CHAPTER 6: MECHANICAL PROPERTIES

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CHAPTER 6 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?
Plastic behavior At what point do
dislocations cause permanent deformation?
What materials are most resistant to
permanent deformation?
Toughness and ductility What are they and
how do we measure them?
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INTRODUCTION (I)

• The need for
• standardized language for expressing mechanical
  properties of materials
• STRENGTH, HARDNESS, DUCTILITY, and STIFFNESS
• standardized test methods
• American Society for Testing and Materials
  Standards and others

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INTRODUCTION (II)
The result of mechanical testing is generally a
response curve or a (set of) number(s), in this
case a STRESS vs. STRAIN curve
Courtesy of Plastics Technology Laboratories, Inc
50 Pearl Street, Pittsfield, MA 01201
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Basic Concepts of Stress and Strain

• Need to compare load on specimens of various size
  and shapes
• For tension and compression
• Engineering Stress, s F / A0 , where F is load
  applied perpendicular to speciment crosssection
  and A0 is cross-sectional area (perpendicular to
  the force) before application of the load.
• Engineering Strain, e ?l / l0 ( x 100 ), where
  ?l change in length, lo is the original length.
• These definitions of stress and strain allow one
  to compare test results for specimens of
  different cross-sectional area A0 and of
  different length l0.

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Basic Concepts of Stress and Strain

• Need to compare load on specimens of various size
  and shapes
• For tension and compression
• Engineering Stress, s F / A0 , where F is load
  applied perpendicular to speciment crosssection
  and A0 is cross-sectional area (perpendicular to
  the force) before application of the load.
• Engineering Strain, e ?l / l0 ( x 100 ), where
  ?l change in length, lo is the original length.
• For shear
• Shear Stress, t F / A0 , where F is load
  applied parallel to upper and lower specimen
  faces of area A0.
• Shear Strain, ? tan ? ( x 100 ), where ? is
  the strain angle.

These definitions of stress and strain allow one
to compare test results for specimens of
different crosssectional area A0 and of different
length l0.
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ENGINEERING STRESS
Tensile stress, s
Shear stress, t
Stress has units N/m2 or lb/in2
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ENGINEERING STRAIN
Tensile strain
Lateral strain
Applied
Resulting
Shear strain
Strain is always dimensionless.
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COMMON STATES OF STRESS
Simple tension cable
Note s gt 0 here !
Ski lift (photo courtesy P.M. Anderson)
Simple shear drive shaft
Note t M/AcR here.
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OTHER COMMON STRESS STATES (1)
Simple compression
A
o
(photo courtesy P.M. Anderson)
Note compressive structure member (s lt 0 here).
Balanced Rock, Arches
National Park
(photo courtesy P.M. Anderson)
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OTHER COMMON STRESS STATES (2)
Bi-axial tension
Hydrostatic compression
Pressurized tank
(photo courtesy P.M. Anderson)
(photo courtesy P.M. Anderson)
s lt 0
h
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OTHER COMMON STRESS STATES (3)
State of stresses in college life
s2, family
s1, classes
s lt 0
h
s3, friends, etc
s4, daily challenges, etc
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SIMPLE STRESS-STRAIN TESTING
Typical tensile test machine
Typical tensile specimen
Adapted from Fig. 6.2, Callister 6e.
gauge
(portion of sample with

length
reduced cross section)
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.)

• Other types of tests
• compression brittle materials (e.g., concrete)
• torsion cylindrical tubes, shafts.
• hardness surfaces of metals, ceramics

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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.)
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Other Types of Application of Load
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How does deformation take place in the material
at an atomic scale ?

• Two types of deformation
• Elastic
• Reversible, no change in the shape and the size
  of the specimen when the load is released !
• When under load volume of the material changes !
• Plastic
• Irreversible, dislocations cause slip, bonds are
  broken, new bonds are made.
• When load is released, specimen does not return
  to original size and shape, but volume is
  preserved !

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STRESS-STRAIN CURVE
Necking starts
STRESS
sUTS
REGION I
REGION III
REGION II HARDENING OCCURS DISLOCATION MOTION AND
GENERATION !
sYIELD
sFAILURE or sFRACTURE
l0 le
Region I Elastic Deformation Hookes
Law Region II Uniform Plastic Deformation Strain
is uniform across material Region III
Non-uniform Plastic Deformation Deformation is
limited to neck region
E
l0 le lp
STRAIN
eYIELD
eUTS
l0
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ELASTIC DEFORMATION
1. Initial
2. Small load
3. Unload
Elastic means reversible! Bonds stretch and but
recover when load is released.
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LINEAR ELASTIC PROPERTIES
Modulus of Elasticity, E (also known as
Young's modulus)
F
e
Under Load
Hooke's Law (Linear)
s E e
Poisson's ratio, n metals n 0.33
ceramics 0.25 polymers 0.40
e
L
e
L
No load
e
F
n
-
simple
1
tension
test
Units E GPa or psi n dimensionless
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NON-LINEAR ELASTIC PROPERTIES

