TESTING MATERIALS

Chapter 4

Lesson Objectives

EquationsAreaForce

lx

ModulusYoungs

AlR

lAG

Bones under compression and tension

thickthighbone

thinnerarm bone

Bone in compression.Compressive forces squashthe bone.

Bone in tension.Tensile forces stretch thebone along its length.

Bone breaks.A break occurs where acrack develops in thesurface which is in tension.

Bone bends.On the outside of the bend,bone is in tension. On theinside of the bend boneis in compression.

walls compressedby weight of roof

tie beam across roofin tension, stops roofspreading out

weight of buildingpushes down

ground compressedpushes upfoundations

floors bend-stretched underneath

heavy bed loads floor

Tension and compression at home

Logarithmic scale of stress

Each main division represents a factor of 10

Two main divisions represent a factor of10 10 = 100 = 102

You cannot have zero on a logarithmic scale.At the lower end, it goes 0.1, 0.01, 0.001, and so on,getting smaller and smaller but never reaching zero.

100,000

10,000

1,000

100

10

1

0.1

0.01

105

104

103

102

101

100

10–1

10–2

diamond

glass

mild steel,kevlar

wood

foamed polymers

The Young modulus 1

Many materials stretch in a uniform way. Increase the stretching force in equal steps, and the extension increasesin equal steps too, in proportion. That is, the strain is proportional to the stress producing it. This is the sameas Hooke's law – the stretching of a spring is proportional to the stretching force you apply.

stress

strain

00

strain

stress

= FA

3F

2F

F

0 x 2x 3xextension

ratio stress is constantstrain

Young modulus = stressstrain

E =

strain stress ..................... graph is straight line

= xL

The Young modulus 2

The Young modulus is a property of the material not the specimen. Units of the Young modulusMN m–2 or MPa; for stiff materials GN m–2 or GPa. Same as units of stress, because strain isa ratio of two lengths, e.g. extension is 1% of length

The Young modulus is large for a stiff material (large stress, small strain). Graph is steep.

large strain for little stress _material is flexible, easy tostretch

little strain for large stress_ material is stiff, hard tostretch

strain strain

00

00

e.g. polymer e.g. diamond, steel

0

100

200

300

400

0.1 0.2 0.3 0.4 0.5 0.6 0.7 39.0 39.1 39.2strain /%

+

0

fracture

plastic region,extension uniformalong length

plastic region,necking hasbegun

elasticregion

Most Ductile Element Gold 1g can be drawn to a length of 2.4 km

Highest Tensile Strength Boron 5.7 Gpa

5,700,000,000 Nm-2

 Pasted from <http://www.theodoregray.com/PeriodicTableDisplay/Samples/005.1/s9.JPG>  

Least dense solid Silica Aerogels Tiny spheres of bonded silicon 1.9 mg cm-3 (air = 1.2 mg cm-3) Nicknamed “Frozen Smoke”

Pasted from <http://stardust.jpl.nasa.gov/highres/aerogel_peter.jpg>  

 Pasted from <http://stardust.jpl.nasa.gov/images/gallery/aerogelbrick.jpg>  

 Pasted from <http://en.wikipedia.org/wiki/Image:Aerogel_matches.jpg>  

Light through glass

ray point of view

r

i

normal

r r

normal

airglass

airglass

glass

Angles of rays are measured between theray and a line at right angles to the surface– the 'normal '

Snell's law

in this case:

refractive index n =speed of light in air

speed of light in glass

sin isin r = n

i

i

W hen ligh t reaches a boundary betw een m a teria ls in w hichit trave ls a t d iffe rent speeds:

part is re flectedit bends as it en te rs the new m ateria l

Wave point of view

waves gofast in air

air

glass

waves goslower in glass

glass

Light through glass

Logarithmic scale of resistivity and conductivity

resistivity / m

superconductors—zero resistancemetals are the best conductors

alloys generally conduct less wellthan pure metals

semiconductors conduct, but notvery well

insulators conduct very little,almost not at all

conductivity / S m–1

10 6

10 4

10 2

1

10– 2

10– 4

10– 6

10– 8

10– 12

10– 14

10– 16

10– 18

10– 10

10– 6

10 2

10 4

10 6

10 8

10 10

10– 4

10– 2

1 0 8

1

1012

1014

10 16

1018

10– 8silve r, copper, go ldn icke l, ironstee l, bronze

doped germ anium

pure germ anium

pure s ilicon

Pyrex g lass

alum ina

P erspex, lead g lass

po lystyrene

Conductivity and resistivity 1

two pieces end-on conduct half as well as one – so have twice the resistance

conductance G

conductance G resistance R

two pieces side by side conduct twice as well as one – so have half the resistance

length L

area A

area 2A

area A

resistance R

resistance R2

length L

length 2L

conductance 2G

conductance G2 resistance 2R

area A

GA

RL

R 1A

G1L

Conductivity and resistivity 2

Need to know

unit siemens S

length Lcross sectional

area A

G =1R R =

1G

= 1 =

1

to work outconductance Gconductivity

G = AL

= GLA

to work outresistance Rresistivity

R = LA

unit ohm

= RAL

unit munit S m_1