Poisson's
ratio
C steel 207 220 - 250 400 - 500 23 0.30
Stain less steel 193 515 850 10 0.30
Alloy steels 207 860 1280 12 0.30
Al 70 34 90 40 0.33
Al alloys 72 - 85 250 -500 300 - 550 10 -20 0.34
Ti 103 170 240 30 0.34
Ti alloy 114 1100 1170 10 0.34
Mg 45 25 - 40 50 – 60 8 – 10 0.35
Mg alloys 45 220 290 15 0.35
Ni 204 148 460 47 0.31
Ni super alloy 207 517 930 - 0.21
Al2O3 380 550 - 0.16
PET 2.7 - 4 60 70 30-300 0.39
Hardness
Hardness can be defined as resistance
indentation or resistance to scratch.
to deformation or
Hardness
Indentation Scratch Rebound
Indentation hardness is of particularand is most commonly used.
interest to engineers
Indentation hardness can be measured by differentmethods.
Classified based on how it is measured.
The following are the hardness test methods
• Rockwell hardness test
• Brinell hardness
• Vickers
• Knoop hardness
• shore
Hardness Measurement Methods
Hardness
• Resistance to permanently (plastically) indenting the surface of a
product.
• Large hardness means:
--resistance to plastic deformation or cracking in compression.
--better wear properties.
e.g., Hardened 10
mm sphere
apply known force measure size of indentation 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
Rockwell Hardness
In this type of test, depth of indentation at a constant
load is taken as the measure of Hardness.
A minor load of 10 kg is first applied for good contact
between the indenter and the sample surface.
The major load is then applied and the depth of indentation
is recorded on a dial gage in terms of an arbitrary number.
The dial consists of 100 divisions, each division representing
a penetration depth of 0.002 mm.
Rockwell Hardness
Indenter and Hardness Scale
Two types of indenters – 120 diamond cone called Brale
indenter and 1.6 and 3.2 mm diameter steel balls
Combination of indenter and major load gives rise to
different hardness scales.
C - Scale – Brale indenter + 150 kg load, designated as RC.
Range is RC 20 – RC 70. Used for hard materials like hardened
steels.
B-Scale – Steel ball indenter + 100 kg load, written as RB.
Range is RB 0 to RB 100.
Minor loads in RC and RB scales are 10 kg and 3 kg
respectively.
Microhardness
Sometime hardness determination is needed over a very
small area.
For example, hardness of carburised steel surface,
coatings or individual phases or constituents of a material.
The load applied is much smaller compared to
macrohardness.
The indentation is very small. An optical microscope is
used to observe it. Sample preparation is needed.
Two methods are used for microhardness testing.
Microhardness
Vickers Microhardness
This is same as Vickers hardnessload is much smaller so as to cover
The applied load range is 1 – 100
except that the applieda small area.
g.
Hardness: Common Measurement Systems
Callister Table 6.5
HB = Brinell Hardness
TS (psia) = 500 x HB
TS (MPa) = 3.45 x HB
Comparing
Hardness
Scales:
Inaccuracies in Rockwell / Brinell hardness
measurements may occur due to:
An indentation is made too near a specimen edge.
Two indentations are made too close to one another.
Specimen thickness should be at least ten times the
indentation depth.
Allowance of at least three indentation diameters
between the center on one indentation and the
specimen edge, or to the center of a second
indentation.
Testing of specimens stacked one on top of another is
not recommended.
Indentation should be made into a smooth flat surface.
Impact Tests
Toughness of metals is the ability to
withstand impact.
TOUGHNESS
High toughness = High yield strength and ductility
Dynamic (high strain rate) loading condition (Impact test)
1. Specimen with notch- Notch toughness
2. Specimen with crack- Fracture toughness
Is a measure of the ability of a material to absorb energy up to
fracture
Important Factors in determining Toughness:
1. Specimen Geometry & 2. Method of load application
Static (low strain rate) loading condition (tensile stress-strain test)
1. Area under stress vs strain curve up to the point of fracture.
• Energy to break a unit volume of material
• Approximate by the area under the stress-strain curve.
Toughness
Brittle fracture: elastic energy
Ductile fracture: elastic + plastic energy
very small toughness (unreinforced polymers)
Engineering tensile strain,
Engineering
tensile
stress, s
small toughness (ceramics)
large toughness (metals)
Adapted from Fig. 6.13,
Callister 7e.
