PHYSICS OF MATERIALS

1. the property by virtue of which a body tends to regain its original shape and
size when external forces are removed. If a body completely recovers its original shape
and size , i
Elasticity :
t is called perfectly elastic. Quartz, steel and glass are very nearly elastic.
2. if a body has no tendency to regain its original shape and size , it is called
perfectly plastic. Commo
Plasticity :
n plastics, kneaded dough, solid honey, etc are plastics.
3. characterizes the strength of the forces causing the stretch, squeeze, or twist. It
is defined usually as force/unit area but may
Stress
have different definitions to suit different
situations. We distinguish between three types of stresses:
a) If the deforming force is applied along some linear dimension of a body, the
stress is called or or
b) If the force acts normally and uniformly from all sides of a body, the stress is called
.
c)
longitudinal stress tensile stress compressive stress.
volume stress
If the force is applied tangentially to one face of a rectangular body, keeping the other
face fixed, the stress is called tangential or shearing stress.
4. Strain: When deforming forces are applied on a body, it undergoes a change in shape or
size. The fractional (or relative) change in shape or size is called the strain.
Strain = change in dimension
original dimension
Strain is a ratio of similar quantities so it has no units. There are 3 different kinds of
strain:
a) Longitudinal (linear) strain is the ratio of the change in length ( ) to original
length ( ), i.e., the linear strain .
b) is the ratio of the change in volume ( ) to original volume ( )
Volume strain .
c)
L
l l
l
Volume strain V V
V
V
Shearing strain :
Δ
Δ
=
Δ
Δ
=
The angular deformation ( ) in radians is called shearing stress.
For small the shearing strain tan x .
l
θ
θ θ θ
Δ
≡ ≈ =
l
Δx
θ
F
5. Hooke's Law: for small deformations, stress is proportional to strain.
Stress = E × Strain
The constant E is called the modulus of elasticity. E has the same units as stress
because strain is dimensionless. There are three moduli of elasticity.
(a) Young's modulus (Y) for linear strain:
Y ≡ longitudinal stress /
longitudinal strain /
(b) Bulk Modulus (B) for volume strain: Let a body of volume be subjected to a
uniform pressure on its entire surface and let be the correspond
F A
l l
V
P V
=
Δ
Δ Δ ing
decrease in its volume. Then,
B Volume Stress .
Volume Strain /
1/ is called the compressibility. A material having a small value of
P
V V
B
Δ
≡ =−
Δ
B can be
compressed easily.
(c) Shear Modulus ( ) for shearing strain: Let a force F produce a strain as in the
diagram in point 4 above. Then,
η θ
shearing stress / .
shearing strain tan
6. When a wire is stretched, its length increases and radius decreases. The ratio of the
lateral strain to the longitudinal strain is c
F A F Fl
A Ax
η
θ θ
≡ = = =
Δ
alled Poisson's ratio, / . Its value lies
/
between 0 and 0.5.
7. We can calculate the work done in stretching a wire. Obviously, we must do work
against a force. If x is the extension pr
r r
l l
σ
Δ
=
Δ
( )2
0 0
oduced by the force in a wire of length ,
then . The work done in extending the wire through is given by,
2
l l
F l
F YAx l
l
W Fdx YA xdx YA l
l l
Δ Δ
= Δ
Δ
=∫ = ∫ =
( ) ( )
2 1 1volume stress strain
2 2 2
Hence, Work / unit volume 1 stress strain. We can also write this as,
2
1
2
YA l Al Y l l
l l l
W YA l
l
= Δ = ⎛⎜ Δ ⎞⎟⎛⎜Δ ⎞⎟= × × ×
⎝ ⎠⎝ ⎠
= × ×
= ⎛⎜ Δ ⎞⎟
⎝ ⎠
1 load extension.
2
Δl = × ×
8. A fluid is a substance that can flow and does not have a shape of its own. Thus all
liquids and gases are fluids. Solids possess all the three moduli of elasticity whereas a
fluid possess only the bulk modulus (B). A fluid at rest cannot sustain a tangential
force. If such force is applied to a fluid, the different layers simply slide over one
another. Therefore the forces acting on a fluid at rest have to be normal to the surface.
This implies that the free surface of a liquid at rest, under gravity, in a container, is
horizontal.
9. The normal force per unit a
2
rea is called pressure, . Pressure is a scalar quantity.
Its unit is Newtons/metre , or Pascal (Pa). Another scalar is density, , where
is the mass of a small piece of the mater
P F
A
m
V
m
ρ
Δ
=
Δ
Δ
=
Δ
Δ ial and ΔV is the volume it occupies.
( )
10.Let us calculate how the pressure in a fluid changes with depth.
So take a small element of fluid volume submerged within the
body of the fluid:
No
dm=ρdV =ρAdy ∴ dm g=ρgAdy
( )
w let us require that the sum of the forces on the fluid element
is zero: pA p dp A gAdy 0 dp g.
dy
− + −ρ = ⇒ = −ρ
Note that we are taking the origin ( 0) at the bottom of the liquid. Therefore as the
elevation increases ( positive), the pressure decreases ( negative). The quantity
is the weight
y
dy dp ρ g
=
2 1 ( )
2 1 2 1
2 1
per unit volume of the fluid. For liquids, which are nearly incompressible,
is practically constant.
constant .
11. : Pressure appl
g dp p p p gp p g y y
dy y y y
ρ
ρ ρ ρ
Δ −
∴ = ⇒ = = =− ⇒ − =− −
Δ −
Pascal's Principle ied to an enclosed fluid is transmitted to every portion
of the fluid and to the walls of the containing vessel. This follows from the above: if is
the height below the liquid's surface, the
h
( )
( )
n . Here is the pressure at the
surface of the liquid, and so the difference in pressure is . Therefore,
0 . (I have used here the fact that liquids ar
ext ext
ext
ext
p p gh p
p p gh
gh p p
ρ
ρ
ρ
= +
Δ = Δ + Δ
Δ = ⇒Δ =Δ e incompressible). So
the pressure is everywhere the same.
Area A
(p+dp)A
pA
(dm) g