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Chapter 4. Testing Materials. Lesson Objectives. Equations. 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 > . - PowerPoint PPT Presentation
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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
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