# CHAPTER 6 MECHANICAL PROPERTIES(1) by hcj

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CHAPTER 7:
MECHANICAL PROPERTIES
CHAPTER 7:
MECHANICAL PROPERTIES
Stress
Elasticity
• Stress and strain
Strength
Tensile
• Elastic behavior          Elongation
Ductile
• Plastic behavior          Fracture
Tension
• Toughness and ductility   Flexural
Plasticity
• Ceramic Materials
7.2 STRESS & STRAIN
• Tensile stress, s:               • Shear stress, t:

Stress has units:
N/m2 or lb/in2

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Stress (s) for tension and
compression

Strain (e) for tension and
compression

Shear stress

Shear strain      Torsional deformation
g = tan q         angle of twist, f
7.2 COMMON STATES OF STRESS
• Simple tension: cable

Ski lift   (photo courtesy P.M. Anderson)
• Simple shear: drive shaft

Note: t = M/Ac
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OTHER COMMON STRESS STATES
• Simple compression:

(photo courtesy P.M. Anderson)

Note: compressive
structure member
(photo courtesy P.M. Anderson)   (s < 0 here).

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OTHER COMMON STRESS STATES
• Bi-axial tension:   • Hydrostatic compression:

Pressurized tank                        (photo courtesy
(photo courtesy                         P.M. Anderson)
P.M. Anderson)

s h< 0

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ENGINEERING STRAIN
• Tensile strain:     • Lateral strain:

• Shear strain:

Strain is always
dimensionless.

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7.2 STRESS-STRAIN TESTING
• Typical tensile specimen                     • Typical tensile
test machine
Callister 6e.

• Other types of tests:            Adapted from Fig. 6.3, Callister 6e.
(Fig. 6.3 is taken from H.W. Hayden,
--compression: brittle          W.G. Moffatt, and J. Wulff, The
Structure and Properties of
materials (e.g., concrete)    Materials, Vol. III, Mechanical
--torsion: cylindrical tubes,   Behavior, p. 2, John Wiley and Sons,
New York, 1965.)
shafts.                                                       9
Normal and shear stresses on an arbitrary plane

Stress is a function of the orientation

On plane p-p’ the stress is not pure tensile

There are two components
Tensile or normal stress s’ (normal to the pp’ plane)
Shear stress t’ (parallel to the pp’ plane)
ELASTIC DEFORMATIONS
7.3 Stress-strain behavior
• Modulus of Elasticity, E:
(also known as Young's modulus)

• Hooke's Law:
s=Ee
• Poisson's ratio, n:

metals: n ~ 0.33
ceramics: ~0.25
polymers: ~0.40
Units:
E: [GPa] or [psi]
n: dimensionless
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PROPERTIES FROM BONDING: E
• Elastic modulus, E

Energy ~ curvature at ro

E is larger if Eo is larger.

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7.4 ANESLATICITY

Assumed:
Time-independent elastic deformation
Applied stress produces instantaneous elastic strain
Remains constant while elasticity stress is applied
At release of load, strain is recovered

In real life:
Time-dependent elastic strain component: Anelasticity
Time-dependent microscopic and atomistic processes
For metals is small
Significant for polymeric materials: Viscoelastic behavior
7.5 ELASTIC PROPERTIES OF MATERIALS

Poisson’s ratio
n = -ex/ez = -ey/ez

For isotropic materials
YOUNG’S MODULI:
COMPARISON
Graphite
Metals                     Composites
Ceramics Polymers
Alloys                       /fibers
Semicond

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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II. MECHANICAL BEHAVIOR—METALS
II. ELASTIC DEFORMATION

Elastic means reversible!

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II. PLASTIC (PERMANENT) DEFORMATION
(at lower temperatures, T < Tmelt/3)

• Simple tension test:

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II. PLASTIC DEFORMATION (METALS)

Plastic means permanent!

3
7.6 Tensile properties
• YIELD STRENGTH, sy
Stress at which noticeable plastic deformation has
occurred.
when ep = 0.002

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7.6 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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7.6 TENSILE STRENGTH, TS
Maximum possible engineering stress in tension

Callister 6e.

• Metals: occurs when noticeable necking starts.
• Ceramics: occurs when crack propagation starts.
• Polymers: occurs when polymer backbones are
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7.6 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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7.6 DUCTILITY, %EL
Degree of plastic deformation at fracture
Brittle, when very little plastic deformation

• Plastic tensile strain at failure:

Callister 6e.

ductility as percent reduction
in area
• Note: %AR and %EL are often comparable.
--Reason: crystal slip does not change material volume.
--%AR > %EL possible if internal voids form in neck.
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Stress-strain of iron at several temperatures

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RESILIENCE
Capacity to absorb energy when deformed elastically and then upon
unloadign, to have this energy recovered

Modulus of Resilience

For a linear elastic region:
7.6 TOUGHNESS
• Ability to absorb energy up to fracture

Usually ductile materials are tougher than brittle ones
Areas below the curves
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7.7 True stress & strain
Decline in stress necessary to continue deformation past M
Looks like metal become weaker
Actually, it is increasing in strength
Cross sectional area decreases rapidly within the neck region
Reduction in the load-bearing capacity of the specimen
Stress should consider deformation
7.7 True stress & strain
HARDENING: An increase in sy due to plastic deformation.

