1 2 the golden orb spider’s silk is twice as strong as mild steel and can stretch by up to 30% 0f...
TRANSCRIPT
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THE GOLDEN ORB SPIDER’S SILK IS TWICE AS STRONG AS MILD STEEL
AND
CAN STRETCH BY UP TO 30% 0F ITS ORIGINAL LENGTH
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STIFFNESS first investigated by
ROBERT HOOKE, 1648
He suspended various masses from springs, and measured the extension. m
m
4
m
F = mg
e
“Up to a certain level of force, the extension (e)
produced is proportional to the applied force (F).”
e.g. for a spring or wire
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Force F/N
0
2
4
6
8
10
12
0.00 0.50 1.00 1.50
e /m
F /
N
EXTENSION Force
e/m F/N
0.00 0
0.12 1
0.24 2
0.36 3
0.48 4
0.60 5
0.72 6
0.84 7
0.96 8
1.08 9
1.20 10
eF keFk is called the spring constant
k is equal to the gradient of the graph = 8.3 Nm-1
k is a measure of the spring’s stiffness
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force
extension
WORK DONE IN STRETCHING / ENERGY STORED IN A STRETCHED SPRING OR WIRE
e
F
0
which is the area under the graphW = ½ Fe
1. Special case: when F is proportional to e
Work Done =
Average Force x Extension
eF
W
2
0
or, as F = k e W = ½ ke2
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force
extensione
0
w = f e
eefW
0
which again is the area under the graph
WORK DONE IN STRETCHING / ENERGY STORED IN A STRETCHED SPRING OR WIRE
2. The general case
e
f
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STRETCHING OF A POLYMER e.g. RUBBER
force
extension
F F
FF
C C CCCCC C CCCCC C CCCCC C CCCC
Initially it is easy to merely straighten the polymer chains.
F
It then becomes much harder to separate the atoms of the carbon chain
F
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loading
work done in stretching
unloading
energy recovered
STRETCHING OF RUBBER
energy LOST as internal energy
The word HYSTERESIS is used to refer to the energy lost in a cyclic process.
HYSTERESISLOOP
force
extension
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force
extension
Steel is approximately 1½ STIFFER than copper.
A
Which is graph below shows the stretching of a copper bar and which a steel bar under loading?
B
ANSWER WE CANNOT TELL!
Extension depends upon:(i) Material Properties(ii) Geometry of Bar (i.e. L and A)
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TENSILE STRESS and TENSILE STRAIN are used to compare the stiffness of different
materials.TENSILE STRESS, σ = force applied per unit cross sectional area
A FA
F =
TENSILE STRAIN, ε = fractional change in length under load= extension ÷ original length
Original length l Extension,e
l
e =
ε
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UNITS
A
F =
STRESS N m-2 = Pa
STRAIN
l
e =
ε NO UNITS
Strain can also be expressed as a percentage.
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stress
strain
Steel is approximately 1½ STIFFER than copper.
A
B
ANSWER B must be COPPER
WHICH IS COPPER, A or B?
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stress
strain
YOUNG’s MODULUS OF ELASTICITY - E
E measures stiffness
E = gradient of the stress – strain graph
strain
stressE
e A
F l =
E UNITS of E are Pa (GPa)
leA
FE
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YOUNG’s MODULUS OF ELASTICITY
TYPICAL VALUES
MATERIAL E ( MPa )
Carbon Fibre 270
Steel 210
Copper 130
Kevlar 124
Bone 28
Rubber 0.02
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STRESS – STRAIN GRAPHS
stress
strain
Copper – a Ductile Material
L
Y FU
L = Limit of Proportionality
Y = Yield Point
U = Ultimate Tensile Strength (UTS)
F = Fracture
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STRESS – STRAIN GRAPHS Copper – a Ductile Material
Yield Strength
UTS
stress
strain
L
Y FU
ELASTIC
REGION
PLASTIC REGION
(permanent deformation)
Strain hardening
Necking
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stress
strain
Y
STRESS – STRAIN GRAPHS
Some of a specimen’s elasticity may be lost before the yield point is reached.
If the load is removed a Permanent Set remains in the sample.
PermanentSet
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stress
strain
AREA UNDER STRESS – STRAIN GRAPHS
Energy stored per unit volume
l
A
Al
Fe21
l
e
A
F
2
1
Energy stored per unit volume = ½ STRESS X STRAIN
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STRESS – STRAIN GRAPHS
stress
strain
STEEL
Copper for comparison
Steel
LOWER YIELD POINT is the point at which the main plastic deformation begins.
YY = (UPPER) YIELD POINT
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STRESS – STRAIN GRAPHS
stress
strain
BRITTLE SUBSTANCES
e.g. Cast Iron or Glass
X
BRITTLE SUBSTANCES
FRACTURE AT THEIR ELASTIC LIMIT
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BEAM
YOUNG’S MODULUS APPARATUS
test wire
support wire
main scale
fixed load keeps system taut
venier scale
F = mg
variable load
l
Two identical wires are suspended from the same support.
This counteracts any sagging of the beam and any expansion due to change in temperature.
Extensions, e, are measured with the vernier scale.
Diameter of the wire, D, is measured with a micrometer.
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2DA
Plot F vs. e F
e
A
lgradient
eA
FlE