Mechanical Properties of solids

Physics

Elasticity

The property of a body, by virtue of which it tends to regain its original size and shape when the applied force is removed. the deformation is elastic deformation

Plasticity

The property of a body, by virtue of which has no gross tendency to regain its original size and shape and get permanently deformed are plastic

Elastic examples

Spring, rubber band

Plastic examples

clay, mud, putty

Stress

The restoring force developed in the body when the body is subjected to external deforming force is equal and opposite to the applied force.

This restoring force/area is called stress.

F/A

SI unit of Stress

N m-2 / Pa (Pascal)

Dimension of Stress

[M1L-1T-2]

Longitudinal Stress

Normal Stress

Tensile and Compressive.

Change in Length

Force is normal to the body

Shearing Stress

Tangential Stress

Force is parallel to the body

Change in Area

Hydraulic Stress

Volumetric Stress

Force applied acts perpendicular to all points on the surface of body

Change in volume

Strain

Amount of deformation of a body when stress is applied.

Change in dimension / Original Dimension

SI unit and dimension of Strain

Unitless and dimensionless

Because the units cancel e/o

Longitudinal Strain

Delta L/L

Shearing Strain

Delta x/L = tan theta

sigma s

Volumetric Strain

Delta V/V

Hooke's Law

Law of elasticity

Small amount of stress is directly proportional to strain under elastic limit.

Stress = k.Strain

K is modulus of elasticity.

O-A in stress strain graph

Linear curve.

Body regains og dimension after force is removed and is elastic

Hooke's law is obeyed

A-B

Stress and strain are not proportional.

But body will regain its og dimensions and is elastic

B

Yield point, body has yield strength ( sigma y ) also Elastic limit.

B-D

Body will deform, will not regain og dimension.

Here when body does not regain og dimension it is said to have permanent set.

strain inceases rapidly for small amt of stress

Body goes through Plastic deformation.

D

Proportional limit // ultimate tensile strength of body (sigma u)

E

Fracture Point

body breaks

D-E

If d-e is close to e/o the body is brittle

if d-e are far apart body is ductile.

Elastic tissue of aorta

Does not follow hooke's law even thought its region is very large.

no well defined plastic region.

Elastomers

Bodies that can be stretched to cause large strains

Modulus of elasticity

Ratio of stress/strain

Young's modulus

(Y) = (F/A) / (Del L/L)
= (F x L) / (A x Del L)

Y= sigma/eta

SI- N m-2 / Pa

To find Y of a material of wire (under tension)

Y = (Mg x L) / (pi r square x Del L)

Shear modulus

Modulus of Rigidity

(G) = (F/A) / ( del x/ L)
= (F x L) / ( A x del x)

SI - N m-2 / Pa

G is generally less than Y

G is approx. Y/3

Sigma s = G x theta

G = F/(A x theta)

Bulk modulus

(B) = -p/(del V /V)

SI - N m -2 / Pa

-p shows with inc in p , dec in v
+p shows with dec in p , inc in v

in equil B is always +

Of solids is larger than liq and gases

Compressibility

Reciprocal of bulk

(k)

The fractional change in volume per unit increase in pressure

k= (1/B)
= -(1/ del p) x ( del V/V)

Lateral Strain

Strain perpendicular to the applied force

(decrease in diameter of wire in young's modulus exp)

Lateral strain is directly proportional to Longitudinal Strain

Poisson's Ratio

ratio of Lateral Strain / Longitudinal Strain

(del d/d) / (del L / L)

Ratio of 2 strains, therefore unitless and dimensionless, pure no.

Depends only on nature of material.

Work done to elongate L of wire

W = 1/2 x Y x (l/L) square x AL

Y - youngs mod
(l/L) square - strain squared
AL - Volume of wire

W is stored as U
U- elastic potential limit

U per unit volume - u

u= sigma x eta
i.e., stress x strain