• Curve fit to the stress-strain response:

n = hardening exponent
n = 0.15 (some steels)
n = 0.5 (some copper)
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7.8 Elastic Recovery After Plastic Deformation
7.9 Compressive, Shear, and
Torsional Deformation

Similar to tensile counterpart

No maximum for compression

Necking does not occur

Mode of fracture different from that of
tension
III. MECHANICAL BEHAVIOR—CERAMICS
Limited applicability, catastrophic fracture in a brittle
manner, little energy absorption

7.10 FLEXURAL STRENGTH
Tensile tests are difficult
difficult to prepare geometry
easy to fracture
ceramics fail at 0.1% strain
bending stress
rod specimen is used
flexure test
7.10 MEASURING STRENGTH
• Flexural strength= modulus of rupture
= fracture strength = bend strength

• Type values:

Si nitride   700-1000 300
Si carbide    550-860 430
Al oxide      275-550 390
glass (soda)    69     69
Data from Table 12.5, Callister 6e.
7.11 Elastic Behavior (for
ceramics)

Similar to tensile test for metals

Linear stress-strain

Moduli of elasticity for
ceramics are slightly higher
than for metals

No plastic deformation prior
to fracture
7.12 INFLUENCE OF POROSITY ON THE
MECHANICAL PROPERTIES OF CERAMICS
Powder as precursor
Aluminum oxide           Compaction to desire shape
E = Eo(1 – 1.9P + 0.9P2) Pores or voids elimination
incomplete
Residual porosity remains
Deleterious influence on
elasticity and strength
Volume fraction porosity P

Eo = modulus of elasticity of
the non porous material                     Aluminum oxide
-Pores reduce the area
-Pores are stress concentrators
sfs = soe    -nP

-tensile stress doubles in an
isolated spherical pore
IV MECHANICAL BEHAVIOR—POLYMERS

7.13 STRESS—STRAIN BEHAVIOR

Stress-strain curves
15.1, Callister 6e.
Inset figures along
elastomer curve
Fig. 15.14, Callister
6e. (Fig. 15.14 is from
Z.D. Jastrzebski, The
Nature and Properties
of Engineering
Materials, 3rd ed.,
John Wiley and Sons,
1987.)

• Compare to responses of other polymers:
--brittle response (aligned, cross linked & networked case)
--plastic response (semi-crystalline case)
7.13 T & STRAIN RATE: THERMOPLASTICS
• Decreasing T...
--increases E
--increases TS
--decreases %EL

• Increasing
strain rate...
--same effects
as decreasing T.
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7.14 Macroscopic Deformation

Semicrystaline polymer

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7.15 Viscoelasticity Deformation

Amorphous polymer:
Glass at low T
Viscous liquid at higher T
Small deformation at low T may be elastic
Hooke’s law
Rubbery solid at intermediate T
A combination of glass and viscous/liquid
Viscoelasticity
Elastic deformation is instantaneous
Upon release, deformation is totally recovered
7.15 Viscoelasticity Deformation

Totally elastic

Viscous

Viscoelastic

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Relaxation Modulus for viscoelastic
polymers:

Amorphous polystyrene
A viscoelastic polymer
Polystyrene configurations

Almost totally crystalline isotactic

Viscoelastic creep
Creep modulus Ec(t)
amorphous
V. Hardness & Other Mechanical Property Considerations

7.16 Hardness

Measure of material resistance to localized plastic deformation
Early tests: Mohs scale 1 for talc and 10 for diamond

Depth or size of an indentation

Tests:
Mohs Hardness
Rockwell Hardness
Brinell Hardness
Knoop & Vickers Microindentation Hardness
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Hardness Conversion
Correlation between Hardness and Tensile Strength

Tensile strength and Hardness
measure metal resistance to plastic
deformation

For example:

TS(Mpa) = 3.45 × HB

or

TS(psi) = 500 × HB
7.17 Hardness of Ceramic Materials

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7.18 Tear Strength & Hardness of Polymers

Thin films in packaging
Tear Strength: Energy required to tear apart a cut specimen of a
standard geometry
VI. Property Variability and Design/Safety Factors
7.19 Variability of Material Properties: Average and
standard deviation
7.20 DESIGN/SAFETY FACTORS
• Design uncertainties mean we do not push the limit.
• Factor of safety, N           Often N is
between
1.2 and 4

• Ex: 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.

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d = 47.5 mm                              29
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.

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