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CHAPTER 7: 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?.

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chapter 7 mechanical properties
CHAPTER 7: 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?

  • Ceramic Materials: What special provisions/tests are
  • made for ceramic materials?

1

elastic deformation
ELASTIC DEFORMATION

1. Initial

2. Small load

3. Unload

Elastic means reversible!

2

plastic deformation metals
PLASTIC DEFORMATION (METALS)

1. Initial

2. Small load

3. Unload

Plastic means permanent!

3

engineering stress
ENGINEERING STRESS

• Tensile stress, s:

• Shear stress, t:

Stress has units:

N/m2 or lb/in2

4

common states of stress
COMMON STATES OF STRESS

• Simple tension: cable

Ski lift(photo courtesy P.M. Anderson)

• Simple shear: drive shaft

Note: t = M/AcR here.

5

other common stress states 1
OTHER COMMON STRESS STATES (1)

• Simple compression:

(photo courtesy P.M. Anderson)

Note: compressive

structure member

(s < 0 here).

(photo courtesy P.M. Anderson)

6

other common stress states 2
OTHER COMMON STRESS STATES (2)

• 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.

8

stress strain testing
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.)

9

linear elastic properties
LINEAR ELASTIC PROPERTIES

• 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

10

properties from bonding e
PROPERTIES FROM BONDING: E

• Elastic modulus, E

• E ~ curvature at ro

E is larger if Eo is larger.

11

other elastic properties
OTHER ELASTIC PROPERTIES

• Elastic Shear

modulus, G:

simple

torsion

test

t = Gg

• Elastic Bulk

modulus, K:

pressure

test: Init.

vol =Vo.

Vol chg.

= DV

• Special relations for isotropic materials:

12

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.

13

useful linear elastic relations
USEFUL LINEAR ELASTIC RELATIONS

• Simple tension:

• Simple torsion:

• Material, geometric, and loading parameters all

contribute to deflection.

• Larger elastic moduli minimize elastic deflection.

14

plastic permanent deformation
PLASTIC (PERMANENT) DEFORMATION

(at lower temperatures, T < Tmelt/3)

• Simple tension test:

15

yield strength s y
YIELD STRENGTH, sy

• Stress at which noticeableplastic deformation has

occurred.

when ep = 0.002

16

yield strength comparison
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

17

tensile strength ts
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.

18

tensile strength comparison
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.

19

ductility el
DUCTILITY, %EL

• Plastic tensile strain at failure:

Adapted from Fig. 6.13, Callister 6e.

• Another ductility measure:

• Note: %AR and %EL are often comparable.

--Reason: crystal slip does not change material volume.

--%AR > %EL possible if internal voids form in neck.

20

toughness
TOUGHNESS

• Energy to break a unit volume of material

• Approximate by the area under the stress-strain

curve.

21

hardening
HARDENING

• An increase in sy due to plastic deformation.

• Curve fit to the stress-strain response:

22

measuring elastic modulus
MEASURING ELASTIC MODULUS

• Room T behavior is usually elastic, with brittle failure.

• 3-Point Bend Testing often used.

--tensile tests are difficult for brittle materials.

Adapted from Fig. 12.29, Callister 6e.

• Determine elastic modulus according to:

23

measuring strength
MEASURING STRENGTH

• 3-point bend test to measure room T strength.

Adapted from Fig. 12.29, Callister 6e.

• Typ. values:

• Flexural strength:

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.

24

tensile response elastomer case
TENSILE RESPONSE: ELASTOMER CASE

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)

25

t and strain rate thermoplastics
T AND STRAIN RATE: THERMOPLASTICS

• Decreasing T...

--increases E

--increases TS

--decreases %EL

• Increasing

strain rate...

--same effects

as decreasing T.

Adapted from Fig. 15.3, Callister 6e. (Fig. 15.3 is from T.S. Carswell and J.K. Nason, 'Effect of Environmental Conditions on the Mechanical Properties of Organic Plastics", Symposium on Plastics, American Society for Testing and Materials, Philadelphia, PA, 1944.)

26

time dependent deformation
TIME DEPENDENT DEFORMATION

• Data: Large drop in Er

for T > Tg.

• Stress relaxation test:

(amorphous

polystyrene)

--strain to eo and hold.

--observe decrease in

stress with time.

Adapted from Fig. 15.7, Callister 6e. (Fig. 15.7 is from A.V. Tobolsky, Properties and Structures of Polymers, John Wiley and Sons, Inc., 1960.)

• Relaxation modulus:

• Sample Tg(C) values:

PE (low Mw)

PE (high Mw)

PVC

PS

PC

-110

- 90

+ 87

+100

+150

Selected values from Table 15.2, Callister 6e.

27

hardness
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.)

28

design or safety factors
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

• 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

29

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.

Note: For materials selection cases related to mechanical behavior, see slides 20-4 to 20-10.

30

announcements
ANNOUNCEMENTS

Reading:

Core Problems:

Self-help Problems:

0