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slide1

Special Assignment

  • Add figures/graphics to all slides
  • Use bullets instead of short sentences
  • For the 15’ presentations use fonts 18 or bigger; however, for the 50’, font sizes 10, 12, 14 are fine. You may use 16 or 18 for titles.
  • Add your summary slide
  • Graphics should help to explain the topic
chapter 7 mechanical properties3
CHAPTER 7: MECHANICAL PROPERTIES

Stress

Strain

Elasticity

Strength

Tensile

Elongation

Ductile

Fracture

Tension

Flexural

Plasticity

ISSUES TO ADDRESS...

• Stress and strain

• Elastic behavior

• Plastic behavior

• Toughness and ductility

  • Ceramic Materials
7 2 stress strain
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

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Strain (e) for tension and compression

Compressive load

Tensile load

Shear stress

Shear strain

g = tan q

Torsional deformation

angle of twist, f

7 2 common states of stress
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
OTHER COMMON STRESS STATES

• Simple compression:

(photo courtesy P.M. Anderson)

Note: compressive

structure member

(s < 0 here).

(photo courtesy P.M. Anderson)

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other common stress states8
OTHER COMMON STRESS STATES

• Bi-axial tension:

• Hydrostatic compression:

Pressurized tank

(photo courtesy

P.M. Anderson)

(photo courtesy

P.M. Anderson)

s< 0

h

7

engineering strain
ENGINEERING STRAIN

• Tensile strain:

• Lateral strain:

• Shear strain:

Strain is always

dimensionless.

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7 2 stress strain testing
7.2 STRESS-STRAIN TESTING

• Typical tensile specimen

• Typical tensile

test machine

Adapted from Fig. 6.2,

Callister 6e.

• Other types of tests:

--compression: brittle

materials (e.g., concrete)

--torsion: cylindrical tubes,

shafts.

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.)

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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
ELASTIC DEFORMATIONS7.3 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
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

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7.5 ELASTIC PROPERTIES OF MATERIALS

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Poisson’s ratio

n = -ex/ez = -ey/ez

For isotropic materials

young s moduli comparison
YOUNG’S 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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ii elastic deformation
II. ELASTIC DEFORMATION

1. Initial

2. Small load

3. Unload

Elastic means reversible!

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ii plastic permanent deformation
II. PLASTIC (PERMANENT) DEFORMATION

(at lower temperatures, T < Tmelt/3)

• Simple tension test:

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ii plastic deformation metals
II. PLASTIC DEFORMATION (METALS)

1. Initial

2. Small load

3. Unload

Plastic means permanent!

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7 6 tensile properties
7.6 Tensile properties

• YIELD STRENGTH, sy

Stress at which noticeableplastic deformation has

occurred.

when ep = 0.002

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7 6 yield strength comparison
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
7.6 TENSILE STRENGTH, TS

Maximum possible engineering stress in tension

Adapted from Fig. 6.11, Callister 6e.

• 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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7 6 tensile strength comparison
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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slide28
7.6 DUCTILITY, %ELDegree of plastic deformation at fractureBrittle, when very little plastic deformation

• Plastic tensile strain at failure:

Adapted from Fig. 6.13, 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
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

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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
7.7 True stress & strain

HARDENING: An increase insy 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

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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

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III. MECHANICAL BEHAVIOR—CERAMICSLimited applicability, catastrophic fracture in a brittle manner, little energy absorption7.10 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

three of four point loading technique

flexure test

7 10 measuring strength
7.10 MEASURING STRENGTH

• Flexural strength= modulus of rupture

= fracture strength = bend strength

• Type values:

Si nitride

Si carbide

Al oxide

glass (soda)

700-1000

550-860

275-550

69

300

430

390

69

Data from Table 12.5, Callister 6e.

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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 priorto fracture

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7.12 INFLUENCE OF POROSITY ON THE MECHANICAL PROPERTIES OF CERAMICS

Powder as precursor

Compaction to desire shape

Pores or voids elimination incomplete

Residual porosity remains

Deleterious influence on elasticity and strength

Volume fraction porosity P

Aluminum oxide

E = Eo(1 – 1.9P + 0.9P2)

Eo = modulus of elasticity of the non porous material

-Pores reduce the area

-Pores are stress concentrators

-tensile stress doubles in an isolated spherical pore

Aluminum oxide

sfs = soe-nP

iv mechanical behavior polymers 7 13 stress strain behavior
IV MECHANICAL BEHAVIOR—POLYMERS7.13 STRESS—STRAIN BEHAVIOR

Stress-strain curves adapted from Fig. 15.1, Callister 6e. Inset figures along elastomer curve (green) adapted from 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
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

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7.15 Viscoelasticity Deformation

Totally elastic

Load

Viscous

Viscoelastic

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Relaxation Modulus for viscoelastic polymers:

Amorphous polystyrene

A viscoelastic polymer

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Polystyrene configurations

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Almost totally crystalline isotactic

Lightly crosslinked atactic

Viscoelastic creep

Creep modulus Ec(t)

amorphous

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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

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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

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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

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VI. Property Variability and Design/Safety Factors

7.19 Variability of Material Properties: Average and standard deviation

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7 20 design safety factors
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.

5

d = 47.5 mm

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summary
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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