PHY 231
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PHYSICS 231
Lecture 21: Some material science
Remco Zegers
Walk

in hour: Thursday 11:30

13:30 am
Helproom
gas
liquid
solid
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States of matter
Solid
Liquid
Gas
Plasma
difficult
to
deform
easy to
deform
easy to
deform
easy to
deform
difficult
to
compress
difficult
to
compress
easy to
compress
easy to
compress
difficult
to flow
easy to
flow
easy to
flow
easy to
flow
not
charged
not
charged
not
charged
charged
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Phase transformations
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solids
amorphous
ordered
crystalline
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The deformation of solids
Stress
: Tells something about the force causing the
deformation
Strain
: Measure of the degree of deformation
For small stress, strain and stress are linearly correlated.
Strain = Constant*Stress
Constant:
elastic modulus
The elastic modulus depends on:
•
Material that is deformed
•
Type of deformation (a different modulus is defined for
different types of deformations)
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The Young’s modulus
L
A
FL
L
L
A
F
Y
Y
0
0
0
2
/
/
L/L
:
strain
tensile
]
(Pa)
Pascal
[N/m
F/A
:
stress
tensile
strain
tensile
stress
tensile
Beyond the
elastic limit
an object
is permanently deformed (it does
not return to its original shape if
the stress is removed).
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example
An architect wants to design a 5m high circular pillar with
a radius of 0.5 m that holds a bronze statue that weighs
1.0E+04 kg. He chooses concrete for the material of the
pillar (Y=1.0E+10 Pa). How much does the pillar compress?
5m
0
2
0
/
)
/(
/
/
L
L
R
g
M
L
L
A
F
Y
pillar
statue
R=0.5 m L
0
=5m Y=1.0E+10 Pa M=1.0E+04 kg
L=6.2E

05 m
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Ultimate strength
Ultimate strength: maximum force per unit area a material
can withstand before it breaks or fractures.
Different for
compression and tension.
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example
A builder is stacking 1 m
3
cubic concrete blocks. Each blocks
weighs 5E+03 kg. The ultimate strength of concrete for
compression is 2E+07 Pa. How many blocks can he stack
before the lowest block is crushed?
The force on the low end of the lowest block
is: F=Nm
block
g.
N: total number of blocks
m
block
=mass of one block
g=9.81 m/s
2
Ultimate strength: 2E+07=F/A
=Nm
block
g/1
N=408 blocks.
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The Shear Modulus
x
A
Fh
h
x
A
F
S
S
/
/
x/h
:
strain
shear
]
(Pa)
Pascal
[N/m
F/A
:
stress
shear
strain
shear
stress
shear
2
x
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Moving earth crust
30 m
100 m
A tectonic plate in the lower crust (100 m deep) of
the earth is shifted during an earthquake by 30m.
What is the shear stress involved, if the upper layer
of the earth does not move? (S=1.5E+10 Pa)
h
x
A
F
S
/
/
strain
shear
stress
shear
F/A=4.5E+09 Pa
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Bulk Modulus
Compressibility: 1/(Bulk modulus)
pressure
P
V
V
P
V
V
A
F
B
B
0
0
0
2
/
/
/
V/V
:
strain
volume
]
(Pa)
Pascal
[N/m
F/A
:
stress
volume
strain
volume
stress
volume
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example
What force per unit area needs to be applied to compress
1 m
3
water by 1%? (B=0.21E+10 Pa)
0
/
/
V
V
A
F
B
V/V
0
=0.01 so,
F/A=2.1E+07 Pa !!!
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Some typical elastic moduli
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Density
)
/
(
3
m
kg
V
M
)
4
(
/
C
water
material
specific
o
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Pressure
Pressure=F/A (N/m
2
=Pa)
Same Force, different pressure
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example
A nail is driven into a piece of wood with a force of 700N.
What is the pressure on the wood if A
nail
=1 mm
2
?
A person (weighing 700 N) is lying on a bed of such
nails (his body covers 1000 nails). What is the pressure
exerted by each of the nails?
P
nail
=F/A
nail
=700N/1E

06m
2
=7E+08 Pa
P
person
=F/(1000A
nail
)=700/1E

03=
7E+05 Pa
(about 7 times the atmospheric
pressure).
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