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).