Izod test
Strikes at 167 Joules.
Test specimen is held
vertically.
Notch faces striker.
Charpy impact test
Strikes form higher
position with 300 Joules.
Test specimen is held
horizontally.
Notch faces away from
striker.
ExamplesEx.1. A 15 mm long and 13 mm diameter sample shows the
following behavior in a tensile test. Load at 0.2% offset – 6800
kg, maximum load – 8400 kg, fracture occurs at 7300 kg,
diameter and length after fracture – 8 mm and 65 mm
respectively. Find the standard mechanical properties.
Solution: Ao = (13)2/4 = 132.7 mm2, Af = (8)2/4 = 50.3 mm2
= 620 MPax 9.8)/132.7 = 620 N/mm2UTS = Pmax/Ao = (84000.2% proof stress = (6800 x 9.8)/132.7 = 502 N/mm2 = 502 MpaBreaking stress = (7300 x 9.8)/132.7 = 539 Mpa
%elongation = 100*(Lf – Lo)/Lo = 100 x (65 – 50)/50 = 30%% area reduction = 100*(Af – Ao)/Lo = 100(132.7 – 50.3)/132.7 =
62%
ExamplesEx.2. A metal experiences a true strain of 0.16 at a true stress
of 500 MPa. What is the strain hardening exponent of the
metal? K = 825 MPa. What will be the true strain at a stress of600 MPa?
Solution: n = (logs - logK)/log = (log 500 – log 825)/log 0.16= 0.271
s= Kn
()0.271 , strain = 0.3Strain at 600 MPa: 600 = 825
Quiz
1. Define hardness. What is Mohs scale of hardness?
2. Why it is necessary to specify load-indenter combination in
Rockwell hardness test?
3. How is Brinell hardness measured. Show that BHN varies
as P/D2 where P is the load and D is the indenter diameter.
4. Why is the included angle between opposite faces of theVickers indenter 136?
5.6.
7.
8.
9.
What
What
What
What
is
is
is
is
microhardness? Why sometime it is necessary?
engineering stress and strain?
Hook’s law?elastic and proportional limit?
How is the elastic modulus measured from the stress-strain
curve?10. What is yield stress?
Quiz
11. What is 0.2% proof stress?
12.13.
14.
15.
How is the ductility measured?
WhatWhat
What
is
is
is
ductile and brittle behavior?resilience? What is toughness?
true stress and strain. Deduce the relationship
between true and engineering stress ad strain.16. Why does the engineering stress-strain curve peak and
drop where as the true stress-strain curve keep on going up?a flow curve?
shear stress and strain
Poisson's ratio?
17.18.
19.
20.
What
What
What
What
is
is
is
are structure-sensitive and structure insensitive
properties?21. What is Poisson's ratio?
Quiz22. A 15 mm long and 120 mm dia cylindrical rod is subjected
to a tensile load of 35 kN. It must not experience either plastic
deformation or a diameter reduction of more than 0.012 mm.
Which of the listed materials is suitable for such a requirement
and why? Al (E= 70 GPa, YS = 250 MPa, = 0.33), Ti (E= 105
GPa, YS = 850 MPa, = 0.36), Steel (E= 205 GPa, YS = 550MPa, = 0.27), Mg (E= 45 GPa, YS = 170 MPa, = 0.35).
23. A metal experiences a true strain of 0.1 at a true stress of
415 MPa. What is the strain hardening exponent of the metal?
K = 1035 MPa. What will be the true strain at a stress of 600MPa?
Quiz24. The following data were obtained in a tensile test of a low-
carbon steel of diameter 12 mm and gage length 50 mm.
Plot Engineering and True stress-strain curve and find thetensile properties.
Load, kN Elongation, mm Load, kN Elongation, mm
2 0.0041 25.2 0.51
4 0.0082 28 1.52
6 0.0132 30 2.03
8 0.0183 34 3.05
10 0.0226 38.4 4.57
12 0.0267 40 6.60
14 0.0310 40.4 7.62
16 0.0351 40.8 12.7
18 0.0391 40.2 14.7
20 0.0445 38.6 15.7
22 0.0485 36.4 17.8
24 0.0518 32.4 19.3