1 PHYSICS 231 Lecture 21: Some material science

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Nov 29, 2013 (4 years and 1 month ago)

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PHY 231

1

PHYSICS 231

Lecture 21: Some material science

Remco Zegers

Walk
-
in hour: Thursday 11:30
-
13:30 am

Helproom

gas

liquid

solid

PHY 231

2

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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3

Phase transformations

PHY 231

4

solids

amorphous

ordered

crystalline

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5

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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6

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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7

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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8

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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10

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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11

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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12

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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13

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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14

Some typical elastic moduli

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15

Density

)
/
(
3
m
kg
V
M


)
4
(
/
C
water
material
specific
o




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16

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).