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PHYSICS 231 Lecture 21: Some material science. Remco Zegers Walk-in hour: Thursday 11:30-13:30 am Helproom. liquid. solid. gas. States of matter. Phase transformations. solids. ordered. crystalline. amorphous. The deformation of solids. - PowerPoint PPT Presentation
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PHY 2311
PHYSICS 231Lecture 21: Some material science
Remco ZegersWalk-in hour: Thursday 11:30-13:30 am
Helproom
gas liquid solid
PHY 2312
States of matterSolid Liquid Gas Plasma
diffi culttodeform
easy todeform
easy todeform
easy todeform
diffi culttocompress
diffi culttocompress
easy tocompress
easy tocompress
diffi cultto flow
easy toflow
easy toflow
easy toflow
notcharged
notcharged
notcharged
charged
PHY 2313
Phase transformations
PHY 2314
solids
amorphousordered
crystalline
PHY 2315
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)
PHY 2316
The Young’s modulus
LA
FL
LL
AFY
Y
0
0
0
2
/
/
L/L :strain tensile
](Pa) Pascal[N/mF/A :stress tensile
strain tensile
stress tensile
Beyond the elastic limit an objectis permanently deformed (it doesnot return to its original shape ifthe stress is removed).
PHY 2317
exampleAn architect wants to design a 5m high circular pillar witha 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 /
)/(
/
/
LL
RgM
LL
AFY pillarstatue
R=0.5 m L0=5m Y=1.0E+10 Pa M=1.0E+04 kg
L=6.2E-05 m
PHY 2318
Ultimate strength
Ultimate strength: maximum force per unit area a materialcan withstand before it breaks or fractures.
Different for compression and tension.
PHY 2319
example
A builder is stacking 1 m3 cubic concrete blocks. Each blocksweighs 5E+03 kg. The ultimate strength of concrete forcompression is 2E+07 Pa. How many blocks can he stackbefore the lowest block is crushed?
The force on the low end of the lowest blockis: F=Nmblockg. N: total number of blocksmblock=mass of one blockg=9.81 m/s2
Ultimate strength: 2E+07=F/A=Nmblockg/1
N=408 blocks.
PHY 23110
The Shear Modulus
xA
Fh
hx
AFS
S
/
/
x/h :strainshear
](Pa) Pascal[N/mF/A :stressshear
strainshear
stressshear
2
x
PHY 23111
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 layerof the earth does not move? (S=1.5E+10 Pa)
hx
AFS
/
/
strainshear
stressshear
F/A=4.5E+09 Pa
PHY 23112
Bulk Modulus
Compressibility: 1/(Bulk modulus)
pressureP
VV
P
VV
AFB
B
00
0
2
//
/
V/V :strain volume
](Pa) Pascal[N/mF/A :stress volume
strain volume
stress volume
PHY 23113
example
What force per unit area needs to be applied to compress1 m3 water by 1%? (B=0.21E+10 Pa)
0/
/
VV
AFB
V/V0=0.01 so, F/A=2.1E+07 Pa !!!
PHY 23114
Some typical elastic moduli
PHY 23115
Density
)/( 3mkgV
M
)4(/
Cwatermaterialspecific o
PHY 23116
Pressure
Pressure=F/A (N/m2=Pa)
Same Force, different pressure
PHY 23117
example
A nail is driven into a piece of wood with a force of 700N.What is the pressure on the wood if Anail=1 mm2?A person (weighing 700 N) is lying on a bed of such nails (his body covers 1000 nails). What is the pressureexerted by each of the nails?
Pnail=F/Anail=700N/1E-06m2=7E+08 PaPperson=F/(1000Anail)=700/1E-03=
7E+05 Pa (about 7 times the atmospheric pressure).