Material Science: Stress, Strain, and Moduli, Slides of Physics

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Material Strength

Stress vs Strain

^

A graph of stress versusstrain is linear for smallstresses. ^

The slope of stress versusstrain is a

modulus

that

depends on the type ofmaterial. ^

For normal stress this isYoung’s modulus

Y

^ 

Y

 Stress

Strain



stiff material

elasticmaterial

Inelastic Material

^

The linear behavior ofmaterials only lasts up to acertain strength – the

yield

strength

^

Materials can continue todeform but they won’t restoretheir shape. ^

For very high strain amaterial will break.

 Stress

Strain

breakingstrength 

yieldstrength

Shear Modulus

^

Materials also have amodulus from shear forces. ^

Shear modulus

S

also

matches with a springconstant. ^

The angle

^

=^

 x

/ L

is

sometimes used for shear.

F^

 x A^ (goes into screen) L

x

k

x

SA L

F

x

FLA

L

x

A

F

S

s s

 ^ 

Bulk Modulus

^

Pressure changes volume,not length. ^

Bulk modulus

B

relates

changes in pressure andvolume. ^

The negative sign representsthe decrease in volume withincreasing pressure.

P

 V V A^ (surface area)

V

P V

V

V

A

F

B

V V

 

Under Pressure ^

Steel has a bulk modulus of B^

= 60 GPa. A sphere with a volume of 0.50 m

3 is

constructed and lowered intothe ocean where

P

MPa. ^

How much does the volumechange?

^

Use the relation for bulkmodulus.^ 

B

= -(

 P

) / (

 V

/ V

)

^

 V

= -

V^

 P

/^ B

^

Substitute values:^ 

(-0.50 m

3 )(2.0 x 10

7 Pa) /

(6.0 x 10

10

Pa)

^

 V

= -1.6 x 10

4 m

3