• Some materials will exhibit a non-linear elastic
  behavior under stress ! Examples are polymers,
  gray cast iron, concrete, etc

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Linear Elastic Deformation (Atomic Scale)
Chapter 2 Inter-atomic Bonding ! Youngs
Modulus a (dF/dr) at ro , what else ? If we
increase temperature, how will E behave ?
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Other Elastic Properties
Elastic Shear modulus, G
t G g
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YOUNGS MODULI COMPARISON
Graphite Ceramics Semicond
Metals Alloys
Composites /fibers
Polymers
E(GPa)
Based on data in Table B2, Callister
6e. Composite data based on reinforced epoxy with
60 vol of aligned carbon (CFRE), aramid (AFRE),
or glass (GFRE) fibers.
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USEFUL LINEAR ELASTIC RELATIONS
Simple tension
Simple torsion
Material, geometric, and loading parameters
all contribute to deflection. Larger
elastic moduli minimize elastic deflection.
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PLASTIC DEFORMATION (METALS)
1. Initial
2. Small load
3. Unload
Plastic means permanent!
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PLASTIC (PERMANENT) DEFORMATION
(at lower temperatures, T lt Tmelt/3)
Simple tension test
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YIELD STRENGTH, sy
Some materials do NOT exhibit a distinct
transition from elastic to plastic region under
stress, so by convention a straight line is drawn
parallel to the stress strain curve with 0.2
strain. The stress at the intersection is called
the yield stress !
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HARDENING
An increase in sy due to plastic deformation.
Curve fit to the stress-strain response
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YIELD STRENGTH COMPARISON
Room T values
Based on data in Table B4, Callister 6e. a
annealed hr hot rolled ag aged cd cold
drawn cw cold worked qt quenched tempered
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TENSILE STRENGTH, TS
Maximum possible engineering stress in tension.
NECKING
Adapted from Fig. 6.11, Callister 6e.
FRACTURE
Metals occurs when noticeable necking
starts. Ceramics occurs when crack
propagation starts. Polymers occurs when
polymer backbones are aligned and about to
break.
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TENSILE STRENGTH COMPARISON
Room T values
Based on data in Table B4, Callister 6e. a
annealed hr hot rolled ag aged cd cold
drawn cw cold worked qt quenched
tempered AFRE, GFRE, CFRE aramid, glass,
carbon fiber-reinforced epoxy composites, with 60
vol fibers.
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DUCTILITY, EL
Plastic tensile strain at failure
Adapted from Fig. 6.13, Callister 6e.
Note AR and EL are often comparable.
--Reason crystal slip does not change material
volume. --AR gt EL possible if internal
voids form in neck.
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Mechanical Strength of Materials
Yield Strength, Tensile Strength and Ductility
can be improved by alloying, heat and mechanical
treatment, but Youngs Modulus is rather
insensitive to such processing ! Temperature
effects YS, TS and YM decrease with increasing
temperature, but ductility increases with
temperature !
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TOUGHNESS RESILIENCE
Energy to break a unit volume of material
Approximate by the area under the stress-strain
curve.
RESILIENCE is energy stored in the material w/o
plastic deformation ! Ur sy2 / 2 E TOUGHNESS
is total energy stored in the material upon
fracture !
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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.
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TRUE STRESS STRAIN
sT s (1 e ) eT ln (1e)
The material does NOT get weaker past M
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HARDNESS
Resistance to permanently indenting the
surface. Large hardness means
--resistance to plastic deformation or cracking
in compression. --better wear
properties.
Adapted from Fig. 6.18, Callister 6e. (Fig. 6.18
is adapted from G.F. Kinney, Engineering
Properties and Applications of Plastics, p. 202,
John Wiley and Sons, 1957.)
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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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Hardness Measurement
Table 6.5
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HARDNESS !!

• Relatively simple and cheap technique
• Non-destructive
• Related to many other mechanical properties

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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
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Design or Safety Factors
Design uncertainties mean we do not push the
limit. Factor of safety, N
Often N is between 1.2 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.
d 0.067 m 6.7 cm
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SUMMARY
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).
Plastic behavior This permanent deformation
behavior occurs when the tensile (or
compressive) uniaxial stress reaches sy.
Toughness The energy needed to break a unit
volume of material.
Ductility The plastic strain at failure.
Note For materials selection cases related to
mechanical behavior, see slides 22-4 to 22-10.
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ANNOUNCEMENTS
Reading Chapter 6 and Chapter 7
Homework Core Questions 6.11,6.16, 6.20,
6.37, 6.44 Bonus Questions 6.6, 6.7, 6.45
Due date 06-11-2009
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